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EPISTEME
Physis e Sophia nel III millennio
An International Journal
of Science, History and Philosophy
N. 6 - 21 dicembre 2002
2
Redazione ([email protected])
"Episteme"
c/o Dipartimento di Matematica e Informatica
Università degli Studi
Via Vanvitelli - 06100 Perugia
Direttore Responsabile
Euro Roscini (Supplemento semestrale ad: Arte in Foglio, Pubblicazione
registrata presso il Tribunale di Perugia, N. 36/1991)
http://www.robotics.it/episteme
http://www.dipmat.unipg.it/~bartocci
(per ottenere ~ tenere premuto Alt mentre si compone il numero 126 con i simboli numerici nella parte destra
della tastiera)
Numeri arretrati on line: http://itis.volta.alessandria.it/episteme
PORZI editoriali
ISSN 1593-3482
3
PARTE II/
SECOND SECTION
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EPISTEME
Physis e Sophia nel III millennio/Physis and Sophia in the III millennium
An International Journal of Science, History and Philosophy
N. 6 - 21 dicembre 2002 / 21st Dec. 2002
[La diffusione via Internet di sezioni della rivista avviene prima della data indicata - Sections of Episteme are
available in Internet even before the previous date]
Parte I
Informazioni editoriali/Editorial Policy
Pubblicazioni ricevute/Received books and journals
1 - Lia Mangolini: La vera natura del "magico Shamìr" - A proposito di un'antichissima
tecnologia per la lavorazione della pietra senza l'uso di strumenti metallici
2 - Emilio Spedicato: L'Eden riscoperto: geografia, questioni numeriche ed altre storie
3 - Felice Vinci: L'optimum climatico, il paradiso indoeuropeo e il giardino dell'Eden
4 - Sabato Scala: Il culto gnostico della Maddalena - Dal mosaico di Otranto alle basiliche
paleocristiane di Cimitile, attraverso opere letterarie ed architettoniche, fino agli ultimi
custodi, i Catari ed i Templari
5 - Arcangelo Papi: La facciata profetica del Duomo di S. Rufino in Assisi
6 - Prospero Calzolari: Presenza occulta e manifesta dell'Imperatore Federico II nella
Basilica di San Francesco ad Assisi - Frate Elia e la congiura del silenzio
7 - Giuseppe Pirazzo, Francesco Vitale: Il mistero degli indiani Mandan
8 - Ludwik Kostro: When, Where, and How Was Decalogue Created? - Historical Origins
and Evolution of the Ten Commandments
9 - Umberto Bartocci: La vera identità di Cristoforo Colombo - Osservazioni e congetture
10 - Pier Costanzo Brio: Cristoforo Colombo, la nascita - Verità storica e leggenda purista
11 - Ezio Albrile: Una eresia di luce
12 - Rosario Vieni: Sul termine greco ανθρωπος … e dintorni
13 - Oktawian Nawrot: Liberty as a Relation
14 - Sante Anfiboli: Il canto delle gru - Un racconto iniziatico
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15 - Bruno d'Ausser Berrau: Ατοπον − Relazioni spazio-temporali e metafisica tradizionale
16 -
"
"
"
: Solvet saeclum in favilla - In attesa del Dies Irae?
17 - Umberto Lucia: Il ruolo del trasferimento tecnologico nello sviluppo sostenibile
Reprints
Paolo Manzelli, Mariagrazia Costa: Il tempo come coordinata - Gli studi di Giorgio
Piccardi (1895-1972)
Omero Speri, Piero Zorzi: Atomo, Energia, Uomo
Commenti ricevuti/Received Comments
Sante Anfiboli: A proposito del Vexillum Templi, e altra simbolica templare...
Alberto Bolognesi: Il Big Bang ha fatto flop?
Lino Lista: Le tre Grazie - Una chiave per dischiudere il giardino della Primavera
Arcangelo Papi: Il caso Majorana - L'<<ipotesi Klingsor>>
Francesco Pullia: Manlio Farinacci, studioso fuori dal coro
Recensioni/Reviews
Luca Bianchini, Anna Trombetta: Goethe, Mozart e Mayr, fratelli illuminati
Paolo Cortesi: Alla ricerca della Pietra Filosofale - Storia e segreti dell'alchimia
(Gerardina Cesarano)
Gianni Grana: L'invenzione di Dio
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Parte II
(Sezione speciale, tutta dedicata alla teoria della relatività, e "filiazioni"... - A
special section, wholly dedicated to the theory of relativity, and "derivations"...)
- A Letter from the Editor to the Readers
- Alternative Physics On Line
1 - Umberto Bartocci: Looking for Special Relativity's Possible Experimental Falsifications
2 - Christopher Jon Bjerknes: S. Tolver Preston's Explosive Idea - E = mc 2 and the
Huyghens-Leibnitz Mass/Energy Identity as a Heuristic Principle in the Nineteenth Century
3"
"
" : Einstein's Irrational Ontology of Redundancy - The Special
Theory of Relativity and Its Many Fallacies of Petitio Principii
4 - Alberto Bolognesi: La nuova teoria del cielo - La cosmologia osservativa di Halton Arp
5 - George Galeczki: Beyond Maxwell-Lorentz Electrodynamics
6 - Delbert J. Larson: The State of Experimental Evidence for Length Contraction, 2002
7-
"
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: The Most General Fundamental Failures of Modern Physics
8 - Emidio Laureti: Le basi sperimentali della propulsione non Newtoniana
9 - Rocco Vittorio Macrì: Neopitagorismo e Relatività
10 - Jarosław Mrozek: Did Einstein Claim That Nature Has Mathematical Structure?
11 - Francisco J. Müller: The Problem of Reciprocity and Non-Reciprocity in Relativity
Theory
12 - Vladimir Onoochin: On the Impossibility to Describe the Fields of the System of
Uniformly Moving Charges in the Frame of Special Relativity
13 - Sabato Scala: Simmetrizzazione delle equazioni di Maxwell con l'introduzione del
campo gravitazionale, un'idea bizzarra?
14 - Gianfranco Spavieri, Miguel Rodríguez, Edgar Moreno: Recent Developments in the
Relativistic Electrodynamics Controversy
15 - Tuomo Suntola: Dynamic Space Converts Relativity Into Absolute Time and Distance
16 - Paramahamsa Tewari: Nature of Energy, Light, and Einstein's Light Principle in
Special Theory of Relativity
17 -
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: On the Space-Vortex Structure of Cosmic Bodies
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18 - Theo Theocharis: Louis T. More, Prophet of the 20th Century
19 -
"
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: Ultimate Creative Ignorance
20 - Tom Van Flandern: What the Global Positioning System Tells Us about the Twin's
Paradox
Reprints
Emilio Almansi: Sulle attrazioni newtoniane di origine idrodinamica
Stefan Marinov: Annus Horribilis - (The Story of) A Payed Advertisement Published by
Nature
N. Moisseiev: Intorno alla legge di resistenza al moto dei corpi in un mezzo pulviscolare
Carl A. Zapffe: Exodus of Einstein's Special Theory in Seven Simple Steps
Recensioni/Reviews
Christopher Jon Bjerknes: Albert Einstein, The Incorrigible Plagiarist
(Thomas E. Phipps, Jr., from Infinite Energy Magazine, N. 47, 6 October, 2002)
(A brand new Appendix to the book: A Short History of the Concept of Relative Simultaneity
in the Special Theory of Relativity)
Franco Selleri (a cura di): La natura del tempo (Propagazioni super-luminali - Paradosso
dei gemelli - Teletrasporto)
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INFORMAZIONI EDITORIALI
Episteme è soprattutto una rivista "non convenzionale" on-line, reperibile presso i seguenti
siti:
(Numeri arretrati: http://itis.volta.alessandria.it/episteme).
Articoli, commenti e altro materiale sono benvenuti, e possono essere presentati per la
pubblicazione da parte di ciascuna persona interessata. La spedizione può essere effettuata
vuoi a mezzo Internet, a:
[email protected]
(inviare eventuali attachments soltanto in formato txt, o doc - si prega di non usare tex! - ed
eventuali figure, tabelle, etc. in formato jpg),
vuoi facendo pervenire un dischetto tramite posta ordinaria, all'indirizzo:
"Episteme"
Dipartimento di Matematica e Informatica, Università
06100 Perugia - Italy.
Respingendo ogni forma di "monopolio linguistico", Episteme intende mantenersi
plurilingue, pertanto i lavori potranno essere redatti in qualsiasi (quasi!) lingua, vale a dire
Francese, Inglese, Italiano, Spagnolo, Tedesco (etc.?!).
L'accettazione degli articoli è decisa dagli organizzatori - in base alla conformità con la linea
della rivista - che ne informeranno in modo tempestivo i proponenti, riservandosi
eventualmente di acquisire pareri di esperti (le opinioni ricevute saranno eventualmente rese
note agli interessati), e/o di chiedere agli autori chiarimenti o modifiche.
Il materiale ricevuto anche se non utilizzato non si restituisce.
- La diffusione via Internet di parti della rivista avviene in qualche caso prima della data
prevista per la pubblicazione ordinaria, dopo la quale però ogni correzione ai lavori messi a
disposizione in rete viene segnalata in un apposito Errata Corrige.
- Si fa notare che la versione on-line di Episteme è talora necessariamente "semplificata"
rispetto a quella a stampa (per esempio in presenza di caratteri o simboli speciali). Il file
originale in formato doc dei vari articoli (o dell'intero fascicolo) verrà inviato gratuitamente
dalla redazione (come attachment) a chiunque ne farà richiesta.
"Episteme" è più in generale un "progetto culturale", che non ha fini di lucro, e non è
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ad Episteme) al sopra citato indirizzo.
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Oltre alla diffusione on-line, si produce anche un certo numero di copie cartacee della rivista,
tra l'altro per distribuirle, a cura e spese degli organizzatori, presso Biblioteche, Istituzioni,
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postale, e come contributo generale per la gestione e il mantenimento in vita del progetto. Si
ringraziano pertanto in anticipo coloro che vorranno richiedere la versione a stampa della
rivista.
EDITORIAL POLICY
Episteme is mostly an on-line publication, but it does produce even printed copies. In order to
obtain some of these (15$ each), a request should be sent to the editor, at one of the addresses
indicated below.
Episteme is interested in publishing papers which illustrate unconventional points of view that is to say, which do not usually appear in other academic journals - in Science, History
and Philosophy.
Since Episteme is thought of as a multi-linguistic journal, papers are accepted and possibly
published in Deutsch, French, English, Italian, Spanish (etc.?!).
Episteme will communicate to contributors as soon as possible whether submitted papers are
in agreement with the journal's criteria, or not.
Files of the papers, in doc or txt format (please avoid tex!), together with possible illustrations
in jpg format, should be sent either by attachment, to:
[email protected]
or by diskette, through ordinary mail, to:
"Episteme"
Dipartimento di Matematica e Informatica
Università, 06100 Perugia - Italy.
Episteme can be found at the following web sites:
(Back numbers: http://itis.volta.alessandria.it/episteme).
- Sections of this journal are available in Internet even before the publication of the printed
version; afterwards, any modification of the material made available in the web is registered
in a suitable Errata Corrige.
- The Internet version of Episteme can sometimes be defective, in presence for instance of
special characters or symbols. The original file in doc format of the various articles (or of the
journal's whole issue) will be sent free (as an attachment) from the editorial office to every
people asking for it.
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A Letter from the Editor to the Readers
This special number of Episteme, attached to the ordinary December 2002 issue, is intended
to celebrate the first three years of the journal (which has grown up more and more from its
first number, meeting encouraging appreciation from an increasing number of readers), and to
face - in as "professional" way as possible - one of the greater obstacles to the diffusion of the
principles of Cartesian rationality. Namely, the assertion that man, conceived as a "young
animal", and as a recent and still "simple" product of blind evolution and chance from nonliving matter, has not (at least in the present moment of his history, but perhaps he will never
have) an intellect able to make an intuitive image of the real underlying structure of the
Universe. This is, in our opinion, the answer to the question which Theocharis [a well known
physicist, who is present in this number of Episteme, as well as in N. 4, Sep. 2002] asks in:
"Where science has gone wrong"?1 The turning point could be in fact recognized in the 1859
publication, and worldwide success, of Darwin's theory2, which immediately led to the 1872
"revolution" in the foundations of mathematics (the voluntary renouncing of intuition in
favour of a formalistic point of view, which first of all destroyed the foundational rôle of
euclidean geometry3), and shortly afterwards to the 1905 relativistic revolution (fostered once
again by mathematicians, those people which one could call the Göttingen men4). As a matter
of fact, relativity was the first physical theory to introduce the idea that one could not
anymore interpret all natural phenomena in a "classical way" (the reason for that would be
that man's intellect does not have experience of the large, and small, scale universe), and thus
supported the necessity of unconventional mathematics in physics 5 (the famous successive
Einstein's "qualms of conscience", in front of a physics which had rapidly grown up highly
counter-intuitive, appear entirely adequate to his "original sin").
No more explicit manifesto of this philosophy we could find but in the words of a leading
XXth Century physicist, the 1965 Nobel prize winner Richard Feynman, who warns that:
"What I am going to tell you about is what we teach our physics students [...] and you think I'm going
to explain it to you so you can understand it? No, you are not going to be able to understand it. [...] It
is my task to convince you not to turn away because you don't understand it. You see, my physics
students don't understand it either. That is because I don't understand it. Nobody does. [...] It's a
problem that physicists have learned to deal with: They've larned to realized that whether they like a
theory or they don't like a theory is not the essential question. Rather, it is whether or not the theory
gives predictions that agree with experiment. [...] The theory of quantum Electrodynamics describes
Nature as absurd from the point of view of common sense. And it agrees full with experiment. So I
hope you can accept Nature as She is - absurd "6.
In front of a Nature which is irreparably "absurd", and can be only manipulated, but not
understood, a rather nihilistic-irrational7 drift has spread in "natural philosophy", and from
physics it has "infected" all fields of science and of Western Weltanschauung. This trend has
given rise to a sort of epistemological resignation8, which has supported the common feeling
that purely practical satisfaction should be the only consequence of the scientific enterprise. It
also implies the supremacy of practical-echonomical values (or even simply aesthetical) over
ethical, as well as metaphysical, ones (regarding as such the pursuit of pure knowledge). And
this is one of the worst "sins" of our "advanced" civilization, which aims to propose itself sometimes even resorting to the force - as the unique, and the best, for the whole mankind.
Perhaps, another interesting quotation 9 would be useful in order to realize what kind of
epistemology is born from such premises.
11
Constructing a scientific theory means forging a new system of concepts for interpreting the world.
Such a construction has a great deal in common with the process of creating a fictional world [...] In
either a work of fiction or a work of science, the task of creation is the same [...] "the boundary line
between the two is not as clear as is generally believed" [here the author quotes Vladimir Nabokov's
Lectures in Literature, ed. by Fredson Bowers, Harcourt Brace Jovanovich, New York 1980] [...]
There is no discontinuity between the thinking processes underlying modern science and the thinking
represented in the ancient myths. [...] The scientist is a mythopoet who constructs a system of concepts
for interpreting experience and weaves them into a coherent story. But science adds the discipline of
prediction, testing, and building upon the results of the others. Science is mythology plus discipline.
[...] Even physics, the standard of precision for all experimental science, is a mythology created by
human minds guided by the paradigms of the day. [...] In modern western culture, science has largely
taken the place of traditional religions [...] Many millennia ago, orally recited myths represented the
best scientific thought of the time. Today, "objective" science is one of our most widely accepted
myths.
The author goes on describing the shock that some students experience when confronted
with this "truth", and explaining the reason for the "success" of only a few of them.
Bright students with high scores in mathematical aptitude arrive eager to learn all the wonderful truths
of science. For the first two years, they really believe it. But in the third year, they study issues in the
philosophy of science and discover that it is all a myth. It is a myth with high predictive value, and no
other myth has been found to be more accurate. Yet it is not an Eternal verity, but simply our best
guess about the universe works. When they come to that realization, many of the students go through a
profound emotional crisis. Some of them never recover. But the best ones emerge with a deeper
understanding of science and a better ability to do original research.
These "skeptical" opinions (which are similar in some sense to those of the well known
epistemologist Paul K. Feyerabend) are of course in part right, in part wrong, and in part,
moreover, paradoxical. Yes, even if most of contemporary physics could be well described
indeed as a work of idealistic "fiction", all the same the aim of any "true" science should
always be, at the contrary, to try to assemble (as far as it is possible) a rational image of the
world, which, at least in principle, cannot be but the same for all human beings, since they
share the same experiences and thought-categories10. That is to say, even if a scientist should
always show himself well aware of the limits of his knowledge, and of its possible
hypothetical nature, science cannot but reduce the space for arbitrariness of opinions, and a
"proof" of this is the fact that very often quite independent scientists, coming from all the
parts of the world, and from absolutely different cultures, elaborate the same kind of scientific
theories, as this volume shows in some extent.
The "paradox" arises when one takes note of the existence of a curious factual situation [see
for instance the paper of Bolognesi about the "big-bang", or the professional experiences
sketched in Marinov's reprint], namely that, this "liberal" epistemology notwithstanding,
scientific paradigma are defended by the establishment like dogmas, critical research on the
"foundations" is discouraged, official journals would not take even in consideration papers
like most of the ones published here, for instance those which express doubts about relativity,
under the conviction that this theory is "beyond a shadow of a doubt" 11, and that only a crank
would challenge Einstein. Briefly, the paradox is that a self pretended (in words) liberal
environment, shows itself quite illiberal in the facts!
It is not difficult to realize how much of this debate is influenced even by politicalsociological purposes, since the appreciated value of tolerance would be, in the persuasion of
many, better favoured by the absence of any "truth", including "scientific" ones. As a matter
of fact, there are instead effective arguments concerning the possible coexistence of freedom
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and truth, for instance that there are not too many truths to be afraid of12, or that every
generation has anyway the right, even better the duty, to doubt (this is the Cartesian
methodological doubt) any opinion received from the previous generation. As Federigo
Enriques brilliantly says: "For the values of the spirit, as well as for those of economy, a
degradation law holds: men cannot peacefully enjoy their hereditary possession, but must
renew and recreate these values, in an effort to understand and to get over them"13.
Carrying on this discussion, we would risk to write down a manifesto of proto-modern
epistemology, opposed both to modern and post-modern (an example of this is given by the
quoted Feynman and Sowa), not to say pre-modern!, epistemologies; that is to say, to make
explicit the general aptitude, and expectations, which inspired the rational work of people like
Galilei, Descartes, etc., and so we stop here, spending instead a few words in order to make
understood how the editor (who is a mathematician, and not a physicist!) came to realize the
unexpected influence of a reductionist materialist philosophy on the "foundations" of
mathematics and physics, and of the existence of strong (usually overlooked) connections
between the last two. He used to teach modern formalistic mathematics, telling his students as it is usual under these circumstances - that the highly sophisticated approach they were
called to follow (since the very foundations), was necessary, due to the "well known" great
achievements of physical research at the beginning of XXth Century. Most teachers roughly
satisfy the need of motivations in this way, but the editor decided, at some point of his career,
to study with more attention the previous statement, in order to be able to persuade better
(mostly himself!) that the renunciation to intuition, which was demanded by the formalistic
approach to the "nature" of mathematical objects, was rather justified, and wise notwithstanding his long personal teaching experience, which, quite at the contrary, had
shown very clearly to him that mathematics could have been taught in a quite simpler way by
using at the beginning the intuition of ordinary space (euclidean geometry, measuring, real
numbers) and time (arithmetics, counting, natural numbers, order), instead of abstract
structures. So he went on studying the physical connection, analysing in some detail the
famous historical experiments, which led people such as Feynman to claim that "classical"
explanations were " absolutely impossible". When he started this research he was quite sure
that he would have found all in perfect order, and that he would have come back to his
beloved pure mathematics in a very short time: but 20 and more years have elapsed since
then, and he has found himself more and more sinking into a deep bog, and he was persuaded
at last that the "magnificence", and the experimental ground, of some theories as relativity, or
quantum mechanics (in its widespread "irrational" Copenhagen interpretation) was more an
effect of propaganda, rather than of objective science (namely, a science which is based on
certain experimental data, and deductions), or of logical "impossibilities".
This persuasion of the necessity of a new literal re-volution, of the restoration of ordinary
rationality in Natural Philosophy, appears - we would dare say - a common thread connecting
the papers collected in this volume, wholly dedicated to criticism and alternative to the pillars
of XXth Century physics, relativity, relativistic cosmology, etc.. We must admit that we are
well aware of the fact that some of this criticism could be in its turn criticized, since not
always the arguments are free of errors, or of misunderstandings. All the same, in our opinion,
this does not diminish the interest of such attempts for a long overdue renewal of science,
since we are not in front of mathematics, where a mistake in a line of a proof of a theorem
usually makes the whole discussion worthless. Matters in physics appear more complex, and
subtle, and one can take advantage of even "unperfect" papers, which however express good
ideas14.
We are ending this "foreword" explaining briefly the criteria which inspired the choice of
the reprints. As Friedwart Winterberg says very keenly, the promising attempts of physics at
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the end of XIXth Century, aimed towards a knowledge of the aether's structure, "were brought
to an abrupt end by Einstein's rejection of the ether and its replacement by his well-known
postulates"15. Both the papers of Almansi and of Moisseiev appeared as a good example of
this assertion, even if they, especially the second one, were written after the publication, and
the rather fast acceptance16, of Einstein's theory. "Explanation" of gravitation as a possible
phenomenon of hydrodynamical origin, and the analysis of the resistance to the motion
through a fluid medium, could have been quite well proposed as studies concerning possible
properties of "physical space" (pressure, pressure waves, resistance, etc.), supposed either a
continuous or a powdery (an hypothesis which we personally find more likely) medium. The
publication of Marinov's "paid advertisement" in Nature, was something due, a tribute to the
memory of on unforgotten friend, and in most sense a "master". Not all his opinions appear
acceptable, since he never believed in an "aether", yet he defined himself an "absolutist", a
situation which led him to statements like: there are no "fields", there is no (finite speed)
propagation of interaction, there exists energy coming from "nothing", and so on. The same
applies for the choice of Zapffe's "exodus": a commemoration of a physicist which always
disputed relativity as a an adequate "model" of physical reality 17. His magnetospheric theory
sounds quite attractive, unfortunately one must repeat what has been said in Marinov's case,
not all his opinions appear acceptable18.
Notes
1 - Nature, 1987, 329; Nature, 1988, 333 and 389.
2 - The connection with darwinism is essential in order to understand all the development of Western
science and culture during the last 150 years. A very interesting virtual book [Adnan Oktar (Harun
Yahya), The Evolution Deceit] dealing with this matter is freely available at the web page:
http://www.evolutiondeceit.com/ . Needless to say, this does not mean that everything before was
quite good, and that were not irrational obstacles interposed against free thought - which is the
indispensable condition for the progress of any knowledge - but the Darwinistic pessimism and
aggressiveness had a very bad influence on the field itself of "rationality".
3 - U. Bartocci and J.P. Wesley eds., Proceedings of the Conference on Foundations of Mathematics
& Physics in 20th Century: the Renunciation to Intuition, Benjamin Wesley Publ., Blumberg,
Germany, 1990.
4 - See for instance the very interesting Lewis Pyenson's book, The Young Einstein - The advent of
relativity (Adam Hilger Ltd, Bristol and Boston, 1985), in particular Chapter 5: "Physics in the
shadow of mathematics".
5 - Ibidem, p. 83.
6 - QED - The strange theory of light and matter, Princeton University Press, 1985, pp. 9-10.
Feynman goes over on this opinion at the beginning of his celebrated lectures about Quantum
Mechanics (The Feynman Lectures on Physics, Addison-Wesley Publ. Co., 1965): "We choose to
examine a phenomen which is impossible, absolutely impossible, to explain in any classical way, and
which has in it the heart of quantum mechanics. In reality, it contains the only mystery". Of course,
from an aether-theoretical point of view, all the pretended "impossibilities" are rooted instead on the
post-relativity disappearance of the concept of aether, as responsible for all quantum phenomena. B.H.
Lavenda and E. Santamato assert for instance that: "Quantum indeterminism is explainable in terms of
the random interactions between quantum particles and the underlying medium in which they
supposedly move" ("The Underlying Brownian Motion of Nonrelativistic Quantum Mechanics",
Foundations of Physics, Vol. 11, N. 9/10, 1981, p. 654); and elsewhere that: "It might perhaps be
possible to develop a completely classical formulation of quantum mechanics based upon the irregular
motion of a single Brownian particle immersed in a suspension of lighter particles" ("Stochastic
Interpretations of Nonrelativistic Quantum Theory", Int. J. of Th. Physics, Vol. 23, N. 7, 1984).
14
7 - The word "irrational", which could evocatively qualify some contemporary physical theories, is
introduced just in opposition to "classical physics", namely to physics which makes use only of
ordinary rationality (that is to say, founded on ordinary space, time, causality), but we must
explicitely remark that to go beyond this ordinary rationality does not necessarily mean to fall into
inner contradictions, as some too naif criticism - for instance of relativity - seems to believe. The
situation is similar to the famous case of non-euclidean geometries. They are logically acceptable
intellectual constructions, but they do not describe the intuition of ordinary space which is "rooted" in
man's mind. Exactly as non-euclidean geometries show that there are many possible "models" of space
which could be thought of, relativity show that it is possible to conceive many abstract mathematical
models of space-time, and the important question to ask is not whether these counter-intuitive spacetimes are "illogical" in themselves (since after all they are mathematical models, and thus they are
"logical" in the same measure as all mathematics is logical), but if their introduction is really
necessary in order to describe Nature's laws.
8 - As it has been called by Franco Selleri, in La causalità impossibile - L'interpretazione realistica
della fisica dei quanti, Ed. Jaca Book, Milano, 1987, p. 13.
9 - From the chapter "Science as a Mythology", in John F. Sowa: Conceptual Structures - Information
Processing in Mind and Machine, Addison Wesley, 1984, pp. 353-356.
10 - "There can exist but one correct method of viewing any subject or question whatever", see in this
same Episteme's issue the paper of C.J. Bjerknes dedicated to S. Tolver-Preston.
11 - From the title of the Chapter: "Special relativity: Beyond a Shadow of a Doubt", in: Clifford Will,
Was Einstein right?, Oxford University Press, 1988. No less enthusiastic appears the famous
mathematician Hermann Weyl (which the author appreciates very much in different contexts), when
he claims (in Space - Time - Matter, Dover Pub., NY, 1952) that: "Einstein's Theory of Relativity has
advanced our ideas of the structure of the cosmos a step further. It is as if a wall which separated us
from Truth has collapsed" ("Truth" has a capital initial letter in the original English text, but one
should take into account that in the German original the corresponding term "Wahrheit" had to be
written with a capital initial by a general rule of that language). Nevertheless, orthodox physicists are
not so unwise do not acknowledge that any physical theory cannot be a perennial certainty, and that it
could be shown wrong in certain respects, an approximation of limited validity to reality. For example,
many physicists would easily accept that the theory of relativity (both special and general) may be
imprecise when applied in the domain of very small distances, or that it may not be adequate when
applied to extremely large ones (for instance, of the order of the presumed "size" of the universe). But,
even if these possible breakdowns would not cause concern, it appears very unlikely that the
establishment would be willing to recognize that relativity gave a quite misleading image of the
universe, and that they followed a completely wrong path for more than 100 years.
12 - We would say, either of a logical-mathematical nature, or of an experimental one, while "general
theories" do almost always depend on the choice of principles a priori, which as such are obviously
free. Any discussion acknowledging the different rôles of hypotheses, facts and deductions (or even
inductions and abductions), should always develop with extreme tolerance, very often establishing not
one single truth, but just a graph of possibilities, which was the the ideal of Leibniz's calculemus.
13 - Le matematiche nella storia e nella cultura, Ed. Zanichelli, Bologna, 1936, p. 153. Editor's
translation, with obvious apologies, here and elsewhere, for the poor English!
14 - We could add that, in the worst case, some mistakes have the instructive consequence to show
how a counter-intuitive treatment of physics could lead even educated scholars into intellectual
bewilderment.
15 - "The Goal Towards Unified Theory of Elementary Particles and the Ether Hypothesis" (in
Physical Interpretations of Relativity Theory. Proceedings, London, 1988).
15
16 - At least from the greatest part of the scientific Western establishment, with some curious
exceptions, which would not today politically correct to discuss with absolute freedom of opinion and
expression.
17 - He was even one of the contributors to the Proceedings of the International Conference "What
Physics for the Next Century?", Ischia, 1991, Ed. Andromeda, Bologna: "Bradley Aberration and
Einstein Space-Time", pp. 197-198.
18 - For instance, as numerous critics of relativity, he falls in the "trap" of the so-called Dingle
Syllogism, which is unfortunately not so good a weapon against special relativity (it would just
emphasize that relativity is not completely a "relativistic" theory, since the difference between inertial
and accelerated motions is an "absolute feature" in Minkowski space-time; see for instance our "Most
Common Misunderstandings About Special Relativity", at the web page:
http://www.dipmat.unipg.it/~bartocci/ERRORSVF.htm).
*****
The following words, coming from a private communication, seem to be very appropriate to
put an end to this Introduction.
Aether as a continuum is the Solution
Glory to experts in Aether models! While people are wondering how the universe began and
evolved, The Answer seems to depend upon Aether as the continuum in Fluid Mechanics.
Hydrodynamics provides an analogy to the physical pictures of simplicity in fundamental
Nature. In the simplest continuum analogous to vacuum, quantum uncertainty is not yielding
particles but actually, mini vortices. Vortices are stable, interactive, and able to form particlelike patterns. Vortices are actually spinning strings in Superstring Theory.
The beginning of the Universe is just the quantum fluctuation of Aether or the fabric of space.
Quantum field is a vacuum continuum. While other physicists are still searching for the
reality of superstring, aether continuum physicists or fluid mechanics physicists are keen on
the reality and application of vortices.
[Wishing a prosperous development and promotion of Aether models],
Wu Chi Kay - Aether model developer
16
Alternative Physics On Line
As stated in the previous "Letter to the Readers" which opens this volume, during the second
half of the last Century (after World War II, and after the worldwide consecration of Albert
Einstein's "authority"- by the way, due to a doubtful connection between relativity, the famous
formula E = mc2 , and the construction of the atomic bomb - as a result of the nuclear
explosions at Hiroshima and Nagasaki), the publication of papers expressing criticism of or
alternatives to relativity has almost been banned by "normal" scientific journals (justified by
the claim that: only a crank would challenge Einstein). This attitude has on the one side
almost totally discouraged the production of free critical thought, and on the other side has
crystallized the foundations of established Physics in a system of dogmatic immobility - a
situation which forced many intellectuals (not only physicists) to understand scientific
knowledge as a kind of "religion" (a thought system in which beliefs cannot be checked by
laymen, or not even really "understood" - see for instance, in this same issue of Episteme,
Marinov's complaints, or Theocharis' contributions).
Even today, things are continuing in this manner, as far as leading scientific journals are
concerned, but the increasing diffusion of the Internet has allowed greater freedom of
expression and communication, and this has supported the acquisition of unconventional news
and points of view, thus showing that discomfort towards the actual establishment's
philosophy of Nature and of Science is rather widespread. In this page, we offer some
interesting examples of this "resistance", which becomes more and more worth of attention,
the more some investigations could lead to unexpected and very positive practical
consequences (see for instance Aspden's mention below of an "unseen sea of energy that we
inhabit in ignorance of its overwhelming power").
We are ending this short presentation with an almost obvious consideration: while censorship
of ideas has become less effective, the web's information content has become so large that
even a willing reader is at risk of getting lost in a maze of too many inputs, some of which
must truly be classified in the realm of day dreams, if not of voluntary disinformation...
[Thanks to Josef Hasslberger, Francisco J. Müller, Delbert Larson, for their valuable support
and cooperation]
*****
"Unconventional" Scientific Journals On Line and General Web Sites
1) Aetherometry - The Science of the Metrics of the Aether,
http://www.aetherometry.com/
2) Aether Sites, http://www.aethro-kinematics.com/wc_sites.html
3) Apeiron - Studies in infinite nature, http://redshift.vif.com/
4) (Various papers about) Extracting Energy from the Active Vacuum,
http://jnaudin.free.fr/html/meg.htm
5) Galilean Electrodynamics, http://www.galileanelectrodynamics.com/
17
6) Infinite Energy Magazine, http://www.infinite-energy.com
7) Journal of New Energy, http://www.padrak.com/ine/
8) Journal of Theoretics, http://www.journaloftheoretics.com
9) Astronomy Research - Scientifically viable challenges to mainstream paradigms,
http://metaresearch.org/
Something has gone wrong in the field of astronomy. Many widely held beliefs fly in the face
of observational evidence. Theories go through such contortions to resolve inconsistencies
that the ideas can no longer be explained in simple language. Alternative ideas are often
rejected out of hand simply because they challenge the status quo. The result... many of
today's theories are unnecessarily complex. Meta Research is dedicated to bringing some
common sense back to this field. Here we challenge ideas that have consistently failed to
make successful predictions, examine new paradigms, and advocate the ideas found to be
most worthy of further consideration and testing. [...]
10) Modern Scientific Theories of the ancient Aether,
http://www.magna.com.au/~prfbrown/aetherqr.htm
11) Natural Philosophy Alliance, http://mywebpages.comcast.net/deneb
The Natural Philosophy Alliance (NPA) is devoted mainly to broad-ranging, fully openminded criticism, at the most fundamental levels, of the often irrational and unrealistic
doctrines of modern physics and cosmology; and to the ultimate replacement of these
doctrines by much sounder ideas developed with full respect for evidence, logic, and
objectivity. Such reforms have long been urgently needed; and yet there is no area of
scholarship more stubbornly censorial, and more reluctant to reform itself.
Reigning paradigms in physics and cosmology have for many decades been protected from
open challenge by extreme intolerance, excluding debate about the most crucial problems
from major journals and meetings. But the founding of the NPA in 1994 provided those
struggling against this irrationality and intolerance with the strength, visibility, and credibility
that comes from numbers and from collaborative, purposeful effort. It has also enabled them
to share, expand, and refine their individual knowledge through contact with many other
critical scholars, at NPA general meetings--held at least once per year since 1994--and by
phone and mail, both postal and electronic. [...]
12) Sapere Aude, http://www.btinternet.com/~sapere.aude/
(from Dec. 2002: http://www.dipmat.unipg.it/~bartocci/fis/sapere_aude.html)
Reclaiming the common sense foundations of knowledge
The site seeks to further the debate about the foundations of knowledge by facilitating access
to the arguments of critics of orthodoxy. Because of the perennially central role the natural
sciences, critical arguments focus on the presuppositions, concepts and methods of modern
physics, and especially on the cognitive revolution associated with special relativity ("antirelativity").
13) The Subspace Project, http://www.martinelli.org/
Why an Aether? Its almost a commonly known fact that the aether was disproven by an
experiment done almost one hundred years ago, by a couple of physicists whom we know as
Michelson and Morely (see "Is the Speed of Light Constant" ). Given that, An obvious
question might be then, "why should we re-visit this idea?". There are a few reasons why we
should. The first point I should make is that the aether theory that was disproven by the
18
Michelson and Moreley experiment was that conceived by 19th century physicists. This only
means the first aether conception was wrong, not that there is no aether.
Furthermore, new scientific research is a process of "turning over stones". We are simply not
smart enough to know which 'stones to turn' or what we will find underneath. Sometimes we
can find things of interest , most times not -- but, sometimes you get "spin-offs".
When it comes to basic research it is unfortunately hard to guess at any kind of a return on
investment. The Michelson and Morley experiment is one example of an unexpected ROI.
They were doing basic research - just doing the sweeping - after all the great discoveries had
finally been made. They were measuring the drift velocity of the earth through the aether.
Every physicist expected that the Michelson and Morley experiment (because of the
extremely precise Michelson Interferometer) would give some number for the earth's drift
velocity through the aether. This number was the expected ROI. Instead they found no drift
velocity whatsoever. In fact, if we were to use their results to calculate the velocity of the
earth with respect to the aether we would have to say that the earth is at absolute rest - not
even orbiting the sun!. This was far more interesting and valuable than the expected ROI.
They found 'gold' - a new principle - a new physical law. … "the speed of light is constant for
all frames." With this new law, physics took a very unexpected turn. This find was one of the
key ingredients to today's modern physics. It gave Einstein the foundation upon which all of
his work was built. And this gives us another observation… As the turn of the century was
approaching, physicists believed that physics was nearly done. This turned out to be wrong way wrong. This is a pattern in science history. In fact, it is not too far off to state this as a
principle, that "established science is often wrong". [...]
Are There Aether Atoms? Yes, but they are not what you might expect. [...]
14) Sur la piste de l'Energie Libre, http://quanthomme.free.fr/CHERCHEURS1.htm
15) 21st Century Science & Technology, http://www.21stcenturysciencetech.com
Some Interesting Papers On Line
1) http://www.energyscience.co.uk/index.html
Aether Science Papers
by: Harold Aspden
This is not a commercial website. It is an educational site operated on a non-profit basis by
Energy Science Ltd. under the direction of Dr. Harold Aspden, who in his retirement years
provides the financial support needed to sustain this venture. Dr. Aspden acknowledges his
gratitude to the Internet facility for providing the means to tell the world about his lifelong
exploration of the unseen sea of energy that we inhabit in ignorance of its overwhelming
power.
The book Aether Science Papers was published in 1996. [...] The 14 papers, reproduced in A4
format from the scientific periodicals in which they were first published, constitute the main
section of the book. The front section of the book is a 68 page commentary entitled The
Creative Vacuum. In view of the importance of making scientists aware of this work, it has
been decided to publish the opening 68 pages here in these Web pages.
About the Title: The 'aether' is a word which says that there is no such thing as empty space.
To say there is no aether is therefore to assert that space can be truly empty, meaning it
contains nothing of an electrical character, it now being a well established fact that there is
nothing having a physical existence that lacks electrical properties. If a scientist expresses
doubt by reference to the 'neutron', I say that the neutron has magnetic properties which are
seated in the motion of electric charge. Otherwise, you need to explain why it has a magnetic
19
moment. If that scientist then mentions the 'neutrino', then I say that the 'neutrino' was only a
notion, a figment of imagination invented as a devious way of declaring that the aether could
absorb or shed energy and momentum without admitting that the aether exists. If that scientist
says that the consensus opinion of professors of physics who deny the reality of the aether can
surely not be discarded, then I ask "Why not?" and can but point to a report on page 12, 6
May 1996 issue, of The Times newspaper in U.K. Science correspondent Nigel Hawkes wrote
under a heading 'The possibility of getting something for nothing': "A physicist at Cambridge
University has produced a new and daring explanation for an old puzzle. If she is right, it
could be the first convincing evidence that it is possible to get something from nothing. The
question Claudia Eberlein addresses in a forthcoming issue of Physical Review Letters is that
of sonoluminescence. If you expose water to a blast of ultrasound, you get a flash of light.
This is deeply puzzling, because visible light has so much more energy than sound that the
energy of the sound has somehow to be boosted by a trillionfold. The wavelength of the light
emitted implies that the source is at a temperature of tens of thousands of degrees C. Ms
Eberlein suggests that the emission of light is a quantum vacuum effect - energy given off by
the vacuum. Quantum theory says that there is in reality no such thing as a vacuum and that
empty space teems with 'virtual particles' including photons which flit in and out of existence.
The theory is open to test. If it turns out to be right, her explanation will be a major coup, the
first observable manifestation of quantum vacuum radiaton."
The energetic vacuum is, therefore, a live issue. The 'aether' is a reality and I believe that it
can, like a fluid crystal, form structure and dissolve that structure, as it latches onto material
substance, but if that substance vibrates excessively then even the aether is confounded and,
in its confusion, it sheds energy! I have, accordingly, chosen the title Aether Science Papers
with deliberation, knowing that, in the end, the 'aether', per se, will have to be recognized,
even though that will confound the non-believers who constitute the modern generation of
physicists.
2) http://mujweb.cz/veda/babiakjoz/MMX%20New%20view.htm
Michelson-Morley's Experiment - A New View
by: Jozef Babiak
Michelson-Morley's experiment carried out in 1887 should determine absolute velocity of the
Earth around the Sun in the hypothetical "aether". Negative results of this experiment, why
the shift of the interference fringes does not appear when rotating the interferometer in the
angle of 900, explained in 1892 Fitzgerald and independently of him Lorentz with the
contraction hypothesis. Einstein in 1905 built his Special Theory of Relativity on validity of
the contraction hypothesis and on the principle of constant velocity of light in vacuum. [...]
The calculation of the shift of the interference fringes that should appear by absolute velocity
of the Earth around the Sun, is in literature given as follows: [...] This calculation of the shift
of the interference fringes in the Michelson - Morley's experiment is incorrect, because it is
calculated according to the laws of the classic Newton's mechanics - using Galileo's
transformations. Michelson - Morley's experiment is a physical experiment with light,
therefore calculation of the shift of the interference fringes should be calculated according to
the optics' laws. Light in its nature (photons, electromagnetic oscillation) and with its way of
propagating in the solid environment (Snell's law, Huygens' principle) differentiates with its
characteristics from solid bodies to that are valid the laws of the Newton's mechanics. Light photons - are atom particles which by interactions with atoms of the solid environment create
the optics' laws, therefore we can not describe the propagation of the light in the solid
environment using the laws of the classic Newton's mechanics. Snell's law defines the
velocity of light beams in the solid environment as c / na , where na is refractive index of light
in the solid environment. In the calculation of the shift of the interference fringes is the
velocity of light beams in the interferometer arms stated incorrectly as c, which is the velocity
of light in vacuum. In the Michelson-Morley's experiment there is no vacuum in the
20
interferometer arms. I present here an argument, that is often presented, that the velocity of
light in the air is just a few less than in vacuum and has no significant meaning for this
experiment. The velocity of light beams in the air in the Earth's atmosphere is less by c - c / na
= 79 km/s than the velocity of light in vacuum c. Michelson's inteferometer can measure he
change of the velocity of light from the shift of the inteference fringes with the accuracy 1 m/s
on the length of one meter. Therefore is unavoidable to state the precise value of the velocity
of light in the arms of the Michelson's interferometer. Huygens' principle of propagation of
the light in the solid environment defines, that every point to which the oscillation comes,
becomes the source of the elementary oscillation. Huygens' principle avoids adding the
velocity of light beams with the velocity of light, because the source of the light oscillation
becomes each point of the solid environment which the oscillation reaches. Sound is
propagated in the solid environment using the same principle. Pressure wave - sound is
propagated in the solid environment progressively from point to point with the velocity given
by the parameters of the solid environment. We can observe this phenomenon very well and
graphically on the flying plane. The velocity of the sound coming from the flying plane is not
added to the velocity of the plane, the sound is propagated from the flying plane in the air
with the velocity given by the air parameters. The velocity of the movement of the sound
source has no influence to the velocity of the sound. Only the sound frequency is changing,
according to the Doppler's principle. Michelson-Morley's experiment has been measured in
the air, therefore the light beams in both interferometer arms were moving in the air. The air
in both interferometer arms is at rest with respect to the interferometer, therefore the velocity
of the light beams with the respect to the interferometer is in both arms c / na . [...]
3) http://www.paradox-paradigm.com/
From Paradox to Paradigm
by: Johan Bakker
Foreword: Quantum mechanics and the Relativity Theory are incompatible. Somewhere
something must be wrong. In 1727 Bradley observed the star y-Draconis and measured the
stellar aberration. Science concluded unjustly from these measurements that the influential
ether could not exist. Michelson and Morley proved without doubt, with their famous
experiment in 1887, that absolute ether could not exist.
After both ethers were denied the Special Relativity Theory of Einstein was inevitable. The
propagation of forces and light through vacuum became mysterious and almost
unexplainable; time and space became relative.
In the 20th century quantum mechanics developed and gained momentum through the rapid
development of computer science, mathematics and technological development. The
mathematical solutions are staggering, though even the greatest scientists admit they do not
comprehend the physical implications of quantum mechanics totally. In atomic and subatomic
physics math has taken over. The flaw of quantum mechanics is the lack of physical
understanding; it's become an empirical science.
When we consider that science unjustly rejected the hypothesis of the influential ether, in
theory the possibility of this alternative still exists. Exploring the possibilities of the
influential ether, it was "easy" to find mathematical and physical explanations for relativistic
observations and the Lorentz factor. The scientific explanations the ether gives for
unexplained and mysterious physical phenomena are vast.
Elementary and atomic particles like electron, positron, proton, neutron, deuteron, photon and
neutrinos reveal their existence in simple non-relativistic mathematics. The physical
background of quantum mechanics becomes clear. The dual character of particles and
uncertainty principle of quantum mechanics coincides with the ether. Nuclear fusion is better
understood. Even the cause for gravity emerges.
21
Theoretical physicists are not able to disprove the ether theory. They however,
understandable, reject the possibility of ether because it differs too much with the present
scientific perception; their opinion is pre-determined. [...]
Summary: The concrete indications science should look in depth at the possibilities of the
ether theory are:
- In the 19th and 20th century science did not give enough attention to the possibility of the
influential ether after this medium was denied prematurely. The influential ether describes the
stellar aberration perfectly and therefore science should admit the ether theory is a possible
alternative theory.
- The drag coefficient of Fresnel was confirmed by the experiment of Fizeau. This
confirmation had no scientific meaning at all, because the drag coefficient was introduced ad
hoc without a valid physical explanation. It was already certain a "drag factor" would be
measured after Arago's observations. The perfect match of the experiment of Fizeau with the
assumption of ether is a different case and should puzzle scientists.
- The ether theory, described in a simple basic manner in the previous chapters, give all the
explanations you need to explain relativistic observations.
- The inert qualities of the ether gives an explanation for the observed, yet unexplained,
synchrotron radiation.
Often one hears scientists declare the more simple a theory is the more valid it becomes. The
ether theory, with only two forms of energy and related forces, is extremely simple and
explains a lot. Why do scientists reject the ether theory without validated arguments? The
comfort the ether theory explains the revelation of stable particles from ether should mean
something to scientists and produce wondering. The, in a simple way, derived radius of the
neutron combined with the basic equation of the energy of an oscillation eliminates the
constant of Planck and derives a simple classical non relativistic presentation of the
mysterious photon. What is the chance this can happen if it is pure coincidence? The strong
magnetic force, the electrostatic force and the electromagnetic oscillation energy in the
deuteron, the aligned proton and neutron, gives a basic explanation for the quantum mechanic
properties of atomic nuclei and particles. The speculative, but yet simple and consistent,
explanation of gravity emerging from atomic nuclei in matter opens the possibility the ether
theory becomes "the theory of everything" when science gives it proper attention.
Measurements on magnetic currents with directed magnetic spin indicate that there might be a
relation between mass and magnetic energy that exceeds the relation E=Mc2 .
These are the arguments I found pro "ether", by assuming there might be ether after all. The
described ether can explain many othernot mentioned phenomena. For example it is not hard
to see that it is impossible for a proton to merge with an electron when conditions are not
extreme dense. The properties of the mysterious neutrino become clear etc.
Also in favor for the ether theory are contradictions like:
- The Relativity Theory and quantum mechanics contradict each other. There must be
something wrong somewhere!
- The American spacecraft's, the Pioneer 10 and 11 moves through space with a different
direction than calculated with the Relativity Theory. The differences are small but undeniable
and unexplained.
- In astronomy calculations bare large uncertainties. The estimations of the age of the universe
are between 7 and 20 billion years. Factors of importance in astronomy are speed, distance,
mass and time. All the astronomic measurements need relativistic corrections, which
corrections will differ slightly when ether is assumed. Possible the accuracy of these
calculations increases when astronomic data is corrected, according to ether, in a slightly
different way?
- And "last but not least" there are the paradoxes the Relativity Theory and quantum
mechanics imply. If there is no other explanation, the paradoxes have to be real, but without
22
having to explain the paradoxes, the outcome of science is much clearer and therefore much
more preferable.
When I started to write "From Paradox to Paradigm" I just knew in what direction I had to
look. I was not satisfied with the perception of science of the world we do not experience.
Science does not yet have all the answers. When you look what science achieved the last
century you have to be impressed. The information technology and mathematics opened a
world that was fast explored. Scientists eager to explore the unknown had found the code to
decrypt the inexplicable. It had to be the truth what they discovered because the math matched
the experience so well and suddenly what we experienced was no longer valid. Scientists use
the validated argument that what we see is not necessary correct. But they misuse a similar
argument when they say that math describes the data and therefore must be true. They forget
that math is only a tool to describe the events observed and therefore only describes the
mathematical solution of that part of reality. Quantum mechanics describe the experienced
atomic and subatomic world very well. The achievement of science in this area is enormous.
One has to be impressed, but science is also the achievement of men and therefore there is a
change it overestimates itself: science itself can become arrogant. Science should be aware of
its limitations. Quantum mechanics describe the behavior of (sub) atomic physics very well,
this however does not mean that quantum mechanics are the answer to the whole truth. It is
not, nothing is. It describes only a part, the observed in a mathematical way, and can therefore
not be absolute. Quantum mechanics are even more limited in its revelations when derived
relations are extrapolated. The value of extrapolated mathematical solutions is seriously
limited by the fact that one does not know what the math describes exactly. It is a
mathematical solution for a limited outcome of part of the process. Quantum mechanics
describe the mathematical relation between observed data. These mathematical solutions do
not explain the physical process that takes place. Quantum mechanics has no validation to
pretend to describe the physical processes completely.
It would be arrogant to state that the ether is a better way to understand physics, but it is not
when you state that it might be. As long as science denies the possibilities of the ether without
valid arguments science is arrogant. In theoretical physics there are many contradictions that
cannot be resolved, and therefore set aside. The possibilities of the ether theory to combine
the uncertainty principle and duality of quantum mechanics and the deterministic aspects of
classical physics are vast.
The main reason to write "From Paradox to Paradigm" is not be "right" or "wrong". If science
took a path that is not completely correct, the perception quantum mechanics provides may
not be totally valid. The consequence will be that we are not able to foresee that some
interpretations are not entirely correct. We cannot adjust, because the only hold we have is the
math and math only describes the direct relation of the data in a mathematical way. The ether
described in this book gives strong indications that nuclear fusion will not be achieved, in an
economic profitable way, by means of thermal nuclear fusion. The approach according to the
ether should be totally different.
When atomic nucleus are captured and guided by strong magnetic fields the uncertainty
principle can be contained and Controlled Cold Nuclear Fusion (CCNF) becomes
theoretically possible. No one denies the necessity of abundant and clean nuclear fusion
energy for our modern society. The high costs, pollution, global warming and limited reserves
of natural energy resources will become disastrous in due time. And yet science denies society
to explore this possibility by not taking the ether seriously.
[The book is accessible and can be printed, free of charge, at the web site above]
4) http://www.einsteinontrial.com/
Einstein on Trial, Or Metaphysical Principles of Natural Philosophy - A collection of
essays written over a period of a quarter of a century
23
by: Jorge Céspedes-Curé.
In 1905, Einstein set the scientific community on an innovative and, at the time, controversial
course abandoning the Newtonian concept of space and time and upholding the MaxwellLorentz electrodynamics. Was this a leap forward or has the 20th century followed a
misleading course? In a thoroughly readable and exhaustively philosophical analysis, backed
by rigorous mathematical arguments, Jorge C. Curé places Einstein's conceptions on historic
scrutiny. By unifying the Newtonian and classical relativistic conceptions of nature, he
establishes a New Physics. A fitting revolution for the new millennium.
In Chapter 1, the author examines the philosophical knowledge Einstein had about the
ontological and epistemological foundations of physics. He finds, in this respect, that Einstein
was one of the few creators of 20th century physics who knew precisely what he was doing in
the philosophical foundations of physics. In Chapter 2, Curé deduces a generalized HamiltonJacobi equation (HJ) from Newton's axiom of motion. This generalized HJ equation contains
an extra term, which Curé calls the "quantum collective potential" (QCP). Curé goes on to
show the ontological origin of the QCP based on a philosophical consideration when applying
Newton's axiom of motion. He then shows that Schrödinger's equation is a particular case of
the generalized HJ equation. In this chapter, Einstein is found not guilty, at all, in accusing
quantum mechanics for being an incomplete theory. In Chapter 3, a vast collection of
Electrokinetics (EK) and Electrodynamics (ED), which were scattered in the history of
physics of the 19th and 20th centuries, are examined. They are classified and also translated to
a modern vector notation. In Chapter 4, Newton's three principles are extended from three to
five. Curé accepts Einstein's challenge to deduce "formally and logically" a Newtonian
Gravitodynamics and Electrodynamics. Then he shows theoretically and experimentally the
existence of a new ED field proportional to the square of the electric current. He also presents
the revival of Eddington's model of the neutron as a miniature hydrogen atom. In Chapter 5,
Curé re-examines the cosmic ether concept, discovering how Einstein himself resuscitated the
concept in 1920. The author explains the light deflection of remote stars by the solar energy
field, using the classical phenomenon of refraction. Curé's calculations show a much better
agreement with Merat's empirical law of solar light deflection, than Einstein's calculations. In
Chapter 6, Curé demonstrates that Newton provided, in his Principia of 1687, an original
explanation about the perihelic rotation of planet Mercury. Curé defends General Relativity
Theory (GRT), in the event that the sun is oblate. Curé uses the measured starlight deflection
by the energy field of the sun to determine the stellar density of energy. At the end of this
chapter, the author speculates on an alternative explanation of the starlight redshift. This work
has profound implications on the Big Bang theory and modern cosmology. In the last Chapter
7, Curé begins with the analyses of four essays written by Einstein, between 1930 and 1948,
about "Science and Religion." The author points out that Einstein, through the four essays,
foresaw the advent of a future scientific theology. Einstein believed that through a "cosmic
religious experience" man could acquire transrational knowledge by a transcendental
reconnection with the Supreme Intelligence. In the rest of this chapter, Curé pursues, to its
finality, the consequences of these initial theological intuitions of Einstein. In this way, Curé
establishes the foundations of "Cosmotheism" or Scientific Theology.
5) http://ourworld.compuserve.com/homepages/jlnaudin/html/elecmtr.htm
Electrogravitics - Experiment With A Motor
By: Patrick Cornille
6) http://www.orgonelab.org/miller.htm
Dayton Miller's Ether-Drift Experiments: A Fresh Look
by: James DeMeo
The history of science records the 1887 ether-drift experiment of Albert Michelson and
Edward Morley as a pivotal turning point, where the energetic ether of space was discarded
24
by mainstream physics. Thereafter, the postulate of "empty space" was embraced, along with
related concepts which demanded constancy in light-speed, such as Albert Einstein's relativity
theory. The now famous Michelson-Morley experiment is widely cited, in nearly every
physics textbook, for its claimed "null" or "negative" results. Less known, however, is the far
more significant and detailed work of Dayton Miller.
Dayton Miller's 1933 paper in Reviews of Modern Physics details the positive results from
over 20 years of experimental research into the question of ether-drift, and remains the most
definitive body of work on the subject of light-beam interferometry. Other positive etherdetection experiments have been undertaken, such as the work of Sagnac (1913) and
Michelson and Gale (1925), documenting the existence in light-speed variations (c+v > c-v),
but these were not adequately constructed for detection of a larger cosmological ether-drift, of
the Earth and Solar System moving through the background of space. Dayton Miller's work
on ether-drift was so constructed, however, and yielded consistently positive results.
Miller's work, which ran from 1906 through the mid-1930s, most strongly supports the idea of
an ether-drift, of the Earth moving through a cosmological medium, with calculations made of
the actual direction and magnitude of drift. By 1933, Miller concluded that the Earth was
drifting at a speed of 208 km/sec. towards an apex in the Southern Celestial Hemisphere,
towards Dorado, the swordfish, right ascension 4 hrs 54 min., declination of -70° 33', in the
middle of the Great Magellanic Cloud and 7° from the southern pole of the ecliptic. (Miller
1933, p.234) This is based upon a measured displacement of around 10 km/sec. at the
interferometer, and assuming the Earth was pushing through a stationary, but Earth-entrained
ether in that particular direction, which lowered the velocity of the ether from around 200 to
10 km/sec. at the Earth's surface. Today, however, Miller's work is hardly known or
mentioned, as is the case with nearly all the experiments which produced positive results for
an ether in space. Modern physics today points instead to the much earlier and less significant
1887 work of Michelson-Morley, as having "proved the ether did not exist". [...]
http://www.orgonelab.org/
7) http://www.norbertfeist.de/english.htm#Absatz4
Ether Theory or Relativity Theory?
by: Norbert Feist
The missing aberration of terrestrial sources, a new analysis of the Michelson Experiment and
analogous acoustic experiments with the result of a new identical propagation equation for
light and sound call the premises of relativity theory into question. They speak for the
existence of a luminiferous ether as absolute frame of reference and propagation medium for
electromagnetic waves.
8) http://rosarioclub.com/ciencia.htm
La Aventura del Razonamiento - Ciencia & Descubrimiento
by: Ricardo Gómez Kenny
La comunidad cientifica, si bien evoluciona, es cerrada, ciega y sorda. El inesperado
descubrimiento, anunciado por un argentino hace ya varios años, hoy deja sin respuesta a los
matemàticos. Entre las opiniones que han podido recibirse - todas con alguna excusa - se
puede leer "entre lìneas" , algo asì como...".!Ah, yo no fuì! Dirìjase a fulano." Si el error
puntualizado llama la atenciòn, (por lo simple y razonable), la causa de todo sorprende mucho
màs aùn. Los equipos de cientìficos, oficialmente reconocidos y que dicen "estar a favor de la
acciòn interdiciplinaria", nunca quisieron tomar en cuenta la opiniòn racional de los grupos
llamados comunmente "proyectistas". En sìntesis: Segùn este investigador ... todos los dibujos
que representan experiencias en los libros de fisica, (En el tema Relatividad), estan mal
confeccionados. No responden a las reglas preestablecidas para objetos en movimiento.
Obviamente, la crìtica no se refiere a errores propios del dibujante sino de aquèl que concibiò
25
dicha forma de representaciòn.¿Tienen validez los razonamientos que le siguen? Podrìamos
resumir toda esta situaciòn en esta frase: "Un arquitecto moviò la estanterìa. Los matemàticos,
desconcertados, se reùsan a debatir". [...]
9) http://www.hasslberger.com/
Vortex - The Natural Movement - Considerations on Light, Matter, Gravity And
Magnetism
by: Josef Hasslberger
Physics, the science which should be explaining to us how the universe came about and what
it consists of, seems to have arrived at the end of a blind alley. Its descriptions of the origin
and the workings of our universe get more and more complex, less and less agreed-upon and
they are definitely not going to accompany us into the 21st century. We are at the beginning
of the space-age. In order to survive in that new age, we need clear and unequivocal
descriptions of physical phenomena. [...] The trouble is not where physicists commonly look.
It seems to be more a question of philosophical or religious outlook. Our view of nature was
conditioned first by the great philosophers of ancient Greece and then, for a long time, by the
orthodox religions prevalent in current western civilization. Ironically, the physicist who
denies the action of a creator, just by this very denial limits the scope of his investigations. He
has become "inversely religious", which to an independent scientific investigation is no less
limiting than the stand of the dogmatic religionist. So it might be that progress in our time has
become dependent again on philosophy, on that science of thinking, of looking at basics and
drawing conclusions that is unencumbered by the specialization so prevalent in the physical
sciences. The following is a speculative description, in simple terms, of the basic workings of
the universe. [...]
10) http://www.dipmat.unipg.it/~bartocci/H&KPaper.htm
Hafele & Keating Tests; Did They Prove Anything?
by: A.G. Kelly
Abstract: The original test results were not published by Hafele & Keating, in their famous
1972 paper; they published figures that were radically different from the actual test results
which are here published for the first time. An analysis of the real data shows that no credence
can be given to the conclusions of Hafele & Keating.
... A leader in Nature in 1972 [11] said that "the agreement between theory and experiment
was most satisfactory". ... The Hafele 1971 report said "Most people (myself included) would
be reluctant to agree that the time gained by any one of these clocks is indicative of anything"
and "the difference between theory and measurement is disturbing" ...
11) http://personales.ya.com/carlosla/model/
EVE, a model of the aether
by: Carlos Laborde
Introduction: The main purpose of this work is to define a model of aether within a given
description scheme. The description scheme used is considered a matter of free election. This
election must only be judged "a posteriori" by its power to organize in an economic and
simple way as much knowledge of the physical world as possible. The description scheme is
the following classical one:
- The space/geometry chosen for the description is the Euclidean with three dimensions.
- The time concept chosen for the description is the Absolute Time.
Such Space and Time are well defined mathematical concepts that behave according to the
postulates. This does not necessarily imply that, in the absence of known external forces,
every material mechanism used in some local context as a clock and that every, so called,
rigid bar should always behave classically (i.e. remain constant when compared with
standards). It must be considered satisfactory enough if the experimental behaviour of such
26
clocks and rigid rods can be described in a consistent way within the description scheme
chosen, invoking perhaps some new phenomena. Clocks are used to measure time, not Time,
and rigid rods are used to measure space, not Space, (in a similar way that gas pressures,
electric currents, etc, are measured by the corresponding instruments). The Time and Space
are theoretical bricks of the description that are not measured in the physical world but
defined in the model world.
It is considered that the goal of adjusting the physical laws to a classic descriptive scheme
should not be abandoned since it promises more advantages than the relativistic point of view
which adjusts the description scheme to some crude experimental observations. First, when
seeking a global description of the positions and movements of the celestial bodies, the use of
General Relativity seems condemned to lead to circular arguments due to the fact that the
metric used in the description is itself altered by the gravitation fields of the bodies that aim to
be installed in that metric. Second, if succeeding instead to describe the Universe with a 3-D
Euclidean metric together with an absolute Time, the models so constructed are easily
understood by our minds (used to treat with these kinds of relations in our everyday life). In
this case, intuition becomes a powerful tool to suggest new inferences.
The descriptive point of view defended in this work is the same adopted by the majority of
physicists before the arrival of Relativity. It is not ignored that the theory of Relativity
became a safety raft when the efforts made at the beginning of the 20th century failed to
explain the new experimental facts within the classical description frame. This work may be
considered just a call to make one more effort in the old line impelled by two new facts: First,
our knowledge of physical phenomena is now greater (quantum mechanics, vacuum
fluctuations, existence of a preferred reference frame associated with the dipolar anisotropy of
cosmic microwave radiation...). Second, today's official description of Physics seems again
unsatisfactory to an increasing number of physicists.
Abstract: A very simple aether is postulated. This aether is represented by an ensemble of
moving point entities (aetherinos) that pervade all space. The aetherinos are not material
particles. They have no intrinsic material properties (mass, charge, magnetic moment, spin...)
but are responsible for the appearance of these properties in matter, which is postulated to be
an ensemble of entities of another kind (Simple Particles). In principle this aether is fully
described by its aetherino's velocity distribution (which can change in space and in time) and
by an hypothesis about the effects of the collisions of the aetherinos with matter. (The
aetherinos do not collide with themselves).
No attempt is made in this work to deduce the exact local distribution consistent with the
experimental facts. With the help of a plausible example distribution and a very simplistic
model of matter it is "shown" nevertheless that many fundamental laws of physics can be
"explained" instead of just stated. [...]
Light is considered a space - time modulation in the aetherino's velocity distribution. The
"spread out" space - time propagation of the disturbance resembles more the idea of light as a
wave than that of light as a particle (photon). The corpuscular properties of light should then
be ascribed only to its emission and absorption by matter and explained by its cooperative /
destructive interaction with the wave-type disturbance. [...]
12) http://www.dipmat.unipg.it/~bartocci/larson.htm
A Derivation of Maxwell's Equations from a Simple Two-Component Solid-Mechanical
Aether
by: Delbert J. Larson
Abstract: Maxwell's equations are derived from a postulated, mechanical, two-component
aether.
[Two more papers by the same author at http://www.dipmat.unipg.it/~bartocci/listafis.htm,
point N. 20]
27
13) http://www.geocities.com/hlindner1/Writings/Space/Physics.htm
Flowing Space
by: Henry H. Lindner
Abstract: A simple theory of Cosmic space and motion explains the experimental results,
unifies our understanding of the effects of motion and of gravity, produces no paradoxes, and
makes more predictions than Relativity.
Key words: absolute space, atomic clocks, black holes, entrainment, gravity, inertia, light,
mass, motion, paradoxes, principle of equivalence, Relativity, space, time.
http://www.geocities.com/Athens/Atrium/8041/
14) http://www.scientificexploration.org/jse/articles/mccausland/toc.html
Anomalies in the History of Relativity
by: Ian McCausland
Abstract: In November 1919 it was announced to the world that observations of a solar
eclipse that occurred in May 1919 supported Albert Einstein's general theory of relativity.
That announcement was one of the most influential events of 20th-century science, since
Einstein's instant rise to enormous fame arose directly from it. In spite of the confidence with
which the announcement was made, however, it was later realized that the accuracy of the
observations was insufficient to constitute a reliable confirmation of the phenomenon that was
predicted. Furthermore, another of the formulas published in the general theory, for the
variation in the perihelion of the planet Mercury, had already been derived by another
scientist several years earlier using another method. In spite of the fact that the experimental
evidence for relativity seems to have been very flimsy in 1919, Einstein's enormous fame has
remained intact and his theory has ever since been held to be one of the highest achievements
of human thought. The resulting deification of Einstein has had some unfortunate effects:
critics of his theory are often dismissed as cranks, and the search for better theories has been
inhibited. It is suggested that the announcement of the eclipse observations in 1919 was not a
triumph of science as it is often portrayed, but rather an obstacle to objective consideration of
alternatives.
Abstract (first page of article) - Introduction - The General Theory of Relativity - The Eclipse
Expeditions & their Observations - Announcement of the Eclipse Results - The Perihelion of
Mercury - The Special Theory of Relativity - Discussion - Acknowledgement - References
15) http://www.aetherpress.com/
Aether and Gyrons
by: Frank Meno
Present physical theories are based on numerous postulates for such things as forces,
momenta, energy, mass, charge, etc., which are not defined in terms of comprehensible
concepts. For example, a force that causes attraction through empty space is clearly
impossible to comprehend. Although one can obtain some useful results by manipulating
mathematical expressions based on such postulates, this approach has neither yielded progress
in philosophy, nor has it enabled further progress in practice. Common sense tells us that, to
investigate something effectively, we should know what we are dealing with. As I describe in
my book [Cats, Atoms, Gyrons, Aether, and the Universe], the ancient Greeks have delineated
the basic questions, but they failed to develop the required mathematics, and have not
performed the necessary experiments to verify their hypotheses before their civilization
collapsed. Nevertheless, the Greek philosophers came to the correct conclusion that there
exists a fundamental substance which must be atomistic. This means that the ultimate
constituent parts of this substance must not be further divisible. Furthermore, since the
observed physical reality is changing, these fundamental entities, which they called atomos,
28
must be in perpetual motion. The issue that was not effectively resolved regards the shape and
size of these 'atoms' (gyrons). [...]
Aether Gyron
Each gyron moves in a straight line while at the same time rotating around its center. These
gyrons, colliding with each other, comprise the gas called aether. Gyrons are very small on
our scale, their length probably corresponds to the Planck length, which is 1.6 x10^-35 m. In
comparison, the diameter of a proton is 1.5 x10^-15 m. The gyrons are spread throughout the
universe, and the majority of them are undergoing random collisions with each other. In this
condition they are comprising what we call the vacuum. Thus, vacuum is not empty, it
contains the random moving gyrons whose motion represents the potential energy. The
average gyron speed corresponds to the speed of light, while some of them move slower, and
some faster.
Like in material substances, if the equilibrium condition is disturbed, waves can propagate in
the aether. The most commonly observed aether waves are called electromagnetic waves, to
which belongs light. In these waves the gyrons move as a group in a non-random spiral
pattern which is called a photon. The intensity of light depends on the number of photons
moving together. If the spiral trajectories of the participating photons move in unison, then the
light is termed coherent. Coherent light is generated in lasers, while incoherent light comes
from the sun and common illumination.
As in material fluids, there can also exist vortices in the aether. In an aether vortex the gyrons
move non-randomly in a closed circular pattern. The simplest aether vortex is called electron.
Since there are possible only right-handed, and left-handed rotations, we have also only two
kinds of electrical charge. The charge is conserved because the rotation in the vortex is
conserved. However, if a right-handed, and a left-handed vortex meet, the rotation cancels,
and charge disappears. This is termed annihilation of matter with anti-matter. The disturbance
associated with such an event causes the generation of photons. The images below show the
organized trajectories of gyrons manifested as photons, and electrons. [...]
16) http://mywebpages.comcast.net/deneb/muller.htm
An Experimental Disproof of Special Relativity Theory (Unipolar Induction)
by: Francisco J. Müller
Here is an experiment that invalidates Relativistic Electrodynamics. To facilitate
understanding it will be presented in two parts, each one in turn subdivided into a rotational
case and a translational one. [...]
17) http://jnaudin.free.fr/html/troutnbl.htm
A Successful Trouton-Noble experiment
by: Jean-Louis Naudin and Patrick Cornille
18) http://www.ece.drexel.edu/ECE/AR/Aether_Model.pdf
An Aether Model of the Universe
by: Allen Rothwarf
Abstract: An aether model based upon a degenerate Fermion fluid, composed primarily of
electrons and positrons in a negative energy state relative to the null state or true vacuum, is
proposed and its consequences are explored for physics and cosmology. The model provides
both insight and quantitative results for a large number of phenomena for which conventional
theory provides no answers or unsatisfactory answers. Among the concepts treated are: waveparticle duality, the nature of spin (a vortex in the aether), the derivation of HubbleÕs law;
electric fields (polarization of the aether); Zitterbewegung (a bare particle orbiting within a
vortex core); inflation in cosmology; the arrow of time; the Pauli exclusion principle
(repulsion between parallel spin vortices); the nature of the photon (a region of rotating
polarized aether propagating with a screw-like motion); neutrinos (a spin vortex with no
29
particle in its core); redshifts; g-ray bursters; and a number of other topics. A key assumption
is that the speed of light is the Fermi velocity of the degenerate electron-positron plasma that
dominates the aether. As a consequence the speed of light decreases with time on the scale of
the age of the universe.
Keywords: Aether, Quantum Mechanics, Cosmology, Relativity, red-shift, Hubble's law,
speed of light, vortices, wave-particle duality.
1. Introduction
We live in a universe of interacting fluids. While oceans in which gases are dissolved, and an
oxygen-nitrogen atmosphere with water vapor and other trace gases are readily accepted, the
third fluid, the aether, which penetrates everything is ridiculed as a relic of a bygone era in
science. Yet, while rejecting an aether, the science establishment has no problems swallowing
waves in vacuum, mysterious probability waves, ad hoc cosmological constants, vacuum
fluctuations that can generate anything, and time and space expanding and shrinking. To the
true believer, the fact that they work is the only justification for the major theories in physics;
Maxwell's equations, the Schrodinger equation, and Relativity, and is used as evidence that
we know everything, that Science is Dead, and humanity's brightest should move on to more
challenging tasks. Some of us, however, are heretics. We would actually like to understand
the physics, rather than just use it as a magic wand to create technology. In this pursuit of
understanding, which is also ridiculed by the establishment as asking meaningless questions,
we have found that the aether is not only a useful concept, but that it is a real substance with
an origin that coincides with the birth of our universe and whose properties determine the
speed of light, the other physical constants, and the missing insight lacking in present
theories.
Before expounding upon the aether and how it explains so many phenomena in a simple way,
let me point out that contrary to popular belief, science is not logically based. Instead, it, like
all human activity is based upon chance and trial and error. [...]
http://www.ece.drexel.edu/ECE/AR/Rothwarf_home.html
19) http://get.ilja-schmelzer.net/
General Lorentz Ether Theory
By: Ilya Schmelzer
An old and seemingly discredited notion of ether has found its new incarnation in a "metric
theory of gravity" by I. Schmelzer, who managed to find for his new ether a consistent and
instructive interpretation in terms of condensed matter physics. (Prof.V.A. Petrov)
General Lorentz ether theory (GLET) is a metric theory of gravity with a predefined
Newtonian framework with preferred coordinates Xi, T. It generalizes Lorentz-Poincare Ether
Theory to Gravity. The ether has density, velocity and stress tensor, and fulfills the classical
conservation laws [...]
20) http://www.journaloftheoretics.com/Links/Papers/Seto.pdf
Unification of Physics
By: Ken H. Seto
Abstract: In the final days of his life, Einstein tried in vain to unite gravity with the
electromagnetic force. The reason for his failure was due to his incomplete understanding of
the physical space. A new description of physical space along with a new understanding of
matter was formulated. This new model of the current universe gives rise to a new theory of
gravity and at the same time it unite gravity with the electromagnetic force naturally. Also this
new model predicts the existence of a new fifth force - called the CRE force. In addition, the
unification of all physics is within the scope of this model.
http://www.erinet.com/kenseto/
30
[The author is already known to Episteme's readers for his article "The Resurrection of the
Light Conducting Medium for Modern Physics" which appeared in the issue N. 3, April 2001]
21) http://metaresearch.org/cosmology/speed_of_gravity.asp
The Speed of Gravity - What the Experiments Say
By: Tom Van Flandern
Abstract: Standard experimental techniques exist to determine the propagation speed of
forces. When we apply these techniques to gravity, they all yield propagation speeds too great
to measure, substantially faster than light speed. This is because gravity, in contrast to light,
has no detectable aberration or propagation delay for its action, even for cases (such as binary
pulsars) where sources of gravity accelerate significantly during the light time from source to
target By contrast, the finite propagation speed of light causes radiation pressure forces to
have a non-radial component causing orbits to decay (the "Poynting-Robertson effect"); but
gravity has no counterpart force proportional to v/c to first order. General relativity (GR)
explains these features by suggesting that gravitation (unlike electromagnetic forces) is a pure
geometric effect of curved space-time, not a force of nature that propagates. [...]
*****
Call for papers for a book of essays
The Editors of a proposed book on classical electrodynamics to be published
by Rinton Press, Inc. (USA) invite submission of papers.
The name of the compilation will be
Has the last word been said on classical electrodynamics?
(Classical electrodynamics: new horizons)
All papers to be submitted by e-mail
to dr. Andrew E. Chubykalo (preferable)
[email protected]
or to Dr. Vladimir Onoochin
[email protected]
or to Dr. Roman Smirnov-Rueda
[email protected]
or to Dr. Augusto Espinoza
[email protected]
in LaTeX, LaTeX"\documentstyle" format is preferable (i.e. not "\documentclass"!).
Figures for papers should be presented in eps-format (encapsulated postscript
format). Page size should not be more than 22.86 x 15.24 см. Papers should be
approximately 15 pages in length and must not exceed 20 pages (except special
cases agreed with the Editors).
All received papers will be evaluated by independent referees.
31
Deadline is 1st of June, 2003
After publication of the book all contributors receive two printouts of their
contributions.
EDITORIAL AIMS AND OBJECTIVES
In the last decade, it is observed an emergence of revived interests towards classical
electrodynamics. While the conventional Maxwell's theory remains one of the few cornerstones of modern physics and cradle of Einstein's relativity, an throughout study on it may
lead us to a better and deeper understanding on electromagnetism which has a nearly two
century history and may bring us nice surprises. In spite of all its visible successes, there are
still reasons to believe that either Maxwell's equations or the conceptual background of
electromagnetism needs to be modified.
There are also attempts in these directions. R. Feynman was one of these who had
some doubts on the completeness of classical electrodynamics, and he once commented: "…
this tremendous edifice (classical electrodynamics), which is such a beautiful success in
explaining so many phenomena, ultimately falls on its face. When you follow any of our
physics too far, you find that it always gets into some kind of trouble. …the failure of the
classical electromagnetic theory. Classical mechanics is a mathematically consistent theory; it
just doesn't agree with experience. It is interesting, though, that the classical theory of
electromagnetism is unsatisfactory theory all by itself. There are difficulties associated with
the ideas of Maxwell's theory which are not solved by and not directly associated with
quantum mechanics…".
Many unresolved and forbidden problems of classical electrodynamics seem to be
more serious in view of frustrated intentions to make fully compatible Einstein's relativity
(based mainly on Maxwell's equations) with quantum mechanics. According to Bohm, this
significant incommensurability has to lead to discover an entirely new order to physics at a
fundamental level with all its implications for classical theory. It will be helpful if there is a
forum where arguments of both for and against modification of standard Maxwell's approach
are presented, and thus, an objective discussion of all possible alternative views logically
sound and based on a rigorous mathematical ground is conducted.
This review volume as entitled above will provide such a forum. The editors would
call scientists who are actively working in electromagnetic theory to send in your review or
research papers on classical electrodynamics, especially these on unsolved and annoying
problems.
The Editors:
Dr. Andrew E. Chubykalo (Mexico)
Dr. Augusto Espinoza (Mexico)
Dr. Vladimir Onoochin (Russia)
Dr. Roman Smirnov-Rueda (Spain)
32
Looking for Special Relativity's
Possible Experimental Falsifications
(Umberto Bartocci)
1 - Introduction
We already had the opportunity to describe, in the Letter... which opens this special number
of Episteme, the fundamental reasons which should inspire a general criticism of relativity, or,
better, of the "philosophy" which was (and is) the ground of Einstein's success. This paper is
an attempt to analyse the strictly physical (phenomenological) situation, in order to give a
suggestion where to look for possible experimental falsifications of the theory (from now on
SR, special relativity1), in the conviction that this is the only possible manner to show that the
main assumption of "abstract physics" supporters is wrong: namely, that the renouncing to
ordinary space, time, causality, was not a "nihilistic caprice", but a necessity forced by facts2.
This analysis is not so easy as it could appear, since to decide whether a given experiment,
or phenomenon (two paradigmatic examples: annual stellar aberration, Sagnac's experiment),
could be explained in a relativistic manner or not (or else, from the other side, that it could
not be explained in a "classical" way), is an engagement which can be pursued only with a
great care, and a good knowledge of the theory one is aiming to prove or to disprove3.
Our main points will be that:
I - There are not so many convincing (direct) experimental arguments in favour or SR, as it is
vice versa usually emphasized by "orthodox" physicists - which sometimes add, on these
premises, that a pretended phenomenon possibly disproving SR would be like a vox clamantis
in deserto, and that this justifies the cautious establishment's response in front of such claims.
II - Moreover, there is not even a crowd of experimental data against Einstein's physics. In
simple words, we do not have until now enough evidence in favour of neither a point of view,
which shows that it would be rather unwise, at least for the moment, to dismiss all attempts
aiming to provide a "rational" description of how Nature works.
1.A Cartesian Physics vs Special Relativity
In order to achieve our goal, let us give a sketch of what relativity essentially is. First of all,
it is a theory which, contrarily to the common opinion, should be considered more
conservative than revolutionary in its essence. In order to explain this assertion, we must go
back to the very beginning of physics as a science, and to the opposition between Cartesian
conception of space as a plenum, and Newtonian contrary point of view4, an empty space not
endowed of any physical objective, measurable, property. Of course, from this quite simple
starting point5, divergences grow up in an increasing complexity, but the substance of all
conflict is there. After the success of Newton on Descartes, the image of the empty space - in
which a mysterious action at a distance ruled the trajectories of all celestial bodies, and in
which movement could only be relative, according to Galileo's famous ship's argument6 dominated the scene of science for more than one Century. The conception of a space acting
as an indispensable medium for all physical interactions, came back during electromagnetic
studies in XIX Century: Ampère, Oersted, Faraday, Neumann, the great Maxwell's Treatise,
etc.. At the end of that Century the situation in theoretical physics was indeed an
33
uncomfortable one. There was the image of the world given by Newtonian mechanics, which
marked, even in a symbolical way, the "victory" of science over the supporters of darkness
and superstition. But there was an aether too, which was clearly "seen" for instance in the
lines of force surrounding a magnet. When Einstein appears on the stage 7, a solution was
really needed, and there were only two possible way out. Either to accept the evidence for an
electromagnetic aether, to refuse the principle of relativity (from now on PR), and to frankly
acknowledge that Newton's party was wrong; or, at the contrary, to maintain the foundation of
Newton's physics8, even in a quite different space-time set up, really undreamed of until
Einstein's age (and this would be the "revolution").
It is obvious that, from our point of view, the really true courage would have been to choose
the first option, while Enstein did exactly the opposite. He maintained Newton's empty space,
proposing PR as one of the essential Nature's laws, and at the same time "borrowed" from
aether's physics concepts like the independence of light's speed from the speed of the source,
the finiteness of the speed of propagation of all aether's "disturbances" (fields), etc.. He
showed in such a way that it was possible to assemble a general theory, but he was forced,
however, to give up ordinary space and time conceptions. Thus, it is not a "paradox" to assert
that Einstein followed rather closely Newton's tracks9, and that its only true opponent is
Cartesian fluid-dynamical physics10. One could as well assert that SR is similar to a proof ab
absurdo: the only way to keep together the abstract RP, and the experimental
electromagnetism, is to abandon ordinary space-time, and since this is absurd, we must
choose between the principle and the facts. Needless to say which should have been, in our
opinion, the right choice.
1.B Special Relativity's True "Heart"
As we have mentioned, SR is made up of two postulates (Voraussetzungen), RP plus LSP
(Light's Speed Principle)11. In an empty space RP is "acceptable", because of a kind of
insufficient reason principle: there is no reason why an inertial observer 12 should experience a
physics different from another one, seeing that there exists nothing which could decide which
one is really moving, or still. In an aether theory, and in a wave theoretical approach to the
nature of light (perhaps not the only possible one), LSP is acceptable (even in a stronger
form, see the next section 4). So, from the point of view of a critic of SR, this is 50% correct,
and it is not LSP the assertion which should require a careful scrutiny, but SR's true
foundation, that is to say PR13. Indeed, it is PR which, added to LSP, makes LSP quite
counter-intuitive, and such that all the attention of people goes to the very qell known strange
features of relativistic speeds, but, we repeat it, LSP has nothing wrong in itself, and it
becomes "bad" when one changes the independence from the speed of the source with the
independence from the speed of the observer!
At this point, the fundamental question is: which are the direct experimental arguments in
favour of PR?
We believe that an "honest" answer should be, at least for the moment being, that there are
not. The greatest part of the pretended experiments in favour of SR - whose correctness one
could even accept, mostly if he is not a professional physicist, like the present writer - could
be, first of all, easily re-interpreted in an aether theory, finding in fact in such a context their
better (proper) "explanation" (the "increasing" of the inertial mass as a phenomenon of
"resistance"; the finiteness of the speed of propagation of interactions, perhaps equal for many
different phenomena, the consequent "retardation", etc., obvious; for the so-called "time
dilation", see the next section 3; and so on, we must confess that we find most of all worth of
some attention the claims about the experimental validity od the so-called transverse Doppler
effect). Second, that part of experiments which seem to validate PR, have only used the
34
hypothetical motion of the Earth through the aether 14, thus showing that theoretical physics
has not made, in this field, a great progress since XVII Century! The possibility that this
motion does not exist at all - or that it is too small to be detected 15 - is seldom taken into
consideration in popular divulgations of Einstein's theory, while Descartes-Leibniz's vortex
theory16 implies exactly this inexistence. Only experiments performed in reciprocally moving
laboratories would give some evidence in favour of the one or of the other conflicting points
of view, and these experiments have been almost never done 17! In 20 years study of this
problem, and innumerable discussions with colleagues (usually worried to avert a friend from
bad companies), the author has never heard of such experiments, while at the contrary
everybody claimed that it was practically impossible to reach those speeds which could have
been significant in order to test RP. Moreover, they added that the required accuracy of
measures would have been irreparably disturbed by the forced movement (see even Marinov's
remarks, in the next section 2.A).
And so then? Why one should believe in something which has not yet been proved beyond a
shadow of a doubt18??
It is at this point unavoidable the doubt that the motivations of Einstein's followers are not
of a strictly scientific nature (mathematicians for instance greeted with enthusiasm the "birth"
of SR, since it showed that their sophisticated tools would have shown their practical utility
too19), and we feel obliged to carry on a long research work like the present one.
1.C The Theory of the "Dragging Aether"
It is clear from the above that the general theory which we feel the most trustworthy opponent
of SR is the so-called theory of the dragged aether20, a denomination which shows
nevertheless an implicit relativistic conditioning. If we consider a physically active aether,
why should we accept - in obedience to the opinion that any motion could not be but relative that it would be the same thing to say either that the aether is dragged, or that the aether is
dragging, as it is quite more likely? This misunderstanding is not only of a linguistic nature,
since it is at the origin of a pretended "proof" against the theory we are aiming to propose as
the possibly "true" one. As a matter of fact, most text-books recall the famous Fizeau's
experiment as a "crucial" one proving that the aether is not (at least completely) dragged by
moving bodies (in this case water, forced to move in a pipe), but this has really nothing to do
with Descartes-Leibniz's theory21!
At this point one could ask whether there are other arguments against the dragging aether
(the usual name for an hypothesis of this kind is Stokes theory, but we believe, as we have
said, that we are in front of similar but different theories), and one would be perhaps surprised
acknowledging that, according to the well known Resnick's book 22, only Fizeau's experiment
and annual stellar aberration are quoted as such "proofs". Of the first one we have just said,
the other one appears as a possible new great misunderstanding, one of the many which affect
theoretical physics, which the author, not accustomed to this kind of situation in mathematics,
discovered with great amazement23. As a matter of fact, it has been shown very clearly by
Giancarlo Cavalleri et al.24: "Some special relativity textbooks assert, without giving a
detailed history of the question of aberration, that Stokes theory is wrong [...] their argument
is grounded on a misunderstanding: precisely, the aether which they consider is not
irrotational". Moreover, we feel that is not even impossible to explain Bradley's aberration
introducing a "model" similar to the local magnetosphere (quite compatible with the general
theory of the dragging aether) discussed in the reprint of Zapffe's paper in this same volume,
namely, that this question is still well open.
35
This is the general conceptual frame25 in which one should fit the observations and
proposals below, which represent a kind of Summa, trying to collect the "best" acquired in
many years research and frequentation of "alternative physicists", to whom all (dead or
alive) go the author's warmest thanks.
2 - Does RP Hold in Electromagnetism?
We begin our analysis restating the fundamental question in more specific words: does
electromagnetic phenomenology really allows physicists to propose RP as one of the most
fundamental Nature's "laws"?
It is obvious that, from the point of view of the "Cartesian physics" sketched in the previous
section, the expected answer of Nature should be a clear and strong not, and not only in
electromagnetism, but in principle even in mechanics, with the only difference that it is very
likely that mankind has not been able to observe until now significant mechanical violations
of RP, as men have been confined in their small planet, and in the realm of "low velocities".
It is rather instructive to quote at the opposite the words of a physicist (taken from an
Internet group discussion), who claims that:
The experimental evidence confirming the principle of relativity is actually overwhelming, in
the sense that in no field has one ever discovered any dependence of the forms of the laws of
physics on the velocity of the reference frame.
Is this an opinion, or objective science (as far as science can be objective in the limits of our
present knowledge)? The fact is that exactly Maxwell's Electrodynamics (from now on ME),
the supposed pillar of Einstein's SR26, provides a mathematical set-up which can have
different interpretations as a physical theory (which is a mathematical theory, plus a set of
more or less explicit, and formalized, assumptions, rules of codification and decodification,
from the reality to the abstract intellectual "model", and conversely, which are not so rigid),
some of which interpretations do not satisfy RP.
To this question the author has dedicated a paper 27, in which it is shown that the
phenomenon of the electromagnetic induction, the only one which Einstein choosed as a
motivation for his proposal of a complete symmetry between "inertial frames", is indeed a
good example (internal to ME) of a symmetrical interaction 28, but it should have been
regarded as an exception (which has to do with the circumstance that we are in this case in
front of closed circuits) in classically interpreted ME, and not as a rule. As a matter of fact,
general Maxwell's treatment (which is "aether-based") suggests instead that we are possibly
in front of an asymmetrical phenomenology, in which velocities with respect to a priviliged
frame make a great difference. One must admit, of course, that SR show how it is possible to
interpret ME even in a conceptually symmetrical framework, but one should admit too that
we are indeed in front of two different physical theories, even if they are "sharing" the same
equations. Which one is "true", we actually do not really know. Physics is believed to be
above all an experimental science, but the most meaningful and widespread convictions
appear to be more theoretical in essence (we do not want to say: ideological) than
experimental, and it was really a surprise to realize that some endless discussions could have
been put to an end with experiments that nobody has ever properly done (but almost every
physicist thinks, and acts, as if they had been done!).
36
2.A The Direct and the Inverse Rowland Experiments
It seems convenient, for many reasons, to start with an "experiment" which could be thought
of as the possible key for understanding the nature of the eventual electromagnetic
asymmetries we are talking about. The dear unforgotten friend Stefan Marinov explains the
situation is his Divine Electromagnetism (1993), pp. 169-173, and we quote below some of
his very clear words.
Rowland [Rowland H.A., Sitzungsberichte der K. Akademie der Wiss. zu Berlin, p. 211 (1876)] carried
out in 1876 the following experiment: A disk was charged with positive (or negative) electricity. There
was a magnetic needle in the neighbourhood of the disk. When the disk was set in rotation, the needle
experienced a torque due to the magnetic action produced by the convection current of the charges
rotating with the disk. I call this the DIRECT ROWLAND EXPERIMENT.
According to the principle of relativity, if the disk will be kept at rest and the needle will be set in
rotation, the same torque has to act on it. Such an experiment is called by me the INVERSE
ROWLAND EXPERIMENT.
[...] The above two experiments can be called ROTATIONAL Rowland experiments. It is easy to
transform them into INERTIAL experiments. So if we charge a conveyer belt and set it in action, the
motion of the charges can be considered as inertial (i.e., with a velocity constant in value and in
37
direction) over a considerable length of the belt and we shall realize thus the inertial direct Rowland
experiment.
[...] As far as I know nobody has carried out either the rotational nor the inertial inverse Rowland
experiments.
Now I shall show that, contrary to the prediction of the princople of relativity, the inverse Rowland
experiment must be null, i.e., a magnet moving with respect to charges at rest does not experience
torque.
[...] I carried out the rotational direct and inverse Rowland experiments. [...] Of course, because of the
mechanical vibrations and the Earth's magnetism, it was pretty difficult to establish such a null effect
and my experiment, naturally, needs confirmation carried out in a first class laboratory. According to
me, the inverse Rowland experiment has been not carried until now not because of technical
difficulties but because of a fear that the result will be null [...]
Marinov's words describe a situation which we will face later on in other conceptually
similar contexts, but we wish to remark since now that, apart from possible theoretical and
experimental questions arised by the "Rowland case"29, they testify our same experience:
direct fundamental experiments, the only ones which should allow Einstein's enthusiasts to
assert that SR is really beyond a shadow of a doubt, have never been performed30!
2.B Some Theoretical Remarks About ME
Before going on, it is convenient to be more precise about ME as a mathematical theory. By
this we mean the system of the four Maxwell's equations (expressed in standard differential
notation, in the MKSQ unit system):
∂B
∂t
(1)
curl(E) = -
(2)
curl(B) = µ0 (ε0
(3)
div(E) =
(4)
ρ
ε0
div(B) = 0 ,
∂E
+ j)
∂t
which can be reduced to the two D'Alembert wave equations for the electric and magnetic
potentials Φ , A :
(5)
(6)
ρ
,
ε0
A = -µ0 j ,
Φ = -
where appear the charge density ρ(x,y,z,t) and the density current j(x,y,z,t) (which satisfy
∂ρ
the charge continuity equation div(j) = ).
∂t
The potentials Φ , A are connected by the Lorentz gauge condition:
(7) div(A) = -c-2
∂Φ
(where: c-2 = ε0µ0 ) .
∂t
38
The electric and magnetic fields E, B are expressed in terms of the potentials by the
equations:
(8)
(9)
∂ A
∂t
B = curl(A) ,
E = -∇Φ -
and the force acting on a charge q , movin with velocity v , is the Lorentz force:
(10) F = q (-∇Φ -
∂ A
+ v×curl(A)) = q E + q v × B .
∂t
There is indeed in the theory a further assumption, which can be viewed as a restriction on
the way fields originate from sources 31: we assume that for a given ρ and j, (5) and (6) have a
unique solution which is physically relevant, namely the one given by the so called LiénardWiechert retarded potentials:
r
1
ρ (x' , y' , z' , t - )dx ' dy ' dz '
(11) Φ(x,y,z,t) =
,
c
4π ε 0 ∫ ∫ ∫
r
(12)
µ
A(x,y,z,t) = 0
4π
∫∫∫
r
j (x' , y' , z' , t - )dx ' dy ' dz '
,
c
r
where r'(x,y,z;x',y',z') is the ordinary distance
[(x - x' ) 2 + (y - y' ) 2 + (z - z' ) 2 , and the
integration is made on the whole space (one gets smooth solutions if one starts from smooth
data for ρ and j ).
The previous formulae (11) and (12) are in truth not so simple to understand. Their
"physical" meaning is that the contribution of a point (x',y',z') to the integrals is not given for
instance by the charge which is in this point at the time t , but only by the charge which was
r
in (x',y',z') at the retarded time t - , that is to say by the charge which is seen from (x,y,z)
c
in the point (x',y',z') at the time t .
The equations introduced above must be thought of - in ME's classical interpretation - as
valid only in a set of privileged reference frames K , the so-called aether frames (in principle
they are unique up to spatial rotations and translations, and up to a time homothety, but do not
forget what has been said in footnote 25), where the ordinary concepts of classical mechanics
can be used. In their relativistic interpretation, one must add an additional hypothesis, which
ensures the validity of the theory in all inertial reference frames K' , namely the ones moving
with a uniform velocity with respect to K (connected to K by means of a Lorentz-Poincaré
transformation):
(13)
(j,ρc) and (cA,Φ) are 4-vectors of the Minkowski space-time.
Only this assumption enables to write the Maxwell's equations in a covariant form, but one
must remark that (13) is a genuine new physical assumption, which is logically independent
of the previous ones, and that it is perfectly legitimate to use ME in a "classical" space-time
theory without any connection at all with relativity. We shall show now some of the
39
differences which can arise between different physical interpretations of the same
mathematical theory.
2.C Trouton-Noble Type Experiments
Let us study more carefully the different previsions which a Cartesian and an Einsteinian
physicists (from now on: C and E ), can do with the same mathematical theory.
Let K(x,y,z,t) be an inertial coordinate system of the space-time. K will mean for C a
(possibly local) rest-frame in the aether (or even an aether-frame). Measures of space and
time (for instance, synchronizations of remote clocks) can be made exactly as Einstein
requires, so that even E can accept K as one of his inertial coordinate system. Until this
moment, the only difference is that C would not accept as a "good" coordinate system any
other similar system K' which would "move" with respect to K with a uniform velocity, and
most of all that C would not accept the method that E could indeed use (rightly, from his
point of view) in order to simplify the effort to give an answer to some theoretical questions.
Namely, to change the coordinate system, choosing another one K' more "suitable" with
respect to the physical situation under discussion; make computations in K' ; then go back to
K
using some coordinate transformation (in the present case, Lorentz-Poincaré
transformations). In other words, C cannot use sometimes of the facilities of E , but it does
not really matter, since they agree at least in the choice of K , and most of all in the system of
equations that they have in order to describe electromagnetic phenomenology.
Let us think of an electric charge Q moving in K with some uniform velocity
v = (v,0,0) along the x-axis (let us even suppose that x = vt , y = z = 0 , are the equations of
the motion of Q ), and let us ask, to both C and E : which are the electric and magnetic
potentials associated with Q ?
The question is such that both C and E will give the same answer32:
(14)
(15)
ΦQ =
1
4π ε
AQ =
µ0
4π
Q
( x − vt ) 2 + (1 − β 2 )( y 2 + z 2 )
0
,
Qv
(x − vt ) 2 + (1 − β 2 )( y 2 + z 2 )
(where, as usual, β =
v
).
c
The coincidence of these potentials both for C and E , which could be extended to any
system of a finite number of charges (since we are in front of a linear theory), could make
believe that C and E would share even the same "physics", at least in the electromagnetic
field, but this is not true, as we should immediately understand, now and later in the next
section.
Let us in fact introduce another charge q , in the (xy)-plane, which in the instant t = 0 has
coordinates (Rcos(θ),Rsin(θ),0) , as in the following picture, and let us ask which is the total
electromagnetic force acting on q in virtue of Q in the case q is supposed to move with
velocity w = (w,0,0) parallel to v (in particular, comoving with Q with the same velocity v
, or standing still in K , case w = 0 ) :
40
∂ AQ
+ w×curl(AQ)) ,
∂t
straightforward computations give the following values for the three terms in the right hand
side of the previous expression of the required force:
Starting from (10), namely, in our case,
1
4π ε
-∇ΦQ =
-
∂ AQ
µ
= - 0
∂t
4π
curl(AQ) =
Q
[
0
( x − vt ) 2 + (1 − β 2 )( y 2 + z 2 )
Qv
[
µ0
4π
( x − vt ) 2 + (1 − β 2 )( y 2 + z 2 )
[
( x − vt ) + (1 − β )( y + z )
2
1
4π ε
-
1
4π ε
0
0
2
2
(x-vt,(1-β2)y, (1-β2)z)
3
v(x-vt)
3
]
(1-β2) (0,-z,y)
3
[
( x − vt ) + (1 − β )( y + z )
2
2
2
2
[
R cos (θ ) + (1 − β ) R sin (θ )
qQ
2
[
2
2
2
2
R cos (θ ) + (1 − β ) R sin (θ )
qQ
vw
2
1
4π ε 0 c 2
=
1
4π ε
[
2
2
R
2
R cos (θ ) + (1 − β
2
2
qQ
2
]
3
(1-β2) (0,-y,-z)
3
(Rcos(θ),(1-β2)Rsin(θ),0) +
3
β2 Rcos(θ) ix +
1 1
µ0
=
:
4π ε 0 c 2
4π
qQ
+
0
2
]
= q (-∇ΦQ -
Qvw
and so, remembering that
Fq =
]
Qv
µ
w×curl(AQ)) = 0
4π
(16)
Fq
[ 1− β
2
sin (θ )
2
]
3
2
2
]
]
) R sin (θ ) ]
2
2
3
(1-β2) (0,-Rsin(θ),0) =
(1-β2) [ (cos(θ),sin(θ),0) -
vw
sin(θ) iy ] =
c2
41
1
=
4π ε
qQ
R2
0
(1 − β 2 )
[ 1− β
2
sin (θ )
2
]
3
[u-
vw
sin(θ) iy ] ,
c2
where ix , iy are the unit vectors of x and y , and u is the unit vector of the vector Qq in the
instant t = 0 .
This formula gives the exact expression of the required interaction in ME , with no
difference whatsoever whether we are following a classical point of view or a relativistic one.
1
It is in fact rather instructive, since it is made up of two terms. The first one, namely
4π ε 0
qQ
R2
(1 − β 2 )
[ 1− β
]
3
u , does represent the complete force acting on q when the velocity of
sin (θ )
q is equal to 0 , or even when the velocity of Q is equal to 0 , no matter which is w . When
both v = w = 0 , this term is equal precisely to the well known Coulomb's law for the
interaction of static electric charges.
For any v , different from 0 or not, this "partial" (if w is not zero) force is "almost" equal
- that is to say, up to second order in β - to Coulomb's force, and if we think of a "rigid rod"
which connects the two charges Q and q , this term is annihilated by the reaction of the rod.
For our purposes, the interesting term is the other one, which in the comoving case
β 2 (1 − β 2 )
1 qQ
( w = v and not zero) becomes: 3 sin(θ) iy .
4π ε 0 R 2 1 − β 2 sin 2 (θ )
This force is not directed along u , so it is not annihilated by the reaction of the rod. Up to
second order in β , the projection of this force along the vector
u' = (-sin(θ),cos(θ),0) , namely the unit vector orthogonal to u such that the pair (u,u') has
the same orientation as (ix,iy) , is equal to:
2
2
[
(17)
-
1
4π ε
0
]
qQ 2
β sin(θ) cos(θ) u' .
R2
The "symmetric" computation of the force acting on Q by means of q , always in the
comoving case, gives a similar force, but with opposite sign, which implies that we are in the
presence of a couple of forces, having linear momentum equal to:
(18)
M = -
1
4π ε
0
1
qQ 2
β sin(θ) cos(θ) iz = 4π ε
R
0
qQ 2
β sin(2θ) iz .
2R
A very "small" momentum indeed, but enough, from the point of view of C , to let him
predict that the rod would turn clockwise (if we suppose the two charges of the same sign)
with respect to z , in order to reach the equilibrium position parallel to v (for θ = 0 the
π
momentum vanishes, but it vanishes even if θ =
).
2
This is indeed a violation of the Newton's action-reaction principle, a violation which
appears not only in classical electromagnetism, but even in SR (see footnote 29). It appears
indeed quite "understandable" in an aether theory, since it would be due to the retardation due
to the finite speed of propagation of the electromagnetic interaction. But why have we said:
"from the point of view of C ", if we have even asserted that C and E agree with their
computation? Because E , the previous formula notwithstanding, is forced to predict that the
42
rod would not rotate! As a matter of fact, C has no other means to ground his prevision of a
rotation, while E could argue in the following way too. If I think of an observer X on the
rigid rod, then from the point of view of X the rod is standing still, and since X is a "good"
observer as I am, then the forces acting on the two charges at the extremities of the rod would
be for X exactly equal and opposite, directed along the direction of the rod, as they are for
me when v = w = 0 . Since this reference frame K' which I could think of, comoving with
the rod, is physically quite equivalent to the one, K , in which I am standing still, and since in
K' there should be no rotation (in SR, the action-reaction principle holds in the "proper
frame" of the given physical situation), then a rotation should there be not even in K !
This analysis of E is in fact rather easy, but it is not so trivial to understand why E would
conclude that, even if the previous momentum in K is indeed different from zero for him too,
then the rod would remain nevertheless still. This is why the two forces acting on q and Q
at the same instant t in K (we have supposed t = 0 , but it could be any other instant) are not
acting in the same instant in K' . That is to say, E thinks that from K we see only an
"apparent" momentum, due to the fact that the two forces "appear" to act simultaneously in K
, while in the proper system K' , comoving with the rod , the two forces which are "really"
simultaneous do not produce a momentum. In conclusion, E would claim that C's
prediction is wrong, since he is trying to estimate physical quantities standing far away from
the moving object. C could easily object that it is E which is wrong, because when he is
thinking of an "observer" E' comoving with the rod, E' would be in motion with respect to
the aether ("absolute" motion), and so the Einstein's synchronization of clocks performed by
E' is uncorrect. This is the reason why E' believes that the two forces acting simultaneously
with respect to him on q and Q do not produce momentum, while they do33.
We have proved that, even starting from the same equations, and making the same
computations, there is not a physical agreement between C and E . But who is really right
(perhaps no one of the two!)? Thought of a true rod like the previous one, uniformly moving
with respect to a frame which one has some right to consider "inertial" (with a "good
approximation"), does this rod rotate or not?? An experiment inspired to the situation above
was indeed attempted by Trouton and Noble in 1903, and it is one of the few truly
electromagnetic experiments aimed to prove the consistence of SR. Unfortunately, Trouton
and Noble tried, as usual, to make in evidence a pretended motion of the Earth through the
aether, which as we have said very likely does not exist34. To people who are influenced by
the rôle of the famous Michelson-Morley optical experiment as one of the principal
motivation for the birth of SR, we say that experiments of the previous kind, at the same
manner that the one proposed in the next section, aimed to put in evidence the possible
electromagnetic effects of the "aether wind" due to an absolute motion, should be regarded as
electromagnetic "Michelson-Morley experiments", and that they should be performed for
instance in a "train" like the one of the Buys-Ballot's test (see footnote 17).
2.D The Cardone-Mignani Experiment
We have seen in section 2.C that it is not enough to share the same mathematical equations in
order to have the same physics. Moreover, even if C and E have a common starting point in
Maxwell's equations, to compute the same expressions for the potentials (and for the fields),
is not the general rule. We have analysed before a very simple case, in which potentials are
indeed equal for C and E , but this agreement does not exist anymore when they are in front
of non-uniform motions, like the ones which appear for instance in the case of a circular
current.
As an example of this, we suggest to compute (in a given aether-frame K as before;
remember what has been said on the "agreement" of C and K about this frame) the force
43
which does act at the instant t = 0 on a test-charge q placed in the center of a circular circuit
S , as the effect of a stationary current I flowing in S , when the circuit and the charge are
comoving with a uniform speed v = (v,0,0) as in the previous section.
The situation is described in the following picture (the current is supposed to flow in the
anticlockwise direction from x to y with respect to z), and so by the parametric motion's
equations (both for C and E ):
x = Rcos(θ) + vt , y = Rsin(θ) , z = 0 , 0 ≤ θ ≤ 2π ,
while the motion's equations of q are obviously:
x = vt , y= 0 , z = 0 :
The author did extensively deal with this not simple computation (which requires a direct
integration of Maxwell's equations) in the paper quoted in footnote 27, and the result is that
the force acting on q , from the point of view of C , is equal to (up to second order effects in
β ):
(19)
F =-
µ 0 qI v
iy .
4R
Thus, C would expect a force which is not equal to zero, and which does depend both on
the intensity and on the direction of the current.
From the point of view of E , at the contrary, the prediction is quite different, and he will
not agree at all with (19). As a matter of fact, in the proper reference frame K' , comoving
with the circuit ( S will be no more circular in K' , but this does not really matter), the 3force acting on q must obviously be equal to zero ( E maintains the validity of Clausius'
postulate in K' ), and this implies that it must be zero even in K .
So the important question is: in which point E , which is using the same Maxwell's
equations as C , do not forget it, will differ by the formula (19) when doing his computations
in K ?
Here they are, in order to answer precisely to this question, the exact expressions of the
potentials of the circuit S computed by C 35 :
(20)
ΦS = 0
44
2π
(21)
( − sin(θ ), cos(θ ),0)
µ
dθ ,
AS = 0 IR ∫
4π
( x − vt − R cos(θ )) 2 + (1 − β 2 )[( y − Rsin(θ )) 2 + z 2 ]
0
and now the expressions of the same quantities as computed by E :
v Ax'
(20') Φ*S =
1− β
2
(where Ax' is the first component of the magnetic vector potential in the proper frame K' of
S ; we are using the simplest possible case of a Lorentz transformation)
2π
( − sin (θ ), 1 − β 2 cos(θ ),0)
µ0
dθ .
(21') A*S =
IR ∫
2
2
2
2
2
4π
0
( x − vt − R 1 − β cos(θ )) + (1 − β )[( y − Rsin(θ )) + z ]
The great difference between (20), (21) and the corresponding (20'), (21'), is that Clausius'
postulate (see footnote 35) does hold in SR only in the proper frame of S , while it is no more
valid in K , according to the transformation rules (which are consequences of (13)):
Φ*S =
ρ*S =
Φ '+ v A x '
1− β
2
v Ax'
=
1− β
v
j
v
c 2 x' = 2
c
1− β 2
ρ '+
2
j x'
1− β
2
(where the apices designate quantities computed in K' ).
These equations imply that the moving circuit "appears" to have a non-zero density charge
in K , and so a non-vanishing electric potential. In classically interpreted ME, at the contrary,
the expression for ρS is simply given by the general formula:
ρ(x,y,z,t) = ρ0(x-vt,y,z,t) = 0 ,
where ρ0 represents the density charge in the case v = 0 .
An analogous "classical" formula describes the relation between the density current terms 36:
j(x,y,z,t) = j0(x-vt,y,z,t) + ρ0(x,y,z,t) ,
while the same equation, from the point of view of SR, is given instead by:
jx(x,y,z,t) =
j x ' + vρ '
1− β
2
=
j x'
1− β
2
(the other two components of j remains unchanged in the passage from K' to K ).
45
This shows37 that Maxwell's equations have relativistic solutions only when relativistic
treatment of charges and currents is introduced, while they can have equally good "classical"
solutions when these terms are defined in a classical way.
Let us remark too that the difference between AS and A*S is "very small", since the two
potentials are indeed equal up to second order in β , but that it is not so small to be neglected
(see footnote 32), since, in force of (7), one must have (and one has):
div(AS) = - c-2
∂Φ S
,
∂t
∂ Φ *S
div(A*S) = - c-2 ∂ t
,
and these formulae show that the small difference becomes essential in the second case, when
a small term (the divergence of the magnetic potential) is multiplied by c 2 , and thus it gives a
meaningful non-zero time-variation of the electric potential, a potential which cannot vanish
(in the first case, instead, the divergence of the magnetic potential is exactly equal to zero).
In conclusion, we should ask once again: who is really (that is to say: experimentally) right,
C or E ? The aforesaid divergence can be elaborated in view of the proposal of a new
gedankenexperiment aimed to discriminate between classical and relativistic interpretations of
ME . One could either try to perform direct measures of the force acting on the charge q , or
better of the electric potential difference across a thin linear conductor T placed along a radius
with an extremity in the centre of C and the other one close to the current wire, as in the
following picture:
We could attempt to make in evidence a possible Earth's absolute velocity (and this is why
the sensor and the circuit's plane have been projected to be able to rotate, since this velocity is
unknown), but, as we already said many times, the apparatus should be put in a real motion
with respect to an ordinary Earth's laboratory, before saying that this test has given all
possible information.
The fact that the force predicted by C does depend both on the intensity and on the
direction of the current, should make it possible to separate a non-zero effect from other
possible "disturbances" (due for instance to the electromagnetic fields existing in the
terrestrial reference frame, and to other sources of systematic errors, or even to the possible
46
non-validity of Clausius' postulate - see footnote 35). Moreover, by increasing I and/or q ,
one might be able to observe an effect even if the velocity of the moving laboratory is very
small, as presumably it has to be, compared with c .
We show below another picture, showing the experimental apparatus which we38 have tried
to use in an amateurish way (in Foligno, near Perugia, in 1990):
An experiment of this kind has been in fact performed in a professional way by CardoneMignani39, with results which are difficult to interpret. Anyway, their apparatus was still in an
Earth's laboratory, and so it could have possibly put in evidence only an unlikely "absolute"
Earth's velocity.
In conclusion, we want to repeat it once again that:
* - Apart the fact that the most conspicuous phenomena alleged in favour of SR (namely the
increasing of the inertial mass and the mean-life of speedy particles) appear rather more
compatible with an "absolute theory", than conversely (in absence of any evidence about a
symmetry of these phenomena), it is possible to predict from ME physical effects which
would depend from an absolute velocity, and this shows that the observation at the beginninf
of section 2 - in no field has one ever discovered any dependence of the forms of the laws of
physics on the velocity of the reference frame - is wrong (at least from a theoretical point of
view, but the assertion appears to be theoretical, and not experimental).
** - Electrodynamical experiments (charges-and-currents) to test SR have been
undeservedly neglected, to our actual knowledge, in favour of optical ones, and they
moreover (of both kinds) have never (or seldom) been performed in moving laboratories with
respect to the Earth.
These statements should "prove" our assertion that SR has not been tested so much as it is
usual to claim, by those physicists who appear anxious to persuade their audience that
Einstein was the greatest scientist of all times, and that a doubt about SR would be the same
as a doubt about the Copernican system40.
3 - An (Impossible?!) Gedankenexperiment with Moving Clocks
There is little doubt that one of the most impressive, and counter-intuitive, consequences of
SR, is the so called time dilation, which could be roughly41 expressed as (from the same
Internet group discussion quoted before, in section 2):
The lengthening of the period of a moving clock in the ratio γ =
1
1− β
2
.
47
It would be quite better to say that, for any observer Ω , the time interval ∆τ which has
elapsed for Ω between two events E , F in its life is equal to:
F
(22)
1
2
∆τ = ∫ − ds
cE
(where ds2 is the pseudo-metrics of Minkowski space-time),
and that, when expressed in any Lorentz coordinate system K(x,y,z,t) , then (22) becomes:
F
(23)
F
1
1
2
2
2
2
2
∆τ = ∫ − dS + c dt = ∫ − v + c dt =
cE
cE
F
∫
1 − β 2 dt ,
E
since now ds2 = dx2 + dy2 + dz2 - c2dt2 = dS2 - c2dt2 , and where v =
observer Ω with respect to K , and as usual β =
dS
is the speed of the
dt
v
.
c
Of course, if this speed is a constant, for instance when Ω is an inertial observer, then we
can write:
F
(24)
∆τ =
1− β
2
∫ dt
=
1− β
2
[t(F) - t(E)] =
1− β
2
∆t ,
E
or even:
(25)
∆t = γ ∆τ ,
which means that the coordinate time which has elapsed between the two events E , F is γ
times the so-called proper time which has elapsed between the same two events with respect
to Ω .
This is all, as far as the mathematical theory of "relativistic time" is concerned. Thereafter it
is the moment of phenomena, which go from the observed increasing of the mean-life of
speedy particles (with respect to an Earth's laboratory), to the so called twin-paradox, which
seems to have been experimentally confirmed by the famous Hafele-Keating clocks' travel
around the world (an effect which is more complicated by the presence of a theoretical time
dilation due to the gravitational potential, which must be taken into account by people which
are confident in relativity, either special or general).
Well, as far as this last experiment is concerned, we share the strong doubts which are
illustrated in the very important paper by A.G. Kelly listed at the point N. 17 in the chapter
dedicated to "Alternative Physics on Line" in this same volume of Episteme, and so we
propose a similar test, remarking that, at least in principle, this "twin effect" could be checked
also by comparing the time elapsed for a rotating clock (with constant speed, which makes the
formula (24), or (25), applicable, even if we are not in front of an "inertial" clock) with a
reference clock, which remains still in an Earth's laboratory:
48
One cannot of course hope to be able to reach very high speeds v of C' , but one could
think to take advantage from the fact that C' could be rotated for a long period of time. If for
instance we take for the radius R of the rotating platform R = 1 m , and an angular speed ω
= 2πν which is corresponding to a frequency of ν = 50 Hz, then v is just about 300 m sec1
, which is almost exactly the Earth's rotation speed. From the formula (24) we have ∆τ =
1 − β 2 ∆t , which is almost equal (namely, once again, up to second order in β ) to:
(26)
∆τ ~ (1 -
1 2
1
β ) ∆t = ∆t - β2∆t .
2
2
This last equation shows that the rotating clock C' should loose
1 2
β ∆t sec for each
2
second which is measured by the reference clock C , and since actually:
β =
v
1 2
1
3x102
=
= 10-6 ,
β =
10-12 ,
8
c
2
2
3x10
then we have that in an hour time the rotating clock should theoretically (according to SR)
loose 18 x 10-10 sec , which is about 2 nano-seconds, a value perhaps great enough to be
detected (even in the Hafele-Keating test quoted above the "game" is played around a few
nano-seconds).
Going on with our pure theoretical (pre-experimental) speculations, what could we expect,
from a qualitative point of view, from such an experiment?
Well, according to SR, one should observe not only the expected time retardation, but even
that all kind of clocks should show exactly the same slowing down. From an aethertheoretical point of view, instead, a time retardation is not strictly necessary; moreover, if
there is one, then it should be explained by some "absolute" effect, namely a real physical
effect due to the interaction of the moving clock with the aether. Along this path of thought, a
Cartesian physicist should expect that different clocks (atomic, mechanical, etc.) could
experience different time dilations (and, why not?, even contractions), at different rates.
The author can hear "orthodox" physicists saying: "this experiment has to do with one of the
phenomena which we observe every day in our particle accelerators", but we object that the
increasing of the mean-life of a particle (and let us even accept that the corresponding rate is
exactly the one predicted by SR, and moreover equal for all particles) is not exactly the same
thing proposed before. As an example of a physical cause (coherent with the hypothesis of a
dragging aether) which one could think of, in order to explain the increasing of this mean-life,
let us give the following one, which comes from an analogy (analogies are methodologically
49
fundamental in Cartesian philosophy). Let us imagine an ordinary cartesian orthogonal
reference frame, with an origin O and three axes Ox, Oy, Oz , and a rain falling down along zaxis with intensity s (for instance millimeters of rain for time unity: so s has the physical
dimension of a speed). This means that, if we take a container (a tea-cup!) in form of a
paralleliped (suppose that it has a vertex in the origin, and the three sides coming out from
this vertex along the three axes of the given reference frame being such that the length along
x-axis is L , along y-axis L' , along z-axis L'' ; so the volume is V = LL'L'' ), then, after a
period of time T , we will find a volume of water inside the container which is equal to
LL'sT . Suppose now to rotate the cup along the y-axis of an angle θ , less than 90°, and then
ask the same question: what will be the volume of water inside the cup after a time T ? It is
clear that the answer will be LL'sTcos(θ) , and so far so good. Suppose now that the cup with sides parallel to the three axes - is moving along x-axis with a velocity v = (v,0,0) , and
then ask once again the same question: after the same time T , what will be the volume of
water inside the cup? It is rather clear that, from the point of view of an observer moving with
the cup at the same velocity v , the rain will not fall anymore along the perpendicular to the
"base" of the cup, since one must take in account a kind of "composition of velocities"
(classical aberration, see next section!), and that the rain will fall for him along the direction
s
(v,0,s) , "aberrated" of an angle θ , with respect to z-axis, such that: cos(θ) =
.
2
s + v2
This obviously means that the case we are studying now is exactly the same as before, as if
the cup was simply rotated along y-axis of the same angle θ , and then the answer will be
once again:
LL'sTcos(θ) = LL'T
1
s2
s + v
2
2
= LL'T
1+
v2 .
s2
When comparing this value with the value LL'sT found at the beginning, we find, as it was
obvious to expect, that the water inside the moving cup is less than the water inside the
standing cup, and, pushing further our analogy, if T = U/LL's is the time required for getting
a given volume U of water in the standing cup, then this same time will be equal to:
(27)
T(v) =
U
v2
v2
1+ 2 = T 1+ 2
LL' s
s
s
in the case of a moving cup, a time which is bigger than T .
Of course, we claim that we could possibly be in front of a "similar" phenomenon in the
case we wished to "explain". Let us call T the mean-life, for instance of a muon, in a
terrestrial laboratory: then this T will be, presumably, a function of the given particle and of
its interaction with the "surrounding aether". Then we know that a speedy particle will appear
to have, from the point of view of the terrestrial laboratory, a bigger mean-life, equal to:
(28)
T(v) = γT =
T
1− β
2
~ T(1+
1 2
β ) (up to second order in β ),
2
which is the value predicted by SR, and which we admit agrees with the experimented value.
But let us now compare (28) and (26), by putting in the first equation, as it would be quite
"natural", s = c . Then, up to second order in β , the two equations appear to be identical! In
conclusion, could we be quite sure that the "true" physical reason of the discussed
50
phenomenon is not of the kind of the "moving cup" model, at least in absence of any evidence
of symmetry, which would be essential for the relativistic explanation?
Coming back to the argument of different clocks, and in view of the possible objection of
relativity's supporters (if the proposed experiment would fail their expectations), that the
"failing" clocks are not "good" ones, the question which must receive a clear answer is: but
which is a "good" clock for SR? (remember that at Einstein's times atomic clocks were not
available, not even in theoretical speculations). As a matter of fact, the answer is not difficult,
since the only one clock which is good for relativity is the light-clock, which is described in
the following figure (which we take, with the description below, from Marinov's book:
Classical Physics, Part III, High-Velocity Mechanics, 1981, p. 7):
A short light pulse (i.e., a group of photons) is generated at a given initial moment. The pulse flies ...
to mirror B, ... it returns to A, where it puts a counter ... showing the number "1" and generates (after
amplification) a second pulse which flies to mirror B again; after the return of the second pulse the
counter will show the number "2"...
It is rather clear why this the ideal, perfect clock in SR, and it is curious to remark 42 that
even from an aether-theoretical point of view a light-clock would experience some time
dilation when in (absolute) motion through the aether. If we suppose that the absolute velocity
is (v,0,0) along the horizontal arm of the clock 43 (say that its length is L , in such a way that
2L
the period of the clock44 is T =
), then the moving period would be:
c
(29)
T(v) =
2L
1
L
L
2 Lc
+
= 2
=
= T
,
2
2
(1 − β 2 )
c(1 − β )
c− v
c+ v
c − v
NT
ticks with respect to
T
an aether-rest light-clock, then the same time interval will be measured with N' ticks with
respect to the (absolutely) moving light-clock, in such a way that:
which implies that, if one measures some time interval ∆t as N =
(30)
N' =
NT
= N (1 - β2) .
T (v )
The previous formula can be interpreted as a time dilation effect due to the absolute velocity
1
v , and when compared with (26) one realizes that only a factor
is missing (of course, the
2
same is true for (29) and (28)). If one introduces a "real" length contraction too, again due to a
possible interaction with the aether, then one would get exactly the same factor of the
relativistic time dilation. But since we do not have enough information whether this length
contraction must be conjectured or not (see in this same Episteme's volume the first Larson's
paper), we prefer to leave (30) as it is, because it gives, after all, an instructive example of
other possible time dilations factors, not necessarily equal to the unique one predicted by SR.
51
In other words, if for instance from an aether-theoretical point of view, the previous tea-cup
model would be able to predict a time dilation for moving atomic clocks equal to the
relativistic time dilation, for light-clocks this dilation could be different, and so on, so on...
In conclusion, let us repeat it, even if it was true - at least in some measure - that absolute
speed effects are such that to imply a perfect quantitative identity with SR predictions, then all
the same this would not mean that we are in front of identical physical theories (or of
equivalent physical theories, as many physicists like to say), since the proper time should be
interpreted, from the point of view of the aether physics, only as an apparent time, while the
true time would always be only the coordinate time measured in an (absolute) aether-frame45.
4 - On Relativistic Light's Aberration
We end this paper by proposing at last an optical experiment, but not a test like the usual
ones, aimed to measure speeds, or speeds' differences. Rather, we feel that a very important
consequence of relativity is the so-called light's aberration, which could easily been explained
as follows.
Think, in a coordinate system K of Minkowski space-time as above, of a photon emitted at
the time t = 0 along the y-axis by a light source S standing still in K , say for instance at the
L
point (0,L,0) . Then, at the time
, the photon will arrive in the spatial "origin" of K , the
c
point (0,0,0) . Suppose instead that the source is moving with respect to K with some
velocity v = (v,0,0) , and suppose to introduce a proper system K'(x',y',z',t') comoving with
S (with spatial axes "parallel" to x, y and z). Then the photon will go along a straight line in
L
K' , but not in K , which implies that, at the time γ
(now it appears, as it must in SR, the
c
time dilation factor!), the photon will meet the x-axis in the point (βγL,0,0) , and not in the
point (0,0,0) as before.
So, the aberration angle θ is given (in K ) by:
(31)
tg(θ) =
βγL
= βγ ,
L
or even, up to second order in β :
(32)
tg(θ) ~ β =
v
,
c
which is the classical formula for astronomical aberration46.
A few mathematics would perhaps describe better the situation.
Motion's equations of the photon in K , when the source is still in K :
x = 0 , y = L - ct , z = 0 ; 3-velocity of the photon in K (0,-c,0) ; speed = c .
Motion's equations of the photon in K' , source moving in K :
x' = 0 , y = L - ct' , z' = 0 ; 3-velocity of the photon in K' (0,-c,0) ; speed = c .
Motion's equations of the photon in K , source moving in K :
v
x' = x - vt = 0 , y = L - c(t - γ 2 ) , z = 0
c
52
x = vt , y = L - γct + βγvt = L - γct(1 - β2) = L - ct 1 − β
arrival of the photon at y = 0 : L - ct 1 − β
3-velocity of the photon in K : (v,-c 1 − β
2
,z=0
L
c
,0) ; speed2 = v2 + c2(1 - β2) = c2 .
=0 , t=γ
2
2
This relativistic analysis of aberration shows that, if it is true, according to SR, that the
light's speed c does not depend from the source's motion (in our case from v ), then the
light's vector velocity can depend from v . As a matter of fact, in the 3-velocity (in K ) of
the photon the quantity v does appear explicitely, even if it disappears in the formula which
gives the speed.
Well, from a possibly strict aether-theoretical point of view, when supposing the
independence of light's propagation from the "source's movement", we could think that the
whole vector velocity would not depend from the source, and not only the speed. That is to
say, there is possibly in this point a divergence between aether-grounded previsions and the
corresponding relativistic previsions. So, is it possible to compare relativistic predictions with
analogous aether-theoretical ones, outside from the realm of astronomical observations? In
other words, is it possible to test the relativistic aberration of light in an Earth's laboratory??
We suggest to use a circular platform P like in the following picture:
First suppose that P is at rest, and place a mono-directional (the most possible point-like!)
photon's source S in the rim of the platform, near to a "fixed" point p in the laboratory.
Direct the source towards the centre of P , in such a way that a "fixed" light's detector S*
(once again, the most possible point-like), placed near the "antipodal" point p* of p , can
detect the arrival of the photons emitted by S . Then, we can make the platform rotate, and
arrange things in such a way that, in "stationary" conditions for the angular velocity of P , S
does emit photons only when it is in front of p . The goal is to check whether S* will
continue to detect these photons, as an aether theory would foresee, or not, as relativity would
instead predict. That is to say, one could test whether light is really "dragged" by the velocity
of the source, or not.
One could even think to take both detector S* and source S fixed in the laboratory, and to
use as a moving source a mirror M (almost possibly point-like, as before!), placed in the rim
of P . S does emit photons directed towards the centre A of P , and these photons are
reflected only when M passes in front of A (that is to say, with a period equal to 2πR/v =
2π/ω - of course, from relativity's point of view, one must specify that this is the period with
respect to the laboratory coordinate system). The trace of the backwards photons can be
detected by a fixed screen-detector S* .
In order to avoid S and S* to be too much close one to the other, one could think to place
a semi-transparent mirror M' at some inessential distance from S , orthogonal to the photon
beam, and at a distance L 1 from A , in such a way that the emitted photons can pass through
53
M' . One could then place S* at some distance L 2 from A , in order to detect the backwards
photons reflected by the "other" face of M' , like in the following picture:
One could even think to increase the expected effect by repeated reflections, introducing
another "mirror" placed between the platform and the detector S* .
It is easy to give quantitative evaluations for this Gedankenexperiment. For a given radius
R , and a given angular speed ω , then the distance between the impact point A° of the
inwards non-aberrated photons, and the impact point A1 of possibly aberrated backwards
photons would be equal, in force of (32), to:
(33)
δx = δx' + δx" = (L1+R)tg(θ) + (L1+L2)tg(θ) = (2L1+R+L2)tg(θ) ,
which is almost equal (up to second order in β ) to:
(34)
δx ~ (2L1+R+L2)β = (2L1+R+L2)
ω R
.
c
This identity shows, first of all, that the described test would be called to measure a first
order effect in β . For 1 meter radius, a distance L1 = L2 equal to 25 meters, an angular speed
ω once again corresponding to 50 Herz, then, according to SR, one should have a "shifting
effect", after just one reflection, of:
76 x
3x102
= 76 x 10-6 m ,
3x108
namely an effect of a few microns, which is perhaps not so small to start with. This effect
could afterwards be emphasized - as we have suggested - and finally detected.
It would perhaps be even better, from practical purposes, to replace the rotating platform
with a "very sly" vertical spinning rotor - as in the following picture - in order to get always
an angle of 90° between the inwards beam, and the reflecting mirror M :
In such a way, the proposed "experiment" would rather be similar to the famous Fizeau
cog-wheel experiment. Summing up, the light emitted by S is periodically reflected by M .
54
Then, after a new reflection by M' , the beam hits the mirror-detector S* , from which it is
once again reflected to M' , and so on. If SR is correct, then one should be able to appreciate
an increasing displacement of the trace of the reflected photons, compared with the original
one, corresponding to photons which have not been reflected (and hence are not aberrated). At
the contrary, if the aether-theoretical prevision is correct, then one should not observe any
displacement. The qualitative side of this last experiment could be perhaps one of its most
attractive features47.
Notes
1 - "Special" refers to the first 1905 Einstein's theory, which did not yet include a treatment of
gravitation (Newtonian gravitation was irremiadably out of the requested relativistic "covariance").
After the building of general relativity (GR), we could say that SR is the theory of a flat space-time (a
4-dimensional connected time-oriented Lorentz manifold; in truth, to the property of flatness, one has
to add simply connectedness and completeness in order to get the characteristic properties of
Minkowski space-time), namely that part of relativity which does neglect gravitational effects due to
the presence of the space-time curvature induced by matter. In this sense, SR deals only with
electrodynamics in Minkowski's space-time.
2 - One should perhaps emphasize that any "relativistic space-time" in GR, must be be regarded as a
purely logical admissible construction, whose only "fault" is that it does not describe the "space" and
"time" thought-categories which are rooted in the human mind (a statement this one with which even
relativity supporters generally agree). Hence one can just discuss whether these new space-time (or
others, there is no limit to abstract mathematical constructions) do correspond in some extent to
reality, or not. This remark implies that attempts to prove that relativity is "logically inconsistent"
(contradictory in itself) are worst than useless as arguments against relativity (one case for all, the socalled Dingle syllogism, see section 5 in our "Most Common Misunderstandings...", quoted in footnote
18 in the quoted Letter...). This does not exclude, of course, that such attempts could teach, in any
case, something interesting (see footnote 14 in that same Letter...).
3 - We say that in the conviction that some of the usual criticism against relativity is, unfortunately,
ineffective (see the paper mentioned in the previous footnote).
4 - We must acknowledge that, during his many years of activity, Newton did not always push his
criticism against Descartes up to the point to completely refuse the aether. Anyway, what does really
matters in this discussion, is the manner in which Newton's ideas have been interpreted - and
developed - by his followers, and not which was his original, authentic, thought about this, or others,
argument (if there ever was such a "thought", since it could have changed from an age of life to the
other, or could have been uncertain, undecided). The historical fact is that the hypothesis of the aether
was dismissed after Newton in the conviction that the conception of a "plenum space" was
incompatible with the gravitation's law which ruled the the movement of celestial bodies (see also
footnote 10), and this is enough for our "judgement". Of course, the two conflicting options influenced
the conjectures about the nature of the light too, which was thought of as made up of "corpuscules" in
one case, or conceived as a "wave" (perturbation of the medium) in the other (Huyghens).
5 - Which grounds in something like an "antinomy of the pure reason". The conception of an empty
space does in fact correspond to the mental space of euclidean-intuitive geometry, the "space"
regarded as a "transcendental form" of the human intellect, and it should not by any means be
confused with the space of physical reality.
6 - Besides, a rather old argument, expressed for instance almost in the same words by Nicholas of
Cusa and Giordano Bruno (traces of its influence can be found even in Copernic). It was at that time
needed in order to rebate the objection: "why the pretended Earth's movement around the Sun is not
detected by Earth's inhabitants?". This shows that the chief argument which opposes relativity to the
aether's physics was already fully active not only at the beginning of XVII Century, but at an earlier
55
date too. As we shall see, the most popular experiments alleged in favour of relativity show only that
this pretended movement (the famous aether's wind) cannot be detected in a terrestrial laboratory.
7 - By the way, there were already important studies about the question which gave only to him an
unprecedented fame, see Bjerknes' book reviewed in this same volume.
8 - Which - and this could be thought of as a "paradox" - does not include Newton's gravitation's
theory itself, since, as it is well known, this was the first victim of the requirement that all physics'
laws should be expressed in a covariant form. Of course, people seeing this much beloved theory
disappear, together with the "classical" space-time which Newton too used in his work (as everybody
else until the beginning of XXth Century!), fall in the mental trap of identifying classical physics with
Newtonian physics, and do not realize the importance of the fact that the conception of "physical
space" is identical in Newton's and Einstein's approach.
9 - Even the introduction of the term "inertial" (by no means an easy concept to understand: Einstein
in fact did not make any attempt of explanation, and just used the language of "ordinary" Newtonian
mechanics), show the asserted conservative side of SR.
10 - We feel dutiful a reference to the "unknown" Italian physicist Marco Todeschini, who studied
deeply this argument, and advanced the question to investigate Newton's objections to Descartes'
"gravitational theory", in order to realize whether they are, at the light of advanced physical and
mathematical knowledge, still well-founded or not. See for instance some information about this
scientist in: http://www.dipmat.unipg.it/~bartocci/todes.html (in Italian only).
11 - And many other "implicit" assumptions, see footnote 9.
12 - This restriction to inertial observers appears indeed a conceptual weak point of SR, since a fully
relativistic approach should perhaps make no difference at all between "states of motion" with respect
to nothing (see even the footnote 18 mentioned in the previous footnote 2).
13 - One should not forget that, if Maxwell's theory is "correct" (an assertion, however, which should
be investigated with more care: see for instance, both in this same volume, Galeczki's article, or the
"Call for papers": Has the last word been said on classical electrodynamics?), then LSP would be a
direct consequence of RP, since there is nothing in that theory which connects the speed of an
electromagnetic wave to the speed of its source.
14 - Not to say of their "accuracy", either theoretical or instrumental. Flaws appear sometimes
unintentional, sometimes more suspicious (see for instance Kelly's paper mentioned in section 3). One
of the most interesting examples of this situation, is the analysis of Michelson-Morley's experiment
made in: Marco Mamone Capria, Fernanda Pambianco, "On the Michelson-Morley Experiment"
(Foundations of Physics, 24, 6, 1994), or the refusal of subsequent Miller's results - obtained during
many repetitions of this same experiment - which is discussed in DeMeo's paper listed at the point N.
6 in the chapter dedicated to "Alternative Physics on Line" in this same volume of Episteme. We
consider worth of attention under this point of view many papers by the (well known as a critic of
relativity) Italian physicist Roberto Monti, in particular his "Theory of Relativity: A Critical
Analysis", Physics Essays, Vol. 9, N. 2, 1996, pp. 238-260 (see also his papers published in Episteme
N. 3 and N. 4).
15 - The Earth's revolution speed is about 30 km/sec , and it was not detected for instance by
Michelson and Morley, Trouton and Noble (see section 2.C), and many others. The Earth's rotation
speed in the 24 hours is a more likely candidate for this detection, and it is about 300 m/sec , so an
hundred of times less than the previous one, which implies that, for experiments of-second order in β,
the factor β2 = v2/c2 becomes 10.000 times less. We believe that this could be the reason for the
experimental "anomalies" pointed out for instance in Van Flandern's paper about GPS (see this same
volume of Episteme), but the trouble is that the "detection" of this speed (already realized by
Michelson-Gale's experiment, or by variations of Sagnac-kind experiments) would easily be
56
considered uninfluential to our purposes by relativity's supporters, since it does concern non-uniform
motions!
16 - See for instance Alessandro Moretti: "L'universo intellegibile, ovvero, la gravità descritta da
Leibniz", in Episteme N. 3 (2001) (in Italian only).
17 - One of the very rare exceptions is the experiment that the Dutch meteorologist Buys-Ballot (18171890)
"conducted in order to confirm the Doppler shift. "He put a group of
musicians on a train and took up his position on a station platform. He asked the train driver to rush
past him as fast as he could while the musicians played and held a constant note, and was able to
detect the Doppler shift (as a change in pitch) as the train passed him (D. Filkin, S. Hawking: Stephen
Hawking's Universe: The Cosmos Explained, BasicBooks, New York:, 1997, p. 65)". From:
http://scienceworld.wolfram.com/physics/DopplerEffect.html .
18 - From the title of the chapter: "Special relativity: Beyond a Shadow of a Doubt", in: Clifford Will,
Was Einstein right?, Oxford University Press, 1988 - quoted also in the Letter... which opens this
volume.
19 - See for instance Pyenson's book, quoted in the aforesaid Letter... (previous footnote).
20 - We repeat that it seems necessary to accept as a fact the failure of too many experiments aimed to
detect an "appreciable" aether's wind in a terrestrial laboratory, and so we confess to have some
suspicion towards those people who claim for instance to have proven the existence of an Earth's
absolute movement of almost the same amount of the famous speed with respect to the background
radiation (and of course these numerical evaluations have been given only a posteriori).
21 - See for instance: Giuseppe Antoni, Umberto Bartocci, "A Simple 'Classical' Interpretation of
Fizeau's Experiment", Apeiron, Vol. 8, N. 3, July 2001 (available on line at:
http://www.dipmat.unipg.it/~bartocci/fizhoek.html ).
22 - Robert Resnick, Introduction to Special Relativity, Wiley, New York, 1968.
23 - It is very famous the alleged Hilbert's remark: "Physics is too important to be left to physicists"
(see for instance Pyenson's book quoted in footnote 19, p. 183). Unfortunately, from one side it is true
that theoretical physics should always be carried on with all the logical exactitude which
mathematicians display in their researches. For instance, it is surprising to see how often physicists
assert that something cannot be done, giving as only proof the fact that they did not succeed in doing
that, when it is well known that any assertion of this kind in mathematics is very difficult to prove (a
good example: Paul Cohen's 1963 proof of the independence of the so-called "continuum's hypothesis"
from the Zermelo-Fraenkel-Skolem axioms for a set theory; or perhaps, even better known, Galois'
proof that it was not possible to give a "general" formula for the solutions of an algebraic equation
with degree greater than 4, it would have been certainly not enough to claim this impossibility on the
basis that mathematicians did try for some time to find this formula, and that they did not find it!). But
from the other side, it is even true that mathematicians have in many recent circumstances shown
themselves perhaps worst, with their propensity to aesthetical canons, formalistic abstractness, etc.,
and that these propensions are one of the not minor causes of the physical "philosophy" we are
criticizing (see again Pyenson's book in footnote 19, or, of the present author: "'Cattivi maestri',
ovvero, a proposito di un morbus mathematicorum (ma non solo!) recens", at the web page:
http://www.dipmat.unipg.it/~bartocci/st/goedel6.htm - in Italian only).
24 - G. Cavalleri, L. Galgani, G. Spavieri, G. Spinelli, "Esperimenti di ottica classica ed etere Experiments of classical optics and aether", Scientia, Vol. 111, 1976, pp. 667-673.
25 - We should perhaps explicitely remark that in this theory could even happen that observers in
effective relative motion could be both in absolute rest, a situation which implies that all aetherframes, or rest-frames, should be considered only as local ones.
57
26 - "The special theory of relativity grew out of the Maxwell electromagnetic equations. So it came
about that even in the derivation of the mechanical concepts and their relations the consideration of
those of the electromagnetic field has played an essential role" (A. Einstein, "Elementary Derivation of
the equivalence of Mass and Energy", Bulletin of the American Mathematical Society, 41, 1935). See
the second Bjerknes' paper in this same volume of Episteme.
27 - "Symmetries and Asymmetries in Classical and Relativistic Electrodynamics", with Marco
Mamone Capria, Foundations of Physics, 21, 7, 1991; availabe on line at:
http://www.dipmat.unipg.it/~bartocci/symm.html .
28 - Einstein's source was very likely Alfred Föppl's: Einführung in die Maxwell'sche Theorie der
Elektricität, 1894, but this case was well known to Maxwell himself (A Treatise on Electricity and
Magnetism, 3rd edition, 1892, p. 601).
29 - See for instance: G. Cavalleri, G. Spavieri, G.Spinelli: "On the Action and Reaction Principle in
Special Relativity", Nuovo Cimento B, 5, 1988; G. Spavieri: "Proposal for Experiments to Detect the
Missing Torque in Special Relativity", Found. of Phys. Lett., 3, 1990.
30 - Some people question whether even Marinov did really perform all the experiments he claimed to
have done, or whether they were "professionally" performed, which is perhaps true, at least to some
extent. But this could be so only because Marinov, after his exile from Bulgaria, was a poor man, and
did everything with his own money and enthusiasm, not having access to public funds, often not used
in the best way by luckier establishment's physicists. As far as the strictly experimental situation is
concerned, we should perhaps add that Marinov did not use an electric coil, or a magnetic needle, in
order to try to detect the torque which was, at last, missing, and that he claims to have used an Hall
detector.
31 - The solution below gives the "right" behaviour of fields E and B at infinity, and excludes the
so-called advanced potentials as having no possible physical meaning. We could perhaps point out
that Roberto Monti (see footnote 14) remarks that in equation (2) it should be added a term σ0E ,
where σ0 is the possible vacuum conductivity, and that the conventional present-day choice of
putting σ0 = 0 is not experimentally so well established as it should be. Even if this observation, in
case it was experimentally confirmed, would destroy all pretended covariance of Maxwell's
electrodynamics, one must acknowledge that in non-cosmological contexts (such as the ones we shall
be dealing with) σ0 seems to be really negligible. In other words, that this would be one of those
possible violations of SR on a large scale which would not worry relativity's supporters (see also
footnote 11 in the often mentioned Letter...).
32 - See for instance the celebrated Feynman Lectures on Physics, Addison-Wesley Publ. Co., 1965,
"Electromagnetism and Matter". The author warns (21-5) that it is not so trivial to get (14) and (15)
from (11) and (12), since at first sight "almost everyone" would claim that after integration it should
appear, in the denominator of the fractions, the retarded distance (namely, the distance from the point
in which the charge is seen at the time t), which is not the case. We could perhaps emphasize that the
distance which appears in (14) and (15), and the "ordinary" distance , differ only up to second order
in β , but their difference - which a physicist willing to uncautiously approximate computations since
the beginning, and not only at the end, would risk to neglect! - is essential to further developments.
33 - One should perhaps meditate about the circumstance that this possible factual divergence between
classically interpreted and relativistic Maxwell's electrodynamics is in principle meaningful even for a
small length of the rod, or for a "low" absolute speed v .
34 - But see also the analysis and the experimental results mentioned in the paper listed at the point N.
17 in the chapter dedicated to "Alternative Physics on Line" in this same volume of Episteme. As far
as Trouton-Noble's type experiments is concerned, see also the paper by G. Spavieri, et al., again in
this same volume.
58
35 - In the calculation which leads to formula (20) we did use the fact that Φ = 0 , and then ∇Φ = 0 .
This is the so-called Clausius' postulate: "For a circuit in which is flowing a stationary current, the
charge density is zero" (another electromagnetic "principle" which is not explicitely stated in ME).
Recent reports (for instance: O. Jefimenko, "Demonstration of the Electric Fields of Current-Carrying
Conductors", Am. J. of Phys., 30, 1962; T. Ivezic, "The 'relativistic' electric fields produced by steady
currents: comparison with experiments", Phys. Lett. A, 156, 1-2, 1991; A.K.T. Assis, W.A. Rodrigues,
A.J. Mania, "The Electric Field Outside a Stationary Resistive Wire Carrying a Constant Current",
Foundations of Physics, 29, 1999), both experimental and theoretical, have questioned its validity, but
this would not change the essence of the present discussion. As a matter of fact, both classical and
relativistic Maxwell's electrodynamics should take into account the same modification, and moreover
a charge situated right in the centre of a circular circuit should not be affected by the force arising
from this nonzero electric potential, apart from "asymmetries" in the circuit (not to say of the fact that
the special features of the force (19) could be, at least in principle, allow its detection between other
forces).
36 - It is perhaps useful to remark that the charge continuity equation does hold for these classical
values of the density charge and of the density current, as well as it does hold for the corresponding
relativistic values.
37 - By the way, as one should always expect: mathematics can never give explicitely at the end
anything more than it had in itself implicitly, in the original assumptions one started from!
38 - Umberto Bartocci, Marco Mamone Capria, Luigi Mantovani; see Umberto Bartocci: "On a
Possible Experimental Discrimination Between Classical and Relativistic Electrodynamics",
Proceedings of the International Conference "What Physics for the Next Century?", Ischia, 1991, Ed.
Andromeda, Bologna, pp. 88-94.
39 - Umberto Bartocci, Fabio Cardone, Roberto Mignani: "New electromagnetic test of breakdown of
local Lorentz invariance: Theory and experimental results", Foundations of Physics, Vol. 14, N. 1,
2001 (see point N. 10 in: http://www.dipmat.unipg.it/~bartocci/listafis.htm, with figures).
40 - Tullio Regge, Cronache dell'Universo , Ed. Boringhieri, Torino, 1981.
41 - This is indeed a popular description of time dilation, but we find it misleading - that is to say, a
source for possible misunderstandings - to speak of a "moving clock", since in Minkowski's spacetime nothing is really "moving" (space and time are "tied" together, and can be untied only in
particular coordinate systems), and so the period of a clock remains always unchanged.
42 - As it is curious to remark that the ideal clock of SR (which, as far as our actual knowledge, has
never been realized in practice!) cannot be thought of as point-like, since a length is necessarily
required (one could object that any real clock cannot be thought of as point-like, but here the question
is different, since the light-clock has even a privileged direction). This shows that, at least in principle,
it is not possible to think of a light-clock in an accelerated frame (for instance in the "rotating
platform" of Sagnac's experiment: see section 3 in "Most Common Misunderstandings...", quoted in
footnote 2), without meeting serious conceptual troubles. This observation refers for instance to the
well known difficulties of SR when one wishes to introduce in it some "simple" physical concepts,
like for instance the concept of rigid body.
43 - Not fortuitously we have decided to neglect to analyse any "transversal" motion of the lightclock's behaviour from the point of view of an aether theory! It is clear that to discuss this question
would be exactly as to discuss the Michelson-Morley experiment, and we have serious doubts about
the correctness of its usual theoretical descriptions (see for instance the paper by Mamone Capria and
Pambianco quoted in footnote 14). It is obvious that, at least in the case of high absolute speeds, a
light-clock should in general simply cease to work.
44 - This period of time is quite suggestive, since it would imply that, thought of a minimum possible
length (an hypothesis rather natural in the fluid-dynamical conception of space), call it for instance a
59
metron, then one would have as a consequence a minimum possible time, call it for instance a cronon:
1 cronon = 1 metron / c . Just to give an idea of the possible quantitative size of these units, if we
conjecture that a metron has something to do with the so-called Planck length, whose magnitude is
about 10-35 m , then the cronon would be about 10-43 sec .
45 - About the supposed equivalence of different physical theories (would the pretended equivalence
mean that all possibly conceivable experiments should give the same result? Or that this would be true
for only some of them??), it is rather instructive the reading of: Gianfranco Spavieri, "Nonequivalence of Ether Theories and Special Relativity", Physical Review A, 34, 1986.
46 - This light's relativistic aberration was studied by Einstein since his first 1905 paper, since he had
to explain the known phenomenon of the annual stellar aberration, discovered by James Bradley in
1728. As a matter of fact, this phenomenon could have thought of, at first sight at least, a physical fact
contrary to relativity's principle. We have to admit that Einstein seems to have succeeded in his
purpose, and that annual stellar aberration has a good relativistic explanation too - that is to say, one
must even admit that this phenomenon has - and it had before Einstein - other "classical" explanations.
In truth, this is a rather controversial argument, and are numerous the Einstein's critics which assert
instead that SR cannot provide a good explanation for astronomical aberration (see for instance:
Thomas E. Phipps Jr., "Relativity and Aberration", Am. J. Phys., 57 (6), June 1989). The point is that,
according to SR, only the relative speed between the Earth and the moving star should be the reason
for the observed phenomenon, while all stars appear equipped with the same aberration, which does
depend only from the Earth's revolution speed v around the Sun. This is of course wholly correct, but
the point is that, always according to SR, the phenomenon does depend from a comparison between
two positions of the same star in a 6 months interval, when the Earth should be thought of in an
(approximatively) inertial frame K' different from the one K in which it was 6 months early ( K' is
then moving with respect to K with a speed 2v ). If this argument appears able to "save" SR, at least
on this question, and in general, one could object that the indispensable hypothesis for the relativistic
explanation of stellar annual aberration is that the relative speed Earth-star does not change
significatively in this 6 months time, and that this could not be always the case, for instance when
dealing with binary stars, which have a revolution period comparable with that of the Earth, but show
the same aberration of all other stars. At this point, relativity's supporters find another ad hoc
explanation for these stars, etc., and the question does not appear settled once for all (but see the
chapter dedicated to aberration in Reflections on Relativity, http://www.mathpages.com/rr/s2-05/205.htm).
47 - For instance one could think to invert the rotation of the platform, or of the wheel, and to see what
happens: that is to say, whether there is "symmetry" in the observed patterns (the case in favour of the
aether hypothesis), or not (which would be the case in favour of SR). Needless to say, one should
discuss many more practical details of this "experiment", such as the necessity to provide for a
suitable photon source, since a "real" laser beam is much more similar to a divergent cone, rather than
to a cylinder, as one should instead need in the actual case. These practical imperfections
notwithstanding, a SR supporter should yet predict that one would truly find an asymmetry in the trace
of the photons in S* , depending on the direction of rotation.
----[A presentation of the author can be found in Episteme N. 1]
[email protected]
60
S. Tolver Preston's Explosive Idea
E = mc and the Huyghens-Leibnitz Mass/Energy Identity as a
Heuristic Principle in the Nineteenth Century
2
(Christopher Jon Bjerknes)
Abstract. In 1875, S. Tolver Preston published a prophetic treatise, which set forth his
arguments for the existence of an aethereal medium in space. The title of this work is Physics
of the Ether. Its purpose is to discredit the spiritualistic concept of "action at a distance" and
to evince the irrationality of the principle of "potential energy", and replace these mythologies
with "physical causes capable of rational appreciation." Among the many achievements of
this heuristic masterpiece are Preston's arguments for atomic energy, the atomic bomb, a
luminal speed for the propagation of gravity, and the heuristic principle that E = mc2.
Introduction
Samuel Tolver Preston [b. 1844, was the son of Daniel Bloom Preston (b. 1807) and Mary
Susannah Tolver] set forth arguments in the nineteenth century, which were to condition life
in the twentieth century, and beyond. In an early attempt to apply Herbert Spencer's "Social
Darwinism" in a constructive way (as opposed to the horrific racism it furthered), Preston
argued for the collegiate education of females, on the grounds that it would strengthen the
genetic stock of males and generally increase the intelligence of human beings.[1] This
opposed the longstanding tradition that the Church is the bride of Christ, and is obedient; and,
therefore, a woman must obey her husband and shun professional work. In a letter to Darwin,
Preston professed rationalistic words to the effect of, "self-interest as a motive for conduct is a
thing to be commended - and it certainly [is] I think ... the only conceivable rational motive of
conduct: and always is the tacitly recognized motive in all rational actions."[2] Preston's
equally pragmatic aether theories led him into diverse fields. For example, Preston speculated
on the nature of "Free Will" and brain dynamics - another of his scientific challenges to the
religious ontology and traditions pervasive in his time.[3]
Preston's profound physical insights were the result of a rational analysis of
phenomena he conducted in the refined language and images of the eighteenth century
homme d'esprit George-Louis Le Sage. Preston's work was in part a self-described scientific
reaction to contemporary "theories of a vague nature" which proposed "phantom agencies" to
account for known phenomena. His Physics of the Ether [4] is a scientific synthesis derived
from the hypotheses that aether is rarified mass, mass, concentrated aether; and that aether
particles must be in motion and this motion is conserved. For Preston, as for many of his
contemporaries, all things are modes of motion. These premises evolve subtly into a
definition of terms, identities, and mathematical expressions described in compelling prose,
which assert, among other things, that energy is proportional to mass times the speed of light
squared, yielding incredibly potent kinetic effects,
"165. To give an idea, first, of the enormous intensity of the store of energy attainable by
means of that extensive state of subdivision of matter which renders a high normal speed practicable,
it may be computed that a quantity of matter representing a total mass of only one grain, and
possessing the normal velocity of the ether particles (that of a wave of light), encloses a store of
energy represented by upwards of one thousand millions of foot-tons, or the mass of one single grain
contains an energy not less than that possessed by a mass of forty thousand tons, moving at the speed
of a cannon ball (1200 feet per second); or other wise, a quantity of matter representing a mass of one
61
grain endued with the velocity of the ether particles, encloses an amount of energy which, if entirely
utilized, would be competent to project a weight of one hundred thousand tons to a height of nearly
two miles (1.9 miles)."
Towards a Comprehensive Theory of Dynamics Based on Motion as a
Unifying and Vivifying Cause
Preston set a high standard for his work, which many today would consider naïve,
"there can exist but one correct method of viewing any subject or question whatever." Before
we can come to understand Preston and evaluate the nature of his conclusions and determine
his method for arriving at them, we should first explore the historical context, which led him
to question the mythologies prevalent in his day, and to propose alternative points of view
based on a Le Sagian materialism, which originally arose as a materialistic exposition on the
Epicurean theory of "universal attraction".[5]
Le Sage argued that if space were to contain an extremely fine particulate aether of
"ultramundane particles" moving at light speed in all directions, these particles would
bombard bodies. In the case of a comparatively isolated body, the bombardment would,
statistically, be even on all sides, and a sort of equilibrium pressure would result. However,
bodies would cast "shadows" on other bodies by blocking out those "ultramundane" aether
particles which strike them. This proposed shadowing effect would cause a net force of
attraction between bodies, in conformity with Newton's inverse square law.
In Preston's day, as today, there was a lingering religious opposition to any such
mechanistic exposition on the cause of gravity, which would obviate the governance and
active intervention of God as the cause of gravity. Many, Roger Cotes, Richard Bentley and
Voltaire, among them, considered the idea of "universal attraction" to be a scientific proof of
the existence and active governance of God. Just as the Church had opposed any refutation of
Aristotle's Physics and Metaphysics, religious extremists opposed and oppose any mechanistic
exposition on a proposed cause of "mutual attraction". This corrupt attitude toward pure
science, which is an offense against religious freedom, not an expression of it (Descartes,
Huyghens and Leibnitz, who were vocal advocates of aethereal gravitational theories, were
deeply religious men), is exemplified by Bentley's A Confutation of Atheism from the Origin
and Frame of the World, written pursuant to Newton's letters,[6]
"And first as to that ordinary Cant of illiterate and puny Atheists [***] That such a mutual
Gravitation or spontaneous Attraction can neither be inherent and essential to Matter; nor even
supervene to it, unless impress'd and infused into it by a Divine Power. (3.) That though we should
allow such attraction to be natural and essential to all Matter; yet the Atoms of Chaos could never so
convene by it, as to form the present System: or if they could form it, it could neither acquire such
motions, nor continue permanent in this state, without the power and Providence of a Divine
Being."[7]
This religious persecution had a chilling effect on research into the physical causes of
gravity and magnetism. The subject became and remained largely taboo, with a few notable
exceptions. Colin Maclaurin's writings evince how lightly one had (has) to tread when
proposing a physical theory of gravity. He was a diplomatic apologist for such an approach:
"14. As we cannot but conceive the universe, as depending on the first cause and chief mover,
whom it would be absurd, not to say impious, to exclude from acting in it; so we have some hints of
the manner in which he operates in nature, from the laws which we find established in it. Tho' he is the
source of all efficacy, yet we find that place is left for second causes to act in subordination to him;
and mechanism has its share in carrying on the great scheme of nature. The establishing the equality of
action and reaction, even in those powers which seem to surpass mechanism, and to be more
immediately derived from him, seems to be an indication that those powers, while they derive their
62
efficacy from him, are however, in a certain degree, circumscribed and regulated in their operations by
mechanical principles; and that they are not to be considered as mere immediate volitions of his (as
they are often represented) but rather as instruments made by him, to perform the purposes for which
he intended them. If, for example, the most noble phaenomena in nature be produced by a rare elastic
aetherial medium, as Sir Isaac Newton conjectured, the whole efficacy of this medium must be
resolved into his power and will, who is the supreme cause. This, however, does not hinder, but that
the same medium may be subject to the like laws as other elastic fluids, in its actions and vibrations;
and that, if its nature was better known to us, we might make curious and useful discoveries
concerning its effects, from those laws. It is easy to see that this conjecture no way derogates from the
government and influences of the Deity; while it leaves us at liberty to pursue our enquires concerning
the nature and operations of such a medium. Whereas they who hastily resolve those powers into
immediate volitions of the supreme cause, without admitting any intermediate instruments, put an end
to our enquires at once; and deprive us of what is probably the most sublime part of philosophy, by
representing it as imaginary and fictitious: by which means, as we observed above, they hurt those
very interests which they appear so sanguine to promote; for the higher we rise in the scale of nature,
towards the supreme cause, the views we have from philosophy appear more beautiful and extensive.
Nor is there any thing extraordinary in what is here represented concerning the manner in which the
Supreme Cause acts in the universe, by employing subordinate instruments and agents, which are
allowed to have their proper force and efficacy; for this we know is the case in the common course of
nature; where we find gravity, attraction, repulsion, &c. constantly combined and compounded with
the principles of mechanism: and we see no reason why it should not likewise take place in the more
subtile and abstruse phaenomena and motions of the system. "[8]
Preston courageously and unapologetically confronted the religious bias and dogma
against mechanistic theories of gravitation. He cautions us to not "attach two ideas to [a]
fundamental conception[.]" Motion is the sole cause, for Preston. He also notes, regarding
theories of a vague nature, "that their very vagueness, in which their real weakness consists, is
employed as a defence against argument: hence the long life of such theories." This is a
reaction against the vague and "spiritualistic" notion of "action at a distance" as a "cause".
The cause of gravity is to this day considered by some a divine mystery not meant to be
understood by humankind.
Consider Cotes' preface to Newton's Principia, where he intimates that the search for a
physical cause for gravity, as opposed to a blind faith in (mythological and numerological)
theological forces, is heresy. Cotes, seemingly together with Newton, asserts that induction
resolves gravity to the will of God as the ultimate cause of the phenomenon,
"Without all doubt this World, so diversified with that variety of forms and motions we find in
it, could arise from nothing but the perfectly free will of God directing and presiding over all. [***]
All sound and true philosophy is founded on the appearance of things; which if they draw us never so
much against our wills, to such principles as most clearly manifest to us the most excellent counsel
and supreme dominion of the All-wise and Almighty Being; those principles are not therefore to be
laid aside, because some men may perhaps dislike them. They may call them, if they please, miracles
or occult qualities; but names maliciously given ought not to be a disadvantage to the things
themselves; unless they will say at last, that all philosophy ought to be founded in atheism. [***] He
must be blind who from the most wise and excellent contrivances of things cannot see the infinite
Wisdom and Goodness of their Almighty Creator, and he must be mad and senseless who refuses to
acknowledge them.[9] Newton's distinguished work will be the safest protection against the attacks of
atheists, and nowhere more surely than from this quiver can one draw forth missiles against a band of
godless men."[10]
Voltaire, also, threatened those who would attempt a Cartesian exposition on gravity,
"The cause of this cause is among the Arcana of the Almighty. 'Procedes huc, et non amplius.'
(Thus far shalt thou go, and no farther.)"[11]
63
Preston's fundamental conception is that all things transform as modes of motion
through the impact of particles. These hypothetical particles bear the measurable properties of
inertia, momentum and energy, and "fill" an otherwise void cosmic "empty space". There is a
tacit monadism lurking in Preston's ideas, which he leaves largely unexplored. He argues
through induction that the gaseous nature of his aether filling "space" is self-evident and need
not be explained in terms of frames of reference, or contained volumes, other than as
ontological absolutes. It is this absolutism, which ultimately leads him to predict that E = mc2,
as an absolute store of energy contained in material bodies, which can be put to work.
For Preston, as for Huyghens and Leibnitz, the identity between mass and energy is
the mode of motion. He argues that "action at a distance" is an impossibility, which requires
the "absurd postulate of an infinite velocity[.]" He further argues that the concept of "potential
energy" is devoid of meaning, because it asserts energy without motion, and confuses terms
by equating, in name only, one state with a completely different state. A living person can
potentially die, and become a dead person, but such a fact does not render a living person,
dead. The state of a mass in a field of force is not the same as the state of a mass in motion, in
terms of the ability to do work. Should a field of force composed of a shower of aether
particles impart motion to a body, then it is this conserved motion which is cause, not spiritual
"potential" which is cause.
Preston substitutes the action of an intervening medium for the two myths of "action at
a distance" and "potential energy", which he finds feed off of one another, the fall of one
necessarily toppling the other. He attempts to logically prove that the conservation of energy
is only satisfied by supposing that the aether is a gas of particles in linear motion, which
expand to fill any contained volume. The "forces" of Nature result from contact with these
moving particles of aether. The velocity of these particles cannot be infinite, for if it were,
then the aether particle which causes the phenomena of gravity and magnetism would have to
concurrently occupy the beginning, middle and end of its journey, an impossibility.
Preston induces the elasticity and speed of aether particles, which of logical and
experimental necessity (by analogy to an aeriform medium) must be in motion, from the
speed of light. He does not delve into the metaphysics of why his proposed aether particles
move at light speed, but instead infers this speed as a logical necessity, his necessary singular
exposition of the known phenomena, his ultimate generalization arrived at through induction
from known experimental results.
We see here many of the elements of the theory of relativity, stated in scientific terms,
as opposed to the metaphysics, which later replaced the scientific hypotheses of this aether
theory. "Action at a distance" must occupy time, due to the fact it is through the action of an
intervening medium that the effects known as "action at a distance" arise. This speed is the
normal speed of aether particles, known through induction to approximate the speed of light gravity propagates at the speed of light, a speed which nothing can exceed, for speed depends
upon the size of a particle and an aether particle is perhaps the smallest fathomable
subdivision of matter, and the fastest motion. Preston induces these Le Sagian ideas from the
properties of light propagation. Le Sage simply wrote, "we assume for the [gravitational]
corpuscles the velocity of light[.]"
From these basic inductions to general principles, Preston begins to synthesize these
generalizations into fantastic and useful conclusions,
"The above deduction, as to the high speed of the ether particles in their normal state, throws
at once a light upon the existence of a vast store of energy in space of a very intense character,
competent to produce the most forcible observed molecular motions, such as the phenomena of
chemical action, combustion, the explosion of gunpowder, and other remarkable cases of the
development of motion or work, all such effects finding their explanation in an interchange of motion
between the ether and the molecules of matter under special conditions[.] "
64
The bombardment of aether particles flying about in space, each with great energy due
to their high velocity, produces an enormous pressure in space. Taking note of the fact that the
tensile strength of steel wire is enormous and again appealing to reason, Preston holds that
matter cannot cohere with the immense force it does if it is simply composed of isolated
masses suspended in empty space. There must be a "material agent" which causes this effect,
which effect Preston attributes to a pressure differential, as a logical necessity,
"As to the precise physical process by which a reduction of the pressure of the intervening
medium can take place in the presence of vibrating matter, we shall reserve the consideration of this
point for the present; but it may be noted that the inference is none the less essential, that a reduction
of the ether pressure does take place in the presence of the opposed vibrating molecules of the wire,
since there remains no other conceivable means of explaining in a realizable manner why these
portions of matter (molecules), already completely disconnected from each other in the normal state of
the wire, should require this enormous force to shift their positions in the act of breaking the wire,
unless in this act there were something further to be accomplished than merely to change the positions
of molecules in space. [A change in position of the wire itself, without breaking it, requires no such
powerful force.]"
Preston goes on to attribute the pressure differential to a rarefaction of the aether
between vibrating bodies caused by "stationary waves" between them, "We have observed
that a vibratory movement of matter, under such conditions that the waves are reflected and
thereby stationary vibrations are formed in the medium, is well qualified to disturb the
equilibrium of pressure of the medium," and makes clear that he does not see cohesion as the
ultimate pressure differential between normal volume elements of aether and of vacuum; and
he gives the example of chemical bonds as a state of pressure differential far exceeding the
force of cohesion. His inferences again and again produce an increase in force commensurate
with a reduction in scale. The subdivision results in the attenuation of matter into aether
particles, as a limit. He sets a figure of, "500 tons per square inch as a limiting value for the
ether pressure".
Again, there is no metaphysical attempt to delve into the cause of the normal velocity
of aether particles, but Preston does tacitly and ontologically assume a quite vaguely defined
frame of reference for this velocity. This ontological belief, and Preston's attitudes toward
mechanics, truth, and his epistemological agenda, would today be considered by many to be
naïve and circularly reasoned; but they nevertheless produced predictions which have been
borne out by technological advances in the twentieth century; and one seriously doubts that
these predictions would have arisen in relativity theory, other than as a thinly veiled repetition
(without attribution) of the conclusions drawn by Preston, Olinto De Pretto [Editor's note: see
for instance Umberto Bartocci, Albert Einstein e Olinto De Pretto: la vera storia della
formula più famosa del mondo, Ed. Andromeda, Bologna, 1999; information on line:
http://www.dipmat.unipg.it/~bartocci/listast.htm, points 9 and C] and others, through
relativity theory's more complicated ontological fictions, which have no inductive
justification, and which reify purely abstract conceptualizations of dimension. In contrast to
relativity theory, Preston's ideas are based on quantifiable measurements, on measurable
relations, ultimately resolved into the most scientific expressions of our empirical sensual
experience, the sense of resistance to touch, which is "pressure" and "matter", as a measurable
thing; and the separation of distance through time, which velocity constitutes a measurable
relation. Preston proposes a dynamic "material agency", the aether.
Preston derives the density of the aether. This is quite significant to his later
derivations of the store of energy contained in the density of matter, and the powerful effects
which he predicts will occur should matter be subdivided into aether particles,
"In connection with this subject, it may be of great interest to contemplate the possibility of
the following as a physical problem. If we suppose a given mass of matter and a given volume of
65
space, the volume of the space being supposed vastly greater than that of the mass of matter. Then it
becomes possible, by the subdivision of the this mass of matter (which may be readily conceived to
carried out to any extent), to pervade the entire volume of the space with matter, or there is no limit to
the degree of close proximity into which the particles of matter pervading this space may be brought
by continuous subdivision, the approach of the particles going on continuously without limit as the
subdivision progresses. Thus, with a given mass of matter there is no limit to the extent of space that
may be pervaded by matter by continued subdivision, or there may be no appreciable portion of the
vast volume of space but what contains myriads of particles of matter. The normal state of this finely
subdivided matter may be conceived to be a state of motion or a state of rest; if a state of motion, then
we may observe the physical possibility of the existence of a store of energy of an extreme intensity,
and which, from the minuteness and small length of path of the moving particles, must be concealed;
this motion being also necessarily attended by the production of an intense and at the same time
evenly balanced pressure, the smoothness and uniformity of the pressure, and the consequent
concealment of its existence from the senses, being more and more complete as the subdivision
progresses."
Preston concludes that the aether is made up of subdivided particles of matter, which
conclusion is happily in agreement with the velocity and properties of light propagation. He
infers a posteriori a relation between the subdivision of matter and an increase in the speed of
particles, which ultimately results through the subdivision of mass in aether particles moving
at or slightly above light speed. In a statement of the working principle of the atomic bomb,
Preston avows,
"If now we imagine, merely for illustration, each of these air molecules to be subdivided into a
million parts, and that the speed of each component part has been increased a thousand times. The
presence of the ether within the receiver may be left out of account for the present. Then by this
imaginary process of subdivision, the mean distance of these parts of matter (which we shall term
'particles') would be so reduced as to bring these particles into closer proximity than the molecules of
air outside the receiver (the mean distance of the particles of the subdivided matter being inversely as
the cube root of the their number). The pressure against the interior of the receiver, which is as the
square of the speed of the particles, would now be increased a million-fold; and yet this result is
attained without any increase in the absolute value of the energy of each particle, for the energy has,
by the reduction of mass, remained precisely the same for each particle as before, although the total
energy has become vastly greater, this energy being now subdivided among a large number of
particles, and the pressure maintained by a greatly increased number of moving particles.
We might imagine this process of subdivision, or this reduction of mass combined with
increase of speed, to go on progressively, and thus the total energy would be continually increasing,
and the mean distance and mean length of path of these small moving masses or particles would be
continually diminishing, and therefore the concealment of this motion from the senses would be more
and more complete. The pressure would continually rise in intensity, and at the same time become
more even and perfectly balanced as the number of particles increased.
We might thus imagine this process to go on progressively, until at length the dimensions,
mean distance, and speed of the ether particles themselves had been reached; or its possible thus step
by step to arrive at a just conception of the wonderful intensity of the store of energy that is rendered
physically practicable, and the high static value of the pressure that may be reached, under the simple
mechanical conditions of an extensive subdivision of matter combined with a high speed. "
The "speed of the ether particles" is that of a wave of light, and the "absolute value of
the energy of each particle" when reduced to aether is mc2, which is described in Preston's
prose in section 165 of his book, as quoted here above in the introduction. S. Tolver Preston
provided a qualitative and quantitative theory, which set in motion the search for atomic
energy and weaponry, a search which was ultimately successful. His contributions to science
deserve far greater mention. Preston was indeed a man of science, who did not flinch when
opposing the religious zealotry he confronted. We would do well to follow his example and
66
oppose "theories of a vague nature" which propose "phantom agencies" like "space-time" and
replace them with "physical causes capable of rational appreciation."
Notes
[1] S. T. Preston, "Evolution and Female Education", Nature, (23 September 1880), pp. 485-486;
Revised, Original essays. I. On the social relations of the sexes. II. Science and sectarian religion. III.
On the scientific basis of personal responsibility, with a reprint from an essay on "Evolution and
female education," revised from Nature, September 23, 1880, Williams and Norgate, London,
Edinburgh, (1884).
[2] S. T. Preston paraphrased in F. Darwin & A.C. Seward, Editors, More letters of Charles Darwin,
Volume 2, Chapter 8, John Murray, London, (1903), p. 52, Letter 421.
[3] S. T. Preston, "On a Point Relating to Brain Dynamics", Nature, (13 May 1880), pp. 29-30;
Responses by G. Romanes, Nature, Volume 22, p. 75, and W. C. Ley, Nature, Volume 22, (10 June
1880), p. 121; Reply by Preston, Nature, (10 June 1880), p. 121.
[4] S. T. Preston, Physics of the Ether, E. & F. N. Spon, London, (1875).
[5] G. L. Le Sage, read by P. Prevost to the Berlin Academy in 1782, "Lucrèce Neutonien", Nouveaux
Mémoires de l'Académie royale des Sciences et Belles-Lettres de Berlin,Year 1782, (Berlin, 1784), pp.
404-427; reprinted in Notice de la Vie et des Écrits de George-Louis Le Sage, Chez J. J. Paschoud,
Genève, (1805), pp. 561-604; English translation by C. G. Abbot with an introduction by S. P.
Langley appears in: "The Le Sage Theory of Gravitation", Annual Report of the Board of Regents of
the Smithsonian Institution Showing the Operations, Expenditures, and Condition of the Institution for
the Year Ending June 30, 1898,(U.S.) Government Printing Office, Washington, (1899), pp. 139-160.
W. Thomson, S. Tolver Preston, H. A. Lorentz, and J. J. Thomson, among many others, pursued Le
Sage's shadow theory of ultramundane particles. Maxwell and Poincaré opposed it, on the basis that it
would result in excessive heat accumulation.
[6] I. Newton, Four Letters from Sir Isaac Newton to Doctor Bentley containing Some Arguments in
Proof of a Deity, London, (1756) [Editor's note: see also Episteme N. 5, March 2002]. Edward B.
Davis has presented significant scholarship on Newton's religious views: "Newton's Rejection of the
'Newtonian World View': The Role of Divine Will in Newton's Natural Philosophy", Fides et Historia,
Volume 22, Number 2, (Summer 1990), pp. 6-20; reprinted Science and Christian Belief, Volume 3,
Number 1, (1991), pp. 103-117; reprinted with additions Facets of Faith and Science, Volume 3,
University Press of America, Lanham, Maryland, (1996), pp. 75-96.
[7] R. Bentley, A Confutation of Atheism from the Origin and Frame of the World, Part 3, Phoenix,
London, (1693), pp. 4, 20-21.
[8] C. Maclaurin, "Of the Supreme Author and Governor of the universe, the True and Living God",
An Account of Sir Isaac Newton's Philosophical Discoveries, Book 4, Chapter 9, Patrick Murdoch,
London, (1748), pp. 388-390.
[9] R. Cotes, in I. Newton, The Mathematical Principles of Natural Philosophy, London, (1729), from
"THE PREFACE OF Mr. Roger Cotes", not paginated.
[10] R. Cotes, Cote's preface to the second edition of Newton's Principia. Sir Isaac Newton's
Mathematical Principles of Natural Philosophy and his System of the World, University of California
Press, Berkeley, Los Angeles, London, (1962), p. XXXIII.
[11] F. M. A. Voltaire, "On Attraction", Letters on England, Letter 15.
*****
67
[We believe it worthwhile to add an ending section about the important
question: vis viva versus kinetic energy]
Clash of Leibnitz and Newton Space as Meta-Aether
There was in Preston's day an emerging rejection of the Newtonian ideas of mystical "force"
as a cause of phenomena among "empty space". Fechner stated,
"All that is given is what can be seen and felt, movement and the laws of movement. How
then can we speak of force here? For physics, force is nothing but an auxiliary expression for
presenting the laws of equilibrium and of motion; and every clear interpretation of physical force
brings us back to this. We speak of laws of force; but when we look at the matter more closely, we
find that they are merely laws of equilibrium and movement which hold for matter in the presence of
matter. To say that the sun and the earth exercise an attraction upon one another, simply means that the
sun and earth behave in relation to one another in accordance with definite laws. To the physicist,
force is but a law, and in no other way does he know how to describe it. . . All that the physicist
deduces from his forces is merely an inference from laws, through the instrumentality of the auxiliary
word 'force'." [12]
T. H. Pasley, in 1835, averred,
"Of the nature of matter the knowledge is limited to the principle of inertia. Matter being inert
it can do nothing and bodies formed of inert matter are incapable of acting in any manner: the want of
power cannot originate power: hence cause must consist in means independent of action by matter.
Matter consisting in unorganized molecules, it appeared nothing out of reason to conclude that the
whole and all things they go to form are inert. For if a body be broken its parts are inactive, and the
body itself to be in an acting state requires to be impelled by means such as itself does not possess.
The inertia of matter therefore is evident. Matter being inert it cannot either attract or repel. But then,
how is universal gravitation, acknowledged by all the most learned of the world and demonstrated
mathematically, to be set aside, and wherein is cause of it and attraction be rejected. The difficulty is
as great as the Authorities who make no difficulty of supporting these principles and causes are
exalted in fame. The greatest difficulty however lies in reconciling them with the Inert nature of
Matter. Matter has no acting properties as it is essentially inert. Acting implies being in motion;
motion requires physical impulse foreign to that which is made to act, and from the atoms of matter
being unalterable, by nothing but physical impulse can they be affected, nor can the effect be other
than motion. Wherefore, gravitating, and repelling are not properties of either matter or bodies. [***]
In moral philosophy inertia means inferior ability and ability sluggishly exerted; in Physics it signifies
no ability or power whatever. Making inertia a 'passive power' amounts to no power; power implies
acting, passive power not acting or that can act, but power is never passive. Inertia being an 'inert
force' is the same as force without force: 'vis inertiae' is the force of inactivity, the power of inability.
All bodies are convertible into powers, but are such only while being made to act. To say a body
'resists' by means of its inertia, is making nothing a physical force. Who can conceive force at rest.
Inertia causing 'an endeavour and perserverance in a body to continue in motion or at rest' is a
contradiction in terms [***] Inertia is no cause, it is nothing active or passive. The resistance of a
ponderable body at rest is caused by that which makes it ponderable. Inertia being nothing is
productive of nothing; it may be said to be the zero of cause. " [13]
Pasley identified many of the fatal flaws in the Epicurean mythologies, for example,
"[W]itness the Newtonian Theory of Gravitation, Attraction and Repulsion, which, it is said
'Newton has proved to the whole world direct and regulate the System.' But as gravitating, attracting
and repelling cannot belong to inert bodies, formed as all are of inert matter, the adopted theory, in
these respects, is utterly fallacious and untrue. Gravitating by the Planets of their own accord is as
68
movement in the lifeless; attraction as the will of the dead; and repulsion as antipathy possessed by a
stone. The whole of these and all such monstrocities have origin solely in the theory of Perception
being rejected where most applicable, and in coupling Activity with Inertia. " [14]
Preston wanted to replace these myths with a physical agent, which obeyed the
principle of the conservation of energy. Perhaps the most famous name associated with the
principle of the conservation of energy, the foundation of Preston's natural philosophy, is
Julius Robert Mayer. He sought a meaningful definition of the concept of "force" and this is
likely why Preston, in working out the energy store in bodies through Joule's and Clausius'
methods, deduced Leibnitz' vis viva, as opposed to kinetic energy,[16] as the absolute store of
energy contained in mass. In 1807, Thomas Young defined "energy" in English as,
"The term energy may be applied, with great propriety, to the product of the mass or weight of
a body, into the square of the number expressing its velocity. "[17]
Mayer stated, in 1852, in an effort to provide a "generic conception of 'force,'"
"On the other hand, the product of the pressure into the space through which it acts, or, again,
the product - or half-product - of the mass into the square of the velocity, is named 'force.' In order that
motion may actually occur, it is in fact necessary that the mass, whatever it may be, should under the
influence of a pressure, and, in the direction of that pressure, traverse a certain space, 'the effective
space' (Wirkungsraum): and in this case a magnitude which is proportional to the 'pushing force' and
to the effective space, likewise receives the name 'force;' but to distinguish it from the mere pushing
force, by which alone motion is never actually brought about, it is also called the 'vis viva of motion,'
or 'moving force.' With the generic conception of 'force,' the higher mechanics, as an essentially
analytic science, is not concerned. In order to arrive at it, we must, according to the general rule,
collect together the characters possessed in common by the several species. As is well known, the
definition so obtained runs thus - 'Force is every thing which brings about or tends to bring about,
alters or tends to alter motion'. This definition, however, it is easy to see, is tautological; for the last
fourteen words of it might be omitted, and the sense would be still the same. [***] If a mass M,
originally at rest, while traversing the effective space s, under the influence and in the direction of the
pressure p, acquires the velocity c, we have ps = Mc2. Since, however, every production of motion
implies the existence of a pressure (or of a pull) and an effective space, and also the exhaustion of one
at least of these factors, the effective space, it follows that motion can never come into existence
except at the cost of this product, ps = Mc2. And this it is which for shortness I call 'force.' "[18]
Preston focused on the notion of aethereal pressure (as opposed to mystical "forces" of
gravitation and magnetism exerted upon a mass by a mass via "action at a distance") again
and again in opting for the formulation of the absolute store of energy as E = mc2 , as opposed
to E = ½ mv2. This is perhaps due to the fact that most of the writings on the principle of the
conservation of force from the 1840's focused on Galilean-Leibnitzian style experiments with
falling masses. Leibnitz' arguments for a conserved vis viva against Descartes' momentum
were initially a posteriori and depended upon experiments of gravitation on the Earth.
However, by 1875 it was an anomaly for Preston to not see the "transference of work" done
by a body thrown upwards against the "resistance" of "gravity" as ½ mv2. Preston wrote,
"26. In considering the high normal velocity of the ether particles, it is to be expected
beforehand that this agent must exert an extremely forcible pressure upon the molecules of matter,
even if every allowance be made for the extreme low density of the agent; for it is important to note
that the pressure exerted is as the square of the speed of the particles of the agent, and therefore the
pressure rises in a very rapid ratio as the speed increases; so that taking into account this fact, in
conjunction with the high velocity of the particles, we must be prepared to find this pressure will have
a very high value. In looking to physical phenomena for an indication of this pressure, and also with
the object, if possible, of arriving at a limiting value for its intensity, or the value which this pressure
69
must at least attain on the lowest computation, we will consider one observed fact. [***] 53. Secondly,
it may be shown that an excess of energy is imparted to the surrounding medium by a vibrating mass
or molecule, due to a second separate physical cause, which we shall now consider. We have observed
that the speciality of a vibrating movement is to affect the normal velocity of the component particles
of the medium in such a way that equal increments and decrements of velocity are experienced. But it
is an important principle to observe, that when masses of matter experience equal increments and
decrements of velocity so that the mean velocity remains unaltered, that, nevertheless, the energy
being as the square of the velocity, the value for the energy does not remain unaltered. Thus, if we take
the case of two equal masses having equal velocities, which we may express by V, the energy in each
case being expressed by V 2, and the total energy therefore by 2V 2. If now we suppose one of the
masses to receive an increment of velocity v, its velocity therefore becoming V + v, the other mass
experiencing an equal decrement of velocity, its velocity becoming V - v; then although the mean
value for velocity has remained unchanged, yet the value for energy has by no means remained
unchanged, for the energy of each mass being as the square of its velocity, the total energy now
becomes (V + v)2 + (V - v)2 = 2V2 + 2 v2. Now the value for the total energy before this change of
velocity took place was only 2V2. The total energy has therefore, by merely changing the velocities by
equal amounts (so as not to affect the mean velocity), received a notable increase represented by the
amount 2v2. This is an important point, on account of the direct and practical bearing which it has on
the phenomena of vibratory motion; the above indicating that the change of the velocities of the
component particles of the medium by equal amounts, which it is the special function of a vibratory
motion of matter to effect, is itself a direct cause whereby a certain excess or surplus of energy is
communicated to the medium. [***] 98. Important Influence of Subdivision. - One of the most
important practical consequences following from the extensive state of subdivision, which is the
characteristic of the molecular condition of matter, is the vast extent of surface which is thereby
brought under the action of the ether pressure. This is a fact of importance, by a due appreciation of
which the great energy of the action of the ether upon molecules will appear no longer discordant or
inconsistent, but the fact may be brought into harmony with ordinary mechanical principles, this vast
extent of surface being the fitting mechanical condition for the production of static and dynamic
effects of extreme intensity. [***] [114] III. High Normal Speed of Component Particles. - This
physical quality is absolutely essential to constitute a powerful dynamic agent, for without this high
speed dynamic effects of a high intensity cannot be produced. Second, this high normal speed of the
particles is the sole condition on which the loss of motion sustained by the ether can be replenished
with that degree of speed which is essential to render a continuous dynamic effect of a high intensity
possible to the ether. Third, this high speed of the component particles is the sole quality by which the
loss of motion sustained by the ether in producing a given dynamic effect can be subdivided or
distributed over a large volume of the ether, whereby a notable local disturbance of the equilibrium of
the ether is prevented. Fourth, this quality is essential for the rapid interchange of motion between
masses and molecules of matter at a distance from each other, the rapidity of intercommunication or
exchange of motion being strictly limited by the normal speed of the particles of the intervening agent.
Fifth, this high speed of the component particles is necessary to render possible the existence of a store
of energy of a high value, without the encumbrance of a large quantity of matter in space. Sixth, the
high normal velocity of the ether particles is the necessary mechanical condition to enable an intense
pressure to be exerted by the ether upon the molecules of matter, without the movements of these
molecules and masses being obstructed by the agent exerting the pressure. For, in the first place, by
this high speed of the component particles an intense pressure is attainable (more especially as the
pressure rises as the square of the speed) without the necessity for the agent being dense, by which the
free passage of masses of matter through the agent would be obstructed. In the second place, the high
speed of the component particles enables masses of matter to pass through the agent with the least
disturbance of its equilibrium, or with a minimum of resistance from this cause, the agent becoming
almost impalpable; the exertion of an intense pressure by the agent being itself the necessary condition
to render the agent adapted to control forcibly the molecules of matter in stable equilibrium, as
exhibited in the general phenomena of 'cohesion,' or the aggregation of the molecules of matter
generally. The above may serve as a general summary of the special physical qualities of the ether;
and it may be noted that if the attempt were made beforehand, as a mechanical problem or speculation,
to devise or scheme out what special physical qualities an agent should possess in order to be
mechanically fitted to produce the varied physical effects of the character observed, then the scheme
of the ether would be found to constitute the only possible solution of which the mechanical problem
70
admits; or the ether may be contemplated as a piece of mechanism specially adapted to its work. [***]
128. We shall now proceed to consider more closely the mode or general principle upon which
physical processes effect themselves, and it will be our endeavour to show that these processes
resemble one another in a second fundamental aspect, viz. that all these processes are cyclical, i. e.
consist in a transference of motion from the ether through matter to the ether, or consist in a
transference of motion from and to the same source; and therefore that all physical processes, however
diverse and varied, are identical in this fundamental respect; or that every observed motion whatever
came from the ether at one time, and will return to the ether at some subsequent time. This theorem
may be shown to be a necessary consequence resulting from the fundamental principle of
conservation. The normal state of the ether is a state of motion, or the component particles of the ether
transfer their motions among themselves, and this motion is of necessity permanently maintained. The
ether, therefore, constitutes a source of motion. A mass or molecule of matter, on the other hand,
cannot possibly be in motion without continually giving up some of its motion to the surrounding
ether, which motion is rapidly carried off to a distance in the form of waves; so that matter cannot
possibly remain in motion, unless the motion be renewed by the ether as rapidly as it is being
dissipated in the ether, which would constitute a cyclical process. Since, therefore, the motion of
matter is being continually dissipated in the ether, the ether constitutes the receptacle of all the
motions of matter. The ether therefore must, in accordance with the principle of conservation, be the
source of all the motions of matter, for matter cannot evolve motion out of itself. Also, since matter
cannot retain its motion, but must be always dependent on the ether for any supply of motion, matter
therefore cannot in any case constitute a source of motion. The ether therefore constitutes both the
source and the receptacle of all the motions of matter, or this would constitute the theorem that all
physical processes are cyclical, or consist in a transference of motion from and to the same source, and
accordingly that all physical processes are correlated in this fundamental respect. [***] 135. Amount
of energy being dependent on the quantity of matter in motion and on the square of the velocity of
motion, and since motion cannot come into existence spontaneously, or go out of existence
spontaneously, but in accordance with the principle of conservation, the sum of energy must remain
constant; it follows, therefore, that whenever there is a loss of motion by matter, there must be a
simultaneous gain of motion by matter, or the loss and gain of motion must be simultaneous, for a loss
of motion without a simultaneous gain of motion would involve for an interval of time an annihilation
of energy. It follows, therefore, as a necessary consequence from this, that the energy expended in any
physical process whatever can be solely dependent on and due to motion simultaneously imparted, i. e.
imparted at the time of the expenditure of the energy; for unless motion be imparted at the time,
energy cannot be expended at all, for to expend motion without imparting motion would be to
annihilate energy; indeed, the motion imparted is itself the measure of that expended, and is the sole
cause of its expenditure, i. e. motion can only be expended in the communication of motion, and in
that fact lies apparent the principle of the Indestructibility of Motion. [***] 163. Absolute Quantity of
Energy in the Unit Volume of Space. - We shall now consider more particularly the energy enclosed by
the ether, with the endeavour to give some idea of the absolute value of the energy represented by the
motion of the ether particles contained within a given portion of space, with the object, if possible, to
fix upon a limiting value for this energy, or the lowest value consistent with what physical facts would
require. The conditions required in order to determine the amount of energy enclosed in the unit
volume of space are clearly, first, a knowledge of the quantity of matter in the form of ether contained
in the unit volume of space (i. e. the density of the ether); and secondly, the normal velocity of the
ether particles. Now, although we do not know the density of the ether independently, nevertheless
since density is determined by pressure and velocity of component particles, if, therefore, by a known
limiting value for the velocity of the ether particles, a limiting value for the ether pressure can also be
fixed upon, then a limiting value for the ether density is thereby given. The limiting value for the
velocity of the ether particles is given by the measured velocity of a wave of light. As regards the
value for pressure, we take the estimate already fixed upon: that this amounts to 500 tons per square
inch as the lowest limiting value. There are valid grounds for inferring that this value for pressure has
been under-estimated; for we assumed the total ether pressure as a small multiple of the observed
difference of pressure in the case of 'cohesion,' whereas, as before remarked, it is a known fact that the
force required to separate chemically combined molecules must be many times greater, this indicating
the high intensity of the controlling ether pressure, and showing that an estimate of this pressure from
the case of 'cohesion' must be but an inadequate representation of the reality. The tremendous energy
developed in explosives, which is the very energy of the ether itself, is a direct indication of the
71
intensity of the ether pressure, which is the necessary accompaniment of this energy. That this value
for pressure has been under-estimated, a bare consideration of the dependent value for density would
almost show, for the ether density corresponding to this pressure (1/5264800 of the atmospheric
density) represents a density so insignificant as to be less than that of the best gaseous vacua. "
Additional Notes
[12] Fechner quoted in H. Vaihinger's, Philosophy of the 'As if', Barnes & Noble, Inc., New York,
(1966), p. 215; translated by C. K. Ogden.
[13] T.H. Pasley, A Theory of Natural Philosophy, on Mechanical Principles, Divested of All
Immaterial Chymical Properties, Showing for the First Time the Physical Cause of Continuous
Motion, Whittaker & Co., London, (1836), Preface and pp. 145-146.
[14] Pasley, ibid. xcii.
[15] See for example the many works of Marc Seguin and M. F. de Boucheporn, Cf. The Correlation
and Conservation of Forces, D. Appleton, New York, (1867), pp. 4, 76-82; W. B. Taylor, "Kinetic
Theories of Gravitation", Annual Report of the Board of Regents of the Smithsonian Institution, U. S.
Government Printing Office, Washington, (1877), pp. 205-282. Another good example is A.
Anderssohn, Die Mechanik der Gravitation, Breslau, (1874); and Zur Loesung des Problems ueber
Sitz und Wesen der Anziehung, Breslau, (1874); and Physikalische Prinzipien der Naturlehre, G.
Schwetschke, Halle, (1894). See also: G. Hoffmann, Die Anderssohn'sche Drucktheorie und ihre
Bedeutung für die einheitliche Erklärung der physischen Erscheinung, G. Schwetschke, Halle, (1892).
For some, the aether become their embodiment of the Tertullian-Newtonian pantheistic God and Holy
Wind. See, for instance, Philipp Spiller, Die Urkraft des Weltalls nach ihrem Wesen und Wirken auf
allen Naturgebieten, Verlag der Stuhr'schen Buchhandlung (S. Gerstmann), Berlin, (1876).
[16] G. G. Coriolis, Du calcul de l'effet des machines, ou Considérations sur l'emploi des moteurs,
Paris, (1829). Coriolis used the term "force vive". First use of the term "kinetic energy" in English is
perhaps by Thomson and Tait, Good Words, (October, 1862).
[17] T. Young, A Course of Lectures on Natural Philosophy and the Mechanical Arts, Volume
1,Taylor and Walton, London, (1845), p. 59.
[18] J. R. Mayer, translated by J. C. Foster, "Remarks on the Mechanical Equivalent of Heat", The
Correlation and Conservation of Forces, D. Appleton, New York, (1867), pp. 331, 336.
----Christopher Jon Bjerknes is an American historian of science, who has
authored six books and numerous articles on the theory of relativity and on
Albert Einstein. His most recent book, Albert Einstein - The Incorrigible
Plagiarist, is reviewed in this same volume of Episteme.
[email protected]
72
Einstein's Irrational Ontology of Redundancy
The Special Theory of Relativity
and Its Many Fallacies of Petitio Principii
Abstract. Albert Einstein's arguments were almost always fallacies of Petitio Principii. He argued
well-known experimental results as if a priori first principles. Einstein would then induce, as if
deducing, the well-known hypotheses of others, and deduce from these plagiarized hypotheses the
same experimental results as conclusions, which he had first stated as premises. This was Einstein's
modus operandi for plagiarism. In the special theory of relativity, Einstein argued light speed
invariance, a well-known (supposed) experimental result at the time, as if an a priori first principle,
which an empirical measurement cannot be, to then induce through analysis, as if deducing in
synthesis, the "Lorentz Transformation" hypotheses. Einstein then used the "Lorentz Transformation",
the true set of hypotheses of the special theory of relativity, to deduce light speed invariance as a
conclusion, a conclusion which Einstein had already presumed as a premise. Einstein employed the
same fallacious method in the general theory of relativity. Einstein irrationally asserted the wellknown experimental gravitational-inertial mass equivalence of Bessel and Eötvös as if an "a priori"
postulate, which an experimental result cannot be, only to arrive at it as an ultimate conclusion, a
conclusion redundant to the premise. The quasi-postivistic analyses Einstein presented by turning the
synthetic scientific theories of his predecessors on their heads have been applauded, ridiculed and
often misrepresented as synthetic, which they are not.
Method
In 1905, Mileva Einstein-Marity and Albert Einstein [1] coauthored a paper on the
"electrodynamics of moving bodies". Fallacies of begging the question emerge even in the
very introduction to the work. The Einsteins acknowledge in their introduction, that light
speed invariance and the symmetry of electrodynamic phenomena were well-established
phenomena. Well-known specific phenomena are not, by definition, "a priori" general
concepts. However, the Einsteins asked us to abandon reason and assert specific experimental
results and empirical observations, as if a priori general principles. In other words, the
Einsteins engaged in an analysis of the problems of invariant light speed, and of the symmetry
of electrodynamic phenomena in alleged violation of Maxwell's theory, which problems faced
physicists at the end of the nineteenth century; and the Einsteins irrationally pretended that
these two problems were solutions of themselves.
1
Henry August Rowland stated the two main problems facing the physicists of his day,
on October 28th, 1899, and I have italicized that which the Einsteins would later call "two
assumptions", or "postulates":
"And yet, however wonderful [the ether] may be, its laws are far more simple than those of
matter. Every wave in it, whatever its length or intensity, proceeds onwards in it according to well
known laws, all with the same speed, unaltered in direction, from its source in electrified matter to the
confines of the Universe, unimpaired in energy unless it is disturbed by the presence of matter.
However the waves may cross each other, each proceeds by itself without interference with the others.
[***] To detect something dependent on the relative motion of the ether and matter has been and is
the great desire of physicists. But we always find that, with one possible exception, there is always
some compensating feature which renders our efforts useless. This one experiment is the aberration of
light, but even here Stokes has shown that it may be explained in either of two ways: first, that the
earth moves through the ether of space without disturbing it, and second, if it carries the ether with it
by a kind of motion called irrotational. Even here, however, the amount of action probably depends
73
upon relative motion of the luminous source to the recipient telescope. So the principle of Doppler
depends also on this relative motion and is independent of the ether. The result of the experiments of
Foucault on the passage of light through moving water can no longer be interpreted as due to the
partial movement of the ether with the moving water, an inference due to imperfect theory alone. The
experiment of Lodge, who attempted to set the ether in motion by a rapidly rotating disc, showed no
such result. The experiment of Michelson to detect the ethereal wind, although carried to the extreme
of accuracy, also failed to detect any relative motion of the matter and the ether [Emphasis Added]."[2]
The Einsteins turned reason on its head and called these two a posteriori problems, a
priori "postulates". The Einsteins phrased their two "postulates", as follows:
1"1 (a). Examples of a similar kind, as well as the failed attempts to find a motion of the earth relative
to the 'light medium', lead to the supposition, that the concept of absolute rest corresponds to no
characteristic properties of the phenomena not just in mechanics, but also in electrodynamics, on the
contrary, for all systems of coordinates, for which the equations of mechanics are valid, the same
electrodynamic and optical laws are also valid, as has already been proven for the magnitudes of the
first order.
1 (b). The laws according to which the states of physical systems change do not depend upon to which
of two systems of coordinates, in uniform translatory motion relative to each other, this change of state
is referred.
12 (a). [L]ight in empty space always propagates with a determinate velocity c irrespective of the state
of motion of the emitting body.
2 (b). Every ray of light moves in the 'resting' system of coordinates with the determinate velocity c,
irrespective of whether this ray of light is emitted from a resting or moving body. Such that
velocity = (path of light) / (interval of time) ,
where 'interval of time' is to be construed in the sense of the definition of § 1."
Note that the first "postulate", the principle of relativity, refers only to "moving
systems" and the second "postulate", the light "postulate", refers only to a proposed "resting
system". Note further, that the light "postulate" refers only to a proposed source independence
of light speed, but not to an observer independence, because this "postulate" assumes a prior
privileged frame and medium in the 1905 paper, the "resting system". The paper later
presumes that c' = c +/- v, relative to the "resting system".
1Many assert that the Einsteins employed only these two "a priori postulates" in their
theorization, as opposed to FitzGerald, Larmor, Lorentz, and Poincaré, who required the
additional hypotheses of length contraction and time dilatation to arrive at the same
formulation - long before the Einsteins. Ad hoc hypotheses were frowned upon at the time,
due to Newton's admonitions against them, such that the removal of hypotheses was seen as
an improvement. The two postulate myth is substantially and demonstrably false. The two
postulates are not postulates, but rather are the deduced conclusions of the theory summations of the supposedly observed phenomena of the day.
After asserting the two "postulates", the Einsteins raised a straw man argument based a
non sequitur. They asserted that the two "postulates" appeared irreconcilable with each other.
If light speed is constant in the "resting system", then how can it also be isotropic in a
"moving system"? This is a (manufactured) dilemma, because, in some inexplicable way, the
Einsteins argue that the first postulate, the principle of relativity, compels that light speed
from a given light signal be isotropic for all systems in uniform motion with each other.
However, this is clearly a non sequitur, because the principle of relativity no more compels
light speed isotropy for all "moving systems", then the principle of relativity requires that a
body resting relative to one "moving system" k also rest relative to another "moving system"
K, which is in motion relative to the first. Einstein also raised the opposing problem. How can
light speed be isotropic in the "resting system" and also be isotropic in a "moving system"? Of
course, these questions presume the conclusion before it has been proven, the conclusion
being that light speed from any given signal is isotropic in the "resting system" and all
74
"moving systems", which are in uniform translatory motion with respect to the "resting
system". To knock down these straw men, the Einsteins turned the "two postulates" into one
"postulate", the conclusion which is sought. 1The Einsteins asserted that it is the combination
of the two postulates, not either postulate by itself, which "deduces" c' = c between the
moving system and the resting system, by simply asserting that c' = c, before it has in any way
been proven:
"It is easy, with the help of this result, to ascertain the magnitudes ξ, η, ζ, because one
expresses by means of these equations, that light (as the principle of the constancy of the velocity of
light, in conjunction with the principle of relativity, requires) also propagates with the velocity c as
measured in the moving system."
After irrationally presuming this conclusion, the Einsteins proceeded to pretend that
they had not presumed it:
"Now, we have to prove that every ray of light propagates with the velocity c as measured in
the moving system, in case this is, as we have taken for granted, the case in the resting system,
because we still have not offered up the proof that the principle of the constancy of the velocity of
light is reconcilable with the principle of relativity."
However, the combination of the two postulates induces c' = c +/- v, not c' = c. One
must take the supposed empirical phenomenon of c' = c as a point of departure for an
inductive analysis, not a deductive synthesis, to induce a fundamental geometry, which
fundamental geometry then deduces the identity c' = c and the covariance of the laws of
physics, as a synthetic theory. The Einsteins averred, before any proof was offered:
"It is easy, with the help of this result, to ascertain the magnitudes ξ, η, ζ, because one
expresses by means of these equations, that light (as the principle of the constancy of the velocity of
light, in conjunction with the principle of relativity, requires) also propagates with the velocity c as
measured in the moving system. For a ray of light emitted in the direction of increasing ξ at the time τ
= 0, the following equations are valid: ξ = cτ. . ."
Note the non sequitur, which begs the question: That allegedly if the speed of light is
c in the "resting system" the principle of relativity compels that it also be c in the "moving
system"; which, without the prior hypotheses of the Lorentz Transformation, clearly is not a
rational conclusion, for if I rest in the resting system, the principle of relativity does not
compel that I also rest in the moving system. Rather, the Einsteins simply confused their
conclusion as an additional premise, which renders the two "postulates" redundant, or renders
one postulate deducible from the other, and in no sense a postulate.
As Einstein, himself, avowed, "the real basis of the special relativity theory" is not the
conclusion of light speed invariance and the covariance of the laws of physics in Lange's
"inertial systems". As Albert Einstein later admitted, the real set of a priori postulates is the
"Lorentz Transformation", replete with its dreaded ad hoc hypotheses. The Lorentz
Transformation deduces all velocity comparisons, not just invariant light speed, which is a
specific speed, and a derived unit, not a general geometry.
Later formulations of the special theory of relativity change the 1905 light postulate,
from the Einsteins constant speed of light exclusively in the "resting system", into the
invariance of light speed in all of Lange's inertial systems. But this renders the principle of
relativity redundant to, or deducible from, the light "postulate", and, therefore, not a
"postulate", per se, because the light "postulate" then asserts the identity of Lange's inertial
systems as light speed invariance, and the principle of relativity is already proven in the light
"postulate". On the other hand, if we pretend that the principle of relativity is the covariance
75
of the laws of physics embracing Maxwell's theory, given the "Lorentz Transformation" as a
premise, then the second "postulate" is already incorporated in the first "postulate".
If we are to assume that the Einsteins, in their 1905 paper, deduced, not induced, the
Lorentz Transformation from invariant light speed; we would further have to fallaciously
assume that empirically observed Lorentz Transformation metrics provoked the Einsteins to
induce an unobserved invariant light speed and the unobserved symmetry of phenomena, as
self-evident general truths induced a posteriori from empirically observed and reciprocally
measured: length contraction, time dilatation and relative simultaneity. Such is obviously not
what happened, and such is not what is argued in the 1905 paper.
On the contrary, supposedly observed invariant light speed and the supposedly
observed symmetry of electrodynamic phenomena led Voigt [3], FitzGerald [4] and Larmor
[5] to scientifically induce, a posteriori, the general geometry of the (misnamed) "Lorentz
Transformation", which general set of hypotheses supposedly deduced all "known"
phenomena in non-existent hypothetical "inertial systems". The Einsteins pseudoMetaphysics, their ontology of redundancy, simply disguised the more scientific, though
likewise irrational, work of their predecessors, in a way which attempted to make it appear
that the Einsteins had deduced that which must be induced, and had avoided hypotheses,
which they had not avoided, but rather induced, through fallacy of Petitio Principii.
Most of the post-1905 statements of the special theory of relativity substitute a
completely different proposition for the "two postulates". Einstein, himself, substituted one
light theorem, in 1907, for the "two postulates" of 1905:
"the 'principle of the constancy of the velocity of light' [***] for a system of coordinates in a
definite state of motion [as opposed to solely in the 'resting system' as in 1905.]" [6]
which presumes the Lorentz Transformation from which this "postulate" is deduced, and
which presumes the tacit hypotheses of an isotropic and homogenous absolute space [7] and
"a definite state of motion" relative to that absolute space. This new light "postulate"
represents, therefore, not a postulate, but a deduction, a theorem, and a phenomenon. Einstein
admitted, in 1907, that this "postulate" could not be a priori, but must, instead, be a
posteriori:
1"That the supposition made here, which we want to call the 'principle of the constancy of the
velocity of light', is actually met in Nature, is by no means self-evident, nevertheless, it is - at least for
a system of coordinates in a definite state of motion - rendered probable through its verification, which
Lorentz' theory based upon an absolutely resting aether has ascertained through experiment." [8]
1The so-called "postulates" are simply a restatement of supposed experimental facts,
and are not postulates, but empirical facts generalized as "laws" and "theorems". As Robert
Daniel Carmichael stated:
"The experiments which we have described (and others related to them) are fundamental in the
theory of relativity. The postulates in the next chapter are based on them. These postulates are in the
nature of generalizations of the facts established by experiment. [***] In the next chapter we shall
begin the systematic development of the theory of relativity. It will be seen that its fundamental
postulates, or laws, are based on the experiments of which we have given a brief account and on others
related to them. [***] The postulates, as we shall see, are simply generalizations of experimental facts;
and, unless an experiment can be devised to show that these generalizations are not legitimate, it is
natural and in accordance with the usual procedure in science to accept them as 'laws of nature.'" [9]
H. A. Lorentz questioned Albert Einstein's "method" of pretending that induction is
deduction:
76
1"Einstein simply postulates what we have deduced, with some difficulty and not altogether
satisfactorily, from the fundamental equations of the electromagnetic field. [***] I have not availed
myself of his substitutions, only because the formulae are rather complicated and look somewhat
artificial". [10]
1We soon discover in the introduction of the Einsteins' 1905 paper a clear statement of
the fallacious objective of their entire paper:
"These two assumptions are sufficient in order to arrive at a simple and consistent
electrodynamics of moving bodies, taking as a basis Maxwell's theory for resting bodies."
Is Maxwell's theory for resting bodies a third postulate? One of the "two assumptions",
the first "postulate", is that the laws electrodynamics of moving bodies be consistent among
systems of reference in uniform translatory motion with respect to the "resting system". Of
course, the reasoning presented is circular, first assuming via the first "postulate" that the laws
of electrodynamics are consistent, then arguing that this mandated consistency, as a premise,
causes consistency as an effect. It is the first of many circular arguments found in the
Einsteins' 1905 paper. How do we determine that which constitutes an "inertial system", other
than circularly, as in: An inertial system is one in which there is no net force acting on the
system; there is no net force acting on a system, when it is inertial?
Maxwell's theory for resting bodies is Maxwell's theory of the medium, a privileged
frame, the aether. However, the Einsteins alleged that the aether was "superfluous" to their
theory. The Einsteins irrationally wrote with the same pen that the aether was superfluous,
while asserting it as a basis for their theory.
In the introduction to the 1905 paper, we are being primed to venture forth from
Maxwell's theorems for bodies resting in the aether, so that we can return to them, Petitio
Principii, as the covariant laws of moving bodies, while being asked to pretend that the aether
is superfluous, so that we aren't too shocked when simultaneity is claimed to be relative,
again, Petitio Principii, via an impossible light synchronization assumption of light speed
invariance, or c' = c, which premise is also the conclusion of the theory.
For example, Albert 1Einstein stated in 1949:
"[T]he following postulate is [***] sufficient for a solution [***] L-principle holds for all
inertial systems (application of the special principle of relativity to the L-principle) [***] With the
help of the Lorentz transformations the special principle of relativity can be expressed thus: The laws
of nature are invariant with respect to Lorentz-transformations". [11]
Compare Albert Einstein's later statement to Willem de Sitter's statement of 1911:
"The principle of relativity can be enunciated as the postulate that the transformations, with
respect to which the laws of nature shall be invariant, are 'Lorentz-transformations.'*" [12]
Einstein, ever the plagiarist, stated in 1952:
"The whole content of the special theory of relativity is included in the postulate: The laws of
Nature are invariant with respect to the Lorentz transformations."[13]
Modus Operandi for Plagiarism
1
Einstein disclosed his modus operandi for manipulating credit for the synthetic
theories of others, when he stated in 1936:
77
"There is no inductive method which could lead to the fundamental concepts of physics.
Failure to understand this fact constituted the basic philosophical error of so many investigators of the
nineteenth century. [***] Logical thinking is necessarily deductive; it is based upon hypothetical
concepts and axioms. How can we expect to choose the latter so that we might hope for a confirmation
of the consequences derived from them? The most satisfactory situation is evidently to be found in
cases where the new fundamental hypotheses are suggested by the world of experience itself."[14]
This is a clear statement by Einstein that he would have science deduce a thing from
itself, taking the world of experience as a hypothesis, only to deduce the world of experience
as an effect, of itself. Of course, Mileva and Albert were forced to present the real hypotheses,
which they stuck in the middle of their arguments by way of induction, or an attempt at
induction, which analyses they attempted to disguise as deductions from a priori principles,
but which "a priori principles" were well-known summations of phenomena.
Einstein wanted people to believe that it is irrelevant that his predecessors induced the
theories he later copied, because Einstein just invented them, sua sponte, irrationally, after he
had read them, and therefore deserved credit for them:
"Invention is not the product of logical thought, even though the final product is tied to a
logical structure."[15]
Conclusion
Einstein stated, together with Infeld:
"Physical concepts are free creations of the human mind, and are not, however it may seem,
uniquely determined by the external world."[16]
Certainly, the two "postulates" of the theory of relativity were not, "free creations of
the human mind," but were, instead, summations of the empirical observations of the wellknown phenomena of the day framed with the familiar concepts of the day. What Infeld and
Einstein meant by "free" is difficult to fathom, and it is simply repetitive to say that creations
of the mind are creations of the mind. Einstein's vague notions are perhaps the result of his
plagiarizing Newton, Mach, Pearson, and others, on the principle of logical economy and
watering down what they had written with Einstein's simplistic and naïve talk. If "free" is to
mean unrestricted in any sense, no human mind is "free". We are limited in our concepts,
experience, and scope, and we are socialized, indoctrinated and inculcated into certain beliefs.
Despite Einstein's assertions, there is no mutual exclusion between being creative and being
logical. One can create logical hypotheses through creative induction.
It is the Lorentz Transformation which is the product of creative inductive logic, with
its hypotheses of length contraction, time dilatation and relative simultaneity, and which is the
fundamental postulate of the special theory of relativity. Invariant light speed and the
covariance of the laws of physics are deducible from the Lorentz Transformation, the laws of
physics, and the definition of inertial motion, which are more fundamental in the special
theory of relativity, than invariant light speed. Speed must be composed of the more
fundamental elements of distance and duration. Speed is a derived unit. Therefore, the
synthesis of the special theory of relativity comes in deducing invariant light speed from the
hypotheses of an isotropic and homogenous space, Maxwell's theory of the medium, the
theory of inertial motion, and the hypotheses of length contraction, time dilation and relative
simultaneity. This is precisely the conclusion Einstein was obliged to admit, in 1935:
"The special theory of relativity grew out of the Maxwell electromagnetic equations. So it
came about that even in the derivation of the mechanical concepts and their relations the consideration
of those of the electromagnetic field has played an essential role. The question as to the independence
78
of those relations is a natural one because the Lorentz transformation, the real basis of the special
relativity theory[. . .]"[17]
To argue, as the Einsteins did argue in 1905, that invariant light speed and the
mandated identity of Lange's inertial systems deduces invariant light speed and the mandated
identity of Lange's inertial systems, is to argue in fallacies of Petitio Principii, which the
Einsteins did do, in an attempt to hide their plagiarism of the induced hypotheses of
Boscovich, Voigt, FitzGerald and Larmor.[18]
Notes
1 - M. Einstein-Marity and A. Einstein, "Zur Elektrodynamik bewegter Körper", Annalen der Physik,
Series 4, Volume 17, (1905), pp. 891-921.
2 - H. A. Rowland, The Physical Papers of Henry August Rowland, The Johns Hopkins Press,
Baltimore, Maryland, (1902), pp. 673-674.
3 - W. Voigt, "Ueber das Doppler'sche Princip", Nachrichten von der Königlichen Gesellschaft der
Wissenschaften und der Georg-Augusts-Universität zu Göttingen, (1887), pp. 41-51; republished
Physikalische Zeitschrift, Volume 16, Number 20, (October15, 1915), pp. 381-386; English
translation, as well as very useful commentary, are found in A. Ernst and Jong-Ping Hsu (W. Kern is
credited with assisting in the translation), "First Proposal of the Universal Speed of Light by Voigt in
1887", Chinese Journal of Physics (The Physical Society of the Republic of China), Volume 39,
Number 3, (June, 2001), pp. 211-230; URL < http://psroc.phys.ntu.edu.tw/cjp/v39/211.pdf> Lorentz
acknowledged Voigt's priority, and suggested that the "Lorentz Transformation" be called the
"Transformations of Relativity": See: H. A. Lorentz, Theory of Electrons, B. G. Teubner, Leipzig,
(1909), p. 198 footnote; and H. A. Lorentz, "Deux memoirs de Henri Poincaré", Acta Mathematica,
Volume 38, (1921), p. 295; reprinted in Œuvres de Henri Poincaré, Volume XI, Gautier-Villars,
(1956), pp. 247-261. Minkowski also acknowledged Voigt's priority: See: The Principle of Relativity,
Dover, New York, (1952), p. 81; and Physikalische Zeitschrift, Volume 9, Number 22, (November 1,
1908), p. 762. For further discussion of Voigt's relativistic transformation, see: R. Dugas, A History of
Mechanics, Dover, New York, (1988), pp. 468, 484, 494; A. Pais, Subtle is the Lord, Oxford
University Press, Oxford, New York, Toronto, Melbourne, (1982), pp. 121-122.
4 - G. F. FitzGerald, "The Ether and Earth's Atmosphere (Letter to the Editor)", Science, Volume 13,
Number 328, (1889), p. 390.
5 - J. Larmor, "A Dynamical Theory of the Electric and Luminiferous Medium", Philosophical
Transactions of the Royal Society of London A, Volume 185, (1894), pp. 719-822; Volume 186,
(1895), pp. 695-743; Volume 188, (1897), pp. 205-300; and Aether and Matter, CUP, (1900).
6 - A. Einstein, "Über das Relativitätsprinzip und die aus demselben gezogenen Folgerung", Jahrbuch
der Radioaktivität und Elektronik, Volume 4, (1907), pp. 411-462, at 416.
7 - See: A. Pais, Subtle is the Lord, Oxford University Press, Oxford, New York, Toronto, Melbourne,
(1982), p. 142; where Pais refers to Einstein's so-called "Morgan manuscript" of 1921. Einstein
plagiarized this from: N. R. Campbell, "The Common Sense of Relativity", Philosophical Magazine,
Series 6, Volume 21, Number 124, (April, 1911), pp. 502-517, at 505. See also: R. D. Carmichael,
"On the Theory of Relativity: Analysis of the Postulates", The Physical Review, First Series, Volume
35, (September, 1912), pp. 153-176; and "On the Theory of Relativity: Mass, Force and Energy", The
Physical Review, Series 2, Volume 1, (February, 1913), pp. 161-197.
8 - A. Einstein, "Über das Relativitätsprinzip und die aus demselben gezogenen Folgerung", Jahrbuch
der Radioaktivität und Elektronik, Volume 4, (1907), pp. 411-462, at 416.
79
9 - R. D. Carmichael, The Theory of Relativity, Mathematical Monographs No. 12, John Wiley &
Sons, Inc., New York, Chapman & Hall, Limited, London, (1920), pp. 13-14.
10 - H. A. Lorentz, The Theory of Electrons, Dover, New York, (1952), p. 230.
11 - A. Einstein, The Theory of Relativity and other Essays, Carol Publishing Group, (1996), pp. 6-8.
12 - W. de Sitter, "On the Bearing of the Principle of Relativity on Gravitational Astronomy", Monthly
Notices of the Royal Astronomical Society, Volume 71, (March, 1911), pp. 388-415, at 388-389.
13 - A. Einstein, Relativity, the Special and the General Theory, Crown Publishing, Inc., New York,
(1961), p. 148.
14 - A. Einstein, Ideas and Opinions, Crown Publishers, Inc., New York, (1954), p. 307.
15 - A. Einstein, quoted in A. Pais, Subtle is the Lord, Oxford University Press, Oxford, New York,
Toronto, Melbourne, (1982), p. 131.
16 - A. Einstein and I. Infeld, The Evolution of Physics, Simon & Schuster, New York, London,
Toronto, Sydney, Tokyo, Singapore, (1966), p. 31. Compare to the more lucid, prior statements of: W.
K. Clifford, The Common Sense of the Exact Sciences, Dover, New York, (1955), pp. 193-194. E.
Mach, "The Economy of Science", The Science of Mechanics, Open Court, LaSalle, Illinois, (1960),
pp. 577-595. K. Pearson, The Grammar of Science, Second Revised and Enlarged Edition, Adam and
Charles Black, London, (1900), pp. 30-37. H. Poincaré, Dernières Pensées, Flammarion, Paris, (1913);
English translation Mathematics and Science: Last Essays, Dover, New York, (1963), pp. 22-23.
Einstein often plagiarized these works.
17 - A. Einstein, "Elementary Derivation of the equivalence of Mass and Energy", Bulletin of the
American Mathematical Society, Series 2, Volume 41, (1935), pp. 223-230, at 223.
18 - Cf. C. J. Bjerknes, Albert Einstein: The Incorrigible Plagiarist, XTX Inc., Downers Grove,
Illinois, USA, (2002), ISBN 0971962987.
Selected Bibliography
R. D. Carmichael, The Theory of Relativity, Mathematical Monographs No. 12, John Wiley & Sons,
Inc., New York, Chapman & Hall, Limited, London, (1920), pp. 13-14.
H. Dingler, Die Grundlagen der Physik, synthetische Prinzipien der mathematischen Naturphilosphie,
Verlag der Vereinigung wissenschaftlicher Verleger, Leipzig, (1919).
S. H. Guggenheimer, The Einstein Theory Explained and Analyzed, The Macmillan Company, New
York, (1925).
J. Mackaye, The Dynamic Universe, Charles Scribner's Sons, New York, (1931).
W. Kantor, Relativistic Propagation of Light, Coronado Press, Lawrence, Kansas, (1976).
S. Goldberg, Understanding Relativity, Birkhäuser, Boston, Basel, Stuttgart, (1984).
----[A presentation of the author is given at the end of his previous paper published in this
same issue of Episteme]
[email protected]
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La nuova teoria del cielo
La cosmologia osservativa di Halton Arp
(Alberto Bolognesi)
Questo articolo cerca di comunicare informazioni e interpretazioni alternative dell'universo
che sono state a lungo ostacolate e, in qualche caso, perfino soppresse. Sono tutte di natura
osservativa e si basano essenzialmente sui risultati ottenuti al telescopio dall'astronomo
americano Halton Arp, a cui sono legato da lunga e profonda amicizia.
La ragione per cui questi dati stentano tanto a circolare è che la loro accettazione
determinerebbe automaticamente uno sconvolgimento scientifico e culturale paragonabile
almeno a quello che si produsse con la falsificazione del Sistema Tolemaico. "L'astronomia e
l'intera fisica - è stato autorevolmente sancito - dipendono totalmente dalla fisica delle
particelle la quale a sua volta proviene direttamente dal Big Bang. Con il Big Bang e
l'espansione dell'universo - concordano Murray Gell Mann, David Schramm e Stephen
Hawking - astronomia e fisica hanno cessato per sempre di esistere come discipline
autonome".
Amen. E se i biologi molecolari inaugurano le loro indagini sul funzionamento del cervello
umano con riferimenti espliciti alla nucleosintesi prodottasi nella "fornace primordiale", si
dovrebbe aggiungere che non solo fisica, astrofisica e costanti universali, ma chimica,
biochimica, botanica, zoologia, storia e filosofia si trovavano in qualche modo già iscritte
nella prodigiosa formula dell'Inizio, intesa come un tutto creato dal nulla.
L'alternativa kantiana che il tutto sia inaccessibile all'esperienza è una concezione in disuso:
oltre al sottoscritto - che è un dilettante - non conosco più di una dozzina di astrofisici che
dichiarano apertamente che l'unico universo di cui abbia senso parlare è quello osservabile o
potenzialmente osservabile, e che l'espressione "tutto l'universo", "condizioni iniziali" e "fine
dell'universo" sono prive di qualsiasi contenuto scientifico.
Poiché un protone, un neutrone o un elettrone non possono mai essere creati o distrutti
isolatamente in un'interazione di particelle, i cosmologi deducono che il loro numero totale è
stato fissato rigorosamente al momento del "Fireball". Non un fermione di più e non un
fermione di meno. Dio - o chi per esso - ha parlato una volta sola. Dalla massa delle galassie
alle singole stelle, dalla balenottera azzurra al giaguaro, alla zanzara tigre, tutto dipende
interamente e unicamente dalle condizioni iniziali. Tutto. Ma proprio tutto. All'obiezione di
Leibniz - perché c'è qualcosa al posto di nulla? - i teorici della Palla di Fuoco oppongono
l'esistenza del falso vuoto, il magico tappeto delle fluttuazioni virtuali, i formicolii del nulla,
"l'aperto del puro compossibile". Basta associare al mondo fisico un'energia positiva e alla
gravitazione un'energia "negativa" per avere l'universo a costo zero, tutto e nulla
contemporaneamente. Più uno meno uno uguale zero, "poiché nulla era - come già scriveva
Edgar Poe nel 1848 - tutto è". Eureka!
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Una testimonianza a tarallucci e vino di questo trionfo moderno ci è fornita dal bellissimo
libro di Dennis Overbye ("Cuori solitari del cosmo"), che descrive i canti e i lazzi di famosi
astronomi che ridiscendono in pulmann dall'osservatorio Keck, sulla cima del Mauna Kea:
"Sai qual fu la conclusion, dopo molte ore di osservazion? - cantavano festanti - L'universo è
in espansion, sempre in espansion, sempre in espansion …".
Ma qualcosa è andato storto, e nei dispositivi ad accoppiamento di carica applicati ai telescopi
sono apparsi sempre più numerosi enigmatici ponti, filamenti luminosi di materia e sinistre
connessioni che collegano oggetti che dovrebbero essere invece lontanissimi fra loro. Allora?
"La festa appena cominciata … è già finita?.
DILETTANTI DENIGRATORI E RIVOLUZIONI SENZA PROVE
Il preambolo mi consente di fissare drasticamente i termini della questione. Che cosa succede
alla cosmologia, alla fisica delle particelle, ma anche alla fisica ordinaria e all'epistemologia,
se le connessioni fra oggetti di diverso spostamento spettrale sono reali?
L'assunzione fondamentale su cui è costruita tutta la conoscenza attuale dell'universo è che lo
spostamento verso il rosso deve rappresentare una velocità. Non basterebbe infatti che
rappresentasse una mera misura delle distanze come nell'originario "effetto Hubble": per
avere un universo in espansione, velocità e distanza devono in qualche modo coincidere. Uno
spostamento verso il rosso in relazione lineare con la sola distanza eliminerebbe il Big Bang,
darebbe di nuovo un universo statico, togliendo di mano ai cosmologi la sospirata "età
dell'universo" e ai fisici delle particelle la mitica "era di Planck". E perfino ovvio che il
sistema del mondo contemporaneo deve fare quadrato attorno alla recessione delle galassie.
Non ci sono alternative: questo effetto deve essere "universale" e aumentare in proporzione
diretta alla distanza che ci separa da esse. Più elevato è il redshift più lontane sono le galassie,
più lontane sono le galassie più velocemente devono allontanarsi. Anche il profano capisce
facilmente che è una questione di vita o di morte: le velocità devono essere reali.
Ma rispetto a cosa? Se prendiamo tre galassie A, B e C fra loro molto lontane e le disponiamo
su una retta immaginaria, quella che sta in mezzo deve allontanarsi radialmente rispetto alle
altre due che recedono più rapidamente. Come è possibile? Se A e C si allontanano
reciprocamente e proporzionalmente alla loro distanza, come fa B a recedere verso C se C
vede B recedere verso A?
A
B
C
∗←→ ∗ ←→ ∗
←→
Il solo modo di intendere la recessione universale non è evidentemente di assegnare una
velocità alle galassie, ma di attribuire una velocità alle distanze. Non è la fuga delle galassie,
ma la fuga delle distanze! Per aver dichiarato e scritto questo una trentina di anni fa, sono
stato incolpato di "infangare l'immagine pubblica del mondo scientifico" e inserito nella lista
dei proscritti dalla divulgazione scientifica.
In un clima più liberal, oggi i cosmologi ammettono che non sono le galassie a fuggire
attraverso lo spazio separandosi le une dalle altre, ma che è lo spazio stesso a dilatarsi e ad
espandersi trascinando con sé gli oggetti cosmici. Si fa ossessivamente riferimento all'uvetta
di un panettone che cresce nel forno, e così tutto va a posto se si è disposti ad assegnare al
vuoto e alla metrica le qualità di una pasta che lievita col tempo. (Chiedersi poi chi alimenta il
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forno sarebbe "altamente provocatorio"). Ma questa precisazione ha un costo drammatico e i
cosmologi ammettono adesso, con scarso entusiasmo, che lo spostamento verso il rosso delle
galassie "non è dovuto all'effetto Doppler" (J. Gribbin, Enciclopedia di Astronomia e
Cosmologia). Cioè, a rigore non è dovuto alle loro velocità.
Se però vi iscrivete alla Facoltà di Astronomia il redshift cosmologico vi verrà spiegato
sistematicamente in questo modo: "Consideriamo due fotoni che partono dalla sorgente con
un ritardo ∆ t l'uno rispetto all'altro. Poiché in quel ∆t l'universo si espande, la sorgente si
allontana di una quantità vx∆t e il secondo fotone deve percorrere una distanza più lunga
per giungere fino a noi: il ritardo ∆t' con cui lo riceviamo è perciò maggiore". Ma questo è
l'effetto Doppler canonico, e gli educatori sanno bene che c'è qualcosa che non va, perché è
ovvio che la dilatazione deve avvenire nel tempo attraverso lo spazio che lievita mentre i
fotoni sono in viaggio, non quando "il primo e poi il secondo fotone si stacca dalla sorgente"
per intraprendere il suo lungo percorso fino ai nostri strumenti! Come faccia allora una
lunghezza d'onda a "stirarsi" nello spazio che cresce in misura uguale e contraria alla
direzione di propagazione della radiazione elettromagnetica, è un inquietante capitolo di
spettroscopia che attende ancora di essere scritto.
Altri trent'anni di proscrizione? Sarebbe un bel traguardo per un cinquantasettenne.
Prima di passare ad alcune confutazioni osservative raccolte da Halton Arp vorrei chiudere il
greve argomento riportando la lettera di un dilettante pubblicata di recente da una rivista
specializzata. "Che cos'è che veramente si espande? - si chiede con passione il signor Ariberto
Papini di Siena - Perché si fa presto a far dilatare la superficie di un palloncino: è di gomma!
Oppure un lenzuolo: è di stoffa! Ma come si fa a fare espandere, oppure ad incurvare
qualcosa di non materiale: il vuoto, il nulla?". La profonda risposta fu che "gli aspetti della
cosmologia non sono intuitivi, e che alla comprensione dell'espansione dell'universo si arriva
solo per via matematica poiché l'estrema astrazione di alcuni concetti rende ardua una
spiegazione divulgativa. Comunque tenga presente che la gravità frena la materia - rispetto a
cosa?! - ed è la materia ad espandersi. Essa con tale espansione crea lo spazio. Ovvero, le
galassie non si espandono in uno spazio circostante, ma lo spazio stesso è creato
dall'espansione dell'Universo" (Nuovo Orione n. 123, agosto 2002).
Cioè lo spazio è creato dall'espansione dello spazio. Soddisfatti o rimborsati.
RIVOLUZIONI SENZA PROVE?
O gli oggetti di Arp sono tutte illusioni ottiche o i cosmologi difendono un'espansione
dell'universo smentita dall'osservazione astronomica. Non è possibile una soluzione
"salomonica" o di compromesso e questo rende la controversia ancora più aspra e
drammatica. Poiché galassie interagenti con redshift discorde non possono essere
contemporaneamente vicine e lontane, connesse e disconnesse, lente e veloci, il punto di vista
convenzionale è costretto ad invocare sistematicamente effetti di prospettiva, allineamenti e
accavallamenti accidentali nella profondità del cielo.
Né potrebbe accontentarsi di attribuire all'oggetto con redshift eccedente uno spostamento non
cosmologico assegnando a quello con minore spostamento verso il rosso un redshift
sicuramente e interamente cosmologico.
Giudicate voi.
La prima immagine (Fig. 1) che ho selezionato da un gran numero di casi esistenti, mostra un
quasar che cade davanti a una galassia ellittica, la NGC 1199. L'oggetto compatto indicato
con una freccia ha uno spostamento verso il rosso abbastanza elevato (z = 0,044) mentre
quello della galassia è modesto (z = 0,009). Per la legge di Hubble e per la buona sorte della
cosmologia del Big Bang l'oggetto di tipo quasar dovrebbe invece trovarsi dietro (cioè molto
più lontano della galassia ellittica).
83
Fig. 1
L'immagine successiva (Fig. 2) rappresenta la galassia NGC 4319 e il quasar Markarian 205
connesso da un visibile ponte di materia. Ma lo spostamento verso il rosso della galassia è z =
0,006 mentre quello del quasar è di 0,07, cioè dovrebbe trovarsi undici volte più distante
secondo la "legge" che tutela l'espansione dell'universo.
Fig. 2
84
La fotografia seguente (Fig. 3) rappresenta il Sestetto di Seyfert, un gruppo di galassie in
interazioni che hanno all'incirca la stessa magnitudine apparente. Cinque di esse hanno più o
meno lo stesso redshift (z = 0,015) ma quella indicata con la freccia presenta uno spostamento
quasi cinque volte maggiore, il che la renderebbe cinque volte più lontana e di enormi
dimensioni.
Fig. 3
85
La quarta immagine (Fig. 4) mostra la suggestiva catena di galassie blu VV 172. Quattro di
queste galassie hanno un valore di redshift che oscilla intorno a z = 0,05 mentre quella
indicata con una freccia presenta uno spostamento verso il rosso estremamente elevato: z =
0,12. Chi crede davvero che questa galassia non faccia parte della configurazione e che si
tratti di un lontanissimo oggetto blu che si è andato ad incastrare accidentalmente fra quattro
compagne blu lungo la nostra linea di vista, alzi la mano: e chi alza la mano sostiene
implicitamente che si tratta della galassia blu più grande di tutto l'universo …
Fig. 4
86
La quinta immagine (Fig. 5) presenta tre quasar nei bracci a spirale di NGC 1073. C'è una
probabilità su cinquantamila che si tratti di un allineamento accidentale.
Fig. 5
E ancora, in Figura 6, una fotografia profonda di tre quasar intorno a NGC 3842. Qui c'è una
possibilità su un milione di trovare per caso questa associazione.
Fig. 6
87
La settima immagine mostra la spirale barrata a due bracci NGC 1097 con i suoi quattro getti
luminosi. Ci sono almeno cinquanta quasar attorno a questa galassia straordinariamente attiva.
Fig. 7
Fig. 8
(Grafico dei quasar individuati attorno a NGC 1097
da Arp, Wolstencroft e He nel 1979).
Concludo questa "rivoluzione senza prove" con la foto (Fig. 9) ottenuta da N. Sharp della
coppia di galassie NGC 7603 A e B, foto che i lettori di Episteme già conoscono per via della
recentissima e sensazionale scoperta effettuata dagli astronomi M.L. Corredoira e C.M.
Gutierrez. Rappresenta il coronamento di cinquant'anni di ricerche che hanno fruttato ad Arp
soltanto l'allontanamento dall'Osservatorio di Monte Palomar. Sebbene siano stati pubblicati
sulla celebre rivista "Astronomy and Astrophysics", i risultati continuano a circolare nella
comunità astronomica come l'ennesimo, imbarazzante X file.
88
Le due galassie collegate da un evidentissimo ponte di materia hanno rispettivamente uno z:
0,029 per l'oggetto più grande e z: 0,057 per la compagna più piccola. Al momento della
scoperta della clamorosa discordanza (1971) Arp notò subito due condensazioni di aspetto
stellare immerse nel braccio, e auspicò che i futuri spettrografi potessero analizzarne i dettagli
e determinarne gli spostamenti verso il rosso. Impresa riuscita a Corredoira e Gutierrez
trent'anni dopo col N.O.T. di La Palma, e con tecnologia progredita: le due condensazioni
hanno mostrato gli spettri tipici dei quasar con z = 0,391 per l'oggetto più vicino alla galassia
principale e z = 0,243 per quello prossimo alla compagna! Così abbiamo due galassie
interagenti con diverso spostamento verso il rosso e due quasar ad alto redshift nel filamento
che le connette: il mondo avrebbe dovuto fermarsi per questo, almeno per un giorno, ma i
grandi media non ne hanno nemmeno parlato.
Fig. 9
Che dire? C'è una terza condensazione che emerge dal nucleo della NGC 7603A: e basterebbe
un'occhiata dell'Hubble Space Telescope o del Keck per affossare il Sistema del Mondo.
Richiesta di ulteriori osservazioni con il telescopio orbitale a raggi X Chandra e con l'8 metri
del VLT dell'ESO al Cerro Paranal sono state prontamente respinte.
LA NUOVA TEORIA DEL CIELO
Le discordanze di redshift constatate, richiedono che le condizioni di emissione della
radiazione da parte di oggetti interagenti o posti alla stessa distanza mutino da un sistema
all'altro. Si tratta dunque di comprendere un fenomeno fisico in grado di operare su interi
insiemi estesi di stelle, gas e polveri, generando spostamenti intrinseci che non hanno a che
vedere né con la velocità né con la distanza. Un meccanismo che opera ancora più
vistosamente nei quasar, che lungi dall'essere gli astri favolosi più energetici e lontani di tutto
l'universo, svelano la loro natura di oggetti piccoli e poco luminosi, connessi alle galassie.
Questo cambio - val la pena sottolinearlo - non è invocato da una nuova stravagante teoria
dell'universo ma, se non avete già dimenticato le precedenti immagini, dalle osservazioni
stesse.
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Dunque nuova fisica, nuova informazione che dovrebbe esaltare - e non deprimere! - chi
tende ad approfondire la conoscenza della struttura cosmica. Anche se questo sembra
aumentare la nostra ignoranza, allontanandoci da certezze gelosamente custodite.
L'evidenza osservativa dello spostamento verso il rosso intrinseco chiama in causa
direttamente la fisica quantistica e l'azione interparticellare che devono giustificare l'esistenza
del mondo collegandolo al microcosmo. Per gli scopi divulgativi che si propone questo
articolo dirò semplicemente che la varietà dei redshift intrinseci osservati richiede che le
transizioni energetiche di un atomo di idrogeno, di elio, di ossigeno, di magnesio … devono
trovarsi a frequenze e a lunghezze d'onda diverse da quelle che sperimentiamo in laboratorio.
E questo dà già un'idea della immensa posta in gioco. A qualsiasi livello di conoscenza si
trovi il lettore (e lo scrivente!) la falsificazione dell'universo in espansione impone che le
righe degli elementi e le serie spettrali che compongono l'intero spettro elettromagnetico si
trovino realmente alle frequenze osservate.
Si può ben comprendere lo shock stemperato dall'ironia che ha fatto esclamare a un eminente
fisico che "i dati di Arp implicano costanti personalizzate!": Ma questa è esattamente la sfida
osservativa, questa è esattamente la vita sulla frontiera.
"Che cosa determina l'energia di transizione tra due stati atomici dell'idrogeno? - si chiede
Arp - Un fattore è rappresentato dalla carica relativa tra l'elettrone e il nucleo, l'altro fattore
è la massa dell'elettrone che subisce una transizione tra i due possibili stati orbitali. Se le
misure della costante di struttura fine eliminano la possibilità che le cariche elettriche
possono essere diverse, resta solo la massa dell'elettrone"1.
Poiché lo spostamento verso il rosso intrinseco è documentato dalle osservazioni, una delle
poche interpretazioni in grado di spiegarlo efficacemente è di attribuire massa minore a tutte
le particelle che costituiscono la materia dell'oggetto con più alto spostamento verso il rosso.
Ciò darebbe immediatamente frequenze più basse e fotoni più spostati verso il rosso, orbite
elettroniche "allargate" e, in pratica, isotopi più leggeri. Se dunque quasar e galassie
compagne risultano associate a oggetti più massici, come nipotini a spasso coi nonni, una
delle differenze più qualificanti sta nel loro tempo di formazione. E' pensabile - si chiede Arp
- che oggetti connessi da ponti di materia, mobilizzati nei bracci di spirali o immersi in
filamenti luminosi e in gas caldi ad alta e ad altissima energia (X e gamma) abbiano la
medesima età del sistema a cui appartengono?
La soluzione cosmogonica è immediata: gli oggetti cosmici con più alto spostamento verso il
rosso devono essere stati "creati" (espulsi o condensati) in un tempo successivo rispetto a
quelli con basso redshift. "Non appena la materia appare - scrive Arp - essa risulta altamente
spostata verso il rosso. Col passare del tempo diventa più pesante, più grande e più luminosa
e il suo altissimo spostamento decade verso valori più contenuti. Abbiamo in pratica la
rappresentazione empirica di un piccolo quasar con altissimo redshift che evolve in una
galassia compatta con spostamento verso il rosso inferiore e infine in una galassia compagna
con leggera eccedenza nello spostamento verso il rosso" rispetto all'oggetto che l'ha generata.
("Quasar, redshifts and controversies", 1987)2.
E' dunque nei fatti, per Arp, un'evoluzione delle costanti. Ed è ironico - rileva - che il punto di
vista convenzionale ne difenda ad ogni costo l'immutabilità invocando il Secondo Principio
della Termodinamica. La materia creata tutta in una volta dal Big Bang con proprietà
immutabili non rappresenta una violazione, ma le masse delle particelle variabili col tempo lo
sono …. "Mi rendo conto che il mio universo si restringe paurosamente all'universo delle
osservazioni - mi disse una volta - un universo locale dove la materia vi compare
continuamente ricreata, o riciclata. I tuttologi non potrebbero accontentarsi ma ciò è
esattamente quel che osserviamo!". Evidentemente a partire da uno stato particellare
estremamente diffuso - ipotizza Arp - Da un "apeiron" sconosciuto e onnipervasivo che
accende i nuclei delle galassie e che le moltiplica attraverso espulsioni secondarie come una
gragnola ininterrotta di fuochi d'artificio. O come una pianta che germoglia.
90
E' un immagine locale ma grandiosa, che non può (né si vede come potrebbe) pretendere di
fissare tutto l'universo. La sola definizione sensata del Mondo - insiste - è: "tutta la materia
osservabile o potenzialmente osservabile che siamo in grado di sperimentare".
I limiti kantiani vengono immediatamente ristabiliti: siamo all'interno di un perimetro o di una
bolla i cui orizzonti si allargano per mezzo di strumenti sempre più progrediti, ma
continuiamo a permanere confinati al centro del mistero. Più che una condizione umana
sembra una condizione della fisica.
CHE COS'È H ?
O
Ma all'interno della "bolla delle osservazioni", come sull'isola di Kant battuta dai marosi
dell'inconoscibile, possiamo ancora fare scienza. Se la creazione di materia prende posto
nell'universo come un processo continuato, e se i redshift esprimono semplicemente l'età degli
oggetti cosmici e non più la loro velocità e la loro distanza dal mitico Inizio del Mondo, può
ancora avere un significato la determinazione della "costante Ho"?
Sorprendentemente la risposta è sì. La costante di Hubble che nella cosmologia del Big Bang
non è che un numero che quantifica la rapidità con cui l'universo si va espandendo, diventa
nella relazione age-redshift di Arp la chiave di volta per misurare la variabilità della massa in
funzione dello spostamento verso il rosso. L'integrazione che lega lo spostamento spettrale
alla scala delle magnitudini apparenti è immediata, e con essa l'annosa questione dei "redshift
anomali".
La trasformazione della convenzionale legge di Hubble "velocity-distance" in "age-distance
law" e in "age-luminosity law" è fissata nelle equazioni della massa variabile:
m = mo
t2
t0
2
(1)
sul redshift:
2
1+ z =
t0
t2
(2)
2
1 + z1 t 0
=
(3)
1 + z 0 t1 2
e sulla trasformazione delle scale temporali τ = tempo locale e t = tempo cosmico:
τ =
t3
3t 0
2
(4)
in cui la soluzione di Friedmann (Big Bang) viene ricondotta a uno spaziotempo piatto
(euclideo) e a un universo statico.
Il diagramma sottostante (Fig. 10) visualizza le due soluzioni, che a sinistra forniscono il Big
Bang e a destra l'universo di Narlikar-Arp. Ma, ben conscio di perdere in tal modo i contatti
con i lettori che non hanno specifiche esperienze di cosmologia, dirò subito che non intendo
cavarmela con la mera esposizione del formalismo matematico.
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Fig. 10
(da Arp, 1997)
E non è una passeggiata. Limitandomi all'essenziale, è evidente che non tutte le galassie sono
grandi galassie: al contrario, queste ultime sono abbastanza rare. Nella cosmologia del Big
Bang tutte le galassie hanno però all'incirca la stessa età mentre in quella di Arp devono avere
età assai variegate, e dalla loro età deve dipendere la massa, lo splendore e soprattutto lo
spostamento spettrale, mentre nell'ipotesi convenzionale i redshift misurano essenzialmente le
velocità e le distanze prodotte dall'espansione dello spazio.
E' ovvio che anche le galassie "in carriera" di Arp non sono destinate a raggiungere tutte la
medesima massa e luminosità (le differenze morfologiche sono un fatto osservativo), ma in
questo quadro non si presenta il rischio di mescolare sistematicamente oggetti di magnitudini
assolute molto diverse. Che è poi un vantaggio che ha una terribile contropartita, perché in tal
modo non possiamo più dire gran che sulle loro distanze.
Anche una semplificazione così estrema riesce a mettere a nudo la prima cruciale questione:
meglio una distanza sbagliata o una distanza incerta? E' l'eterno tallone d'Achille della scienza
astronomica, che non può misurare nelle due dimensioni disponibili un mondo fisico che ne
ha almeno tre: misure sbagliate non hanno contenuto scientifico, misure incerte non
producono risultati scientifici. Basta questo preliminare per capire perché, a dispetto delle
confutazioni osservative, l'espansione dell'universo è così strenuamente difesa. E' solo in base
all'interpretazione cinematica del redshift che si è potuta sviluppare una tecnica in grado di
scandagliare l'universo e di produrre spettacolari mappe tridimensionali della struttura
cosmica. Che producono mostri, si potrebbe aggiungere, come le grandi muraglie, le "dita di
Dio", le spropositate luminosità dei quasar, le velocità superluminali e le masse dei buchi neri
che aumentano con la distanza.
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Fig. 11
Interpretazioni a confronto - Nella figura precedente appaiono cinque oggetti di debole luminosità
molto vicini fra loro. I dettagli della composizione spettrale sono qualitativamente molto simili per
tutti i componenti ma l'aspetto non puntiforme dei primi tre a sinistra li definisce come "galassie"
mentre i due oggetti di forma sferica (puntiformi) appaiati sono riconosciuti come "quasar". Il redshift
medio è z = 0,435 il che li collocherebbe a più di cinque miliardi di anni luce di distanza da noi, ma il
quasar a destra ha un redshift quasi cinque volte più alto (che anche dopo le correzioni relativistiche
dovrebbe essere spostato a una distanza almeno doppia). L'interpretazione cosmologica richiede che
tre galassie e un quasar si trovino tutti alla stessa distanza mentre il quasar di destra viene a cadere
solo accidentalmente vicino al gruppo per un effetto di prospettiva. Per Arp gli oggetti sono tutti alla
stessa distanza, molto giovani, molto più vicini e molto meno luminosi, e il quasar di destra
rappresenta l'ultimo nato della formazione. Si noti che il quasar più luminoso non mostra alcuna
nebulosità circostante, che dovrebbe invece essere rivelata sul versante del compagno ritenuto più
lontano. Non appare nessuna galassia "ospite" in 1548+144a e il quasar appare "nudo".
(Cortesia di E.M. Burbidge).
Come si fa a distinguere una galassia debole da una galassia lontana?
E' l'eterno dilemma della "distanza secondo luminosità": quando la luminosità apparente di
una sorgente luminosa è pari a un quarto della luminosità apparente di un'altra sorgente di
medesima luminosità assoluta, la prima si trova a distanza doppia. Nella teoria del Big Bang
quando il redshift di un oggetto è doppio, questi deve recedere a velocità doppia, quando il
redshift è quadruplo l'oggetto si allontana quattro volte più velocemente e deve trovarsi
quattro volte più lontano. La circolarità è in agguato: se i rapporti di luminosità apparenti non
tornano, o coincidono sopra valori di redshift differenti, basta aumentare (o diminuire) le
luminosità assolute. E se due galassie morfologicamente identiche e del medesimo splendore
apparente, ma individuate in posizioni contrapposte del cielo presentano spostamenti verso il
rosso discordi, si chiamano in causa "espansioni asimmetriche dell'universo". Non si può …
sbagliare.
L'alternativa di Arp è il crollo dell'espansione dell'universo, e questo implica che le distanze
siano sbagliate di un fattore che può superare 100, le masse e le luminosità di un fattore
10.000, le età assegnate in base al "look back time" di un fattore fino a 10 10: un'alternativa da
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Sant'Uffizio, si potrebbe dire, quando i detentori del potere temporale per colpa di un piccolo
cannocchiale si trovavano a dover riconsiderare l'inviolabile architettura del Cielo.
Ma il "look back time", cioè l'effetto di osservare gli oggetti cosmici allo stato non attuale per
via della velocità finita delle propagazioni elettromagnetiche, ha importantissime e decisive
conseguenze su entrambi i modelli di universo. Nello schema immaginario del Big Bang
come in un film girato alla rovescia, l'età delle galassie si abbassa progressivamente e
uniformemente con la distanza, svelando oggetti primordiali, in cui la "metallicità" (cioè la
formazione degli elementi più pesanti all'interno delle prime stelle) tende a scomparire. Le
galassie svaniscono per far posto a singole palle di gas di massa grandissima e di vita
brevissima (l'ipotetica popolazione III). Più in là c'è solo "l'era della radiazione". Nella
cosmologia osservativa di Arp, la scalata verso epoche più antiche dipende invece da un unico
parametro, l'età della nostra galassia. Tecnicamente, quindi, la cosiddetta costante di Hubble
rappresenta l'inverso dell'età delle nostre stelle più antiche! Per esprimermi nei termini più
semplici: come ci apparirebbe la nostra galassia alla distanza di un megaparsec (3,261 milioni
di anni luce)? Se la nostra galassia ha quindici miliardi di anni ci apparirebbe a un'età di circa
14 miliardi novecentonovantaseimilioni di anni. Alla distanza stimata dell'ammasso della
Vergine (circa 16-17 megaparsec), ci apparirebbe di una cinquantina di milioni di anni più
giovane, mentre a 5 miliardi di anni luce si mostrerebbe all'età apparente di 10 miliardi di
anni.
Gli specialisti perdoneranno l'ovvietà della rappresentazione, ma a buon profitto dei non
iniziati dirò che a 10 miliardi di anni luce la Via Lattea ne dimostrerebbe cinque e che a 15
miliardi di anni luce (che è distanza spaziale), la nostra galassia - che pure sta là in tempo
reale - sparirebbe come non fosse mai nata, perché la prima luce partita dalle nostre stelle più
antiche non ha ancora potuto colmare quella distanza. E anche una buona risposta al problema
del cielo buio in un universo statico (paradosso di Olbers) che qui non esamineremo. Come
dovrebbero apparirci galassie molto vicine a noi e della medesima età della nostra?
Ovviamente con uno spostamento verso il rosso molto basso, sul quale graverebbero i moti
peculiari di avvicinamento o di allontanamento sulla nostra linea di vista (effetti Doppler)
dovuti all'interazione gravitazionale. Che è poi, in pratica, ciò che constatiamo nel Gruppo
Locale e nei sistemi a noi più prossimi. Ne parleremo fra un attimo.
Apparentemente non resta che chiederci a quale spostamento spettrale dovrebbero trovarsi
oggetti vicini molto giovani e - se esistono - oggetti vicini più antichi della Via Lattea. La
risposta è molto semplice anche se sorprendente: gli oggetti giovani mostrerebbero un redshift
molto alto che tenderebbe ad aumentare con la distanza. L'"orizzonte" degli oggetti
intrinsecamente giovani diventa piuttosto angusto a causa del look back time. La risposta a
come si presenterebbero sistemi vicini più vecchi nella soluzione di Arp è ancora più facile
essendo intuitiva: galassie più antiche della Via Lattea mostrerebbero un redshift negativo,
cioè in pratica esibirebbero un blueshift rispetto al nostro spettro elettromagnetico.
Nelle parole dello stesso Arp: "M 31(la grande galassia in Andromeda di cui la nostra Via
Lattea è una compagna) anche dopo la correzione per la rotazione galattica continua a
esibire un elevato spostamento verso il blu. In questo caso la nostra galassia apparirebbe
spostata verso il rosso se vista da M 31 così come M 31 risulta spostata verso il blu vista da
noi. Questa è la sfida".
PROFONDO ROSSO O ROSSO POCO PROFONDO ?
Resterebbe da chiedersi a quali frequenze e a quale spostamento spettrale dovrebbero
presentarsi sistemi più antichi del nostro e della stessa M 31 se posti a grandi distanze. Ma è
una risposta difficile anche per uno stregone. Nessuno è in grado di dire quanto "durino" le
più grandi galassie: certo non possono essere eterne, e già questo determinerebbe dei grandi
"buchi di buio", immense interruzioni temporali nella propagazione delle radiazioni; e poi si
renderebbero necessarie conoscenze inaccessibili sull'omogeneità o la disomogeneità della
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materia cosmica su scale tendenti all'infinito (cfr. K.V.L. Charlier, "How Infinite can be built
up", 1922). Ricompaiono tutte le grandi e insolute questioni ottocentesche sul cielo buio o su
come potrebbe mai raggiungerci una sorgente luminosa posta a distanza infinita. La scelta di
Arp è ancora di natura empirica: poiché le galassie che presentano blueshift nell'universo
osservabile sono pochissime, noi ci troviamo evidentemente a vivere in uno dei sistemi più
antichi. Galassie un po' più vecchie della nostra alle più grandi distanze tornerebbero ad
apparirci spostate verso il rosso a causa del look back time, e per il lettore che rischia di
smarrirsi nelle proprietà dell'universo statico farò l'esempio grossolano di un sistema dell'età
di 25 miliardi di anni (cioè di circa 10 miliardi di anni più antico della Via Lattea) alla
distanza di 15 miliardi di anni luce. Se fosse ancora osservabile a quella distanza, ci
apparirebbe più giovane delle nostre stelle più vecchie di circa 5 miliardi di anni, quindi non
spostato verso il blu ma di nuovo verso il rosso.
L'interpretazione cosmogonica di Arp dell'universo osservabile richiede che Andromeda (M
31) sia il capostipite e in pratica l'oggetto più antico di tutto il Gruppo Locale; e ciò risolve
anche un rompicapo di lunga data che resta inspiegato nella cornice convenzionale. E' un
problema che mi ha coinvolto personalmente e riguarda l'enigmatica distribuzione dei redshift
della nostra congregazione di galassie che sono tutte positive rispetto a M 31! Io segnalai
questo risultato all'Astronomia professionale sin dal 1971, all'indomani della pubblicazione
degli spostamenti spettrali allora disponibili dei componenti il Gruppo Locale: ma all'epoca
propagandavo epatoprotettori e antinfluenzali e non venni preso sul serio. Scrissi a Paolo
Maffei e a Livio Gratton che "o il Gruppo Locale si sta disperdendo o gli spostamenti verso il
rosso non c'entrano con l'effetto Doppler".
Il fenomeno tuttavia è stato confermato e ampliato con nuovi dati anche per l'altro gruppo di
galassie a noi più vicino, in Ursa Major, dominato dalla grande spirale M 81, e poi esteso a un
gran numero di ammassi dove la galassia più massiccia risulta possedere sistematicamente il
redshift più basso.
Fig. 12 e 13
Distribuzione degli spostamenti verso il rosso-relativi di tutte le più importanti compagne rispetto alla
loro galassia dominante nei gruppi di M 31 e M 81. (Cortesia di H. Arp)
95
E' aperta la caccia alle galassie "madri" e alle più antiche progenitrici? Un buon metodo
potrebbe essere quello di utilizzare i quasar come indicatori delle distanze, ma bisognerebbe
passare sul cadavere del Big Bang.
Nella loro nuova "veste" di oggetti piccoli connessi alle galassie, giovani e poco luminosi, i
quasar non potrebbero essere osservati intorno a galassie attive molto lontane, per le quali, in
base alla sola relazione "age-redshift" è oltretutto molto difficile stimare la distanza.
L'"estinzione" degli oggetti giovani (quasar, BL Lac, etc.) è una funzione che cresce assai
rapidamente nel modello di universo di Narlikar e Arp cosicché i "progenitori" sono
identificabili con sicurezza solo nel nostro vicinato e tuttalpiù alle medie distanze.
Poiché la creazione di oggetti cosmici è osservativamente un fenomeno continuo,
l'integrazione delle due scale temporali (t = tempo cosmico e τ = tempo locale) comporta
notevoli complicazioni che qui risparmieremo al lettore. Mi limiterò a rilevare che si
potrebbero anche osservare oggetti con il medesimo redshift (cioè con la medesima etàapparente) a distanze molto diverse e quindi con età intrinsecamente diverse sulla scala t del
tempo cosmico.
IL NUOVO SCENARIO
Un quesito ricorrente tra i pochi esploratori di questa nuova formulazione del mondo è il
seguente: se i quasar vengono processati e poi espulsi dalle galassie per dar forma a nuove
galassie che a loro volta semineranno nuovi quasar in un processo a cascata, come è apparsa,
come si è formata la prima galassia? Ovviamente, in un universo indefinitamente grande e
antico la domanda è priva di senso: è un po' come cercare l'albero che avrebbe dato origine a
una foresta di dimensioni illimitate: Arp non ha la soluzione complessiva della Natura e non
ne fa mistero.
"Da ciò che possiamo vedere le cose si formano continuamente, e continuamente cambiano
scomparendo e riapparendo: eppure ogni cosa sembra essere in comunicazione con tutte le
altre cose. Se la materia cosmica dispone di un tempo illimitato è possibile che sperimenti
ogni possibilità" (Comunicazione privata, 1993).
E' tuttavia estremamente interessante indagare come avrebbe potuto avere origine la parte
visibile del mondo, l'universo locale delle osservazioni al tempo cosmico t = 0. Essa
comincerebbe con un'esplosione di formazioni di tipo quasaroide di bassa luminosità, circa 15
miliardi di anni fa. Forse a partire da singoli oggetti al centro del Superammasso Locale (che
è oggi la più grande aggregazione di galassie conosciuta) vennero proiettate formazioni
successive poi evolutesi in brillanti galassie della seconda generazione, come M 31 che
occupa il centro del Gruppo Locale. Le analogie con l'Inizio degli Inizi della teoria del Big
Bang sono ingannevoli, perché questa è una creazione continua, continuata e intermittente e
quindi, temporalmente, l'esatto opposto del Big Bang che è invece per definizione un evento
unico a partire dal nulla.
Circa 8 milioni di anni dopo che una galassia come M 31 ha preso a formarsi, essa espelle una
famiglia di compagne di cui la Via Lattea è uno dei componenti: è la foto di gruppo del cortile
di casa, dove le compagne più giovani devono essere generalmente più attive ed aver espulso
molto di recente i quasar del Gruppo Locale (come ad esempio, 3C 120 e i 7 quasar che la
circondano, PKS 0123 + 25, 3C 48 e il BL Lac che si trova nelle vicinanze).
Questo scenario empirico di creazione continua ha celebri eponimi in Fred Hoyle, Hermann
Bondi e Thomas Gold con la Teoria dello Stato Stazionario, e anche nel suggerimento
dell'illustre fisico Paul Dirac che ipotizzò la creazione di materia nell'universo come un
processo "moltiplicativo" preferibilmente in prossimità di precedenti concentrazioni di
materia più vecchia.
Va detto però con chiarezza - ed è lo stesso Arp a farlo - che qui non abbiano nuovo spazio
che sloggia le vecchie formazioni per dar forma a quelle nuove attraverso una metrica in
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espansione, perché gli spostamenti spettrali "anomali" e la relazione age-redshift eliminano
l'espansione dell'universo.
Così le ipotizzate "superfici di massa nulla" di Hoyle e le equazioni della materia di Narlikar a
partire da m = 0 diventano quasi nulle e quasi zero. "Per quanti sforzi si possano fare ammette Arp - non è scientificamente possibile ridurre qualcosa al nulla". O si fa intervenire
un falso vuoto, una radiazione di punto zero, uno stato iperdiffuso di materia-energia o si
sfocia nel misticismo. Anche lui alla fine ha bisogno di un apeiron che accende i nuclei delle
galassie primordiali: "Quale possa essere la connessione fra l'osservata creazione locale e
l'universo in generale pone una questione affascinante ma smisurata. Nei termini delle forme
di vita che stanno lottando con questi concetti, tuttavia è rilevante domandarsi se pure loro,
oltre ad essere continuamente create e ricreate in forme leggermente diverse, possano anche
trovarsi nei loro costituenti più microcospici in continuo contatto informativo con il resto
dell'universo".
IL MISTERO DELLA VERGINE
Se è palesemente retorico chiedersi in quale pozzanghera si sviluppò la prima cellula, è però
del tutto legittimo domandarsi chi fu la madre di M 31. La madre della nostra galassia deve
pure avere una madre, e poiché stiamo parlando del nostro universo locale e non di tutto
l'universo, la "nonna" - se esiste da qualche parte - non dovrebbe poi essere tanto lontana.
Feci questa domanda ad Arp quasi per scherzo una decina di anni fa e lui ammise che gli
sarebbe piaciuto avere una risposta a tutto: aggiunse subito che "sarebbe assai più fruttuoso
conoscere il destino finale delle galassie e della materia che si condensa in stelle piuttosto
che rintracciare una foto dell'antenato da incorniciare". "Hai una risposta anche per questo?
- incalzai malizioso - Ma è molto interessante - fece ignorando la mia provocazione - che le
uniche galassie non locali che presentano spostamenti verso il blu si trovano tutte al centro
del vicino ammasso della Vergine. Sono sei, spirali Sa e Sb, molto simili alle galassie più
vecchie che conosciamo. Se ti fidi della mia relazione age-redshift, è facile calcolare che si
tratta di sistemi più vecchi di una ventina di milioni di anni delle galassie del Gruppo Locale:
il problema è che questo corrisponde solo ad un incremento dello 0,1% rispetto alle nostre
stelle più antiche, così se ti occorre anche la bisnonna dovresti forse trasferirti lassù per
continuare la tua ricerca genealogica …".
Gli spostamenti verso il blu delle galassie della Vergine non trovano spiegazioni soddisfacenti
nella cornice dell'universo in espansione: alla distanza stimata di 16-17 Mpc le galassie più
massicce hanno redshift equivalenti a velocità di recessione di circa un migliaio di chilometri
al secondo, ma c'è una "dispersione" in eccesso enorme e un gran numero di altri membri che
dovrebbero così recedere a velocità doppie, triple, quadruple e oltre. L'effetto viene di solito
"calmierato" sommando a queste galassie "super veloci" un gran numero di nane a basso
spostamento verso il rosso fino a farlo sparire, salvando così l'integrità temporale dei gruppi.
Ma le sei galassie con blueshift vicine al centro dell'ammasso (che altro definisce un
"cluster"?) dovrebbero possedere un moto retrogrado spettacolarmente alto rispetto al flusso
"quieter" dell'espansione cosmica: viene giustificato con movimenti peculiari verso la nostra
linea di vista che si sommano alla direzione di rotazione della nostra galassia, e/o con altre
ipotesi "esotiche" e "oscure", inaccessibili all'osservazione, che qui non menzioneremo. "E'
tuttavia un fenomeno davvero straordinario" ammette il Professor Giuseppe Galletta
dell'Università di Padova. Ma che significa? A tutti gli effetti gli spostamenti verso il blu
accertati al centro della Vergine sono anch'essi da annoverare fra i "redshift anomali" e
costituiscono un'altra formidabile confutazione sperimentale dell'assioma che gli spostamenti
delle righe spettrali delle galassie significano sempre e soltanto velocità.
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LE DITA DI DIO
Il Palladio, la mitica pietra della sapienza caduta dal cielo, non si trova più ad Atene o a Troia.
E' oggi custodito nei penetrali dello Smithsonian Center for Astrophysic ad Harvard, montato
su un rozzo piedistallo in uno dei corridoi dell'ala nuova ricoperta di una smorta moquette
grigia. E' un cubo di plexiglass di circa un metro di lato, all'interno del quale si trovano
migliaia e migliaia di palline colorate in apparente sospensione: sono rosse e azzurre, palline
rosse per le galassie ellittiche e palline azzurre per le galassie a spirale.
Al centro del "diorama" una sferetta bianca marca la posizione della Via Lattea, molto
prossima a un nugolo di palline e più in là a un'altra concentrazione che nelle intenzione del
costruttore dovrebbero rappresentare rispettivamente l'ammasso della Vergine e il più distante
assembramento della Chioma di Berenice. E' la cartografia tridimensionale della struttura
cosmica ottenuta attraverso la misurazione dello spostamento verso il rosso di 2.400 galassie
(palline) in base all'"indubitabile" assunzione che il redshift rappresenta comunque una
distanza e una velocità.
Un'altra di queste mappe di profondità è mostrata nella Fig. 14 che compendia ulteriori
surveys spettroscopiche di una gran numero di galassie.
Fig. 14
Appaiono stupefacenti strutture come "grandi muraglie", filamenti e immense bolle di vuoto.
Presenti in tutti questi diagrammi sono le cosiddette "dita di Dio", smisurati e inspiegabili
allineamenti di galassie che puntano direttamente alla Via Lattea e che vengono giustificati
come "dispersioni di effetti Doppler conseguenti a moti peculiari all'interno degli ammassi"
… (vedi Fig. 15).
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Fig. 15
(Le dita di Dio)
Ma se i cartografi delle tre dimensioni avessero preso la precauzione di annotare la posizione
in base alle luminosità e alle "taglie" delle galassie, avrebbero potuto constatare ad
un'occhiata che le più luminose cadono sistematicamente vicino all'apice delle "dita di Dio":
qualsiasi dilettante puntiglioso potrebbe facilmente dimostrarlo provando una volta per tutte
che quei redshift non possono rappresentare velocità e distanze, e che queste "mappe" sono
prive di significato come indicatori della distribuzione in profondità delle galassie.
CROCI DI EINSTEIN, TOLOMEO E QUANTIZZAZIONE
L'evidenza che i quasar cadono vicini alle galassie non è contestata dai cosmologi di credo
convenzionale: viene attribuita per lo più a "vizi di selezione", a "stastistiche a posteriori" e a
"effetti lente gravitazionali" previsti dalla teoria della Relatività. Anche la presenza di
"materia oscura" - la cui presunta concentrazione al centro e ai bordi degli ammassi
amplificherebbe la visibilità degli oggetti di fondo - è chiamata in causa; e quando si trovano
coppie, tripletti, quartetti di quasar molti vicini e con analogo spostamento verso il rosso,
questi diventano automaticamente "candidati lenti".
"E' anche un buon modo di sfoltire i quasar- feci notare a un influente astrofisico nel corso di
un dibattito - e sarebbe istruttivo per la platea comprendere perché la loro concentrazione
intorno alle galassie attive è una statistica a posteriori, mentre le lenti gravitazionali non lo
sono".
"Naturalmente lei è libero di non crederci - fu la risposta - ma l'ha detto un certo Einstein!
Vada a guardarsi la «croce» che porta il suo nome, e poi mi sappia dire …".
L'immagine della "Croce di Einstein" è riportata qui sotto (Fig. 16), e mostra quattro quasar
centrati nel nucleo di una galassia a spirale che si trova a una distanza stimata di circa 500
milioni di anni luce.
99
Fig. 16
(Einstein Cross)
Poiché i quasar sono ritenuti gli astri più distanti dell'universo e poiché l'osservazione di un
simile raggruppamento profondo (dentro un secondo d'arco) sarebbe per lo meno improbabile,
i cosmologi ne deducono che si tratta dell'allineamento accidentale di un unico oggetto
distante nove miliardi di anni luce "spaccato" in quattro dalla massa della galassia molto più
vicina a noi, che gli cade di fronte sulla nostra linea di vista.
Oppure i quasar sono quattro, e stanno emergendo ortogonalmente dal grembo della galassia
con l'altissimo spostamento intrinseco dovuto alla loro giovane età. Ma così vien giù tutto, la
Croce, il Big Bang e settant'anni di cosmologia.
Improbabile. L'allineamento, tuttavia, dovrebbe essere così esatto che la chance prospettica è
calcolabile in 2 x 10-6, mentre la massa richiesta per il nucleo della galassia che fa da "lente"
dovrebbe essere almeno 1.1 x 1010 masse solari!!
Questo valore eccede quello dei nuclei delle più massicce galassie dell'universo, mentre
qualsiasi astronomo d'osservazione, potrebbe confermare ad un'occhiata che "l'oggetto lente"
in questione è in realtà una galassia nana! Il lettore che cerca affannosamente di decidere dove
stanno i quasar nell'universo, può tornare alla Figura 9, se crede; ma questa non è ancora tutta
la storia della Croce di Einstein, perché Arp e Philip Crane, riprocessando le immagini
ottenute dall'Hubble Space Telescope evidenziarono una linea Lyman alpha che connetteva il
quasar di destra e quello sottostante al materiale di bassa densità della galassia "lente". La
rivista "Nature" si rifiutò di pubblicare il risultato, che tuttavia apparve su "Physics Letters"
(A, 168, 6) nel 1992.
100
Fig. 16 bis
Contorni di immagine che mostrano elongazioni e connessioni di materiale
con il nucleo della galassia centrale (da Arp e Crane, 1992).
La reazione finale fu che Arp e i suoi subalterni non credono nemmeno alla Relatività
Generale, ma anche qui la sottile distinzione è che essi semplicemente non credono che la
"Croce di Einstein" sia davvero un effetto lente gravitazionale.
QUANTIZZAZIONE
Ma esiste un'altra conferma (del tutto indipendente dai dati di Arp) che i redshift delle
galassie e dei quasar non possono essere attribuiti all'espansione dell'universo. Si tratta della
quantizzazione che emerge dall'analisi dell'intera distribuzione spettrale degli oggetti cosmici,
veri e propri numeri magici ricorrenti, per i quali non si può evitare di darne almeno un cenno.
Uno dei risultati più raccapriccianti dell'interpretazione ortodossa è che l'affollamento dei
quasar attorno alle galassie attive comporterebbe immensi coni allungati i cui vertici puntano
invariabilmente verso la Terra. Abbiamo visto che un problema analogo sorge quando si tende
a rappresentare in sezioni profonde la distribuzione delle galassie in base alla relazione
distanza-velocità: appaiono inspiegabili incolonnamenti in fila indiana ("le dita di Dio")
intervallati da enormi "pareti" e zone di vuoto ("struttura a bolle") con la terra ancora al centro
(Figure 14-15).
Un'équipe di ricercatori esaminò i dati disponibili per galassie appartenenti a zone di cielo
contrapposte (T. Broadhurst et alt., Nature, 343, 72, 1990) trovando fronti e muraglie di
oggetti che ricorrevano in mezzo a zone quasi completamente vuote a intervalli regolari di
130 megaparsec! (Fig. 17). Questi dati inattesi provocarono enorme stupore, ma quando fu
chiaro che essi contraddicevano qualsiasi teoria di formazione delle galassie in accordo col
Big Bang, si obbiettò che le porzioni di cielo indagate erano troppo piccole per essere
"rappresentative", e che si imponevano quindi ulteriori investigazioni su sezioni di cielo più
estese e profonde, con telescopi più potenti. Che è poi un'impresa titanica, perché i telescopi
di maggiore apertura hanno un campo d'osservazione ridottissimo (il 10 metri del Keck I
spazia ad esempio 1/250 della grandezza della luna piena) e non è mai chiaro dove si sta
guardando.
101
Fig. 17
Tuttavia le numerose surveys successive hanno "confermato" l'esistenza di muraglie e di bolle
di vuoto o, equivalentemente, che i picchi di redshift risultano sistematicamente quantizzati a
valori preferiti. L'ortodossia rimane "abbottonata" nei confronti della periodicità, perché la
presenza a intervalli discreti di muraglie e gusci concentrici di galassie riporterebbe
trionfalmente Tolomeo al centro dell'universo; le "bolle di vuoto" tuttavia sono in alcuni casi
così grandi che nella cornice del Big Bang non ci sarebbe tempo sufficiente per formarle.
Come ha dichiarato a più riprese l'astronoma Judith Coehn, le grandi strutture avrebbero
potuto formarsi solo accordando un tempo di gran lunga superiore "alla presunta età
dell'universo", cosicché non è più chiaro nemmeno all'ortodossia quale significato accordare
alle molte reclamizzate "mappe di profondità" (vedi Figure 15-16).
L'evidenza che i redshift delle galassie compaiono a valori discreti era tuttavia disponibile da
molto tempo. Nel 1976 l'astronomo del Caltech William Tifft rilevò da un campione
numeroso di galassie binarie che le differenze di redshift cadono costantemente nell'intervallo
di 72-144-216 km/sec. e multipli: il risultato venne subito ridicolizzato in quanto nessuno
sarebbe stato disposto ad accordare velocità di recessioni quantizzate alle galassie binarie.
Inoltre i moti reciproci di interazione avrebbero dovuto cancellare qualsiasi periodicità anche
nel caso che l'effetto fosse stato reale: Arp ricorda che si ironizzò a lungo sulla possibilità di
un annullamento retroattivo del titolo accademico di Tifft. Ma tutte le rilevazioni successive
su coppie di galassie confermarono costantemente questo risultato, che fu nuovamente
evidenziato con misure radio dell'idrogeno neutro, che sono in grado di determinare i redshift
nel modo più accurato. Dove siano andati a finire i moti gravitazionali relativi resta un
mistero insoluto sul tavolo degli astrofisici (e dello stesso Arp!): nel frattempo però è
diventata schiacciante l'evidenza che anche i redshift dei quasar sono fortemente quantizzati
su valori preferiti.
L'astronomo svedese Karl Karlsson trovò che i picchi ricorrenti potevano essere riprodotti da
una formula ∆log(1-z) = costante, che nella tabella riportata qui sotto
z = 0,30
z = 0,60
z = 0,96
z = 1,41
z = 1,96
z = 2,64
z = 3,47
z = 4,49
assume il valore cost. = 0,089.
Il punto di vista tradizionale non è mai intervenuto a smentire la periodicità degli spostamenti
verso il rosso dei quasar perché nella cornice cosmologica del Big Bang la loro collocazione a
102
grandi distanze ha pur sempre un significato che è in stretta relazione con l'evoluzione
dell'universo. Ma non c'è dubbio che qualunque possa essere il meccanismo che impartisce
valori discreti allo spostamento delle righe delle galassie e dei quasar, questa è un'altra prova
decisiva che il redshift non può essere attribuito a velocità.
Val la pena concludere questo blitz nella quantizzazione ricordando che nel sistema
cosmologico a creazione continua di Arp e di Narlikar i redshift degli oggetti cosmici
esprimono le loro età di formazione, ma non necessariamente le loro distanze. Così le loro età
(apparenti) dovrebbero essere miscelate dal look back time in quantità intermedie e cancellare
così ogni traccia della periodicità. La proposta di Arp e che la quantizzazione sia in relazione
diretta a passaggi evolutivi "permessi" che eludono stati intermedi nella "progressione" della
massa variabile, rendendo così la sua evoluzione osservabile solo a certi stati discreti. Questo
riporta l'astrofisica nell'alveo della meccanica quantistica e costituisce una formidabile sfida
per la ricerca e per la scienza del futuro.
LA RIVOLUZIONE PUÒ ATTENDERE?
L'osservazione delle fasi di Venere e di Mercurio non produsse immediatamente
l'Illuminismo, ma una lenta agonia. E' storia nota: grandi differenze nella percezione della
realtà provocano inevitabilmente lacerazioni e conflitti profondi prima di riconciliarsi in un
nuovo paradigma. Ma la rivoluzione di Copernico, la genialità di Keplero o l'evidenza
empirica di Galileo non rappresentarono la vittoria degli illuminati sugli ottusi, dei sapienti
sugli incolti, degli "eretici" sui "collaborazionisti". Al contrario, gli oppositori che all'inizio
erano il mondo intero, furono spesso persone di grande intelligenza.
Il progresso scientifico si realizza però quasi sempre quando qualcuno, nella bonaccia
dell'unanimità, esclama: "E' sbagliato!". O grida, come nella favola di Andersen, che il Re è
nudo. Naturalmente questo non significa che la scienza abbia sempre torto, ma che l'Autorità
istituzionalizzata della conoscenza deve essere perennemente in discussione: è vero che
nessuna futura razionalità potrà mai riportare la terra al centro dell'universo o restituirle una
forma piatta, ma è presumibile che tutte le teorie, compresa quella di Narlikar e Arp, siano
destinate col tempo a essere riformulate. Ciò che non può essere cambiato, o modificato, o
soppresso, sono i bracci, i filamenti, le connessioni osservative di materia che legano oggetti
di diverso spostamento spettrale e che impongono la falsificazione dell'assunzione
fondamentale della cosmologia.
Paradossalmente, è proprio l'accettazione dell'evidenza che si rivela l'ostacolo più difficile.
L'astronomo Massimo Capaccioli ha dichiarato (sottovoce) che "Forse Arp ha ragione, ma
fra cento, o mille anni", e se ciò è vero questo stesso articolo è in anticipo di cento o mille
anni, destinato ad essere fatto a pezzi dalla Contemporaneità in attesa di una eventuale
riabilitazione postuma.
Chi allontana i dati di Arp e ne sospende il giudizio rinviando la questione all'infinito ragiona
più o meno così: "Nonostante queste «scomode» osservazioni non sembra che ce la caviamo
tanto male; abbiamo una teoria della creazione cosmica che è matematicamente corretta fino
all'istante 10-43, un modello della struttura della materia che funziona e un emergente teoria
delle Supercorde che promette di unificare il tutto e il nulla nel rispetto delle leggi della
fisica. E' vero che la predizione di Stephen Hawking di trovare una master equation che
spieghi tutto entro il duemila («da stampare su teeshirts»)non si è avverata, ma chi può dire
cosa troveremo tra dieci anni? Perché l'universo deve essere per forza complesso quando
può essere invece semplicissimo? Non è colpa della scienza se gli eventi sono caotici e
impredicibili, non è colpa della scienza se la natura è competitiva e non cooperativa, o se la
società è sempre più cinica e violenta: mica si può incolpare le GUT (Great Unified
Theories) per la fondamentale irrazionalità dell'esistenza!.
E non c'è dubbio. Se si evita di considerare le confutazioni e le falsificazioni eliminandole
dalla discussione nessuno si chiederà più se la scienza possa avere ottenuto le risposte
103
sbagliate da tutte le più importanti questioni cosmologiche. E se sono sbagliate, anche il Big
Bang, le GUT, le Supercorde e forse "la fondamentale irrazionalità dell'esistenza" sono da
riscrivere. Come sempre in tutte le grandi rivoluzioni, il fatto è più culturale che scientifico.
Vorrei concludere questa mia esposizione della controversia con due aneddoti di natura
sociologico-osservativa, se così si può dire. Il primo è a lieto fine, e riguarda il braccio che
collega le due galassie con redshift altamente discorde NGC 7603 A e B e i due quasar che vi
sono immersi, di cui ho già parlato in precedenza (vedi Fig. 9). Appena mi fu nota, comunicai
questa decisiva scoperta anche a un insigne fisico relativista di Bologna, invitandolo senza
mezzi termini a prendere una posizione.
La cortese risposta fu: "Non rifiuto di guardare nel cannocchiale di Galileo, e, delle due, di
fronte all'immagine trasmessa sono incline a dar ragione a lei. Ma non posso giurarci. Qui
vident sciunt? Mah … nel cannocchiale si vedevano le stelle medicee, ma anche Saturno
tricorporeo … Aspettiamo. Il tempo farà (forse) giustizia".
Avrei dovuto accontentarmi? "Aspettiamo … che cosa? - replicai prontamente - Io guardo
galassie da quarant'anni e a meno di dubitare delle fasi dei pianeti interni, giurerei che le
due galassie in questione sono connesse da un visibile ponte di materia. Lei no? Può anche
tenere i due quasar nello sfondo, se crede, confidando in una possibilità su un milione, ma
non può allontanare le due galassie senza sopprimere l'astronomia osservativa. Il tempo
servirà solo a mantenere lo status quo. Dobbiamo convenire che la storia che si ripete non ci
insegna nulla?".
Dopo qualche tempo ricevetti una comunicazione che mi preannunciava l'inserimento dei dati
di Arp in un'importante Seminario sulla Cosmologia per il dottorato in fisica, e sarò
eternamente grato a quel Professore per il suo atteggiamento costruttivo.
Il secondo episodio è assai meno incoraggiante ed è un esempio tipico di come l'establishment
cosmologico reagisce di fronte a osservazioni di segno opposto.
La Figura 18 mostra una mappa in raggi X ottenuta da W. Pietsch nel 1994 con il telescopio
orbitale tedesco ROSAT centrato sulla galassia attiva ed espulsiva di tipo Seyfert NGC 4258.
Fig. 18
104
Si notano immediatamente due intense emissioni X allineate ai due lati della galassia che è a
sua volta una forte emittente di raggi X. Due sorgenti così perfettamente speculari avrebbero
meno di una probabilità su mille di appaiarsi accidentalmente nello sfondo e in modo così
esatto ai due bordi della galassia su una linea che passa per il nucleo. Era dunque di
straordinario interesse astrofisico approfondire subito la natura di queste due sorgenti: ma un
radioastronomo dichiarò preventivamente che le due emissioni erano in realtà "echi
elettronici dovuti al sistema di rivelazione quando si gira lo strumento, ben noti a chi conosce
la tecnica nel dettaglio"!
Disgraziatamente per lui le due emissioni avevano controparti ottiche che Pietsch, Vogler,
Kahabaka, Jain e Klein ("Astronomy and Astrophysics Letters, 1995) confermarono subito
come candidati quasar. Io non ebbi più notizie del radioastronomo e commentai la cosa su un
giornaletto amatoriale, rammaricandomi che "dopo trent'anni di allineamenti prospettici nel
visibile, abbiamo adesso false eco nei raggi X che possiedono controparti ottiche che poi
risultano essere quasar …".
Ma la storia era ancora ben lontana dalla conclusione, perché nessuno voleva prendere gli
spostamenti verso il rosso dei candidati quasar. Arp riferisce nel suo recente ultimo libro
"Seeing Red" che numerose Istituzioni richiesero l'analisi spettroscopica degli oggetti, senza
alcun esito. Ci riuscì alla fine, due anni dopo, Margaret Burbidge, che con il riflettore di tre
metri di Monte Hamilton rilevò z = 0,65 per il quasar a sinistra e z = 0,40 per quello di
destra. Gli spettri ottenuti sono riprodotti nei grafici che mostro qui sotto, e non è senza
emozione che il lettore può vedere ancora una volta le righe di elementi noti come l'ossigeno,
il magnesio, l'idrogeno, etc. posizionate su lunghezze d'onda lontanissime da quelle che si
formano in laboratorio.
Fig. 19 e 19 bis
E' un'altra decisiva testimonianza di differenti stati della materia cosmica e un'altra cruciale
osservazione a favore della natura riproduttiva delle galassie.
105
La Rivoluzione può attendere? Con commenti indipendenti sopra quel risultato, Arp ed io
adoperammo termini analoghi di "tumulazione della cosmologia corrente": solo che io parlai
di "ultimo chiodo nella bara del Big Bang" e lui di "ultimo fiore". Anche questo, credo, fa la
differenza fra un piccolo dilettante e un grande scienziato.
Note
1
Recenti misurazioni della struttura fine su un campione di quasar effettuato da J. Webb e J. Prohaska
(Physical Review, Sept. 2001) sembrano riproporre la possibilità di variazioni intrinseche nella carica
dell'elettrone. Integrando questi risultati nella cornice cosmologica che colloca i quasar ai confini
dell'universo, Paul Davies e altri hanno suggerito la possibilità che al momento del Big Bang la
velocità della luce tendesse all'infinito! (Nature, agosto 2002). Qui il commento potrebbe essere: che
duro prezzo sono disposti a pagare i sostenitori della Palla di Fuoco per tenere i quasar alle loro
distanze di redshift.
2
L'induzione ricavata da Arp su base osservativa ha una formulazione matematica completa e rigorosa
nella "teoria della massa variabile" sviluppata da Hoyle e Narlikar già agli inizi degli anni Settanta
("Action at Distance in Physics and Cosmology", S. Francisco, 1974). E' chiamata anche teoria
generale della gravità conforme e descrive la massa delle particelle come funzione della posizione e
del tempo. Informazioni dettagliate sono reperibili anche nel nuovo libro di Arp "Seeing Red",
Apeiron, 1998, sull'Astrophysical Journal, Narlikar e Arp, 405:51-56, 1993, in "Origini", Autori vari,
Il Poligrafo, 1994 e nel volume dell'autore di questo articolo, "Eppur non si muove!", - La controversia
sull'espansione dell'universo - Studio Stampa, 1996.
----[Una presentazione dell'autore si trova nel numero 2 di Episteme - si veda anche
il suo contributo nella sezione "Commenti Ricevuti" della I Parte di questo
stesso fascicolo della rivista]
"virgilio" <[email protected]>
106
Beyond Maxwell-Lorentz Electrodynamics
(George Galeczki)
I. Maxwell's Equations
Freeman Dyson published twelve years ago [1] "Feynman's proof of the Maxwell equations".
He recalls that in 1948 Feynman showed him this "proof assuming only Newton's law of
motion and the commutation relation between position and velocity for a single particle."
Although formally obtaining the two "vacuum equations" (i.e. those without source terms),
the claimed "proof" of the full Maxwell equations is wrong mathematically, physically and
conceptually. On top of all this, it expresses the - nowadays common - arrogance of
mathematical physicists giving priority to formalism against empirical facts.
As a matter of fact, Maxwell's equations (ME) represent the mathematical expression of the
experimentally discovered laws of Gauss, Ampère and Faraday and are widely used in
physics and engineering. Several remarks and comments are in order, each of them being
subsequently discussed in more detail:
1/ The basic formulation of ME - as derived from experiments - is in integral form
pertaining to a finite, closed area or volume.
2/ The ME are formulated for continuous fields and are called, therefore, field equations.
3/ ME hold for closed circuits only.
4/ The sources of the fields are continuous charges and continuous current densities.
The discrete, quantized charges introduced in Maxwell's theory are foreign elements.
5/ ME are tautological in the sense that they merely represent relationships between fields
and their sources. One has to provide the initial charge distribution in order to be able to
calculate the field distribution, or vice versa.
6/ ME is unable to describe the interaction between two discrete charges.
7/ ME is unable to supply the equation of motion of one charge in the field produced by all
others.
8/ ME are not suited for the description of open circuits like antennas.
9/ ME are unable to prescribe the exact conditions under which a system will radiate, or not.
The notorious example is Bohr's planetary model of the hydrogen atom.
10/ ME are unable to provide a stable model for the elementary charge.
11/ ME are generally covariant and do not single out the Lorentz transformation (LT) of the
"special" theory of relativity (STR).
12/ ME are formulated in terms of independent, Eulerian coordinates x, y, z, t and partial
derivatives ∂/∂x , ∂/∂y , ∂/∂z , ∂/∂t .
107
ME in their original, integral form and in modern notation are:
∫
E.ds = - ∫ ∫ (∂B/∂t).da
∫∫
D.da =
∫∫∫
∫∫
∫
ρ dV
B.da = 0
H.ds =
∫∫
(1)
(j + ∂D/∂t).da
(2)
Contained in the above is the equation of continuity:
∫∫
j.da = - ∫ ∫ ∫ ρdV
(3)
where ρ and j denote charge and current density, respectively.
In all cases the regions of integration are assumed to be stationary and mechanically rigid.
ME in differential form , as derived from (1), (2) and (3) by means of Stokes' and Gauss'
theorem, are:
∇ × H = j + ∂D/∂t
∇ × E = -∂B/∂t
(4)
∇.D = ρ
∇.B = 0
(5)
and the corresponding equation of continuity:
∇ . j = -∂ρ/∂t
(6)
ME in differential form express the relationship that must exist between the four field vectors
E, D, H and B at any point within a continuous medium (?). In this form, because they
involve space derivatives, they cannot be expected to yield information at points of
discontinuity in the medium. However, the integral form can always be used to determine
what happpens at the boundary surface between different media. It follows then, that the
tangential components of E and H (except perfect conductors) and the normal components
of B and D (if no surface charges are present) have to be continuous at the interface.
II. Maxwell's Equations and "Special" Relativity
As already said, besides generalizing Ampère's circuital law by introducing the "displacement
current", Maxwell's achievment was to express the experimental laws of Coulomb, Gauss,
Ampère, Faraday in mathematical terms. The modern, vector form of ME was introduced by
Gibbs. Einstein's "special" relativity of 1905 has built heavily upon electromagnetism and,
assuming the validity of ME in all inertial frames of reference (IFR's) introduced the
incomprehensible "postulate of light velocity invariance". This constancy is not that refering
to the light source - a wellknown fact in classical wave theory - but to the independence of the
velocity of light from the uniform velocity of the observer/detector relative to the source.
Since in the special case of vacuum-as-continuous-medium the ME displayed covariance (not
invariance!) under the so called Lorentz transformations (LT), ME and STR became
indissolubly tied together, one implying so to say the other. This strategy proved itself very
useful, since every criticism of STR was authomatically seen as criticism of ME, thus
contributing to the survival of the contradiction ridden STR.
The said bi-univocal correspondence between ME and STR is manifested, however, only if
one has in mind the differential form of ME. The reason is that STR is a local, point-event
theory, with local simultaneity and position and velocity dependent time! Due to this
feature of STR, only local conservation laws of energy and momentum are compatible with
108
STR. While valid in the hydrodynamic approximation - a continuum theory - the local,
differential conservation laws fail in the case of discrete, extended systems. The global
time required in this case, independent of position and velocity, is anathema to STR. Farady's
law of induction assumes tacitely such a global time and distant simultaneity, thus allowing
the definition of inductance and self-inductance for macroscopic, closed circuits. Since the
stationary circuits appearing in the integral form of ME are incompatible with STR, it is quite
understandable why the STR "philosophy" gave almost exclusive prominence to ME in
differential form and eliminated the integral form from physics textbooks and monographies.
As a matter of fact, this form - more rich in physical information - is actively in use in
engineering books on electromagnetism [2].
III. General covariance of Maxwell's equations
It was repeatedly and forcefully pointed out by Post [3] that Maxwell's equations are
general covariant. Post quotes that Kottler, Cartan and van Dantzig (KCD), quite
independently of one another concluded on the natural invariance of ME, independent of
any metric or linear connection. Post strongly emphasized the clean functional separation
obtainable between the constitutive equations { D(E), B(H), J(E) } and the field equations.
In this approach the constitutive equations instead of ME carry all the metric
information, while the field equations (4) and (5) are covariant under all possible space and
time coordinate transformations: Galilean, Lorentzian, conform and so on. The use of (E, D,
B, H) rather than two field vectors eliminates the cgs free-space field identification. The latter
tied the cgs situation irrevocably to an inertial reference frame. A free-space inertial situation
is defined by an explicit constitutive relation:
D = ε0E
,
B = µ0H
(7)
Which can be proven to be invariant under the Lorentz group, as well as under scale changes
of the conformal group. Here is the place to mention the qualitative difference between
invariance and covariance: a physical law is said to be invariant under a coordinate
transformation when the vectors/tensors entering the law remain unchanged, while in the case
of covariance the components of the vectors/tensors are transformed, or in Thomas Phipps'
words "scrambled", according to the same rules as the coordinates,. Only after performing this
scrambling the equations in question remain form invariant.
The superiority of the KCD approach is that the field equations retain their form when a
transition is made from an inertial to a non-inertial frame, in particular a rotating frame.
(N.B. Jan Evert Post was the chief theoretician of the ring laser gyro project, which produced
the most sensible detector of rotation, i.e. of the degree of non-inertiality). Moreover, the form
invariance of ME is independent of whether the fields exist in free space or in matter. The
information about the reference frame and the state of motion of the matter therein is
conveyed exclusively by the nature of the constitutive equations. The general form of these
equations is tensorial and the applications to specific problems was intensively investigated
by Post.
IV. The force of Lorentz and Maxwell's equations
It is clear from what has been said till now that the Maxwell field equations (4) and (5)
expresses a law of nature and will retain their validity so long their limitation to closed
circuits is assured. The tautological nature of ME follows from the absence of "detector
charges" in the rhs, since only the source charges and their distribution is considered. It
means that the ME are intrinsically unable to provide either a force law between discrete
charges, or an equation of motion for individual charge within a system of charges. Here I can
109
mention another fundamental difficulty connected with the discrete vs. continuum dichotomy,
reflected in the use of two different kinds of coordinates: the already mentioned four
independent, Eulerian x, y, z, t and the three time dependent Lagrangean coordinates x(t),
y(t), z(t). The former are suited for field theories, while the later for particle dynamics. Fields
are functions of x, y, z, t, meaning that they have different values at the points of a 4D
continuum. They don't "propagate" in the 4D continuum. The solutions x(t), y(t), z(t) of the
dynamical equations of motion, on the other hand, are 3D vectors and the coordinates "move so to say - with the particle". This already shows that STR is at least formally compatible with
pure field theories, but incompatible with (discrete) particle dynamics [4]. Anyway, quite
independently of STR, in order to brake the tautology, ME have to be completed by a force
law and an equation of motion for discrete charges, the very program of Lorentz who
introduced the quantized electrical charges into Maxwell's field theory. The ME supplemented
by the Lorentz force-law (LF) is called Maxwell-Lorentz electrodynamics (MLE). Lorentz
himself remained unsatisfied with his force-law:
FL = q (E + v × B)
(8)
In his own words [5]: "It is got by generalizing the results of electromagnetic experiments.
The first term represents the force acting on an electron in an electrostatic field [F1=qE] . On
the other hand, the part of the force expressed by the second term may be derived from the
law according to which an element of a wire carrying a currect is acted on by a magnetic
field [dF2 = (qv x B , assuming Jds = qv ] . After having been led in one particular case to the
existence of the force [F1 = qE] and in another to that of the force [F2 = qv x B ] , we now
combine the two in the way shown in the equation, going beyond the direct result of
experiments by the assumption that in general the two forces exist at the same time."
(a) The two 'particular cases' here 'combined' are, however, quite incompatible. In one case we
have a charge at rest, in the other the charges are moving.
(b) Experiments with 'a wire carrying current' have to do with neutral currents, yet the
derivation contradicts this neutrality. The discovery of the Hall effect, formally described as a
"modified Ohm's law":
j = σE + k(E × B)
(9)
where σ is the conductivity and k a constant, seemingly supports (8), but everybody familiar
with the experimental set-up used in the Hall effect studies will agree that E and B above
belong to different systems: a dc - or ac - source for E and a completely separated permanent
or electro-magnet for B. Maxwell's theory requires, however that E and B belong to the same
system of charges and currents. As shown elsewhere [6], the Lorentz force should have
been written as:
FL = q (E(1) + v × B(2))
(10)
i.e. a phenomenological external force, rather than fundamental force acting on a charge
belonging to the same system, as implied by ME. The upper indexes (1) and (2) indicate that
the electric, respective magnetic field belong to different systems, therefore ME and LF do
not form a coherent Maxwell-Lorentz theory as claimed in present day textbooks and
monographies! The reason for this persisting mess is the seeming compliance with SRT's
LT. This belief is, however, totally wrong, since: (a) The LT apply only to E and B belonging
to the same system and (b) The velocity v in most applications is a non-uniform velocity
between magnets an current carrying wires, while the velocity entering the LT is the
110
uniform relative velocity between two inertial frames of reference. This confusion goes
back to Einstein's failure to distinguish between his theory involving schesic velocities
referred to abstract "reference frames" and relative velocities between moving masses, as
implied by Mach's program. For this reason STR is not a true relativity theory! Using a
somewhat different terminology - 'principle of relativity vs. 'principle of relative motion' this point was discussed in a paper by Bartocci and Capria [7], too. This explains also why the
aged Ernst Mach unmistakable declined the rôle of spiritual father of the "special" (very
special, indeed!) theory of the young Einstein.
V. Magnetic field, vector potential and induction
In the spirit of the ME in their integral form, B(2) in (10) has always to be produced by a
closed current loop:
B(2)(r) = I'
∫
(ds' × R)/R3
(11)
where R = r - r' and the integral is performed around the closed current loop. Attempts to
generalize the Biot-Savart law for time-variable magnetic fields have been made by
Jefimenco [8] in the form:
B = (µ0/4π) ∫ ∫ ∫ {[j]/r² + (1/rc)∂[j]/∂t} × (r/r) dV'
(12)
where [..] denotes the retardation symbol indicating that the quantities between the square
brackets are to be evaluated for t' = t - r/c , where t is the moment for which B is calculated. It
is interesting to note that that Eq. (12) does not contain displacement currents, thus indicating
that although time-dependent magnetic fields and displacement currents are coupled together,
displacement currents are not sources of magnetic fields in the conventional sense.
Definition (11) of the magnetic field B - rightly called magnetic flux density in older books is incompatible with the "Lorentz transformed E field" definition of B in "special"
relativistic electromagnetism:
B = V×E
(13)
valid for uniform velocity V only! This incompatibility brings us to the most important issue
of (electromagnetic) induction and the status of Faraday's "flux rule". According to textbook
(and also monography) knowledge, electromagnetic induction were always due to a time
variable magnetic flux crossing a closed conducting loop. Although Faraday discovered both
this so called transformer induction as well as the motional induction, only the first is
embedded in the integral form of ME formulated for stationary integration regions. This
deficiency of the integral ME is, of course, transferred to the differential form of the
Maxwellian law of induction:
∇ × E = -∂B/∂t
(4)
The correct expression for the induced electromotive force (emf), in terms of the vector
potential A, follows from the integral form:
emf =
∫
E.ds - (d/dt) ∫ ∫ B.da = -(d/dt) ∫ ∫ (∇ × A).da = -(d/dt) ∫ A.ds
which provides the formula:
(14)
111
Eind = -dA/dt
(15)
for the induced electric field Eind. Keeping the integration region stationary, one gets the
'transformer field':
Eind = -∂A/∂t
(16)
The difference between Eq. (15) containing the total time derivative d/dt and Eq. (16)
containing the partial time derivative ∂/∂t is huge and has fatal consequences for "special"
relativity! This is obvious, since in ME the four partial derivatives ∂/∂x , ∂/∂y , ∂/∂z , ∂/∂t are
on equal footing (see, for example, Eq.(6)) and obey the LT. The presence of the total time
derivative, by giving to the time derivative a distinct status, destroys the Lorentz
covariance of ME!
Here is the place to mention the incompleteness of the traditional formula for the total
derivative of a vector field:
dA/dt = ∂A/∂t + (v.∇)A
(17)
and the time rate of change "seen" by a point moving with velocity v in a vector field A [9]:
dA/dt = ∂A/∂t + (v.∇)A + (A.∇)v
(18)
Although the vector identity:
(v.∇)A + (A.∇)v + A × (∇ × v) - ∇(v.A) = -v × (∇× A) = -v × B
(19)
for v.A = const. and ∇ × v = 0 leads to the 150 years old formula of Neumann:
Eind = -∂A/∂t + v × B
(20)
equation (18) covers all known situation of electromagnetic induction, including those where
Eq. (19) fails. Eq. (20) is still in exclusive use, although it has never been rigorously justified.
Neumann - just like later Lorentz with his force law (8) - just juxtaposed Faraday's and
Maxwell's transformer field and the empirical field found in the unipolar induction
experiments of Faraday and in the (then) recently discovered Hall effect, called motional
induction field. Wesley derived for the first time (!) the most general law of induction which
includes (20) as a particular case. The surprising result is that the law based upon (18) is able
to describe phenomena governed by the term (v.∇)A like the Aharonov-Bohm (AB) effect
and the Marinov motor [10]. The demystification of the "strange quantum-mechanical (AB)
effect" [10] and its explanation in the framework of electrodynamics has been a real tour de
force. The term (A.∇)v is presently insufficiently investigated, but preliminary results seem to
support its explaining the interaction between two toroidal magnets (closed magnetic field
configurations) [11], which, according to Maxwell's electromagnetism should not interact.
The local form of the correct law of induction, involving the total derivative (18), puts an end
to the perennial disputes between the supporters of fields and potentials, respectively. It has
to be clear that the description by means of A is more general than the usual by means of B,
since it provides an induced electric field even if ∇Φ = 0 (Φ denotes here the scalar
potential), ∂A/∂t = 0 and B = ∇ × A = 0 .
One is tempted to say that Maxwellian electrodynamics overcame all difficulties and retained
its original form since, after all, the use of the truncated form (17) for the total derivative was
not Maxwell's fault. The painful fact for STR-supporters is, however, that Eqs. (4) and (5) do
112
not cover all experimental situation and - acutely painful - that they do not remain
Lorentz covariant if one replaces the partial time derivative with the total one!!
VI. Beyond the Lorentz force law
The force law of Lorentz (8) applies only in situations where the fields E and B are static, or
quasistatic, when radiation could safely be neglected. In such situations, however, Eqs. (4)
and (5) decouple in two pairs of electrostatic and magnetostatic equations, respectively:
∇×E = 0
;
∇D = ρ
(21)
∇×B = j
;
∇B = 0
(22)
and
This explains the upper indexes appearing in Eq. (10), indicating that the sources of E(1) and
B(2) are different. Moreover, as already pointed out, the field B has to be produced by a closed
current loop. It follows then, that the force of Lorentz can by no means be applied to a
system of two charges, so that charge (1) moves in the field B(2) and vice-versa:
d(m1v1)/dt = q1(E(2) + v1 × B(2))
;
d(m2v2)/dt = q2(E(1) + v2 × B(1))
(23)
No wonder that this two-body problem would violate the linear momentum conservation
law, since the sum of internal forces would be different from zero! The replacement of
particle linear momentum p by (p - q.A) - as suggested by the "operator formalism" of
quantum mechanics - doesn't save the conservation law.
The inability of Lorentz force to describe the simplest system of two interacting charges is
presented in textbooks and monographies as due to the fact that "at least one charge path has
to be closed", which is obviously false! In a dense plasma, for example, even in external
magnetic fields, where charges are permanently colliding with each other, there may well be
no closed paths at all. The fact that the external magnetic field is produced by the closed
circuits of the electromagnets is irrelevant for the plasma system!
There exists a rich experimental evidence for the failure of Maxwell-Lorentz electrodynamics
at low velocities (v/c << 1), which is lethal to MLE, since the laws of Gauss, Ampère,
Faraday were all formulated according to the experimental results obtained for low velocities.
Moreover, the interactions between electric currents and magnets were all investigated by
using metallic conductors. The microscopic nature of currents in metallic conductors
remained undecided, till Weber introduced atomism, i.e. quantized electric charges in physics.
He assumed that electric currents consists of a stream of electrons and made first the
identification:
Ids = qv
(24)
With this, Weber succeeded to derive Ampère's law between metallic current elements:
d²FA = (I.I'R/R3)[-2ds.ds' + 3(R.ds)(R.ds')/R²]
(25)
(I, I' denote currents and R = r - r') from his interaction law between discrete, moving
electrons in a metallic conductor:
FW = (qq'R/R3)[1 + V²/c² - 3(V.R)²/2c²R² + R.dV/dt.c²]
(26)
113
vhere V = v - v' and dV/dt denote the relative velocity and the relative acceleration
between the moving charges. This truly relativistic (Machian) and instantaneous force law
explains all known experiments at low velocities with metallic currents, including Ampère's
moving bridge one and the 'electromagnetic rail gun' used in frame of the SDI program
[12] which both imply longitudinal forces between parallel metallic current elements. It is
notorious that the Lorentz force - acting perpendicular on current elements - is unable to
account for these experiments. In spite of this, the belief in uniqueness of the GrassmannBiot-Savart-Lorentz (GBSL) force law is so strong, that Ampère's law (25) - called by
Maxwell "the cardinal formula of electrodynamics" - is not even mentioned in the vast
literature on electrodynamics. Once again, this belief is motivated by the seeming compliance
of the Lorentz force (8) with the LT, i.e. with STR. Wesley put his finger on the sorepoint of
the interminable controversy about Lorentz vs. Ampère force. The supporters of the LF cramp
to the equivalence of the two forces when two closed current loops are involved. This is
totally irrelevant as it is only a question of the analysis of the mechanical forces between the
two objects, the metallic bridge and the remainder of the circuit as a mechanical object.
However, Grassmann's derivation of his law (equivalent with that of Lorentz) is only valid
for mechanically rigid electrical circuits. This means that the GBSL law cannot be
applied to the electrical circuit involved in the non-rigid Ampère bridge!
Weber's law correctly describes the motion of electric charges in vacuum - for example in the
electron microscope - since in this case E and B are external and B is produced by closed
current loops. The useful phenomenon of "self-focussing", or "pinch effect" wellknown to
electron microscopist, is also explainable within the traditional frame of Maxwellian
electrodynamics, as attraction between parallel currents.
Remarkably, Ampère's and Weber's laws comply with Newton's third law (actio = reaction),
since the forces act instantaneously along the line joining the current elements, or the
moving charges. This condition for law velocities is one of the requirements for a system
being non-radiating even for charges moving with high (v >> c) velocities. As a matter of
fact, both the hydrogen atom and the 'rotating ring electron model' are conservative, i.e.
non-radiating, provided the forces are of Weber type!
VII. Some comments on rapidly varying fields and radiation
1/ The characteristic feature of Maxwell's equations is the presence of the terms ∂D/∂t and
∂B/∂t which couple the electric and magnetic fields and lead to the existence of
electromagnetic waves, or radiation. The field equations completed with the Lorentz force
law (the MEL equations) are therefore incoherent, since the fields in the LF expression are
static, or quasistatic, which means that radiation is neglected. No wonder that the attempts of
Dirac and others to add "radiation terms" to the equation of motion of the electron leads to
strange "runaway solutions" and other unsolved difficulties.
2/ The 104 years old Liénard-Wichert formula [9] for the retarded potentials corresponding to
a point-charge moving with acceleration a along the positive direction of the x-axis has been
seriously questioned by Chubykalo and Smirnov-Rueda [13] and independently by Wesley
[9]. This indicates that the "special" relativistic Maxwell-Lorentz electromagnetism is an
unsatisfactory theory by itself, although the reason is hidden in the mathematics of
d'Alembert's wave equation, rather than in the ME themselves.
It is textbook knowledge [13] that the solutions of the wave equation (d'Alembertian) are:
Φ =
∫∫∫
[ρ]/R.dV + Φ0
;
A =
∫∫∫
[j]/R.dV + A0
(27)
114
which are the retarded potentials. Φ0 and A0 denote the solutions of the homogeneous wave
equation. This is OK. From here one usually derives:
Φ = q/(R - v.R/c)
;
A = qv/(cR - v.R)
(28)
and the fields:
E = - q(1 v²/c²)(R - vR/c)/(R - R.v)3 + qR × {(R - vR/c) × a}/(R - R.v/c)3c²
(29)
B = (R × E)/R
Chubykalo and Smirnov-Rueda show that formula (29) does not satisfy the d'Alembert
equation along the x-axis at any time. This follows from the fact that the wave equation for
Exdescribes only transverse modes and - on the other hand - the x-component according to
(29) is different from zero. Thus, the Liénard-Wichert potentials, as solutions of the complete
set of Maxwell equations, are inadequate for describing the properties of electromagnetic field
along the direction of an arbitrarily moving charge. Whitney [14] found another inadequacy
of the Liénard-Wichert potentials for describing the properties of relativistic fields. Further, it
is easy to verify that the Poynting vector calculated with Eq. (29) equals zero, i.e. no energy
transport takes place along the x-axis, while the energy conservation law requires both energy
density and divergence of the Poynting vector to be different from zero!
The criticism of Wesley [9] is even more fundamental and relies upon the fact that in the
wave equation of a field theory, the four variables x, y, z, t have to be independent
(Eulerian) as explained also in [4]. Despite this clear mathematical requirement that r' and t'
be independent variables, in the integral representation (28) of the retarded potentials Liénard
and Wiechert argued incorrectly that the independent space variable r' is a dependent
function of the time variable t'.The change in the 'delta function' - which accounts for the
point-like nature of the charge - leads to the correct expressions for the retarded Coulomb
potential:
Φr = q'/Rr
(30)
where Rr = R(t)/(1 - v/c) for an observer moving directly away with v < c from the point
charge.
3/ The ubiquitous presence of radiation, i.e. of electromagnetic fields detached from their
fields requires the existence of a unique, fundamental frame of reference, relative to which the
energy transmission velocity is "c". This is a consequence of the fact that the velocity of light
doesn't obey either the hypotheses of Ritz ("ballistic propagation", or dependence on the state
of motion of the source), or the untenable second postulate of "special" relativity which is
discused in [15]. The existence of a fundamental frame of reference which could be
experimentally approached by successive approximations, is in line with Maxwell theory, but
disagrees with "special relativistic electrodynamics" which states the validity of ME in any
inertial frame of reference.
VIII. Conclusions
- Maxwell's equations (ME) retain their validity for closed current loops.
- ME have to be completed with a force-law and a corresponding equation of motion.
- In all applications the force of Lorentz is a phenomenological external force, with different
115
sources for E and B, the latter being produced by closed circuits.
- MLE fails to explain low-velocity experiments with non-rigid loops.
- Ampère and Weber's force law accounts for all electrodynamic phenomena in which
radiation can be neglected.
- MLE in its accepted form is unable to account for all induction phenomena.
- The correct law of induction is given by the total derivative of the vector potential. This is
compatible with ME, but destroys the Lorentz covariance of the theory.
- The vector potential is of primary importance and is uniquely defined for specific systems.
- There is no "gauge invariance".
- Low-velocity Weber electrodynamics is truly relativistic in the sense of Mach.
- The presence of radiation requires an absolute, fundamental frame of reference.
References
[1] Dyson F. J. "Feynman's proof of Maxwell equations", Am. J. Phys. 58 (1990) 209-211
[2] Jordan E. C. and Balmain K. G., "Electromagnetic Waves and Radiating Systems"
(Prentice-Hall, Inc., New Jersey, 1968) p. 103
[3] Post E. J. "Formal Structure of Electrodynamics" (North Holland Publ. Co.,Amsterdam,
1962); "Kottler-Cartan-van Dantzig (KCD) and Noninertial Systems", Found. of Physics,
9 (1976) 619-640
[4] Galeczki G., "Minkowski Scalar Invariant Incompatible with any Equation of Motion"
(Proc. 2-nd Intrnational Workshop: "Physics as a Science", Koeln, 1997)
[5] O'Rahilly A., "Electromagnetic Theory: A Critical Examination of Fundamentals",Dover
Publ. Inc., New York, 1965) Vol. 2, p. 561
[6] Galeczki G., "What does the Lorentz force have to do with Maxwell's equations?",
Galilean Electrodynamics, 9 (1998) 95-98; Galeczki G., "What does the Lorentz force
have to do with special relativity?", Galilean Electrodynamics 8 (1997) 1-4
[7] Bartocci U. and Mamone Capria M., "Symmetries and Asymmetries in Classical and Relativistic
Electrodynamics", Found. of Physics 7, (1991) 787-801
[8] Jefimenko O. D., "Comment on "On the equivalence of the laws of Biot-Savart and
Ampère", by T. A. Weber and D. J. Macomb [Am. J. Phys. 57, (1989) 57-59]", Am. J.
Phys. 58, May 1990, 505
[9] Wesley J. P.,"Induction Produces Aharonov-Bohm Effect", Apeiron, 5 (1998) 89-95;
[10] Selected Topics in SCIENTIFIC PHYSICS" (Benjamin Wesley, Blumberg, 2002)
[11] "Force between two identical coaxial toroidal solenoids" (in print)
[12] Graneau P. and Graneau N, "Newton versus Einstein: How Matter Interacts with Matter"
116
(Carlton Press, Inc., New York, 1993); "Wesley J. P., Selected Topics in Advanced
Fundamental Physics" (Benjamin Wesley, Blumberg, 1991
[13] Chubykalo A. E., "Action at a distance as a full-value solution of Maxwell equations:
The basis and application of the separated-potentials method", Phys. Rev. E, 53, (1996)
5373-5381
[14] Landau L. and Lifchitz E. M., "Théorie du Champ" (Éditions de la Paix, Moscou, 1965)
[15] Whitney C. K. "A quantum of light shed on classical potentials and fields", Apeiron (?)
[16] Galeczki G. and Marquardt P., "Requiem fuer die Spezielle Relativitaet" (Haag und
Herchen, Frankfurt a. M., 1997)
Acknowledgement
I am indebted to Paul Wesley, Thomas Phipps Jr., Jan Post and Patrick Cornille
for stimulating exchange of ideas during the years.
----George Galeczki received a Licence in Physics from Bucharest University in
1968, M.Sc. (1975) and D.Sc. (1979) degrees from The Technion - Israel
Institute of Technology - in Haifa (Israel), for works in the field of ordered
magnetism. In 1979 he received the Michael Landau for his research beyond his
work toward a degree. After lecturing three semesters at the Technion, he
moved to the governmental research center RAFAEL, where he did (mostly
classified) work on HgCdTe-infrared detectors. After cumulating two sabbatical
years, he left Israel, responding to an invitation from the University of Cologne
(Germany). There he did research on heterodyne HgCdTe-infrared detectors for
astrophysical applications and continued, in parallel, his critical work on
fundamental physics started in 1978 under the influence of Nathan Rosen ("the
EPR one") and Marinov's successful experiment to measure the absolute
velocity of the Earth. He published about 50 papers on magnetism, narrowbandgap semiconductor physics, nanoscopy, and about an equal number of
papers criticizing "special" and general relativities, Copenhagen quantum
mechanics, and Big Bang theory. He is the co-author (with Peter Marquardt) of
REQUIEM TO SPECIAL RELATIVITY (in German, published by Haag +
Herchen, Frankfurt/Main, 1997) and organizer (with P. Marquardt and J. P.
Wesley) of three (1997, 2000, 2002)International Workshops: PHYSICS AS A
SCIENCE. He is presently an independent science consultant, science writer,
president of the Society for the Advancement of Physics, R.S. and member of the
Natural Philosophy Alliance.
Society for the Advancement of Physics, R.S.
[email protected]
117
The State of Experimental Evidence for Length Contraction, 2002
(Delbert J. Larson)
Dedication.
I wish to dedicate this work to the memory of John E. Chappell, Jr. In all my travels I have
never met anyone so singly and heroically devoted to debunking the special theory of
relativity. John led a difficult life, made difficult largely because of his questioning of the
correctness of the scientific status quo coupled with his stubborn refusal to simply go away
quietly and do something else. It is unfortunate that John lived his life when he did. In most of
the recent past centuries, John's view that logic should prevail over absurdity was accepted as
an axiom. It is my hope that most future centuries will return to that common sense notion as
well, sparing future logic-based scholars the torment and ridicule that John had to endure
during his time in this world. The earthly community of space time research has suffered a
severe loss with his passing. We shall miss him.
*****
Abstract. The idea that physical objects become shorter as they move is now well established
in physical theory. Both the classical theories of Lorentz, Larmor, Fitzgerald and Poincare and
the more radical special theory of relativity of Einstein incorporate a physical length
contraction into their worldview. However, no direct measurement of length contraction has
ever been done. One experiment that tried to observe the effect of a length contraction was
done by Sherwin, who found no evidence of a length contraction. This paper will analyze the
assumptions underlying Sherwin's experiment to show that Sherwin's experiment is in fact
equivocal concerning the existence of a length contraction. This paper will also make mention
of another important recent observation that has relevance to the issue of the existence of
physical length contraction.
*****
Introduction.
In an earlier work (see reference 1) I tried to completely analyze the state of evidence for and
against the existence of a length contraction in nature. My conclusion at that time was that one
could not with scientific certainty state that a length contraction really exists. While there was
and is strong evidence for a time dilation (see reference 2), there has never been any direct
measurement of length contraction. In fact, one very important experiment, by Sherwin (see
reference 3), seemed to provide compelling evidence that there was indeed no length
contraction. The intervening years between my earlier work and the present have not changed
the fact that no direct measurement of length contraction has been made. However, I now
understand that Sherwin's experiment may not be as strong a refutation of length contraction
as Sherwin and I had at first believed. In addition, a second set of experiments has come into
existence in the last several years concerning earth tide measurements that has a bearing on
the experimental evidence for length contraction. This paper will look in some depth into the
possible physics behind Sherwin's experiment, and briefly discuss the issues involving
measurements of earth tides at CERN.
118
Sherwin's Experiment.
My earlier work (reference 1) showed that despite the vast majority of experiments done to
that time no firm conclusion could be made as to whether or not a length contraction really
exists. Indeed, the earlier paper showed that if 1) moving observers incorrectly assume that
the speed of light is isotropic and equal to c in their reference frame; and 2) a Larmorian (or
Lorentzian) time dilation exists in nature; then 3) the observers will arrive at the conclusion
that the Lorentz transformations are valid for electrodynamic phenomena, even if a length
contraction does not actually exist in nature. But beyond the issue of electrodynamics (such as
that used in the design of particle accelerators) reference 1 also shows that no other
experiment done can definitely prove that there is a length contraction. Especially important is
the Michelson Morley experiment. Reference 1 goes into detail about the possibility that the
null result of the Michelson Morley experiment might be caused by node entrapment. The
node entrapment theory is that the electromagnetic oscillation is forced to be null at a pair of
boundaries (the mirrors), and it is this enforced boundary condition that also forces zero
fringe shifts to result from the Michelson Morley experiment. Once you remove that famous
experiment (and others directly related to it) from the evidence in support of length
contraction, you quickly find that there are no experiments that show the reality of the length
contraction.
However, while there are no experiments that unequivocally prove the existence of a length
contraction, I emphasized one experiment that strongly suggested the absence of a length
contraction. That crucial experiment was the one done by Sherwin (reference 3).
In Sherwin's experiment, a spring was made to revolve at a high rate. Sherwin realized that if
the Lorentz worldview was correct, that the spring would undergo a length contraction when
it was aligned with its motion through the ether, while it would not experience the length
contraction when it was aligned perpendicular to its motion through the ether. By arranging
for the rotational motion of the spring to be in resonance with the spring's natural harmonic
motion, Sherwin expected to see oscillations excited in the spring. He saw no such
oscillations. Sherwin interpreted the lack of oscillations as experimental support for Einstein's
special relativity (reference 4), and experimental evidence in contradiction to the Lorentz
theory (reference 5). In my earlier work (reference 1) I interpreted Sherwin's null result as
indicating the lack of a length contraction. Further thought indicates to me that the actual
situation is less than clear, and that both Sherwin and I were basing our conclusions on an
unstated assumption.
The relevant issue is what happens to the spring as it makes its rotation, and the essence of
this question gets down to a matter of what fundamentally determines an object's length. As
far as present science is advanced, I would summarize my belief that length is determined by
the spacings between the nuclei of the atoms making up the object. Those spacings can be
analytically determined by quantum mechanics. Within a single atom, the distribution of the
electron cloud is determined by two competing effects. More energy is required for increased
curvature of the wave function - the favored lower energy states would have larger physical
size from this effect. However, the Coulomb potential energy favors smaller physical size.
The equilibrium physical size of an individual electron cloud is determined by minimizing the
total energy found by combining these two effects as approximated by the Shroedinger
equation, and more accurately by QED. For lattices, such as those found in metals and
springs, the calculation is more complicated, but the same basic interplay between wave
function curvature and Coulomb forces is what determines an object's length.
119
The issue of length contraction in Sherwin's experiment can be simplified by looking at
several atoms (or ions) within the spring. Four such atoms are depicted in Figure 1. In the
figure, a circle (or ellipse) indicates that region within which an ion's electron densities are to
be associated with the nucleus at the center of the circle (or ellipse). (In scanning tunneling
microscope pictures of the atoms on a solid surface, one sees bumps and valleys
corresponding to high and low densities of the electron clouds. The circles and ellipses of
Figure 1 would correspond to the valleys of such scans.) Figure 1 depicts the four
representative atoms aligned in the x direction. The figure shows two cases. The first case is a
depiction of the atoms at rest with respect to a Lorentzian ether, while the second case shows
the atoms when they are moving in the y direction through a Lorentzian ether and hence
length contracted.
Figure 1. A cartoon of four atoms within a spring. Top half of the figure corresponds to
a spring at rest with respect to a Lorentzian ether. Bottom half of the figure corresponds
to a spring moving at velocity v with respect to a Lorentzian ether. The velocity v is
assumed to be in the y direction. The spring extends in the x direction.
120
In Sherwin's experiment the spring is constantly rotated. Figure 2 shows the four
representative atoms when they are aligned in the y direction. Figure 2 again shows two cases.
The first case is a depiction of the atoms at rest with respect to a Lorentzian ether, while the
second case shows the atoms when they are moving in the y direction through a Lorentzian
ether. The second case shows the atoms after they are length contracted.
Figure 2. A cartoon of four atoms within a spring. Left half of the figure corresponds to
a spring at rest with respect to a Lorentzian ether. Right half of the figure corresponds
to a spring moving at velocity v with respect to such an ether. The velocity v is assumed
to be in the y direction. The spring extends in the y direction.
Sherwin realized that the length contraction proposed by Lorentz was different than that
proposed by Einstein. The Lorentz contraction was real, whereas the Einstein contraction was
relative. Hence, since any frame is equivalent to any other in relativity, and the spring's
motion in the earth-based inertial frame is symmetric about the center of motion, there is no
orientation dependent length contraction predicted by special relativity as determined by an
earth based observer. Since any inertial frame is as good as any other in special relativity, the
prediction made by special relativity is that no resonant oscillations of the spring should be
observed. However, for the real length contractions of the Lorentz theory, the spring should
truly contract along its long dimension when it is aligned with it's velocity through the ether.
The Lorentzian situation is shown in Figure 3.
121
Figure 3. A cartoon of four atoms within a spring moving through a Lorentzian ether in
the y direction at velocity v. Top half of the figure corresponds to a spring oriented
along its direction of motion. Bottom half of the figure corresponds to an orientation
perpendicular to the direction of motion.
By synchronizing the rotational motion of the spring with the spring's natural harmonic
motion, Sherwin hoped to excite resonantly driven harmonic oscillations of the spring. His
argument was that length disturbances should propagate no faster than the speed of sound
throughout the spring, since that is what they do in any other type of length disturbance.
Therefore, when the longer spring (extended along x) rotates 90 degrees (so that it extends
along y) there isn't enough time for it to come to its new equilibrium, and the natural F=k∆x
forces (from Hooke's Law) will excite oscillations.
Sherwin found no such oscillations. He took this to indicate a lack of a Lorentz contraction. In
my original work (reference 1) I found nothing wrong with Sherwin's original arguments, so I
pointed to his experiment as providing evidence that a length contraction did not exist in
nature. However I now realize that both Sherwin and I were relying on an unmentioned
assumption. We both assumed that the spring was a rigid body - rigid all the way down to its
atomic connections. Looking again at Figure 3, I am assuming that the connection between
atoms is always such that point A connects to point C. That is, I assume that there is a rigid
connection point between each atom, and that as the spring revolves, the centers of the atoms
122
revolve around the spring's rotation point, and the atoms themselves rotate once as they
revolve, ever keeping points A and C connected between each atom in the spring.
But there is another possibility. Rather than being rigidly connected at points A and C, it is
possible that the individual atoms slide along their common boundary as the spring is rotated.
This situation is shown in Figure 4.
Figure 4. A cartoon of four atoms within a spring moving through a Lorentzian ether in
the y direction at velocity v. Top half of the figure corresponds to a spring oriented
along its direction of motion. Bottom half of the figure corresponds to an orientation
perpendicular to the direction of motion.
The situation is further clarified in Figure 5. Figure 5 shows five atoms within the spring in
three possible orientations. If the spring is rotating counterclockwise in the figure, the atoms
start out with their points A and C in contact. After less than a 90 degree rotation, the atoms
are still in contact, but now they are not in contact at points A and C. After a 90 degree
rotation, the atoms have their points B and D in contact.
123
Figure 5. A cartoon of five atoms within a spring moving through a Lorentzian ether in
the y direction at velocity v in three rotated positions.
If the atoms slide along their common boundary, Figure 5 shows how a null result of
Sherwin's experiment can be obtained within a Lorentzian ether. Rather than the speed of the
length contraction be required to propagate along the spring at the speed of sound, the length
contraction is already there! It is just that the contact point moves along the atomic boundaries
as the spring is rotated.
The simple diagrams above show the relevance of slippage versus rigid contact in one
dimension. But of course the springs are three dimensional. Still, the same principle can be
shown to apply for three dimensional objects. Figure 6 shows the case of two rows of atoms
within a spring. Again, if the atoms slide along their common point of contact they are able to
smoothly transition from the case of a longitudinal length contraction of the spring to that of a
transversely contracted spring. For the case of three dimensions one would only need to add
atoms centered above and below the gaps between the two dimensional image shown in
Figure 6.
124
Figure 6. A cartoon of ten atoms within a spring moving through a Lorentzian ether in
the y direction at velocity v in three rotated positions.
From the above analysis it can be seen that if solids behave such that the individual atoms
within them slide along their common boundary as they rotate, then the null result of
Sherwin's experiment can be understood even in the presence of a Lorentzian ether. If
however, individual atoms within a solid maintain rigid contact at the atomic level, Sherwin's
original arguments remain valid. Once again, an underlying assumption about nature must be
made in order to interpret the results of an experiment. Therefore no conclusive statement can
125
be made concerning whether or not Sherwin's experiment can be used to rule out (or in) any
particular space time theory.
Earth Tides.
An additional experiment has also been conducted since the time that I wrote reference 1 that
has bearing on the question of length contraction. CERN researchers have detected changes in
the time it takes particles to orbit their particle storage rings and have correlated those orbital
period changes to lunar position. From these experiments they have inferred a change in path
length that the particles must have traversed, assuming that the speed of the particles was
constant. (At LEP, under standard relativity or the Lorentzian theory, the electron velocity is
constant and extremely close to the speed of light.)
These experiments could, in principle, be used as evidence for or against a length contraction.
If there were no Lorentzian length contraction, and if Lorentzian time dilation alone is
responsible for our inference of a length contraction (as shown in detail in reference 1), and if
the speed of the particles is indeed constant, then the daily rotation of the earth could lead to
different orbit times for the orbiting particles as a function of time of day.
A full analysis of the LEP observations is very worthy of future study.
Conclusion.
At the time I wrote my earlier work (reference 1) I concluded that the experimental situation
was not entirely clear as to whether or not nature contained a length contraction. By looking
at all of the experimental evidence, it is clear that Einstein's relativity is the most in doubt,
because of the experimental tests (reference 6) of Bell's Theorem (reference 7). At that earlier
time I stated that the experiment of Sherwin appeared to support the case that there was no
length contraction, but that Lorentz's theory should not be ruled out solely due to Sherwin's
result. However, given my understanding of the experimental situation at the time, I made the
point that there was some suggestion in the experimental data that a length contraction does
not, in fact, exist.
With the further analysis done herein it is now clear that Sherwin's test does not clearly
indicate whether or not a Lorentzian length contraction exists. In addition, further analysis of
the situation with regard to earth tide measurements at CERN may provide some suggestion
that a length contraction does exist.
But even with the additional insight and experimental data, I remain firm in my conviction
that it will remain questionable whether or not there is a length contraction until a definitive
experiment can be done. A definitive experiment could involve accelerating spheres of
sufficient size so that ultrashort laser pulses could be fired across the spheres as they move.
Then, the shadows thereby produced could be measured. The spheres would then have to be
slowed down and brought to rest again. By measuring their size, as determined by the
shadows of the light, both before, during, and after their motion, a unique measurement could
be done concerning length contraction. (The before and after measurements are required in
order to ensure that the spheres are not somehow mechanically altered during the acceleration
and deceleration processes.) While even that experiment might be questioned (as can any
experiment) it would be a far more direct measurement of length contraction than anything
done to date.
As of July, 2002, it is still not proven that a length contraction exists.
126
References.
1.
D. J. Larson, Physics Essays 7, 476, 1994.
2.
J. Bailey, K. Borer, F. Combley, H. Drumm, F. Krienen, F. Lange, E. Picasso, W. von
Ruden, F.J.M. Farley, J.H. Field, W. Flegel and P.M. Hattersley, Nature 268, 301 (1977).
3.
C.W. Sherwin, Phys. Rev. A. 35, 3650 (1987).
4.
A. Einstein, Ann. Phys. 17, 891 (1905).
5.
H.A. Lorentz, Proc. R. Acad. Amsterdam 6, 809 (1904).
6.
A. Aspect, J. Dalibard and G. Roger, Phys. Rev. Lett. 49, 1804 (1982).
7.
J.S. Bell, Physics (NY) 1, 195 (1965).
July 15, 2002
----Delbert Larson, Ph. D. in Physics in 1986, in the field of particle accelerators,
has published over 50 papers on a variety of physics topics. He has designed
and built several complete particle accelerator systems over the years,
including a 2.5 MeV, ampere intensity electron beam system and a 10 MeV He3 ion beam system for PET isotope production. He served as a leading designer
of the cancelled Superconducting Super Collider, doing longitudinal dynamics
designs for that lab. Dr. Larson has written computer applications for space
charge inclusive transverse ion optics and a separate code for longitudinal
particle optics. Dr. Larson's computer codes have been used at laboratories
around the world. Dr. Larson is presently leading the design of particle
accelerators for use in medical therapy.
[email protected]
127
The Most General Fundamental Failures of Modern Physics
(Delbert J. Larson)
I have some thoughts on the most general and fundamental failures of modern Physics I
would like to share. As I see it, there are three general and fundamental failures of modern
physics:
Failure 1 - Abandonment of Objective Reality.
I believe that the first fundamental failure of modern physics is the forfeiture of the concept of
an objective reality. This failure has it's roots in relativity and quantum mechanics. In their
famous paper, Einstein, Podolski and Rosen (EPR) showed how, assuming an objective
realty, quantum mechanics must be incomplete. Their argument was refined by Bohm, but it
fell to Bell (name forever to be praised) to develop inequalities capable of testing whether or
not quantum mechanics does indeed violate relativitistic causality. The tests have been done,
(Aspect, et al, were the first, but there have been many more experiments since) and quantum
mechanics does indeed predict the correct results of the Bell's inequality experiments. But
underlying the EPR argument was an assumption. The assumption was that relativity was
correct, and it is a readily obtained result of relativity that no cause can create an effect if the
cause is separated from the effect by a relativistic spacelike interval. Faced with the
conundrum of Bell's inequalities being an experimental reality, modern physics therefore
faced a choice. One could either set relativity aside, or set objective reality aside. Modern
Physics chose the latter. I believe that the wrong choice was taken. Einstein was very clear in
his reverence for an objective reality, and so am I. It is clear to me that relativity should have
been set aside as a result of the tests of Bell's inequalities, and that the concept of an objective
reality should have remained paramount. (Note that the Lorentzian theory has no problem
with cause and effect being separated by a relativistic spacelike interval - what is important
there, since simultaneity is absolute, is simply that the cause precede the effect. With absolute
time, the concept of "precede" is well established in the Lorentz theory in all frames, and one
does not need to specify event separations as "space like", "time like" or "light-like".) Also
note that the Lorentzian theory leads to almost all of the same experimental predictions as
relativity. I have discussed this, and other issues, more fully in [1].
Failure 2 - The Trend toward Complexity.
I believe the second fundamental failure of modern physics is it's continued growth into
complexity. Renormalization theory, quark generations, mixing angles, and on and on, have
been considered to be "revolutionary advances" in understanding. And, as each one
individually has come about, each one, individually, does indeed advance understanding. But,
physics has now reached the point where one really needs to study for decades to
"understand" the present state of the art, as many, many single steps keep being added to the
"standard model". I view this situation as being very similar to that which existed just prior to
Copernicus. The "music of the spheres" was a celebrated theory to explain the motion of the
stars and planets in the skies. Now, this theory is much maligned by present day physics, as it
is clear now that the Copernican way (with Kepler, and later, Newton) was far, far simpler.
But rather than ridicule the "music of the spheres" it would be far better if modern physics
stopped to think about what the science was at that time. It took a great deal of careful
observations to map the stellar and planetary motions. It further took a great deal of detailed
128
mathematics to understand the "music of the spheres" theory, as there were many such
spheres that, as a system, came together to accurately - and correctly - predict the motion of
all heavenly bodies. The theory was very complex, and took many years, and a high intellect,
and mathematical study, to understand. But once understood, it passed all experimental tests!
That is why it was so fevently held on to. It wasn't that the scientists of the time were stupid
(as is often smugly inferred). Rather, the opposite was true. They were very intelligent to
understand such a complicated theory. And after devoting decades to understanding things,
building upon the theory year after year, the practitioners were quite understandably reluctant
to consider any simple alternative. Afterall, a simple alternative was - simplistic! And far less
intellect was needed to understand it. Clearly Kepler was just naive!
I have had an amusing incident that is relevant here. I have come up with a "preon" model.[2]
It dovetails into the quark-lepton model, but it only postulates 6 fundamental particles, and it
identifies the weak force as a radioactive decay, reducing the forces of nature from four to
three. Hence, it is FAR SIMPLER that the standard model. (The standard model now employs
6 quarks, plus 6 antiquarks, and they each come in three colors. That's 36 quarks! Then there
are 12 leptons. And gluons, photons, weak intermediate vector bosons and gravitons. Mixing
angles are employed to further explain events. How many spheres do they need?) But in
reviewing my paper for Physical Review Letters, the reviewer quoted Occoms Razor, saying
that the Standard Model employed far fewer "spheres" than did my new proposal. Recalling
Galileo (name forever to be praised) "Shall we Laugh, or Shall we Cry?"
Failure 3 - An Insistance on the Illusion of the Simplicity of Point-like Entities.
I believe that the third fundamental failure of modern physics is it's insistance on point-like
particles. In some sense this harkens back to the ancient particle versus wave argument. But it
is more than that, because a particle would not necessarily have to be of zero size. While the
concept of a point is mathematically simple, it also leads directly to physical infinities, and
the need for "renormalization". It is my view (again see [1]) that while the math might be
more inconvenient with finite distributed bodies, nature might not be mathematically
convenient. But I believe that nature will prefer finite solutions to her problems.
References.
[1] "An Absolute Theory for the Electrodynamics of Moving Bodies", Physics Essays, volume 7,
number 4 1994 page 476.
[2] "The A-B-C Preon Model", Physics Essays, volume 10, number 1, 1997, page 27.
Also, if anyone is interested in a rigorous ether model, please see:
[3] "A Derivation of Maxwell's Equations from a Simple Two-Component Solid-Mechanical Aether",
Physics Essays, volume 11, number 4, 1998.
----[A presentation of the author can be found at the end of his previously published
paper]
129
Le basi sperimentali della propulsione non newtoniana
(Emidio Laureti)
Il concetto di propulsione denominato dall'ASPS (Associazione Sviluppo Propulsione
Spaziale) PNN (Propulsione Non Newtoniana) nel dettaglio propulsione senza espulsione di
massa di reazione (o di fotoni) nasce con la fondazione dell'ASPS nel 1979. Nel 1992 viene
concepito un sistema di propulsione elettromagnetico (SC23) che sfruttando opportunamente
le fasi delle correnti e dei campi magnetici nei circuiti in alta frequenza rendeva possibile in
linea teorica l'apparente violazione del principio di conservazione della quantità di moto nella
accezione newtoniana. Tale apparenza è in realtà dettata dal semplice fatto che in
elettrodinamica proprio per l'inesistenza di una interazione istantanea del campo e.m. (tutte le
interazioni si propagano al massimo con la velocità della luce c) il principio di azione e
reazione nella accezione newtoniana non vale in quanto informulabile [1]. Mentre continua a
valere la conservazione dell'impulso totale, se si include nel sistema dei corpi che esercitano
fra di loro forze di azione e reazione anche il campo e.m..
Attraverso la procedura illustrata nel prototipo denominato SC23 [2] (a cui è stato concesso il
brevetto nell'Aprile del 2000 ) si realizza una sequenza di interazioni e.m. in cui il principio di
azione e reazione non vale mai essendo le forze elettrodinamiche di azione e reazione dirette
nella stessa direzione e verso. Identicamente si ha una sequenza di istanti in cui è appunto
L'INCLUSIONE del campo e.m. nel principio di conservazione della qdm a conservare il
principio stesso [3] in quanto l'impulso totale acquistato dal sistema in una direzione è uguale
e opposto a quello del campo e.m. (va sottolineato [3] che tale impulso non deve essere
confuso con quello del sistema di propulsione funzionante a rinculi fotonici). Tutta questa
procedura passa necessariamente attraverso una condizione sperimentale che non è stata
debitmente controllata per oltre 200 anni.
Sui testi classici di elettrodinamica infatti si nega che possano esistere forze elettrodinamiche
tra circuiti aperti in cui scorre corrente oscillante, ovvero che tali forze abbiano significato per
circuiti aperti solo matematico e non fisico [4], [5]. Tale impostazione era necessaria poichè
l'esistenza stessa di forze elettrodinamiche tra tratti di circuito aperto, in cui scorre corrente
variabile, implicitamente avrebbe dato la possibilità di violare il Principio di Azione e
Reazione come classicamente si definisce, permettendo la propulsione senza espulsione di
massa di reazione. Che tale violazione sia possibile e necessariamente conseguente lo dicono
gli autori stessi che parlano delle formule di Laplace riferite a circuiti aperti [4], [5]. Solo se la
generazione di forze tra circuiti aperti è impossibile, il Principio di Azione e Reazione può
evitare la "particolarizzazione" e il superamento.
Ad esempio il testo di E. Amaldi (uno dei "ragazzi" di via Panisperna) dice che le formule di
Laplace sono "espressioni matematiche vuote di significato fisico" [4]; mentre il testo del
Perrucca dice " ... in casi meno simmetrici, a voler dedurre le azioni elettrodinamiche dalla
successiva applicazione delle due leggi di Laplace non risulta di regola soddisfatto il principio
di azione e reazione … " [5]. L'unica forza elettrodinamica tra circuiti aperti che può esistere
in alta frequenza sarebbe il solo striminzito impulso fotonico p = E/c , dove p è l'impulso
requisivo scambiato, E è l'energia, e c è la velocità della luce.
130
Per dimostrare che queste erano solo assunzioni dovute all'assenza di sperimentazione
sull'elettrodinamica in alta frequenza occorreva verificare soprattutto che la forza
ettrodinamica in alta frequenza poteva essere anche ATTRATTIVA e non solo repulsiva.
In primis va ricordato che ricercatori esterni all'Asps, pur con obbiettivi diversi dalla PNN,
realizzarono alcune configurazioni sperimentali sui circuiti aperti [6]. Questi autori [7] nel
perseguire l'obbiettivo di dimostrare l'inapplicabilità della forza relativistica di Lorentz nel
caso di circuiti aperti, incidentalmente dimostrarono che l'Equazione Cardinale di Ampere
(non relativistica) era valida per i circuiti aperti. Essi scrivono esplicitamente "No where in
the literature before appears such investigation of the forces between physically non closed
circuits … " che è quello che dice pure da tempo l'Asps, con l'aggiunta di una spiegazione
elementare alla mancanza di tale investigation: ovvero che l'accettazione acritica e/o
limitativa delle Maxwell equazioni (nello specifico l'uso che l'autore fa della cosiddetta
"corrente di spostamento") ha in pratica bloccato ogni iniziativa di sperimentazione fisica
sulla dinamica dell'elettromagnetismo ad alte frequenze [8], [9],[10], [11], [12].
Negli anni immediatamente seguenti il 1992 l'Asps iniziò faticosamente a acquisire apparati
sperimentali idonei alla PNN o più correttamente e ad adattare alla PNN l'esistente.
Soprattutto si definirono e si migliorarono progressivamente le tecniche di rilevamento dei
dati sperimentali. Dal 1999 iniziarono sistematicamente i primi esperimenti circa la possibilità
di esistenza di forze elettrodinamiche tra circuiti aperti.
Uno step delle nostre attività sperimentali è stato appunto quello di dimostrare in primo luogo
che tali forze esistono se si approntano gli apparati sperimentali in grado di dimostrarne
l'esistenza.
In un esperimento condotto dall'Asps un conduttore aperto appeso a un pendolo balistico
viene attratto da un dipolo emittente onde e.m. se il conduttore è opportunamente
condizionato e progettato per essere un circuito in cui la corrente di autoinduzione è in fase
con quella della sorgente emettente il campo e.m..
Negli ultimi mesi del 2001 dopo innumerevoli tentativi e modifiche venne realizzata prima
una configurazione sperimentale in cui alcuni dei bracci dei dipoli del sistema di propulsione
non newtoniano SC23 si spostavano in un unico verso della stessa direzione [13] con un
impulso maggiore di E/c ,sotto alimentazione del generatore di potenza SXP2000.
Alcuni bracci di SC23 "nuotano" in pratica nel campo elettromagnetico da loro emesso,
perché ogni campo e.m.,una volta emesso,è indipendente dalla sorgente.
Nello stesso periodo (Dicembre 2001) una sintesi e una reinterpretazione di tutte le
esperienze condotte permetteva di concepire un prototipo finalmente operativo: SC2.12.
Successivamente nel Febbraio 2002 si ottimizzarono alcuni parametri di tale prototipo
portandolo addirittura a competere con le spinte dei motori a ioni.
Si ricapitolano brevemente gli eventi di tale esperienza:
Secondo la procedura già illustrata in Nova 91 Gennaio-Febbraio-Marzo 2002 [14], il
prototipo SC2.12 (vedi foto qui di seguito) è attaccato a un pendolo balistico lungo circa 1
metro, mentre i sistemi che ne rilevano lo spostamento sono un laser che illumina di taglio la
superficie del prototipo e un fascio di luce prodotta da quello che è chiamato "il nostro
occhiale", ovvero un sistema laser + lente che proietta un'iride sulla parete.
131
La scatola contenente la variante di SC2.12 è nascosta da una copertina di Nova Astronautica,
issn: 0393-1005, Organo Ufficiale dell'ASPS. L'occhiale illumina una "appendice-indice"
attaccata in basso sulla copertina che copre il prototipo SC2.12 e proietta una iride circolare
su una parete.
SINTESI:
Un laser illumina la coopertina quasi orizzontalmente, mentre l'occhiale illumina più in basso
l'indice attaccato alla copertina (indice non presente nella foto di SC2.12 con copertina).
Il prototipo sotto alimentazione elettrica irraggia un campo e.m. rilevato dal "Field Strength
Meter" (non presente nella foto di SC2.12 con copertina).
Evento Sperimentale: simultaneamente all'aumento del campo elettromagnetico
rilevato dal "Field Strength Meter" SC2.12 avanza nella direzione dell'osservatore di circa
3,136 millimetri e conseguentemente l'illuminazione del laser si allunga da destra verso
sinistra, per poi tornare indietro quando l'alimentazione elettrica al prototipo viene disattivata.
L'illuminazione dell'indice da parte dell'occhiale è proiettata su una parete del Lab del Dip.
Ra-1 dell'ASPS in forma di iride. L'occhiale è a circa 13 cm dall'indice e a circa 373 cm dalla
parete. L'iride proiettata sulla parete ha un diametro di circa 11 cm.
Evento Sperimentale: simultaneamente all'aumento del campo elettromagnetico
rilevato dal "Field Strength Meter" SC2.12 avanza da sinistra a destra nella direzione
orizzontale con uno spostamento amplificato di circa 9 cm. La proiezione dell'indice torna
indietro quando l'alimentazione elettrica e quindi il campo e.m. viene disattivato.
Il rapporto Fpnn/p tra la spinta pnn Fpnn e il rinculo fotonico p (pag.8 di Nova Astronautica n.
91) [14] era pari a 1363 , se alcuni parametri PNN non erano ottimizzati.
Lo spostamento S in millimetri sul pendolo balistico era pari a:
S=1,045 millimetri
A 50 watt il rinculo fotonico dava una spinta di 0,017 milligrammi (pag.7 di Nova 91).
132
Moltiplicando 1363*0,017milligrammi si ottiene una spinta Fpnn = 23,171 milligrammi per
quanto descritto in Nova 91 [14].
Viene illustrata una spinta ottimizzata con modifica di alcuni parametri di SC2.12
L'Iride in media ha un diametro di circa 11 cm.
Come da riferimento sulla scala graduata sul muro lo spostamento dell'indice è di circa
9 cm in modo che si evince uno spostamento Sm in millimetri del prototipo sul pendolo
pari a:
Sm = 90 millimetri * (13/373) = 3,136 millimetri
cioè è triplo rispetto al precedente (e sempre a 50 watt).
Ricordando i parametri precedenti la spinta Fpnn diventa pari a:
Fpnn=(3,136/1,045)* 23,171 milligrammi = 69,535 milligrammi
Il guadagno rispetto al rinculo fotonico è di circa 4090 volte.
Conclusioni e ulteriori analisi
Le esperienze condotte dall'Asps su pendolo balistico hanno dimostrato che nella definizione
dell'intensità della forza in alta frequenza intervengono anche dei parametri inaspettati ma
sempre legati strettamente alla corrente e al campo magnetico con cui si determina
l'interazione.
L'intensità di spinta Fpnn che la PNN può determinare attualmente è compresa tra circa:
23 milligrammi < Fpnn < 70 milligrammi
Essa è confrontabile con la propulsione ionica ma con il vantaggio di un elevatissimo impulso
specifico dato che il sistema PNN non espelle massa di reazione ma utilizza solo energia e.m.
per generare la spinta.
Come da esperienza riportata in Nova Astronautica n.91 2002 (pag.3-8) [14], anche la
spinta amplificata di SC2.12 nel Febbraio 2002 presentava ROS, ovvero SWR elevati.
Un calcolo successivo portava a quantificare l'utilizzazione di almeno il solo 40% dei 50 watt
erogati dall'alimentatore.
La spinta pnn Fpnn a 70 milligrammi utilizzava pertanto circa 20 watt.
Ora la spinta di un FEEP thruster è di circa 1 millinewton per 60 watt, ovvero 102
milligrammi.
La spinta di SC2.12 a 60 watt utilizzati per la spinta va pertanto triplicata e risulta essere
dell'ordine dei 210 milligrammi ovvero doppia a parità di consumo energetico rispetto a
quella del FEEP Thruster, ovvero dell'ordine dei 2 millinewton.
Da notare che l'Impulso Specifico dei motori dello Space-Shuttle è di 460 secondi.
L'Impulso Specifico dei motori ionici tipo FEEP thrusters è compreso tra 6000 e 10000
secondi.
L'Impulso Specifico Ipnn di SC2.12 è invece:
Ipnn =(23*10-6 Kg x (9 x 1016 metri2/sec2)/50 watt) = 4.14 x 1010 secondi .
133
Ovvero più di un milione di volte più elevato di quello del motore a ioni.
Bibliografia
[1] E. Laureti, "Non validità del Principio di Azione e Reazione in elettrodinamica", Nova
Astronautica, Vol. 20 n.86, 2000.
[2] E. Laureti, "Il Prototipo SC23", Nova Astronautica, Vol.18 n. 77, 1998.
[3] E. Laureti, "La PNN e il Principio di Azione e Reazione", Nova Astronautica, Vol. 19 n. 82, 1999.
[4] E. Amaldi, Fisica Generale II, Università di Roma, 1965, pag. 290-291.
[5] E. Perrucca, Fisica Generale e Sperimentale II, Un. Tip. Ed. Torinese 1949, pag. 627-628.
[6] P.T. Pappas & T. Vaughan, "Stigma Antenna Force Experiments", in The Thorny Way of Truth,
IV, East-West, Graz, 1989, pag. 158-168.
[7] P.T. Pappas,"Forces on a Stigma Antenna", Physics Essays, 3, 3, 211, 1990.
[8] E. Laureti, "Brevetto di SC23 e Attività Sperimentali", Nova Astronautica Vol.20 n. 96, 2000.
[9] A.P.French, J.R.Tessman, Am. J. Phys., 31, 201, 1963.
[10] F.W. Warburton, "Displacement Current, a Useless Concept", Am. J. Phys., 22, 229,1954.
[11l J.C. Maxwell, "A Treatise on Electricity and Magnetism", V2, Dover, New York, 1954.
[12] E. Laureti, "Riflessioni sulla Conservazione della quantità di Moto e Basi sperimentali della
PNN", Nova Astronautica, Vol.21 n. 87, 2001.
[13] E. Laureti, "Per Santa Rita e San Gabriele santi Protettori dell'ASPS Hurra!", Nova Astronautica
Vol. 21 n. 90, 2001.
[14] E. Laureti, "Setup sperimentale di SC2.12", Nova Astronautica Vol. 22 n. 91, 2002.
----Emidio Laureti è nato a Roma nel 1947. Si è laureato in Fisica nel 1974
presso l'Università di Roma, con una Tesi dal titolo "Correzioni Relativistiche al
Fattore di Forma Elettrico del Deuterio". Attualmente è docente di Matematica e
Fisica nelle scuole medie superiori. Fondatore e Presidente dell'Associazione
Sviluppo Propulsione Spaziale (ASPS) nel 1979, si occupa insieme ad altri
collaboratori di attività sperimentali su concetti di propulsione di tipo
"propellantless", all'ASPS definiti Propulsione Non Newtoniana (PNN). Dal
1982 è Direttore Responsabile di Nova Astronautica (issn: 0393-1005), Organo
Ufficiale dell'ASPS.
Associazione Sviluppo Propulsione Spaziale
Via Nino Martoglio 22 , 00137 Roma - Italia
Tel: 06-87131068
134
http://www.asps.it - [email protected]
135
Neopitagorismo e Relatività
(Rocco Vittorio Macrì)
«Da quando i matematici hanno invaso la teoria della
relatività, io stesso non la capisco più» (Albert Einstein)
Ci troviamo in un'epoca che - per la prima volta nell'intero arco del pensiero scientificofilosofico - vede la fisica padroneggiare, porre confini e dettare legge all'interno della sfera
filosofica. Siamo a quasi un secolo di distanza dalla seconda rivoluzione scientifica, la quale
ha scosso i pilastri della stessa gnoseologia: i concetti di spazio, tempo, simultaneità, cosmo,
esistenza… vengono fatalmente rielaborati e trasformati, tallonando la cosiddetta crisi dei
fondamenti della matematica. Gli stessi principi primi aristotelici subiscono "scacco matto":
«Mediante la meccanica quantistica viene stabilita definitivamente la non validità del
principio di causalità» sentenzia Heisenberg1. Nasce la logica quantistica. È la fisica che, per
la prima volta, "ridisegna" la filosofia…
Sulle macerie del pensiero classico aleggia la figura, diventata oramai leggenda, che incarna e
personifica la rottura col passato, l'autorità che ha cambiato per sempre la nostra immagine
del mondo, la scintilla divina con la quale il Fato innescò "la rivoluzione", come egli stesso
ebbe a dire: «Per punirmi del mio disprezzo nei confronti dell'autorità, il Fato fece un'autorità
di me stesso»2. Albert Einstein fu l'artefice della metamorfosi moderna, che avendo posto «la
matematica al centro dell'esperienza», come documenta Gaston Bachelard, e introducendo
una visione elastica dello spazio e del tempo, sarebbe diventato pietra angolare del più grande
cataclisma intellettuale della storia del pensiero scientifico. Nel suo continuo "detonare e
detronizzare", la rivoluzione einsteiniana avrebbe attivato una serie di «choc epistemologici»
nel cuore stesso della comunità scientifica, che - scrive Bachelard nel 1934 - obbligano lo
scienziato a rimettere tutto in discussione: «Il fisico è stato costretto tre o quattro volte da
vent'anni a questa parte a ricostruire la propria ragione, e, intellettualmente parlando, a rifarsi
una vita»3, fino al punto di mettere all'indice le stesse categorie di pensiero che avevano
resistito e brillato per più di due millenni. L'unica possibilità di accesso alle nuove conquiste
relativistico-quantistiche - ammette Abraham Pais - è «quella data da Einstein, è che la stessa
logica classica deve essere modificata»4.
Si tratta ora di analizzare l'influenza, il rapporto e perfino il legame parentale che la
"gaussiana" concezione del pensiero matematico che spazia da Gauss a Cantor fino a Hilbert
ha avuto nei riguardi della sconvolgente ideazione, progettazione ed elaborazione della fisica
e metafisica contemporanee, e se Einstein può essere visto (suo malgrado) come l'anello di
collegamento tra la cosiddetta Scuola di Göttingen e la Scuola di Copenhagen, tanto più che è
ormai ben assodato che la seconda ha completato il lavoro di "svuotamento categoriale"
iniziato dalla prima5. Allora il fisico moderno potrebbe essere considerato un «pitagorico»
non solo perché - come abbozza quel «genio rivoluzionario tra i fisici» 6 - «considera il criterio
della semplicità logica come strumento indispensabile ed efficace per la sua ricerca» 7, ma
soprattutto perché «sostiene che il principio veramente creativo, nella fisica teorica, è quello
della costruzione matematica»8. Anzi, si dovrà ammettere altresì, che si è andati oltre Pitagora
- parliamo appunto di "neopitagorismo" - dal momento che «Einstein accetta il punto di
partenza dell'assiomatica, secondo cui il contenuto logico-formale della matematica è
nettamente separato dal suo contenuto effettivo o intuitivo»9.
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1. Il "ritorno" a Pitagora
Fa parte ormai della mentalità scientifica comune che, «le grandi teorie raramente sono
semplici»10 e per comprenderle «c'è bisogno di un livello davvero elevato nella conoscenza
della matematica»11. «La scienza moderna si fonda quasi per intero sulla matematica» 12.
Raffinati modelli matematici hanno oggi assunto la guida non solo durante la creazione dei
modelli fisici, ma addirittura durante il relativo processo ermeneutico, ridando splendore a
Pitagora e all'affermazione del suo discepolo Filolao: «Senza il numero non sarebbe possibile
pensare né conoscere alcunché». Sotto questa luce le parole di Dirac (1931) appaiono
paradigmatiche: «Il più potente metodo di avanzamento che può essere suggerito oggi è
quello di impiegare tutte le risorse della matematica pura, nel tentativo di perfezionare e
generalizzare il formalismo matematico che costituisce la base esistente della fisica teorica, e,
dopo ogni successo in questa direzione, di tentare di interpretare le nuove forme matematiche
in termini di entità fisiche»13.
«La cultura occidentale è caratterizzata da una sorta di mito della matematica, dalla fede,
forse dovuta a Pitagora, in una sua virtù esplicativa e quasi trascendente. A molte persone,
descrivere in termini matematici una struttura sintattica o delle relazioni di parentela sembra
già una "spiegazione" sufficiente»14. Nel passare dal «Nihil certi habemus in nostra scientia
nisi nostram mathematicam» del Cusano al programma di Dirac («Scoprire prima le
equazioni e poi, dopo averle esaminate, gradualmente imparare ad applicarle […] È più
importante avere bellezza nelle equazioni che trovare accordo tra equazioni ed esperimenti» 15)
transitano 5 secoli, ma visti da una prospettiva epistemologica hanno l'aspetto di un viaggio a
ritroso di due millenni: è, in un certo senso, un ritorno a Pitagora. Contrariamente alle
aspettative di Bertrand Russell che avrebbe desiderato per il Novecento «una ritirata da
Pitagora»16 il sentiero intrapreso dalla fisica contemporanea porta ad una rivalutazione della
Scuola di Kroton, il ritorno cioè «a una tradizione molto antica» 17. «Sembra che i pitagorici
siano stati i primi ad intendere la forza creativa inerente alle formulazioni matematiche»,
bisbiglia Heisenberg18. «Frammisti ai loro discorsi sui numeri amici e nemici, i pentagrammi
mistici, i numeri perfetti, l'armonia delle sfere e così via, troviamo quelle proprietà dei numeri
e delle figure spaziali, chiare da un punto di vista logico, che successivamente troveranno
posto nel limpido giardino degli Elementi di Euclide»19.
È vero che Aristotele denuncia nella sua Metafisica che i Pitagorici abbiano attribuito al
numero quella funzione di causa materiale che gli Ionici attribuivano all'elemento sostanziale
della realtà corporea: «Costoro sembrano ritenere che il numero sia principio non solo come
costitutivo materiale degli esseri, ma anche come costitutivo delle proprietà e degli stati dei
medesimi»20, e che la fisica contemporanea incarna tale credo quasi come "mistero orfico"
seguito dai nuovi adepti con nomi altisonanti quali quelli di Hilbert, Minkowski, Einstein,
Heisenberg, Pauli, Dirac, ecc. Pur tuttavia, la "metrica pitagorica" originaria era ben lontana
dal moderno nichilismo hilbertiano che svuota il pensiero matematico in una asettica e fredda
intelaiatura logica priva di semantica e contenuti intuitivi. Al contrario, era fondata
sull'evidenza e l'intuizione che l'"umano" si ritrovava già nella sua intima costituzione
psichica: l'elevazione mistica e la poetica visione del kosmos come armonia ne danno diretta
testimonianza. In fondo Copernico, Keplero, Galileo, Newton… depositano a favore di questa
prospettiva21. Ma come direbbe ai nostri giorni un Russell: «La logica e la matematica… sono
l'alfabeto del libro della natura, ma non il libro stesso»22.
Esisteva inoltre la visione iperuranica di un sapere matematico che intelaia la struttura del
mondo in modo monolitico, irremovibile, unitario, anelastico, intrasferibile, non
assoggettabile o soggiogabile: professione di fede che da Pitagora, rimbalzando su Platone,
attraversa i secoli come un raggio luminoso riflesso ora da Cartesio, ora da Leibniz fino ad
arrivare a Husserl: «Nessun Dio può minimamente modificare ciò, come non può modificare
il fatto che 1 + 2 = 3 o che sussistano altre verità essenziali» 23. Perfino Hume, dopo aver
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"dissacrato" e "soggettivizzato" ogni supremo principio sotto la guida dell'empirismo, si
inginocchia reverente dinanzi all'«apoditticità» della matematica, a «quelle realtà che sono
sicurissime e certissime»24, come testimonia lo stesso Kant nella sua Critica della ragion
pratica: «Eppure lo stesso Hume non estese l'empirismo al punto da comprendervi anche la
matematica. Egli pensava che le proposizioni matematiche siano analitiche, e, se questo fosse
esatto, esse sarebbero effettivamente apodittiche»25.
Vedremo come questa certezza inizierà a incrinarsi all'inizio dell'Ottocento e come Gauss
segnerà un'era nuova di stampo strumentalista e trans-intuizionista, che porterà prima alla
nascita ed accettazione delle geometrie non-euclidee e successivamente alla matematica
formalista e pragmatista del nostro secolo, attraversando i transfiniti di Cantor. «Dopo quel
radicale mutamento del pensiero matematico - rileva Renato Nobili - anche nella fisica fu
aperta la via alla determinazione di nuove costituzioni di significato e alla costruzione di
modelli matematici astratti, totalmente irriducibili al genere delle rappresentazioni
fenomenologiche del mondo visibile. Parallelamente a ciò, anche le istanze epistemiche
generali del pensiero fisico subirono trasformazioni profonde; cosicché, ad esempio, quelle
nozioni oggettivistiche e metafisiche forti che furono le Verità, le Leggi e i Principi della
Natura nel volgere di pochi decenni furono abbandonate e rimpiazzate da nozioni deboli,
soggettivistiche e pragmatistiche, quali sono le rappresentazioni, le leggi e i modelli
matematici copiosamente fioriti sul diramato albero della fisica teorica contemporanea»26.
2. "Gaussbuster" ovvero all'origine della metafisica moderna
Esiste un curioso parallelismo tra Gauss e Einstein: entrambi hanno messo in moto un
processo epistemologico rivoluzionario - che sbocciò sulle masse come inedite e sbalorditive
immagini del mondo incrinanti l'"autorità", il "senso comune", le "evidenze", le "certezze" del
pensiero classico - più grande di quanto potessero sospettare, un passo più grande di loro
stessi il cui controllo fatalmente sfuggirà di mano e a nulla varranno i tentativi di recupero.
Similmente alla "canonizzazione" avuta da Einstein nel novembre del 1919 per la conferma
delle previsione della sua Relatività generale in seguito alle misure sulla deflessione della luce
durante l'eclissi del 29 maggio 1919 fatte dalla spedizione guidata da Eddington 27, Johann
Carl Friedrich Gauss (1777-1855) ebbe la sua nel dicembre 1802, quando l'astronomo
Wilhelm Olbers, ad un anno di distanza dalla scoperta di Cerere e dalla successiva
scomparsa28, posizionò il telescopio seguendo i dati forniti da Gauss, "riscoprendo" così
l'asteroide dileguato. Il risultato fece di Gauss «una celebrità europea» 29. La riscoperta di
Cerere fu per «il principe dei matematici» un successo clamoroso, a commento del quale
Laplace veniva a definire Gauss «uno spirito ultraterreno in un corpo umano»30.
Con l'avvento dell'era gaussiana la definitiva accettazione e sistemazione dei numeri
complessi31 e la scoperta delle geometrie non euclidee fecero vacillare l'intera struttura
epistemologica, che dovette rinunciare a ogni pretesa di assolutezza: potevano esistere altri
numeri, altre algebre e altre geometrie di pari dignità epistemica. Come ebbe a osservare il
matematico tedesco Felix Klein, «Gauss si erge alla testa del XIX secolo non solo
cronologicamente»32. La nuova visione gaussiana che veniva a imporre i caratteri empiriostrumentaliste sul terreno della teoresi greca doveva però pagare un prezzo altissimo: la
rinuncia all'autoevidenza33. Un tradimento al pitagorismo antico indicato dai Frammenti
rimasti del discepolo più illustre, Filolao: «La natura del numero e dell'armonia non
ammettono alcun inganno perché l'inganno non è loro proprio. La natura dell'indeterminato e
dell'impensabile e dell'irrazionale porta l'inganno e l'invidia». Ciò veniva a manifestarsi sulle
due colonne del fondamento del pensiero classico: l'aritmetica e la geometria, pietre angolari
del pensiero umano dal tempo degli antichi Greci, «fortezze inespugnabili» fondate su verità
autoevidenti che avrebbero trovato un inesauribile campo di applicazione nello studio della
natura. «Coloro i quali credevano - spiega Russell - (come in generale si credeva sul
continente) che fosse possibile una conoscenza del mondo reale certa e indipendente
138
dall'esperienza non avevano che da additar[le]… : soltanto un pazzo avrebbe messo in dubbio
la [loro] validità, e soltanto uno sciocco ne avrebbe negato il riferimento oggettivo»34.
Il carattere certo e unitario che rivestiva la nostra conoscenza del mondo veniva intaccato alla
radice: l'incontrovertibilità delle verità autoevidenti era stata messa in questione da
convenienze empirio-pragmatiste, e «insieme con essa vacillavano secoli di fiducia
nell'esistenza e nella conoscibilità di verità inattaccabili relative all'universo» 35. «Anche se
non abbiamo elementi per stabilire se Gauss sia stato influenzato direttamente dagli scritti di
Hume», appare evidente come Gauss all'inizio dell'Ottocento «pensasse che l'intera
matematica è priva di verità»36. In una lettera a Bessel del 21 dicembre 1811 scrive: «Non
dobbiamo mai dimenticare che le funzioni [di variabili complesse], come tutte le costruzioni
matematiche, sono solamente nostre creazioni; quando la definizione da cui siamo partiti
cessa di avere senso, non dovremo domandarci "che cos'è", ma piuttosto "che cosa conviene
assumere per mantenerla significativa"»37.
Uno sguardo indietro di qualche secolo ci consente di avere un quadro complessivo più
esauriente riguardo le novità concettuali apportate dalla "gaussite" durante la crescita del
pensiero scientifico. Furono la Germania e l'Italia a fornire il maggior numero di matematici
all'inizio del rinascimento, ma l'opera più importante venne composta in Francia nel 1484 da
Nicolas Chuquet: Triparty en la science des nombres. Qui veniva espresso per la prima volta
un numero negativo isolato in un'equazione algebrica. Ciò nonostante, per le radici di
equazioni che comportavano soluzioni immaginarie l'autore così si esprimeva: «Tel nombre
est ineperible»38. Nella prima metà del XVI secolo i numeri negativi cominciavano ad essere
più facilmente "manipolati" grazie all'introduzione della notazione tedesca con i nuovi simboli
"+ e -" al posto della "più sana" notazione italiana "p e m". Pur tuttavia, nonostante si avesse
completa familiarità con le proprietà dei numeri negativi, questi venivano ancora chiamati
"numeri absurdi"39, a testimonianza del forte grado di diffidenza e perplessità diffuso nei
matematici dell'epoca40 (ancora ben lontani da quel morbus mathematicorum recens col quale
Frege accuserà la struttura assiomatica moderna). Soltanto l'uso e l'abuso nella pratica delle
tecniche e procedimenti operativi porterà all'"accettazione perché funziona" tramite la oramai paradigmatica - logica del successo. Si arriva così alla oggettualizzazione delle
procedure, ossia alla cristallizzazione di veri e propri oggetti matematici che acquisteranno
una realtà indipendente dalle circostanze nelle quali sono stati introdotti. Per questa stessa
ragione verranno accettati e accolti i numeri immaginari41.
Scrive Kline: «Senza aver completamente superato le difficoltà connesse con i numeri
irrazionali e con i numeri negativi, i matematici europei accrebbero i loro problemi andando a
inciampare in quelli che noi oggi chiamiamo numeri complessi» 42. Dalla scoperta di Scipione
del Ferro dell'esistenza di una soluzione algebrica dell'equazione di terzo grado, allo stimolo
che questa dette a Nicolò Tartaglia nel sistematizzarla fino all'Ars magna di Gerolamo
Cardano del 1545 che rese di dominio pubblico le procedure risolutrici delle equazioni di
terzo e di quarto grado (grazie all'aiuto di Ferrari), si incominciava a intravedere un residuo
protagoreo sull'opportunità di un utilizzo infido delle radici quadrate di numeri negativi, radici
che tuttavia Cardano chiamava «sofistiche»43. Il passo successivo fu fatto dall'algebrista
Raffaele Bombelli nella sua Algebra del 1560 (ma stampata nel 1572) che tramite
«considerazioni sofistiche»44 - come egli stesso ebbe a dire - arrivò all'«idea assurda» del
seme germinale del concetto di "numero complesso". Fin qui i concetti di numero
immaginario, numero complesso (o, come venivano chiamati allora, numeri "falsi" o
"silvestri"), e quello stesso di numero negativo vengono "supposti" ma non "proposti", ossia
procedono sul filo metafisico della "plausibilità empirica" di stampo protagoreo: «Siccome
funziona, usiamolo». Nel 1629 il matematico francese Albert Girard riconobbe
definitivamente la natura delle soluzioni negative e complesse, e fu così in grado di
perfezionare il lavoro sulla relazione che intercorre tra le radici e i coefficienti di un'equazione
algebrica, già iniziato da François Viète45. Per una copertura epistemico-razionale dovremo
però aspettare fino a Gauss che, grazie ancora una volta all'abuso del "miracolo cartesiano" di
139
collegamento tra il mondo algebrico e quello geometrico riuscirà a proclamare il "diritto di
cittadinanza" a ciò che Eulero nel 1770 definiva entità «immaginarie o impossibili» 46. Come è
stato giustamente inneggiato allo stesso Gauss in occasione del suo cinquantesimo di
dottorato: «Lei ha reso possibile l'impossibile»47.
Grazie al parallelismo geometrico Gauss veniva a dare inizio a una nuova era dove delle
entità metafisicamente contraddittorie48 venivano "addomesticate" perché sovrapponibili
empiricamente a costruzioni geometriche recuperanti l'evidenza perduta dall'altro versante.
Così, d'altra parte, era già stato fatto secoli prima per l'uso dei numeri negativi che, a
quell'epoca, «sollevavano maggiori difficoltà, poiché non potevano facilmente venire
approssimati da numeri positivi, ma la nozione di senso (o di direzione su una linea) li
rendeva plausibili»49. Il sodalizio algebra-geometria ha salvato "in corner" e reso ammissibili
spesso operazioni definiti impossibili dalla prima (come il caso della «lussuria» dei numeri
immaginari, con le parole di Thomas Jefferson del 179950), come questa d'altra parte ha reso
omaggio alla seconda rendendo possibile operazionisticamente quel "salto" che l'intuizione
molte volte non dava licenza di fare, come nel caso della geometria non-euclidea. Gauss
estenderà tale sodalizio anche alla fisica, quando metterà in dubbio - scrutando tra le tre
vette51 - il carattere euclideo dello spazio fisico… e Einstein completerà l'opera.
3. L'eredità di Gauss: dalla "perdita dell'intuizione" alla "libertà cantoriana"
Il sigillo di Gauss recava il motto «pauca sed matura», ma in realtà quello che avvenne fu lo
sviluppo di una serie continua di nuovi oggetti matematici privi di una adeguata fondazione
filosoficamente ineccepibile e accettati in base alla suprema legge del più spregiudicato e
"antieuclideo" pragmatismo: l'applicabilità. Nuove algebre e nuove geometrie venivano ad
accumularsi nell'atanor sempre più "spazioso" dell'esistente matematico. Scrive mirabilmente
Kline: «Dopo tutto, i consueti numeri reali e complessi venivano impiegati con scopi
totalmente differenti e la loro applicabilità sembrava fuori discussione. Nonostante ciò,
l'apparire di nuove algebre bastò per insinuare nella mente dei matematici il dubbio sulla
verità dell'aritmetica e dell'algebra ordinaria proprio come accade a chi, entrato in contatto
con le abitudini di una civiltà sconosciuta, comincia a mettere in discussione il proprio modo
di vivere»52. La "creazione" continua di nuovi continenti matematici sui tracciati metodologici
empiristi, fuori dalla sfera intuitiva, portò una specie di cataclisma concettuale preeinsteiniano nei teorici dell'epoca: «E così la triste conclusione che i matematici furono
costretti a trarre è che nella matematica non esiste verità […] Il tentativo greco di garantire la
verità della matematica partendo da verità autoevidenti e impiegando solo la dimostrazione
deduttiva è stato inutile. Per molti attenti matematici era troppo duro accettare il fatto che la
matematica non fosse un corpo di verità; sembrava quasi che Dio avesse creato una
molteplicità di algebre e di geometrie con il proposito di confonderli, proprio come aveva
confuso le genti di Babele facendo loro parlare lingue differenti»53.
I grandi matematici che avevano affinità o intuito filosofico diedero voce alle obiezioni dei
nuovi universi razionali. Basterebbe pensare a William R. Hamilton («Nessuna persona
sincera e intelligente può dubitare delle proprietà principali delle rette parallele, così come le
espose duemila anni fa Euclide negli Elementi»54), a Francis Masères («Le radici negative…
non dovrebbero mai dovuto essere ammesse in algebra, e bisogna sperare che ne vengano
escluse»55), a Eulero («È chiaro che non si può neppure includere la radice quadrata di un
numero negativo fra i numeri possibili, e bisogna dunque dire che è una quantità
impossibile»56), a William Frend («Gli algebristi […] possono trovare dei numeri impossibili i
quali, una volta moltiplicati fra loro, generano l'unità. Questo è un linguaggio incomprensibile
e ripugna al senso comune; tuttavia, una volta adottato, come tante altre finzioni esso trova i
più strenui difensori fra coloro che amano accettare le cose senza un attento esame e
disprezzano la voce del retto pensare»57), ad Augustus De Morgan («L'espressione
immaginaria… e l'espressione negativa… hanno una caratteristica comune: quando si trova
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una di esse come soluzione di un problema, ciò indica la presenza di qualche incoerenza o
assurdità»58), per non parlare di Cartesio, Newton, Leibniz, Carnot, ecc. Sembrava quasi
materializzarsi l'anatema scagliato da George Berkeley nel 1734 quando provocava i
matematici con: «È vero che [i matematici] non si sottomettono ad alcuna autorità, non
accettano nulla per vero senza prove, e non credono ad argomentazioni inconcepibili? È vero
che essi non hanno i propri misteri, e quel che è più importante, le loro avversioni e le loro
contraddizioni?»59. Come scrisse Poincaré nel 1899: «La logica talvolta genera mostri»60.
Einstein aveva visto giusto quando osservò che «il sogno della conoscenza assoluta aveva
agonizzato a lungo, ma era stato David Hume… a dare il colpo finale ai sogni di Platone» 61.
Fu Gauss che recuperò gli "algoritmi metafisici" di Hume all'interno del pensiero matematico
tramite l'empirismo dell'applicabilità e la logica del successo: «Qui [nella rappresentazione
geometrica] si mostra come il significato intuitivo di − 1 sia del tutto fondato, e per
ammettere queste quantità nel dominio degli oggetti dell'aritmetica non è necessario
nient'altro»62. La "spinta gaussiana" avrebbe portato successivamente al nuovo paradigma
euristico accettato in matematica. Il motto di De Morgan - «Ricordatevi di − 1 »63 - ne
rappresenta l'archetipo. «Ma fu ancora Gauss - scrive Kline - ad accorgersi della conseguenza
più rivoluzionaria [della geometria non euclidea]. […] Gauss… essendosi reso conto che la
geometria euclidea non è necessariamente la geometria dello spazio fisico, cioè non è
necessariamente vera, mise la geometria nella stessa classe della meccanica e affermò che il
carattere di verità deve essere attribuito soltanto all'aritmetica (e all'analisi che ne costituisce
uno sviluppo). Questa fiducia nell'aritmetica è di per sé curiosa. L'aritmetica, infatti, non
possedeva in quel periodo nessuna fondazione logica e la sicurezza che l'aritmetica, l'algebra e
l'analisi fornissero delle verità sul mondo fisico derivava unicamente dall'esperienza. La storia
della geometria non euclidea dimostra in maniera lampante quanto i matematici siano
influenzati non dai ragionamenti che effettuano, ma dallo spirito dei tempi. Saccheri aveva
respinto gli strani teoremi della geometria non euclidea e ne aveva concluso che Euclide era
stato emendato da ogni neo. Un centinaio di anni dopo, invece, Gauss, Lobačevskij e Bolyai
accettarono fiduciosamente la nuova geometria. Essi pensavano che la loro geometria fosse
logicamente coerente e che perciò fosse altrettanto valida di quella di Euclide. Non avevano
però nessuna dimostrazione di questa coerenza. Anche se dimostrarono molti teoremi senza
imbattersi in evidenti contraddizioni, rimaneva aperta la possibilità che si potesse dedurre una
qualche contraddizione»64.
La scoperta che la geometria euclidea non era una verità unica, necessaria e assoluta riguardo
al mondo fu perciò sbalorditiva, ed ebbe effetti di vasta portata e irreversibili. Essa minò alla
base le concezioni assolutistiche della conoscenza umana in ampie regioni del pensiero: «I
matematici vi si opposero a lungo - scrive Barrow - ma coloro che cercavano di sovvertire le
tradizionali certezze euclidee videro in essa un segnale dell'avvento del relativismo. Il termine
"non euclideo" venne a indicare qualche cosa di più generale di quanto valeva per le linee
nello spazio»65. Una volta spalancata la porta della "trans-intuizione" e della "trans-evidenza"
allora si aprì alla «regina delle scienze» un intero mondo di potenzialità latenti, pronte alla
cristallizzazione per coerenza. La matematica poteva finalmente essere libera e volare
poeticamente attraverso la creatività dello scienziato. «La geometria greca classica - chiarisce
Kline - non aveva soltanto imposto delle restrizioni sul dominio della matematica, ma le
aveva anche impresso un livello di rigore che ostacolava la creatività. Gli studiosi del XVII
secolo avevano spezzato entrambi questi vincoli. Il progresso in matematica richiede un
disprezzo quasi completo per gli scrupoli logici»66.
"Disprezzo" che Cantor coltivò più di ogni altro. «La matematica - scriveva nel 1883 - nel suo
sviluppo è completamente libera e vincolata soltanto all'evidente condizione che i suoi
concetti siano in sé non contraddittori»67. Cantor era sopraffatto dal timore che i vincoli posti
alla ricerca avrebbero potuto tagliare le ali alla creatività matematica, «giacché - egli
affermava - l'essenza della matematica risiede proprio nella sua libertà»68. Senza di questa,
sosteneva Cantor, non ci sarebbero stati i grandi sviluppi registrati nel corso del secolo; non
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avremmo avuto la moderna teoria delle funzioni se Gauss o Cauchy o Jacobi o Weierstrass e
Riemann avessero dovuto «sottoporre le loro idee nuove a un controllo metafisico» 69. D'altra
parte è proprio la completa assenza del «controllo metafisico» che favorirà l'empirismo logico
prima e la «novità relativistica» poi, nel campo della fisica, fomentando - in seno a
quest'ultima - un recupero avventato della "libertà cantoriana" e realizzando così quella che
poi Gaston Bachelard rileverà come «impronta di una induzione così audacemente estensiva
da poter sviare una mente poco abituata alle libertà matematiche» 70. La linea filosoficoprogettuale di Cantor, largamente diffusa tra i matematici, la quale - con le parole e il
disappunto di Gottlob Frege - considera sufficientemente giustificata una definizione che «si
presta spontaneamente a costituire la base dei nostri ragionamenti, senza condurre mai ad
alcuna contraddizione»71, si trasmetterà in seguito nel campo della fisica, tramite Einstein
prima e Heisenberg poi, dove il contagio porterà a una vera e propria epidemia di FLOP 72,
sintomatica peste delle strutture portanti della scienza contemporanea. Già per il campo della
matematica era necessario ricordare che il criterio di non contraddittorietà consente solo di
raggiungere «una certezza empirica» - come aveva fin da allora avvisato Frege - giacché
bisogna «in ogni caso essere pronti a incontrare da un momento all'altro qualche
contraddizione che mandi in rovina l'intero edificio»73. Come esponeva H. Weyl nel 1917:
«Una parte essenziale di quest'edificio è costruita sulla sabbia», ed una delle cause essenziali
di questa circostanza «va ricercata unicamente nell'arbitrio (commesso sin dall'inizio in
matematica) di considerare un campo di possibilità costruttive come un aggregato chiuso di
oggetti esistente in sé»74. Ma oramai si era infiltrato anche nella fisica il nuovo credo dei
matematici, quello che con enfasi scriveva Dedekind all'amico Weber in una lettera del 1888:
«Noi siamo di razza divina e possediamo […] il potere di creare»75.
4. Dagli assiomi ai postulati: il programma di Hilbert tradotto in fisica
«La teoria generale della relatività contrastava con la mirabile struttura euclidea del "sacro
volumetto di geometria" che aveva incantato Einstein in gioventù; ed essenziale, ai fini della
teoria stessa, era la negazione dell'assoluta validità del teorema di Pitagora, per il quale, da
ragazzo, aveva trovato una dimostrazione per proprio conto. […] A quasi tutti gli studiosi
della geometria elementare, un'alternativa valida del sistema euclideo sembrerebbe
impossibile. Invero, il filosofo Kant aveva dichiarato che il sistema euclideo era inevitabile,
una necessità del pensiero umano. Ma, a cominciare dagli inizi del diciannovesimo secolo,
dopo un periodo di incubazione che risaliva fino a Euclide, matematici audaci proposero
effettivamente alternative non euclidee e, come si rese conto Gauss, una volta che Euclide
avesse avuto dei concorrenti, la geometria sarebbe divenuta, per necessità di cose, una scienza
sperimentale»76. Viene così tracciata da Hoffmann e Dukas la linea di collegamento tra Gauss
e Einstein. Le "certezze euclidee" impostate dall'antichità e indicate come rocce inabissabili
«in mezzo ai mari agitati della speculazione umana» 77 venivano poste prima in uno stato
ipotetico e incerto dall'empirismo gaussiano, poi rese costruzioni immaginarie della creatività
umana dal libertinismo cantoriano, e infine ricapitolate nel popperiano mondo 3 delle
congetture perché inadeguate per la neopitagorica struttura del mondo: eccessivamente
semplicistiche e obsolete per l'universo einsteiniano. «E in virtù di queste… rivoluzioni scrive William Clifford - l'idea dell'universo, il Macrocosmo, il Tutto, come soggetto della
conoscenza umana, e perciò di interesse umano, è andato in frantumi» 78. Scrive Russell: «La
rivoluzione di Einstein ha spazzato via tutto...» 79. «Dal punto di vista della dialettica hegeliana
la teoria della relatività era una comoda fonte di antinomie: non era necessario… trovare una
soluzione all'interno della fisica, ma bisognava riconoscere che la materia fosse un'astrazione
irreale e che nessuna scienza della materia poteva essere logicamente soddisfacente» 80. Così
l'universo di Einstein - grazie alla gaussiana mentalità che si era venuta a creare - avrebbe
travalicato i confini pitagorici dell'evidenza e dell'intuizione: «Il mondo di Einstein è un
mondo di numeri; questi non suppongono prima di essi né una verità a priori come la
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condizione della loro espressione formale, né una immagine intuitiva come una condizione
del loro significato fisico»81. La successiva meccanica quantistica ipostatizzerà questa sorta di
metafisica e tramite l'«irrazionale» - per usare i termini di Meyerson -, quell'essenza aberrante
di «aritmetizzazione del possibile», concederà quel "passo" contemplato da Bachelard: «Un
passo ancora e il reale non è più che la causa occasionale del pensiero» 82. Tanto che ai nostri
giorni un Feynman può asserire: «Mi auguro quindi che riuscirete ad accettare la Natura per
quello che è: assurda»83.
Innegabile è dunque il tallonamento della nuova fisica nei confronti dello "svuotamento
semantico-categoriale" della nuova matematica. Lo strano mondo della fisica del Novecento è
intimamente collegato a quello astratto e immaginifico della matematica post-gaussiana84.
Dopo Einstein le geometrie non euclidee non esistevano più soltanto come sistemi logici su
fogli di carta: l'architettura dell'universo era non-euclidea e ciò si poteva toccare con mano.
Così come, dopo Heisenberg, le nuove e strane algebre "non commutative" sviluppate a
partire dai quaternioni di Hamilton85 - riflesso diretto della rivoluzione gaussiana - potevano
finalmente innalzarsi dai "mondi di carta" ed esigere altrettanta dignità "interfenomenologica" del mondo fisico così come lo era stato per le geometrie non euclidee 86. Era
la vittoria del freddo costrutto matematico - esterno e alieno alla sfera dell'evidenza,
dell'intuizione, del senso comune - che trionfava sui detriti delle categorie kantiane,
«completamente annichilite - postillerà Heisenberg - dalle scoperte del nostro secolo» 87.
Hermann von Helmholtz poteva finalmente cantare vittoria - «Essa [l'intuizione] è una
conoscenza empirica ottenuta con l'accumulazione e il rafforzamento di impressioni simili
ricorrenti nella nostra memoria, e non una forma di intuizione trascendentale data prima di
ogni esperienza»88 - così come David Hilbert poteva finalmente vedere realizzato il suo sogno
«di dare una formulazione puramente matematica agli assiomi della fisica» 89, liberando «gli
assiomi che stanno a fondamento delle discipline matematiche dall'obbligo di corrispondere ai
loro significati intuitivi originari e naturali» 90. Siccome per Hilbert «la matematica… possiede
coerenza ma nessun significato»91, era arrivato il momento di trasformare gli assiomi in
postulati92 (portando così a compimento l'ideale del tracciato epistemologico che da Gauss
arriva a Cantor). D'altra parte, sottolinea il matematico Meschkowski, «se sul pensiero di
Hilbert non riluce più, come su quello di Platone, "lo splendore dell'essere"», ciò è
direttamente collegato alla rivoluzione gaussiana: «l'"esistenza" della geometria non euclidea
rende impossibile all'uomo moderno di restare fermo alla concezione spaziale di Platone e di
Kant»93.
Il programma hilbertiano, pur lacerato dal celeberrimo teorema di Gödel, continuò a
sopravvivere sotto le "vesti metafisiche" della fisica del Novecento, da Einstein in poi 94. Lo
sviluppo di un'algebra astratta manipolante enti matematici con procedimenti puramente
formali, evitando ogni interpretazione sulla natura di essi, preparerà il terreno epistemico delle
teorie scientifiche contemporanee, tanto da rendere possibile affermare che «per esempio,
l'integrale di Feynman non corrisponde, per il momento, ad alcun oggetto matematico preciso.
È tuttavia è il pane quotidiano dei fisici teorici»95. L'approccio astratto-assiomatico-formalista
hilbertiano della fisica moderna è nettamente strumentalista, si nutre dell'efficacia empirica
all'interno di un humus positivistico ancorato all'idea machiana di "scienza-formulario"96. È la
filosofia dello 0! = 1 , del (-1) 0 = 10 = 11 = 1! = 0! . Eppure il matematico contemporaneo
giudizioso avverte: «Malgrado lo stato insoddisfacente della matematica, la molteplicità delle
scuole, il disaccordo sugli assiomi da accertare, e il pericolo che nuove contraddizioni,
qualora scoperte, possano invalidare gran parte della matematica, alcuni matematici applicano
tutt'ora questa scienza ai fenomeni fisici»97. Ma lo scienziato della nuova era, accecato dal
potere predittivo della nuova scienza, ha barattato la verità con il successo: «Tutto quello che
si può richiedere da una teoria fisica è che le sue predizioni siano in accordo con le
osservazioni»98. Come osserva Russell: «Il male è intellettuale… Per conto mio, non ho
soluzioni da prospettare; la nostra è un'epoca che sostituisce sempre più il potere agli ideali
primitivi, e ciò accade nelle scienze come in altre cose. Mentre la scienza come
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conseguimento di potere diviene sempre più trionfante, la scienza quale conseguimento di
verità è uccisa da uno scetticismo generato dall'abilità degli scienziati».
5. Conclusioni: le basi metafisiche della teoria della relatività
L'avvento della Relatività, facendo saltare i quadri abituali di riferimento spazio-temporali
insieme all'edificio concettuale della fisica newtoniana - che a Kant appariva come «quella
conoscenza del sistema del mondo chiara e immutabile per tutto l'avvenire» - e rendendo
inintuitivo lo spazio così come il tempo «una creazione del nostro pensiero» 99, veniva a
materializzare sullo sfondo della realtà fisica l'ideale "gaussiano-cantoriano-hilbertiano"
concepito e architettato precedentemente nell'universo del costrutto matematico. La
«rivoluzione copernicana della Relatività» avrebbe apportato un vero e proprio «terremoto dei
concetti» - per usare dei termini che Bachelard dichiaratamente mutua da Nietzsche - sulle
stesse fondamenta gnoseologiche, dove «tutto l'edificio della ragione è "scosso"»: «Con la
scienza einsteiniana incomincia una rivoluzione sistematica dei concetti fondamentali» 100.
Dunque il frutto epistemologicamente più profondo dell'impatto einsteiniano sulla fisica è il
suo stesso sconfinamento dal mondo dei numeri e della materia a quello del pensiero, della
logica e dei pilastri della conoscenza, come sottolinea Hans Reinchenbach: «La teoria della
relatività di Einstein ha dato una forte scossa ai fondamenti filosofici della conoscenza» 101. La
stessa Meccanica Quantistica può essere vista come una conseguenza estrema, una ipostasi
del tracciato epistemico della teoria di Einstein: non abbiamo fatto altro - avrebbe rilevato lo
stesso Born, uno degli artefici della meccanica matriciale - che «avere fedelmente proseguito
sulla via che egli [Einstein] ci aveva indicato nei suoi giorni migliori» 102. Confesserà
Heisenberg: «Avevo soltanto… applicato il tipo di filosofia che egli stesso aveva posto alla
base della sua teoria della relatività ristretta» 103. È stato «Einstein - confermerà Gamow - ad
abbandonare le vecchie idee di "senso comune" sul computo del tempo, la misura della
distanza e la meccanica, … [arrivando] alla riformulazione della "insensata" Teoria della
Relatività. […] Heisenberg ne dedusse che la stessa situazione esistesse nel campo della
Teoria dei Quanti»104. Ecco in sintesi la storia di come si sia arrivato a relativizzare la stessa
logica. Oramai si parla di una «pluralità» di logiche… Scrive B.L. Whorf in Le lingue e la
logica: «Nuovi tipi di logica possono forse aiutarci a capire com'è che gli elettroni […]
sembrano comportarsi illogicamente»105.
Rileva Bachelard che intere schiere di scienziati e filosofi che durante i secoli avevano cercato
un continuo accumulo e perfezionamento nella decodifica del reale sotto l'ombra di un'unica e
primordiale razionalità vengono adesso travolti e devastati dalla «novità relativistica»: una
«scienza senza antenati», la Relatività, in quanto non sarebbe «potuta sbocciare che
nell'atmosfera di una matematica perfezionata; ecco perché la dottrina manca veramente di
antecedenti»106. La matematica assurge così a «vero e proprio metodo di invenzione» 107; da
"descrittore" a "creatore", la sua "carica deduttiva" diventa "induttiva": «L'espressione
matematica da sola consente di pensare il fenomeno» 108. Il calcolo tensoriale è per Bachelard
esempio perfetto di «strumento matematico che crea la scienza fisica contemporanea come il
microscopio crea la microbiologia», «Langevin diceva che: "Il calcolo tensoriale conosce la
fisica meglio dello stesso fisico"»109.
Il «pensiero relativistico» è, dunque, animato da un'«audacia induttiva», una proprietà
"rivelata" dello strumento matematico che nella Teoria gioca un ruolo privilegiato. Ciò, però,
non esime ma, anzi, estremizza «lo scandalo della ragione», per usare ancora una volta dei
termini bachelardiani. Come mette bene in evidenza Bouasse nella sua critica risoluta al
potere esplicativo della teoria di Einstein, decisamente minore rispetto a quella classica: «Si
sopprime l'etere e ci si esime dall'insegnarci con che cosa dobbiamo sostituirlo!» 110. Non
possiamo dunque accettare l'invito di Hume («Allora buttatelo nel fuoco») di bruciare, tramite
Einstein, l'unità del pensiero logico-intuitivo plurimillenario che soggiace nell'"incoscio
collettivo" dell'umanità tutta intera. Noi non facciamo - osserva Bouasse - «i sillogismi
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diversamente da Aristotele: anzi, Aristotele ne conosceva la teoria molto meglio della
maggior parte dei nostri filosofi moderni. Bacon, Descartes… si sbagliavano spesso nelle
applicazioni; ciò non toglie che i loro attrezzi, dei quali talvolta essi si servivano male, erano
esattamente i nostri. Se Bacon, Descartes… risuscitassero, si farebbe loro facilmente
comprendere in che cosa essi si sbagliavano, perché i loro cervelli e i nostri sono costruiti allo
stesso modo», né sono «suscettibili di perfezionamento». E dunque - si chiede Bouasse come è possibile «simultaneamente rigettare i dati intuitivi del nostro cervello sullo spazio e
sul tempo, e serbargli […] fiducia quando si tratta di ragionare? […] Voi dite che il nostro
cervello è un falso testimone, poi conservate la metà della sua testimonianza! […] È assurdo.
[…] Io dico che i dati intuitivi del nostro cervello formano un blocco che non avete il diritto
di dividere. Se ne rigettate una parte, siete fatalmente condotti a rigettare il tutto: cosa che
sopprime ogni possibilità di conoscenza»111.
Bachelard ammette il "cartesicidio" caratteristico della fisica post-relativistica, simbolo di
agonia e sprezzo per la "dea intuizione" e parenti stretti "evidenza", "chiaro" e "distinto":
«Siamo di fronte - egli dice - a una vera dialettica. Si procede sistematicamente negando il
postulato di analisi cartesiana, esattamente nello stesso modo in cui si sviluppa la geometria
non-euclidea negando il postulato di Euclide»112. E se un Cassirer parla di «crisi
dell'intuizione» avvenuta «dopo le geometrie non-euclidee e dopo la relatività speciale e
generale»113, non può essere nascosto al proprio intelletto - "scolasticamente" inteso - che
«come ipotesi metafisica, la teoria di Einstein risulta contraddittoria» 114. Inefficace la
certificazione data da Heisenberg che «"non contraddittorio" si riferisce… alla consistenza e
completezza matematica del formalismo che viene costruito a partire dagli assiomi» 115,
quando è ormai ben noto invece che la formalizzazione matematica di una teoria è ben lungi
dallo schermare la stessa dall'incoerenza latente che sfocia a livello di quello che Bridgman
definisce come «sfondo descrittivo enorme». Dietro alle equazioni c'è una enorme struttura
qualitativa fatta di risultati empirici, ipotesi, generalizzazioni, scelte filosofiche, gusti
personali, convenienze: «Quando si prenda atto, finalmente, di questa ricca realtà
confrontandola con il ritratto della teoria scientifica tramandato dall'empirismo logico, che
vale meno di una caricatura, si comprenderà facilmente che la teoria, accanto ai suoi
innegabili successi, non solo può presentare punti deboli, ma può anche sopravvivere ai suoi
stessi fallimenti»116. Come conferma lo stesso Bridgman: «Ogni sistema di equazioni può
comprendere solo una piccolissima parte della situazione fisica effettiva: dietro le equazioni
vi è uno sfondo descrittivo enorme, tramite il quale esse stabiliscono legami con la natura»117.
È solo grazie all'«oscurità matematica» 118 che regna sovrana sulle nuove teorie che il novello
"apprendista stregone" può ritenersi degno di possedere l'arcana chiave meta-ermeneutica e il
potere ad essa congiunto. Sentendosi appartenente alla pitagorica classe dei neo-mathematicoi
non si abbassa ad una «umana, troppo umana» rappresentazione, figlia dell'intuizione.
L'"ammassato" gruppo degli acousmaticoi - cioè coloro che, come denunciava Cartesio già ai
suoi tempi, «si astengono dall'esaminar molte cose... poiché stimano che possano esser
comprese da altri forniti di maggior intelligenza, abbraccian[d]o il parere di coloro sulla cui
autorità maggiormente confidano»119 - si accascia ai bordi delle corsie preferenziali del
pensiero scientifico, affidandosi ciecamente ai cosiddetti "esperti" («cieca schiavitù al
dogma», direbbe Herbert Dingle120), nella convinzione che quanto non si sia riuscito a
intendere sia dovuto ad un inadeguato e insufficiente numero di neuroni a loro disposizione;
una sorta di "filosofia del rimando" «di cui sono preda non solo tanti studenti, ma anche tanti
docenti»121. Ed ecco così il «mastery, instead of the servitude, of mathematics in relation to
physics» denunciato da Dingle122. Non deve sorprende allora che il matematismo entri a far
parte della nuova ermeneutica contemporanea e a sostituire interi blocchi kantiani della psiche
in altrettanti moduli "gaussiani". Confessa senza malizia un docente universitario di
ingegneria elettrica del calibro di Paul Nahin: «Later, in college, I would learn that the
operation of radio is impossible to understand, at deep theoretical level, without an
understanding of − 1 »123. È la matematica che prende il posto del sillogismo aristotelico.
145
Come manifesta apertamente Dirac: «Le nuove teorie, considerate al di là della struttura
matematica, sono costruite con concetti fisici che non possono essere spiegati in termini di
cose precedentemente note allo studente, che neppure possono essere spiegati adeguatamente
con le parole»124. Riesce facile concepire, a questo punto, come si stia approdando con sempre
più facilità a riconoscere con Bridgman che «tutta la nostra conoscenza è relativa» e che in
questo senso «la relatività in senso generale diventa un puro truismo» 125. Si arriva così alla
signoria della sintassi sulla semantica, all'indebolimento, detronizzazione e perdita del
fondamento126, come anche di una umana comprensione127.
Il pericolo di un matematismo sofisticato e "trans-categoriale" alla guida delle teorie
scientifiche è estremamente elevato, e, se lasciato a se stesso, rischia di diventare un alieno
alla ragione stessa: dovremo allora abituarci a vedere sorpresi e sconcertati gli stessi creatori
delle teorie scientifiche quando i razzi di questo "Math-Alieno" travalicano e sconfinano gli
universi dell'intuizione, come accadde allo stesso Einstein quando si scontrò con la
precessione di Thomas128. Bisogna recuperare lo status baconiano di una matematica al
servizio della ragione e non viceversa: quella che l'Einstein non ancora condizionato dalla
spinta minkowskiana129 era solito sottostare, come dimostra una frase dello stesso riportata da
un suo amico nel 1920: «I'm afraid I'm wrong again. I can't put my theory into words. I can
only formulate it mathematically, and that's suspicious» 130. E nel 1927, in occasione del
secondo centenario della morte di Newton, in una lettera al segretario della Royal Society e
poi riportata su Nature (119) e su Science (65) scrive: «È solo nella teoria dei quanti che il
metodo differenziale di Newton diviene inadeguato, e infatti viene meno la causalità in senso
stretto. Ma non è detta l'ultima parola. Possa lo spirito del metodo di Newton consentirci di
riportare l'armonia tra la realtà fisica e ciò che è alla base di tutto il suo insegnamento: la
causalità in senso stretto». Auspichiamoci la stessa cosa, anzi recuperiamo con Newton
l'essenza stessa della matematica, quando nel 1728 scrisse: «Ma è giusto che le radici delle
equazioni debbano essere spesso impossibili [complesse], per timore che esse debbano esibire
i casi di problemi che sono impossibili come se fossero possibili»131.
Note
1
W. Heisenberg, Il contenuto intuitivo della cinematica e della meccanica nella teoria quantistica, in
S. Boffi (ed.), De Broglie - Schrödinger - Heisenberg, Onde e particelle in armonia. Alle sorgenti
della meccanica quantistica, Milano 1991, p 181.
2
Cit. in B. Hoffmann - H. Dukas, Albert Einstein, creatore e ribelle, Milano 2002, p. 30.
3
G. Bachelard, Il nuovo spirito scientifico, Roma-Bari 1978, p. 156.
4
A. Pais, Il danese tranquillo. Niels Bohr, un fisico e il suo tempo, 1885-1962, Torino 1993, p.75.
5
Per un approfondimento si veda U. Bartocci - R.V. Macrì, Il linguaggio della matematica,
«Episteme», 5, 2002.
6
W. Heisenberg, Fisica e filosofia, Milano 1994, p. 44.
7
A. Einstein, Replica alle osservazioni dei vari autori, in P.A. Schilpp (ed.), Albert Einstein,
scienziato e filosofo. Autobiografia di Einstein e saggi di vari autori, Torino 1958, p. 629.
8
9
V.F. Lenzen, La teoria della conoscenza di Einstein, in P.A. Schilpp (ed.), op. cit., p. 307.
Ibidem, p. 326. Dal rischio reale di una accecante reverenza da parte della fisica nei confronti della
matematica contemporanea, tale da ammaliare e sottomettere l'eredità di Galileo nelle mani della
Scuola di "prestigio matematico" del momento ci mette in guardia Morris Kline nel suo capolavoro
146
Matematica: la perdita della certezza, Milano 1985, p. 15: «Le teorie fisiche più sviluppate, nella
maggior parte dei casi, sono interamente matematiche (pur ammettendo che i risultati di tali teorie
sono interpretati in termini di dati sensibili e di oggetti fisici: si possono sentire i suoni emessi da una
radio pur senza avere la più pallida idea di cosa sia un'onda radio da un punto di vista fisico). Perciò
anche gli scienziati che non si occupano in prima persona del problema dei fondamenti devono
nondimeno porsi il problema di quale matematica possono utilizzare con sicurezza se non vogliono
sprecare anni di lavoro servendosi di una matematica priva di salde basi».
10
M. Polanyi, La conoscenza personale. Verso una filosofia post-critica, Milano 1990, p. 92.
11
P.A.M. Dirac, in D. Monti, Equazione di Dirac, Torino 1996, p. 120. Racconta Sommerfeld che a
seguito del successo che ebbe la teoria di Einstein dopo la spedizione dell'«apostolo ispirato della
dottrina di Einstein, […] Il grande astronomo inglese Sir Arthur Eddington, […] nel 1920, un inviato
della "Kölnische Zeitung" mi chiese qualche particolare su di essa, gli dissi che non era argomento per
il grosso pubblico, sfornito com'è delle conoscenze matematiche necessarie per la comprensione di
questa teoria» (A. Sommerfeld, "Per il compleanno di Albert Einstein", in P.A. Schilpp (ed.), op. cit.,
Torino 1958, p. 53).
12
J.D. Barrow, Teorie del tutto. La ricerca della spiegazione ultima, Milano 1992, p. 316.
13
P.A.M. Dirac, op. cit., p. 116.
14
J.P. Changeux - A. Connes, Pensiero e materia, Torino 1991, p. 12.
15
P.A.M. Dirac, op. cit., p. 122. Esattamente di parere opposto la tradizione dei fisici italiani di inizio
secolo che, intendendo le rappresentazioni fisico-matematiche come parametrizzazioni descrittive di
ciò che non può avere altro fondamento che nel territorio dell'evidenza fenomenica, con le parole di
Antonio Garbasso nel 1910 così si pronunciava: «A voler considerare le cose con pieno rigore, si
direbbe anzi che di necessità il modello analitico [matematico] sia più lontano dalla natura che il
modello, in apparenza più rozzo, della fisica sperimentale. Perché se la percezione fornisce una
immagine della realtà, e l'analogia fisica è già una rappresentazione mediata, il calcolo che traduce
quest'analogia nel linguaggio dell'algebra, costituisce in qualche modo un'icona dell'icona dell'icona»
(A. Garbasso, Fisica d'oggi, filosofia di domani, Milano 1910, p. 118).
16
B. Russell, La mia filosofia, Roma 1995, p. 177.
17
W. Heisenberg, La tradizione nella scienza, Milano 1982, p. 32.
18
W. Heisenberg, Fisica e filosofia, op. cit., p. 84.
19
P.P. Wiener - A. Noland (edd.), Le radici del pensiero scientifico, Milano 1971, p. 1.
20
Aristotele, Metaph., I, 5, 985 b 23 - 986 a 16.
21
Cfr. T.M. Tonietti, Verso la matematica nelle scienze: armonia e matematica nei modelli del cosmo
tra Seicento e Settecento, in M. Mamone Capria (ed.), La costruzione dell'immagine scientifica del
mondo, Napoli 1999. Il mondo antico è completamente intessuto da tale concezione. Cfr., solo per fare
qualche esempio, Proclo, In Platonis theologiam, IV, 34; Boezio, De institutione arithmetica, I, 1 e 2;
Agostino, Ad Orosius contra Priscianum et Origenem, PL 42, 674, e De quantitate animae, 8-12, PL
32, 1042-1047; Alberto Magno, Metaphys., I, tr. 4, c. 2; Bonaventura, Itinerarium mentis in deum, 2,
n. 10; Alano di Lilla, Sermo de trinitate, 255.
22
B. Russell, op. cit., p. 238.
23
E. Husserl, Idee per una fenomenologia, Torino 1981, I, p. 95.
24
Nicola Cusano, La dotta ignoranza, Roma 1991, p. 76.
147
25
E. Kant, Critica della ragion pratica, a cura di V. Mathieu, Milano 1996, p. 53.
26
R. Nobili, La cognizione dello spazio e il principio di dualità, Pavia, preprint 1990, p. 5.
27
Cfr. il paragrafo 16c di A. Pais, «Sottile è il Signore…»: la scienza e la vita di Albert Einstein,
Torino 1991, per una rassegna dei titoli del "Times" e di altre riviste scientifiche e non durante il
momento della "beatificazione" di quel memorabile novembre: «Rivoluzione nella scienza. Nuova
teoria dell'universo. La concezione newtoniana demolita», «Euclide al tappeto», «Notizia
sconvolgente, che farà sorgere i dubbi perfino sull'affidabilità della tavola pitagorica», «Tempi duri
per persone colte», «All'assalto dell'assoluto», ecc.
28
Il 1° gennaio del 1801 l'Osservatorio di Palermo poté vantare una sensazionale scoperta fatta
dall'astronomo Giuseppe Piazzi: il primo asteroide mai osservato, Cerere. Piazzi, tuttavia, aveva
potuto osservare solo 9° dell'intera orbita del pianeta; una porzione fino allora considerata insufficiente
per consentire il calcolo dell'orbita completa. Gauss accettò la sfida e arrivò a calcolare un'orbita
ellittica innovativa rispetto ai tentativi utilizzati fino allora, che in seguito si rivelò esatta.
29
R. Tazzioli, Gauss, principe dei matematici e scienziato poliedrico, Milano 2002, p. 36.
30
Ibidem, p. 39.
31
Gauss completerà l'interpretazione geometrica dei numeri complessi solo a partire dal 1831,
perfezionando il cammino intrapreso nella sua dissertazione discussa a Helmstedt nel 1799, dove è
contenuta la dimostrazione del famoso teorema fondamentale dell'algebra, che afferma che ogni
polinomio a coefficienti complessi ammette almeno una radice complessa. Lo studio delle funzioni
complesse venne poi proseguito da Cauchy che nel 1825 propose una generalizzazione dell'integrale
definito che includesse anche le variabili complesse.
32
Ibidem, p. 6.
33
È vero quanto asserisce Russell: «L'autoevidenza è uno degli argomenti più problematici di tutta
l'epistemologia» (B. Russell, Teoria della conoscenza, Roma 1996, p. 248). D'altra parte la soluzione
tentata da questi sembrerebbe ben lontana da una compiutezza filosofica soddisfacente. Si veda, per
completezza, oltre che Autoevidenza, in B. Russell, op. cit., pp. 248 e sgg., anche La matematica e i
metafisici, in B. Russel, Misticismo e logica, pp. 71 e sgg., dove viene sottolineato che «l'evidenza è
spesso un fuoco fatuo» (p. 74).
34
Cit. in J.D. Barrow, La luna nel pozzo cosmico, Milano 1994, p. 31.
35
J.D. Barrow, op. cit., p. 40.
36
M. Kline, Matematica: la perdita della certezza, op. cit., p. 98.
37
Ibidem. La similitudine con Einstein arriva addirittura nella conversione in età matura e nel rigetto
del proprio credo epistemologico avuto prima della pienezza. Come il "secondo" Einstein nella
maturità rinnegherà il "primo" per aver accettato la metafisica operazionista, anche Gauss, nella fase
matura della sua vita, rimediterà e rimetterà in discussione la matrice empirista e strumentalista che
l'aveva guidato per tutto l'arco degli anni fruttuosi e memorabili. Così come anche tutte e due le
"riconversioni" avverranno troppo tardi in rapporto all'avvio degli sviluppi successivi, che
cristallizzeranno invece il cammino empirio-operazionista della scienza posteriore.
38
C.B. Boyer, Storia della matematica, Milano 1990, p. 322.
39
Ibidem, p. 326.
148
40
«Quanto ai numeri negativi, sebbene essi fossero diventati noti in Europa attraverso i testi arabi, la
maggior parte dei matematici del XVI e del XVII secolo non li accettava come numeri o, se lo faceva,
non li accettava tuttavia come radici delle equazioni» (M. Kline, Storia del pensiero matematico, vol.
I, Torino 1996, p. 294). Racconta Kline che «Pascal considerava la sottrazione di 4 da 0 come una
totale assurdità» e che Cartesio «chiamava false le radici negative delle equazioni sulla base del fatto
che esse pretendono di rappresentare numeri minori di nulla» e soltanto per il fatto da lui dimostrato
che «le radici false possono essere mutate in radici reali, Descartes era disposto ad accettare i numeri
negativi» (Ibidem, pp. 294-295).
41
Termine coniato da Cartesio allorché approfondì l'impossibilità di "trasmutare" le radici complesse
in radici reali, come invece era riuscito a fare per quelle negative: «Esse non sono perciò reali ma
immaginarie, cioè non sono numeri. Descartes tracciò una distinzione più chiara dei suoi predecessori
fra le radici reali e immaginarie delle equazioni» (Ibidem, p. 296).
42
Ibidem, p. 295.
43
C.B. Boyer, op. cit., p. 330.
44
Ibidem, pp.332-333.
45
Sottolinea però Kline che «le opinioni avanzate di Girard non ebbero tuttavia alcuna influenza» (M.
Kline, Storia del pensiero matematico, op. cit., p. 296).
46
Paul J. Nahin, An Imaginary Tale. The Story of
47
Ibidem, p. 82.
− 1 , Princeton 1998, p. 31.
Scriveva De Morgan nel 1831: «Abbiamo dimostrato che il simbolo − 1 è privo di significato,
anzi addirittura auto-contraddittorio e assurdo.» (P.J. Nahin, op. cit., p. 82). Aggiunge ai nostri giorni
M. vos Savant: «Yet it is accepted, and imaginary numbers are used routinely. But how can we justify
using them to prove a contradiction?» (Ibidem, p. 224).
48
49
C.B. Boyer, op. cit., p. 332. Il "sospetto di contraddizione" che nasce dalla manipolazione con i
numeri negativi viene così candidamente spiegata da Paul J. Nahin: «This suspicion of negative
numbers seems so odd to scientists and engineers today, however, simply because they are used to
them and have forgotten the turmoil they went through in their grade-school years. In fact, intelligent,
nontechnical adults continue to experience this turmoil, as illustrated in the following wonderful
couplet, often attributed to the poet W. H. Auden: "Minus times minus is plus. The reason for this we
need not discuss."» (P.J. Nahin, op. cit., pp. 13-14).
50
P.J. Nahin, op. cit., pp. 224-6.
51
«Per verificare l'applicabilità della geometria euclidea e della sua geometria non euclidea Gauss
misurò effettivamente la somma degli angoli del triangolo formato dalle cime delle tre montagne
Brocken, Hohehagen e Inselberg» (M. Kline, Storia del pensiero matematico, vol. II, Torino 1996, p.
1017).
52
53
Ibidem, pp. 106-7.
54
Ibidem, p. 107.
55
Ibidem, p. 132.
56
Ibidem, p. 134.
149
57
Ibidem, pp. 168-9.
58
Ibidem, p. 170.
59
Cit. in B. Russell, La mia filosofia, op. cit., p. 217.
60
M. Kline, Storia del pensiero matematico, vol. II, op. cit., p. 1136.
61
D. Overbye, Einstein innamorato. La vita di un genio tra scoperte scientifiche e passione romantica,
Milano 2002, pp. 126-7.
62
M. Kline, Matematica: la perdita della certezza, op. cit., pp. 172-3.
63
M. Kline, Storia del pensiero matematico, vol. II, op. cit., p. 1139.
64
Ibidem, p. 1026.
65
J.D. Barrow, La luna nel pozzo cosmico, op. cit., p. 35. «All'origine della svolta c'era stata l'opera di
Gauss sulla geometria delle superfici, che iniziava lo studio delle proprietà intrinseche delle superfici,
indipendenti cioè dallo spazio in cui erano immerse» (E. Giusti, Ipotesi sulla natura degli oggetti
matematici, Torino 1999, p. 84). Nell'opera di Gauss del 1828, Disquisitiones generales circa
superficies curvas, l'idea chiave è quella di considerare «la superficie non come la frontiera di un
solido» ma di per sé stessa, con le parole di Eugenio Beltrami «come un velo infinitamente sottile».
L'approccio di Gauss sarà ripreso anni dopo da Riemann, il quale - nella sua lezione di abilitazione
tenuta proprio di fronte a Gauss nel giugno del 1854 - esporrà la sua celebre teoria delle varietà
pluriestese. I perfezionamenti successivi di Beltrami e Ricci Cubastro riveleranno la grande fecondità
dell'idea gaussiana nella formulazione matematica della Relatività generale, come ebbe a sottolineare
lo stesso Einstein: «L'importanza di Gauss per lo sviluppo della fisica moderna e specialmente per i
fondamenti matematici della teoria della relatività è enorme» (Cit. in R. Tazzioli, op. cit., p. 64).
66
M. Kline, Storia del pensiero matematico, vol. I, op. cit., p. 465.
67
Cit. in U. Bottazzini, Insiemi di punti e numeri transfiniti, in Paolo Rossi (ed.), Storia della scienza
moderna e contemporanea, vol. III, tomo I, Milano 2000, p. 62.
68
Ibidem, p. 63.
69
Ibidem. Per questo motivo Kant era odiato da Cantor: «Kant era la sua bestia nera» (B. Russell, Una
filosofia per il nostro tempo, Milano 1995, p. 24). Per un motivo opposto a quello di Cantor, Kant
stava sullo stomaco anche a Russell. Sulla copertina di un libro di Cantor spedito dall'autore medesimo
a Russell c'era scritto: «Vedo che il vostro motto è Kant o Cantor» (Ibidem). Ricorda Alan Wood in
una conversazione avuta con Bertrand Russell la teatrale manifestazione di contrarietà che questi
aveva «circa l'affermazione di Kant riguardo all'esistenza di un elemento soggettivo nella matematica:
il tono della voce può essere descritto solo come di disgusto, simile a quello di un fondamentalista
posto di fronte all'ipotesi che Mosè abbia inventato di sana pianta i Dieci Comandamenti: "Kant mi ha
stufato."» (A. Wood, La filosofia di Russell. Uno studio sulla sua evoluzione, in B. Russell, La mia
filosofia, op. cit., p. 223)". Einstein invece parteggiava per la tesi cantoriana, la quale - oltre a «fare
rivoltare Kant nella tomba» (D. Overbye, op. cit., p. 131) - propendeva per una vittoria della libera
creatività sulla rigidità delle kantiane forme a priori: «Gli assiomi della matematica sono altrettanti
esempi dell'opinione di Einstein per cui i concetti sono libere creazioni della mente umana. […] In
Kant… l'attività creativa della mente era limitata dalle forme a priori dell'intuizione. Ma il pensiero
matematico se ne liberò con la scoperta di geometrie non euclidee, e si capisce quindi come Einstein
abbia dotato il pensiero di una maggiore libertà di creazione che con Kant» (V.F. Lenzen, La teoria
della conoscenza di Einstein, op. cit., p. 327).
70
G. Bachelard, La valeur inductive de la Relativité, Paris 1929, p. 61.
150
71
Cit. in U. Bottazzini, Fondamenti dell'aritmetica e della geometria, in Paolo Rossi (ed.), op. cit., p.
257.
72
FLOP = Falsificatore Logico Potenziale, neologismo del presente autore. Si veda, per un
approfondimento, I FLOP nella trattazione relativistica del tempo, in F. Selleri (ed.), La natura del
tempo, Bari 2002.
73
Cit. in U. Bottazzini, Fondamenti dell'aritmetica e della geometria, in Paolo Rossi (ed.), op. cit., p.
257.
74
Cit. in U. Bartocci, Riflessioni sui fondamenti della matematica ed oltre, «Synthesis», n. 3, anno III,
1994, p. 26.
75
Inevitabile la ricaduta di tale mentalità sulla fisica contemporanea. Scrive Weizsäcker, ad esempio,
che gli elettroni rimangono stabili sulle loro orbite perché le «leggi della meccanica quantistica…
glielo impongono» (Cit. in P. Plichta, La formula segreta dell'universo, Casale Monferrato 1998, p.
177).
76
B. Hoffmann - H. Dukas, Albert Einstein, creatore e ribelle, op. cit., p. 144. Einstein sigillerà
irreversibilmente, in seguito, tale visione gaussiana. Con le parole di Max Jammer: «Fu Einstein che
chiarì come la geometria, allorché viene applicata in questo modo all'indagine dello spazio fisico,
cessa di essere una scienza assiomatico-deduttiva e diviene una fra le scienze naturali» (M. Jammer,
Storia del concetto di spazio, Milano 1981, p. 148).
77
78
W.K. Clifford, Philosophy of the Pure Sciences, in Lectures and Essays, London 1879, vol. I, p.
300, cit. in D. Overbye, op. cit., p. 131.
79
B. Russell, La mia filosofia, op. cit., p. 39.
80
Ibidem, p. 41.
81
L. Brunschvicg, L'expérience humaine et la causalité physique, Paris 1949, p. 410.
82
G. Bachelard, La valeur inductive de la Relativité, op. cit., p. 197.
83
R.P. Feynman, QED. La strana teoria della materia e della luce, Milano 1996, p. 25.
84
Scrive Heisenberg in Fisica e filosofia: «È vero che ci apparirà anche subito chiaro che questi
concetti non sono ben definiti nel senso scientifico e che la loro applicazione può condurre a varie
contraddizioni; ma noi sappiamo tuttavia che essi toccano la realtà. Può essere utile a questo proposito
ricordare che perfino nella parte più precisa della scienza, nella matematica, noi non possiamo fare a
meno di servirci di concetti che implicano delle contraddizioni. È ben noto, ad esempio, che il
concetto d'infinito conduce a contraddizioni che sono state analizzate; eppure sarebbe praticamente
impossibile costruire senza questo concetto le più importanti parti della matematica» (op. cit., p. 233).
85
«L'abbandono dell'antica ipotesi di Euclide ebbe un parallelo nella elaborazione di nuove algebre
che rinunciavano a un altro assunto profondamente radicato, secondo il quale, quando l'operazione A
era seguita dall'operazione B, il risultato doveva essere identico a quello prodotto compiendo prima B
e poi A. […] La costruzione di Hamilton segnò l'inizio di un periodo in cui i matematici presero a
creare liberamente sistemi di simboli servendosi di regole prestabilite e compatibili che ne
governassero le combinazioni reciproche senza curarsi che tali sistemi descrivessero alcunché nel
mondo reale» (J.D. Barrow, op. cit., pp. 38-9).
151
86
Così come «la teoria della relatività - scrive Heisenberg - sembra da principio una cosa astratta ed
estranea», bisogna abituarsi («il nostro pensiero si può adattare solo lentamente all'ampliato dominio
sperimentale e al nuovo mondo concettuale») con la teoria dei quanti «a una rinuncia ancor più
profonda ai concetti finora abituali» (W. Heisenberg, I princìpi fisici della teoria dei quanti, Torino
1987, p. 74). Bisogna solo aspettare, cioè, pazientemente che i nuovi concetti rivoluzionari e astrusi
sedimentino sufficientemente nella nostra mente, come il «Maestro della Scuola Copenhagen»
suggerisce ad Alice, sconcertata dal mondo dei quanti: «Ci farai l'abitudine presto, non temere» (R.
Gilmore, Alice nel paese dei quanti, Milano 1996, p. 78). Rileva a questo riguardo Jenner Barretto
Bastos Filho: «Il paradigma di Copenhagen-Göttingen ha dominato lo scenario della fisica […] Il
positivismo, la sopravvalutazione della misura, la fuga verso il formalismo matematico, e addirittura le
"onde di coscienza", hanno abitato stabilmente nei corsi di meccanica quantistica, operando un vero
lavaggio del cervello» (J.B. Bastos Filho, La dissoluzione della realtà: irrealismo e indeterminismo
nella fisica del microcosmo, in M. Mamone Capria (ed.), op. cit., pp. 448-9).
87
W. Heisenberg, Fisica e filosofia, op. cit., p. 107.
88
Hermann von Helmholtz, Sull'origine e il significato degli assiomi geometrici, in A. Einstein,
Relatività: esposizione divulgativa, Torino 1967, p. 249.
89
90
R. Nobili, op. cit., p. 3. «Il programma di Hilbert era più innovativo di quanto a prima vista potesse
apparire. Fino ad allora, per accertare la coerenza di una struttura matematica era stato necessario
fornire un'interpretazione particolare (ossia un "modello", come veniva chiamato) degli assiomi in
questione. Se questo modello nel mondo reale esisteva, il sistema matematico veniva considerato
coerente, nella convinzione che la realtà fisica fosse esente da contraddizioni. […] Hilbert abbandonò
questo infruttuoso procedimento per cercare prove di coerenza che non facessero uso di modelli (né
fisici né matematici) del significato degli assiomi» (J.D. Barrow, op. cit., p. 198).
91
J.D. Barrow, op. cit., pp. 194-5. Scrive Bertrand Russell: «La matematica pura è interamente
costituita da asserzioni per effetto delle quali, se un tale enunciato è vero per qualcosa, allora il tale
altro enunciato è vero per quella cosa. È essenziale non discutere se il primo enunciato è realmente
vero, e non indicare quale sia la cosa per la quale si suppone che sia vero. […] Così la matematica può
essere definita come la materia nella quale non sappiamo mai di che cosa stiamo parlando, né se ciò
che stiamo dicendo è vero» (B. Russell, Misticismo e logica, op. cit., pp. 71-2).
92
La differenza sta nell'autoevidenza: i primi sono di per sé «chiari e distinti» direbbe Cartesio, mentre
i secondi dovranno sottostare alla "spada di Damocle" di una possibile ventura contraddizione,
cantorianamente potenziale. Mentre gli assiomi sono, nelle parole di Benjamin Fedorovich Kagan
(1869-1953), «verità ammesse da ogni uomo, alle quali l'uomo inevitabilmente ricorre tanto in
ciascuna scienza, quanto in qualsiasi ragionamento quotidiano», i postulati costituiscono precise
richieste che «il lettore deve accettare accingendosi allo studio di una disciplina, affinché i
ragionamenti successivi non suscitino obiezioni da parte sua» (Cit. in R. Tazzioli, op. cit., p. 66).
93
H. Meschkowski, Mutamenti nel pensiero matematico, Torino 1973, p. 87. Come rileva giustamente
Umberto Bartocci: «Logicismo, formalismo, crisi dei fondamenti, etc., sono tutti riconducibili
nell'illustrato contesto ad esiti naturali del tentativo di espungere la geometria euclidea dai fondamenti
della matematica» (U. Bartocci, op. cit., p. 24).
94
È paradigmatico «il detto di Einstein che "la base assiomatica della fisica teorica… deve essere
liberamente inventata"» (F.S.C. Northrop, La concezione della scienza di Einstein, in P.A. Schilpp
(ed.), op. cit., p. 341).
95
96
J.P. Changeux - A. Connes, op. cit., p. 16.
Scrive, ad esempio, Roger Penrose: «La teoria ha due argomenti molto efficaci a suo favore e solo
uno, di scarso rilievo, a sfavore. Innanzitutto, la teoria è sorprendentemente esatta rispetto a tutti i
152
risultati sperimentali fino ad oggi ottenuti. In secondo luogo [...] si tratta di una teoria di straordinaria e
profonda bellezza dal punto di vista matematico. L'unica cosa, che può essere detta contro di essa, è
che, presa in assoluto, non ha alcun senso!» (Cit. in A. Zeilinger, Problemi di interpretazione e
ricerca di paradigmi in meccanica quantistica, in F. Selleri (ed.), Che cos'è la realtà. Dibattito nella
fisica contemporanea, Milano 1990, p. 123).
97
98
S.W. Hawking - R. Penrose, The Nature of Space and Time, Princeton 1996, p. 116.
99
E. Schrödinger, L'immagine del mondo, Torino 2001, p. 115.
100
G. Bachelard, La dialettica filosofica dei concetti della relatività, in P.A. Schilpp (ed.), op. cit., p.
511.
101
H. Reichenbach, Relatività e conoscenza a priori, Bari 1984, p. 59.
102
Cit. in F. Selleri, La fisica del novecento. Per un bilancio critico, Bari 1999, p. 94.
103
W. Heisenberg, La tradizione nella scienza, op. cit., p. 127.
104
G. Gamow, Trent'anni che sconvolsero la fisica, Bologna 1966, p. 107.
105
Scrive il logico americano Alonzo Church: «Noi non attribuiamo alcun carattere di unicità o di
verità assoluta ad alcun sistema logico particolare… possiamo considerare l'analogia di una geometria
tridimensionale utilizzata nella descrizione dello spazio fisico… può esservi, e in realtà vi è, più di una
geometria il cui uso è lecito nella descrizione dello spazio fisico. Analogamente, esiste senza dubbio
più di un sistema formale che può essere utilizzato come logica, e di questi sistemi uno può essere più
proficuo o più comodo di un altro; non si può, però, dire che uno sia giusto e l'altro sbagliato» (Cit. in
J.D. Barrow, op. cit., p. 43).
106
G. Bachelard, La valeur inductive de la Relativité, op. cit., p. 99.
107
G. Bachelard, Il nuovo spirito scientifico, op. cit., p. 39.
108
Ibidem, p. 50.
109
Ibidem.
110
H. Bouasse, La question préalable contre la théorie d'Einstein, Paris 1923, p. 18.
111
Ibidem, pp. 18-20. La trad. it. è a cura di M.R. Abramo in Gaston Bachelard e le fisiche del
novecento, Napoli 2002, pp. 21-2.
112
G. Bachelard, L'expérience de l'espace dans la physique contemporaine, Paris 1937, p. 42.
113
E. Cassirer, Determinismo e indeterminismo nella fisica moderna, Firenze 1970, p. 243.
114
H. Bouasse, op. cit., p. 17.
115
W. Heisenberg, La tradizione nella scienza, op. cit., p. 137.
116
F. Selleri, Introduzione, in F. Selleri (ed.), La natura del tempo, op. cit., p. 22. Dinanzi al
voltafaccia dell'Einstein maturo che cambia rotta e fa una "inversione a U" sul tracciato
epistemologico intrapreso negli anni memorabili, Max Born - sbigottito e dispiaciuto per la «tragedia»
di aver perso «il nostro capo e portabandiera» - ammette: «Dobbiamo accettare il fatto che anche nella
153
fisica, come in tutte le altre attività umane, le convinzioni fondamentali vengono prima del
ragionamento» (M. Born, Le teorie statistiche di Einstein, in P.A. Schilpp (ed.), op. cit., p. 68).
117
P.W. Bridgman, La logica della fisica moderna, Torino 1965, pp. 83-84.
118
M. Mamone Capria, La crisi delle concezioni ordinarie di spazio e di tempo, in M. Mamone Capria
(ed.), op. cit., p. 347.
119
R. Descartes, Regulae ad directionem ingenii, in Opere filosofiche, vol. I, a cura di E. Garin, RomaBari 1991, p. 64.
120
H. Dingle, Science at the Crossroads, London 1972, p. 13.
121
U. Bartocci - R.V. Macrì, Il linguaggio della matematica, op. cit..
122
H. Dingle, op. cit., p. 130.
123
P.J. Nahin, op. cit., p. XV.
124
F. Selleri, La causalità impossibile. L'interpretazione realistica della fisica dei quanti, Milano
1988, p. 45.
125
P.W. Bridgman, op. cit., p. 52. Ciò viene tradotto all'interno dell'immagine scientifica del mondo
come un continuo susseguirsi di teorie rivoluzionarie senza arrivare mai alla verità: una «corsa che
non avrà mai fine» (F.A. Levi, Esplorazione del tempo e dello spazio, Milano 1981, p. 126), quando
invece lo stesso artefice della nuova visione del mondo si affannava per trovare la chiave "definitiva".
Ciò fu osservato distintamente da Wolfgang Pauli, il quale a proposito della tenacia e dell'inventiva di
Einstein a garantire ogni anno una nuova teoria unitaria scrisse: «È interessante dal punto di vista
psicologico che per qualche tempo la teoria corrente sia ritenuta dal suo autore "la soluzione
definitiva"» (Cit. in R. Highfield - P. Carter, Le vite segrete di Albert Einstein, Padova 1994, p. 190).
126
Un approfondimento si ha in R.V. Macrì, Relativismo e pensiero debole: la perdita del fondamento,
«Episteme», n.1, 2000.
127
L'esasperato formalismo matematico che accompagna l'immagine scientifica del mondo nella nostra
epoca sembra voler spezzare il nesso storico ed epistemologico tra scienza e filosofia, dimenticando
che la prima è figlia della seconda: «La filosofia e la scienza sono assai più intimamente legate che
non credano gli scienziati che disprezzano la prima e i filosofi che ignorano la seconda» (A. Garbasso,
"Scienza realistica", in Scienza e poesia a cura di J. de Blasi, Firenze 1934, p. 220). Bisogna dunque
domandarsi perché per una parte considerevole della comunità scientifica l'opera di divulgazione è
temeraria e temuta: per la paura legittima di inquinare ciò che è puro (matematico) o non piuttosto per
la paura di scoprire in uno stato chimerico quello che si credeva matematicamente compreso? Può la
(falsa) matematica ostruire il cammino ad una "umana" (o fisica, o filosofica) comprensione? A sentire
lo stesso Einstein il pericolo non è illusorio: «Da quando i matematici hanno invaso la teoria della
relatività, io stesso non la capisco più» (A. Sommerfeld, Per il compleanno di Albert Einstein, in P.A.
Schilpp (ed.), op. cit., p. 54).
128
129
Cfr. A. Pais, "Sottile è il Signore…", op. cit., cap.7 (7a.3), pp.158-159.
Scrive Lewis Pyenson nel suo meritevole The young Einstein: the advent of relativity (Bristol Boston 1985, p. 80): «Minkowski thought that by mathematising special relativity he clarified the
essential physical features of Einstein's theory. Although Einstein accepted Minkowski's
mathematisation as only a technical improvement on his own work, many other physicists and
mathematicians attempted to extend Minkowski's formulation of matter and electromagnetism. Few
realised that there were major differences between Minkowski's and Einstein's approaches to the
principle of relativity». Per quanto riguarda l'influenza dei matematici su Einstein, in particolare della
Scuola di Göttingen, oltre al suddetto testo di Pyenson si cfr. anche S. Walter, Minkowski,
154
Mathematicians and the Mathematical Theory of Relativity, in H. Goenner et al. (edd.), The
Expanding Worlds of General Relativity, Birkhäuser 1999.
130
Cit. in L. Pyenson, op. cit., p. 28.
131
I. Newton, Arithmetica universalis, 2ª ed., 1728, p. 193.
----[Una presentazione dell'autore si trova nel numero 1 di Episteme]
"RVM" <[email protected]>
*****
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Did Einstein Claim That Nature Has Mathematical Structure?
(Jarosław Mrozek)
Abstract
This paper is an attempt to analyse some of Einstein's utterances concerning the relationship
between mathematics and the world and its ontological structure. The author tries to interpret,
in a non-standard way, Einstein's standpoint expressed in the words: as far as the proposition
of mathematics refer to reality, they are not certain; and as far as they are certain, they do not
refer to reality. Einstein's words prove that he rejected a possibility of direct correspondence
of mathematics and the world. Therefore the author of the paper questions the view according
to which Einstein claimed that nature is mathematical. It seems that Einstein's words can be
interpreted as claiming the possibility of applying mathematics to the study of nature, about
which we don't need to assume that it is mathematical. Such an approach better explains the
successes as well as failures of applications of mathematics. Mathematically 'indifferent'
nature can be examined to some degree using mathematical methods and it can also resist
these methods. Thus the hypothesis of amathematicality of nature is closer to the 'scientific
practice' of naturalists.
*****
Albert Einstein was probably the most outstanding physicist of the XXth century. His
scientific authority is so great that - although he wasn't a professional philosopher, his
philosophical views deserve full attention. It is known that Einstein was an advocate of a
realistic standpoint in ontology - he maintained that the world exists and that in its essence it
is deterministic. As regards his epistemological views, I would like to expose his conviction
that it is possible to get to know the world and that it can be understood thanks to the harmony
present in the world. Einstein expressed his conviction in an aphorism: Raffiniert ist der
Herrgott, aber boshaft ist er nicht (God is sophisticated, but he is not malicious). It is just this
possibility of getting to know the world which, despite its complexity, seems to Einstein to be
the greatest mystery of epistemology - bordering on a 'miracle'.
The reported Einstein's utterance sometimes has a 'stronger' interpretation. This aphorism is
treated as Einstein's expression of mathematical structure of the world. Physics - as a science
examining nature - uses mathematics as its tool. For this to be possible - in accordance with
this interpretation - nature must be mathematical, that is, it must possess the structure
corresponding to the structure of mathematics. God, while 'creating' the world, was
sophisticated, creating it as a highly complicated and complex system, but he wasn't
'malicious' because the structure of the world can be deciphered using theoretical
(mathematical) means available to man.
Indeed, in the philosophical works of Einstein we find fragments and phrases, which can be
considered as utterances about the mathematical character of nature, for instance: 'nature is
the realisation of what is the simplest to think of as regards mathematics' 1. However other
utterances of Einstein show that he didn't find mathematicality to be an immanent
characteristic of nature. Einstein - in my opinion - treated the issue of the ontological structure
of the world rather in the categories of intelligibility or rationality of the world. Nevertheless,
we cannot exclude other interpretations of Einstein's ideas. Besides, he encourages
philosophers to treat distrustfully the declarations found in the works of scientists, claiming
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(in a slightly different context): if you want to learn from physicists theoreticians something
about the methods they use, I propose to stick to this rule: Don't listen to their words, but
watch their deeds2. I think that by tracing Einstein's practice of applying mathematics to
physics, an attentive researcher can feel encouraged to adopt a slightly different approach to
mathematics. The argument supporting such a possibility is that, when confronted with the
question "[h]ow can it be that mathematics, being after all a product of human thought which
is independent of experience, is so admirably appropriate to the objects of reality?"3, Einstein
answers it without referring to the mathematical structure of the world.
Einstein characterizes mathematics as a science whose theses are absolutely certain and
unquestionable, favouring here a widespread conviction that the status of mathematics differs
from the status of natural sciences. According to him mathematics is a formal-logical science,
not empirical. In this context, for Einstein as a physicist and a philosopher, the usefulness of
mathematics in the examination of the world is just amazing. If Einstein shared the view
about mathematicality of nature, there wouldn't be anything surprising there. Everything
would be clear. Why can we refer mathematics to reality? - because nature has mathematical
structure; why do we apply mathematics in natural sciences? - because it is mathematics that
is the 'key' to the knowledge of the world of nature. Einstein, however, gives a different
answer: "[i]n my opinion the answer to this question is, briefly, this: as far as the propositions
of mathematics refer to reality, they are not certain; and as far as they are certain, they do not
refer to reality"4.
It seems that Einstein's words can be interpreted as a viewpoint claiming that it is possible
to apply mathematics to examine nature, about which we need not assume that it is
mathematical. It follows from the suggestion that if mathematical propositions refer to reality,
they are not certain. If nature were mathematical, then - as I understand Einstein - referring
mathematical propositions to it wouldn't lead to the loss of their certainty because then the
whole operation would occur between isomorphic domains - nature having mathematical
structure and mathematical theories. With such an approach, the only problem could be to
discover, identify or construct a suitable - for a given area of reality - mathematical theory
which would provide notions for the adequate modelling of physical processes.
Let's consider this issue 'from the point of view' of mathematics - as long as propositions are
certain, they don't refer to the world. Mathematical propositions refer to the possible formal
relations between mathematical entities, which we approach mentally and then they are
apodictic. The certainty of its theses is a result of the previously accepted premises and the
agreement as to the acceptable methods of reasoning. It is, thus, aprioric in the
methodological sense - it can develop autonomously and it is most often created
independently of external or extramathematical influences. Mathematics as such cannot say
anything about objects imagined or real. However let's notice that such an approach to this
issue excludes only the possibility of direct reference of mathematics to the world. It doesn't
follow from it that mathematical propositions should not be referred to reality. It is possible
and - as mathematical natural science shows - very fruitful.
However the application of mathematical propositions leads to the loss of certainty (if we
refer mathematical propositions to reality, they cease to be certain). But it is not the reason
that would make it impossible to refer mathematical propositions to the world. Einstein in
'practice' shows that although mathematical propositions in themselves don't refer to reality,
with the help of suitable physical procedures they can be applied in order to grasp the
characteristics of natural reality, gaining real meaning. However it should be remembered that
in such a case mathematical propositions lose their absolute certainty. Mathematics applied to
physical phenomena cannot guarantee by itself the truthfulness of conclusions to which it
157
leads by making use of a deductive method appropriate to it. It operates, after all, on
unfamiliar ground. In the 'kingdom' of physics there applies methodology which is suitable
for an empirical science - that means standards and rigours of justification and acceptance of
propositions, different than in formal sciences. Therefore mathematical propositions, showing
some possibilities of such and not a different behaviour of a physical system, on the ground of
physics are not able to predict the real course of a phenomenon as this course can be
ascertained by means of methodological criteria, appropriate to the domain of natural
sciences.
Summing up, Einstein's standpoint concerning the relation between mathematics and the
external world can be formulated like this. What gives some content to mathematical notions
does not belong to mathematics but is a physical interpretation. Therefore Einstein in his work
of applying mathematical methods introduces some 'medium' between mathematics and the
world. This intermediary field, in which mathematical structures and really existing nature's
structures meet, is obviously physics. Reconstructing Einstein's standpoint expressed by the
words: as far as the proposition of mathematics refer to reality, they are not certain; and as far
as they are certain, they do not refer to reality, we can state that instead of abstract
considerations of the relation between mathematics and the world, in his scientific work
Einstein in fact considers the triple connection: nature - physical theories - mathematics,
because mathematics itself does not refer to reality.
In this light, if the issue of the structure of reality itself is concerned, it shouldn't be
approached dogmatically. In particular, with reference to Einstein's standpoint, we could
hypothetically assume that natural reality is neither mathematical nor non-mathematical, it is
simply amathematical (similarly as it is not moral or immoral, but simply amoral). Such a
neutral approach to the problem of nature's structure has its advantages. Thanks to this it is
possible, in my opinion, to avoid the difficulties of realistic standpoint, as well as overcome
the hurdles of instrumental interpretation of mathematics' applications. Mathematically
'neutral' nature can - to some extent - be 'approached' with mathematical methods, as well as to some extent - resist these methods.
In this context, successes and failures of applications of mathematics become well
understood. Naturalists know that to apply mathematics effectively, a lot of effort is needed to
'tailor' mathematical methods so that they 'work' in accordance with the accepted premises.
Let's mention here at least the problem of infinite remains, appearing in the quantum theories
of the field, which are removed by ad hoc5 mathematical means, or Hawking's attempts to
eliminate, on the ground of the quantum theory of gravitation, the boundary conditions for the
Universe6, described by Robert Mathew as 'mathematical hocus pocus' 7. Obviously such
'inconvenient' facts are not exposed by the enthusiasts of effectiveness of mathematics in
natural sciences, but they can be traced in the whole history of mathematics' applications in
physics.
Suspending the judgement as to the issue of mathematical structure of nature, we don't
exclude at the same time that some of its aspects can be subjected to mathematical
description, are 'approachable' or 'interpretable' mathematically. Amathematicality of nature
does not exclude a priori the elimination of mathematical methods from natural sciences.
Mathematical methods, as outstanding physicists have shown in their scientific activity,
supported by physical principles, can become a highly effective tool for expressing at least
some aspects of the surrounding nature.
It seems that Einstein's standpoint as to the issue of the relation between mathematics and
the world contains a significant novum compared to classical approaches (Platonic,
158
Aristotelian, Cartesian and Kantian). It is the treatment of the correspondence between
mathematics and the world as the relationship which is generated in the course of the
development of natural scientific theories applying mathematics. Such an approach does not
require the acceptance of strong metaphysical assumptions about the nature and structure of
the world and mathematics as it does not assume that correspondence of mathematics and the
world is a guaranteed state, something existing in advance, a priori - but it treats this
correspondence as something worked out in the process of knowledge development.
In my opinion Einstein showed in his works that the epistemological role of mathematics is
not just restricted to grasping - or not - the structure of the world in itself (as realists
understand it) or only the external and intermediary participation in the articulation of the
contents of natural scientific theories (in accordance with instrumentalist convictions). It
seems that the process of examining the external world has a more basic and essentially
creative character. It doesn't consist only in fitting mathematical categories to the examined
object but rather in co-creating or constituting this object - that is reality. (The 'range' of this
process is the simultaneous generation of mathematical categories). In this way the relation
between mathematics and the world ceases to be only the juxtaposition of these two different
domains and becomes a process, the effect of which is the epistemological grasping of reality
by means of mathematical categories. Mathematicized physical theory makes use of the
categorial apparatus worked out in formal sciences, in particular of mathematical notions and
methods, however at the same time it still remains a physical theory, having 'contact' with
physical reality. This contact ensures mathematical notions an operational scope by
entangling them in physical meanings ( in the course of applying them) and in this way by
assigning them real contents on the ground of natural sciences.
The mechanism of effectiveness of mathematics is, as I think, conventional - adaptive and
generally speaking it consists in, on the one hand, forcing physical aspects of reality to fit
mathematical formulas and, on the other hand, creating mathematical theories that correspond
to physical data or modifying these theories in order to get adapted to this data. There is
nothing like prefect congruence between mathematics and the world - this congruence has a
rather pragmatic character and is conditioned by these physical theories in a more basic way
than it seems to us.
Notes
1
See, A. Einstein, On the Method of Theoretical Physics, Clarendon Press, Oxford 1933
2
Ibidem
3
A. Einstein, Geometry and Experience, in: A. Einstein, Ideas and Opinions, Crown Publishers, Inc.
New York 1954, p. 233
4
Ibidem, p. 233
5
See. S. W. Hawking, A Brief History of Time: From the Big Bang to Black Holes, A Bantam Books,
New York 1988
6
Ibidem
7
See, R. Matthews, Unravelling the Mind of God. Mysteries at the Frontier of Science, Virgin
Publishing Ltd, 1992
-----
159
University of Gdańsk
Institute of Philosophy and Sociology
ul. Bielańska 5, 80-851 Gdańsk, Poland
Jarosław Mrozek, (born 1955), assistant professor in Department of Logic,
Methodology and Philosophy of Science, University of Gdańsk, Discipline:
Philosophy of Mathematics, Philosophy of Science. M.A. - University of Gdańsk
(1977), PhD - University of Gdańsk (1985); dissertation: Epistemological
Aspect of Relation Between Mathematics and Outer World. Head of
Department of Logic, Methodology and Philosophy of Science (1997 - 1999); Vdirector of Institute of Philosophy and Sociology, University of Gdańsk (1999 2002), Member of Polish Society of Philosophy. Among others academical
publications: Einstein's Conception of the Relation Between Mathematics and
the World, The General Function of Mathematics in Physical Sciences,
Cosmology and Anthropic Principle, The Problem of Understanding
Mathematics.
[email protected]
160
The Problem of Reciprocity and Non-Reciprocity
in Special Relativity Theory
(Francisco J. Müller)
Abstract: The implications of the two relativistic postulates are analyzed in terms of their reciprocity
and symmetry aspects. Whereas the first postulate entails a perfect equivalence of all frames, the
second postulate, as reflected by the Einstein-Lorentz equations, implies an asymmetry of values (not
of forms) that clashes not only with the first postulate equivalence but with the possibility of
experimental verifications, all of which are "asymmetric" in each concrete case. A double index
notation is proposed at the end, in order to show more clearly these asymmetries, and to interpret in a
realistic way, the referential (physical) meanings of the four space/time variables. Lorentzian versus
Einsteinian relativities are contrasted. The former seems to cope better with the asymmetric
experimental realities. The latter only does so by subreptitiously changing the meaning of the physical
variables.
In the introduction of his 1905 relativity paper (1) Einstein gives a hint that the 2 nd
relativistic postulate about the universal constancy of the speed of light might be "apparently
irreconcilable with the former" postulate, that is, with the first Postulate about the formal
validity of physical laws for all frames of reference. Few physicists have pondered why
Einstein posited this dialectical contradiction at the very beginning of his paper. It is the
purpose of this article to dig into this question. A superficial interpretation of the possible
contradiction views it as the clash between the classical, or Galilean composition of
velocities, and the counter-intuitive "scandal" that light seems to travel at the same speed for
all relatively moving observers. But there are more hidden aspects to this problem. The
prototype of this light "scandal" was provided by the null Michelson-Morley experiment. This
experiment, however, have always been performed in a "proper frame", without even the
possibility of observing it from the viewpoint point of a moving frame (for example, from the
Sun)(2). Yet, the theory elaborated by Einstein, introduces a perfectly "reciprocal" treatment
of the experiment, (in its equivalent gedanken version) both in a proper and in a non-proper
frame.
After all the theoretical work was done by Einstein, arriving at the Lorentz equations,
the reciprocity and symmetry of such equations have been greatly studied and formalized.
Group theory assimilated the equations as part of its program. This theory is perhaps the best
mathematical tool to investigate such symmetry properties of physical phenomena as
rotations, nuclear particles, relativity, Quantum symmetries, hypersymmetries, antisymmetries, etc. etc.
Relativistic formalization versus physical realities
An essential aspect of these formalizations is to consider variables like x,y,z,t with
primed and unprimed characters. The operators, matrices, generators, etc. are said to
"transform" one set of un-primed variables into the primed ones, and viceversa. Reciprocity
and symmetry are, here, practically synonyms. Reciprocity, however, usually refers only to
the relationship (also termed "inverse") between one set of variables and another
"corresponding" set. In contrast, symmetry can be discovered within one such single set. For
example the elements Aij and Aji are equal in a "symmetric" matrix or tensor. In
contrast the word "anti-symmetric" has been used to described the case when Aij =
-Aji . When the reciprocity simply consists in changing (+) and (-) signs some authors
still consider it "symmetric", others "anti-symmetric" and some even "asymmetric".
161
Leaving the heavens of pure mathematics, the physical use of such primed and
unprimed quantities have been mostly to denote variables pertaining to a "moving"
versus a "non-moving"(resting) frame of reference. Yet, on account of the relativity
principle and the equivalence of all frames (First Postulate), nobody takes seriously the
labels "moving" versus "non-moving" any more. Being perfectly "interchangeable" or
"reciprocal", the primes and unprimes become, again, a mere mathematical formality.
This leads to the familiar interpretation of the Lorentz equations, for example, as a
"rotation" in 4-dimensional space. To the performance of succesive Lorentz steps as
mere multiplications in group theory. And to the "raising" of the time variable to an
"equivalent" status as the space variables through the artifact of an X4 = ict terminology.
This enables to write the "fundamental relativistic interval dS" in a very beautiful way.
But the danger of all these mathematical myths is that, by taking them too
seriously, (and isolating them from their referential meanings) the physical reality that
they "signify" becomes more and more obscured , ignored and even confusing. This
confusion applies especially to the concept of "event".
The elusive "event" (physical versus mathematical)
A first problem that arises in this respect is the nature, the uniqueness, or even
the existence, of the "event" (the space/time point) that is being "observed", "seen",
"transformed", by a certain number of observers, (minimally by two) in relative
"motion". Mathematically speaking this event can be common to any set of reference
frames, regardless of their "motions", because the world of Mathematics is intrinsically
static and motionless. If we mark a point XY in the plane of a Cartesian system K and
then refer that "same point" to another frame K' that has been "rotated" respect the
first, there is absolutely no difficulty in expressing X' = RX and Y' = RY where R is the
"rotation matrix". The original point does not "belong" any more to the K system as to
the K' one. In fact, nothing has to move and, indeed, nothing has moved.
But when we return to physical reality a given "event" is not only a set of
coordinates, but a physical entity, a "happening", a phenomenon. This could be a
Coulomb force between two (real) charges; or a photon being emitted or received, or a
ticking clock, etc. Then it is dramatically important to distinguish in which frame the
said entity or event is AT REST and in which it is seen as a "moving" reality. This
physical event is certainly not interchangeable and non-reciprocal. In theory yes, we
could set the physical entities in ANY of the two frames, but in each concrete experiment
one and only one of the frames is the proper one.
It is in this sense that the Lorentz equations yield "asymmetric values", although
being formally symmetric (or anti-symmetric). Panofsky and Phillips, very well
established authors of the 1960's, explicitly recognized this when they described the
Lorentz contraction, X<X', saying (3):
"This relation is asymmetrical in X and X', since it gives the relation between
measurement of a proper length X' (at rest) in Ε' and an improper length X (not at rest) in
Ε.
In another place, however, they say that Lorentz equations show that "except for
the sign of v, [the frames] Ε and Ε' are equivalent, in agreement with the second relativity
postulate".(4) (Both emphases are mine).
So for these authors the (±) anti-symmetry of the velocity v, is in one place judged
as an "asymmetry", yet in another as an "equivalence". Be this as it may, the important
point is not to lose "track" of where the event is proper and where it is not. The labels of
162
"moving" and "resting" are absolutely interchangeable and in that sense they are
"trivialized" Yet, the primed and unprimed notation of formalized group and
transformation theory only pays attention to such irrelevant tags, and is oblivious of the
most important point: the residence of the unique physical reality that confers one
frame the character of being "proper" and the other "non-proper". Even worse, by
ignoring the residence of that unique physical event the primed/unprimed notation
opens the way to the removal, altogether of the unique physical event. Then the scenario
of the twin paradox is wide opened and all its concomitants debates start to proliferate.
Let me expand on this.
Methodological origin of the clock or twin paradox
In the twin paradox the time of each twin plays the role of a proper time. Each
twin's clock is resting in each twin's frame. Why should the "moving" twin return
younger, when in its own proper clock nothing has absolutely happened according to the
first relativity Postulate? From where comes the "asymmetry" of their times or "ages"?
We know the standard relativistic answer: "from the fact that only the 'traveling'
twin accelerated". And we know also the standard non-relativistic objection:
"accelerations are as relative and as interchangeable as the velocities. If distances are
relative and their first derivatives are so, why not their second derivatives?" "Because a
force, indeed" answer the relativists, "must have been used by the 'moving' twin to
produce the acceleration". But again the non-relativists accuse the relativists of
introducing a "non-inertial" element in their theory (a force!), thus violating the logical
presuppositions under which the whole Lorentzian deduction was made. This debate can
keep going on and on. I do not pretend to end it here. But what I want to point out here
is the origin of the debate, which is this: a mis-application of the Lorentz
transformation.
The Lorentz equations, at least as conceived by its original author in 1904 (5),
were only geared to study how that unique physical reality of which I have spoken
before, (an electron, a ray of light, etc), is "seen", or "measured" by TWO observers in
relative motion. We can call this a ternary structure: two observers and ONE physical
event. (2O1E for short). In contrast, the twin paradox scenario uses a binary structure:
two clocks or "twins" in relative motion and no common event independent of their own
clocks or "ages" to be studied or observed. Such a binary scenario leaves the theory
totally empty and devoid of objective purpose. It is futile, in search of some objectivity,
to speak of the twins as "observers" and the clocks as "events". That language is but a
picturesque antropomorphism that has creeped only too much into relativistic
textbooks. (Einstein himself is partially guilty of this antropomorphism when using
expressions like: the observers "judge", or "ascertain", or "declare", etc, etc).
Critical comment
What, then, should we conclude here about the debates on the clock paradox?
That they have been a waste of time. Relativists will keep insisting in their
"asymmetrizing" acceleration factor, while non-relativists will insist in the intrinsic
equivalence of all truly inertial frames. In reality, the struggle here is between the
equivalence, reciprocity and formal symmetry that springs from the First Postulate on
the one hand, and on the other, the (numerical) asymmetry that results from the Lorentz
equations (2nd Postulate) when applied to a concrete situation. Indeed, we have returned
here to that "apparent contradiction" between the two Postulates that Einstein envisaged
at the beginning of his paper. The fact that the Lorentz equations are in harmony with c
= c for both (or all) frames does not remove the clash between the asymmetry of the
163
numerical values it predicts for the rest of the physical realities, in comparison with the
perfect equality and equivalence predicted for those same realities by the First
Postulate.
In reality the reason why physicists do not perceive this methodological (even
logical) "mis-match" between the two relativistic postulates is that they have gone too
far into mathematics and have abandoned too much the real physical qualities. They
imply, following Minkowski, that those qualities are mere "shadows", and only their
mathematical connections in a four-dimensional (mythical) language remain formally
invariant.
In this respect it is frequently said that relativity theory ended the "mechanistic"
philosophy of the etherists. But in reality relativity has "ended" all physical qualities,
(electromagnetism included), in the name of pure games of kinematically related frames.
This is not only mechanistic, but "geometristic". The world of relativity is, thus, a timeless, motionless world. And if we still remember Aristotle we will agree with him when
he said that "if we do not understand motion we cannot understand Nature". So
relativity does not "understand" Nature at all, since "nothing moves" in the relativistic
eternal and timeless heavens.
This critical comment, however, does not entail, in the least, that the effects
experimentally tested like time dilation, mass increase, etc, are not real. But only that
they cannot be predicted from a symmetristic, equivalential, reciprocating, version of
relativity theory as Einstein's version. It seems that only the Lorentzian (nonsymmetristic) version of relativity makes sense. To consider this I will summarize the
previous verbal analysis in a more concise and symbolic way, using a "double index"
notation, a notation that I think has been long time overdue in relativistic textbooks.
Analysis using a "double index" notation
Let A and B be two frames of reference in relative motion. We shall not stipulate
which is moving and which is not. Let any property T (like time) be labelled with two
subindexes: the first indicating: where the event or object is; and the second by whom or
in which frame the observation is made. Thus:
1-
T AA means: the "time" of an event in A as measured by A (a proper value)
2T AB means: the "time" of an event in A as measured by B
value )
3-
(a
non-proper
T BB means: the time of an event in B as measured by B (a proper value)
4T BA means: the time of an event in B as measured by A (a
"coordinate" value)
non-proper
or
a
Whenever the two subindexes coincide, we have a proper value. Whenever they are
mixed, we have a non-proper value (or "coordinate" value) The previous T variables
should be understood as dT's in the case of time intervals. For simplicity I will use the
single letter T . With this notation, and the additional symbol L(±v) for a Lorentz
transformation we can express the First Postulate writing that:
(I)
TAA = T BB
(valid also for all TCC , T DD , T EE , etc)
And the 2nd Postulate by means of the reciprocal Lorentz equations:
164
(IIa)
TAA =L(v)T AB
(IIb) TBB =L(-v)TBA
Notice that in the Lorentz equations the first subindexes have to be equal,
because both frames, A and B are refering to a unique common object either in A,
(Eq.IIa), or in B (Eq.IIb). Thus, an equation like T AA = L(v)T BA would be totally
meaningless.
Are all equations I and II applicable simultaneously in each concrete situation?
Are all four "referential" parameters defined above simultaneously meaningful? Let us
see the possible answers both in an Einsteinian (reciprocal) relativity and in Lorentz's
(non-reciprocal) kind.
For both versions of relativity, the First Postulate should be always applicable.
Unfortunately, due to the limitations of the primed/unprimed notation, there is not even
a way to express Eq-I as done above. To write T = T' with this purpose would be to
invite total confusion when the Lorentz equations later yield T ≠ T' . Especially in this
aspect we see the greater advantage of the double index notation.
Now in the Lorentzian context equations II can only be applied one at a time in
each case. Suppose we are dealing with (IIa), so that the event is proper in A and not
proper in B, (regardless of which "moves" or not). Then T BB and TBA are "empty". No
part of this experiment refers to them and, hence, no paradox arises. We could later
repeat an "identical" experiment in B and apply (IIb), in which case T AA and TAB will
represent nothing of "that" experiment. The conclusion of the experiment is simply, in
the first case, that A has a proper time or "age" T AA and B sees it non-properly as TAB
and in the second, reciprocal case, that B has a proper time or "age" T BB and A sees it
non-properly as TBA . The two reciprocal cases do not "mix" or "apply" together in one
single experiment.
In Einsteinian relativity, however, both equations II are taken as perfectly
reciprocal (which they are) and as applicable simultaneously but in a "mixed" way.
(Typically this is the clock paradox bynary scenario) What happens here is that
relativists speak of the "age" of each twin or clock, in their own proper frames. These
"ages" should be denoted by T AA and TBB in the double index notation. That being the
case, the only conclusion should be what the First Postulate establishes, namely that T AA
= TBB . No possible asymmetric aging can arise. But relativists insist that one frame, for
example A, is "really moving" and asymmetrically accelerating. Then they apply (IIa) to
conclude that TAA = L(v)TAB , a result which they express verbally by saying that the
"age" of twin A is smaller (younger) than the "age" of twin B. But the problem here is
that TAB is not the proper "age" of twin B, but only the non-proper "view" or
measurement that B has of A's age. The proper age of B is still TBB, a fact that relativists
overlook simply because they lack the adequate double index notation that I am
proposing here.
Relativists "transform" conceptually the non-proper measurement T AB made by
B, into the proper age TBB of B. This happens, as explained above, because in the bynary
scenario there is no fixed, unique, common object to be observed. Then the subjectivity
of each observer takes the place of the object to be measured. This is what produces the
"mixing-up" of equations in Einstein's "symmetristic" relativity which I mentioned
above.
This unwarranted "transformation" of the physical meaning of the mathematical
variables is, perhaps, the most persistent and irritating error both in Einstein's original
paper and its descendants. Parameters like x,y,z, and ct that were used to describe the
motion of a "light ray", are suddenly, without justification, used for representing the
165
"positions and times" of a moving clock or rod. Again this all can happen because the
primed/unprimed notation used exclusively by relativists is totally "blind" to the
referential physical meaning of the variables. The prime/unprime notation simply
indicates "moving" vs "non-moving" systems, a tag that is perfectly equivalent,
reciprocal and interchangeable. But the proper vs non-proper elements of the
experiments are, in contrast, non-reciprocal and physically asymmetric. This physical
asymmetry is the only thing that experiments can show and verify, a fact that means
that in practice, only Lorentzian relativity, with its preferred ether frame, is the one in
harmony with experiments. The only way that Einsteinian symmetristic relativity can
cope with experimental facts is by converting itself to the Lorentzian scenario as each
situation demands. A few examples of this suffices.
The experimental asymmetries oppose Einstein's symmetristic relativity
1 - The GPS community, for example, must use a reference frame fixed to the earth and
not rotating with it, in order to account for the Sagnac effect that takes place between
the GPS satellites and the terrestrial stations. This is an example of a preferred frame of
reference, breaking all reciprocities and symmetries. Likewise, the gyrolasers, nowadays
used in commercial aircraft, are based on the "asymmetric" times of flight of two
opposing beams of light, S/(c+v) and S/(c-v), observed by proper observers corotating
with the gyrolaser. Hence they can deduce the speed v from their observations. Again,
Lorentz "wins" and Einstein "looses".
2 - In the Hafele-Keating experiment the results did not show the symmetry they were
supposed to show. Any school boy knows that the term v 2/c2 has even parity (+v and –v
yield the same result). So clocks flying to the East must have behaved exactly like those
flying to the West. But they did not. The clocks that flew westward were accelerated (!)
respect the resting Washington clocks, while the eastbound clocks did show the expected
time dilation. To explain these asymmetric results the authors had to adopt the
"viewpoint" of observers fixed to the North pole, (ie, not rotating with the Earth, just as
the GPS community does). Another triumph for non-reciprocal relativity. In adopting
this "polar viewpoint" Hafele-Keating were implying that the observers at rest in
Washington (themselves) could see what the North pole observer "should" have seen. If
that is the case, then why use any relativistic transformation at all? Regardless of the
sloppiness of Hafele-Keating's experiment it showed a remarkably "neat" violation of
the symmetristic and transformational relativistic scenario.
Final conclusion
In reality what happens in all this is that when we have two really inertial, (noncommunicable) frames of reference, only one side of the story can be verified
experimentally in each case. As mentioned above, we cannot perform the MM
experiment from a non-proper frame, neither can we observe fast mesons, or for that
matter relativistic electrons, simultaneously in the non-proper and proper frame. So
physical reality, by selecting in each case a proper frame and not another, breaks the
theoretical symmetry of Einstein's relativity. From all this two major conclusions can be
derived:
1 - Einstein's symmetristic theory can never be proven right because of methodological
impossibilities. But then it cannot be disproved either, for the same reason. Relativists
will always supply, in their favor, what the "imaginary" observer "must" have seen.
Hence, strictly speaking, applying Popper's falsification methodology, relativity theory is
166
not a scientific theory at all. It springs from ideal, impossibly symmetristic, thought
experiments.
2 - When only primed and unprimed variables are used everything works perfectly in
the mathematical heavens of group theory. But when the more "messy" but physically
more revealing double index notation is used we see how symmetristic relativity becomes
asymmetric by subreptitiously changing the physical meaning of the variables.
167
References
1) Einstein, A, "The Electrodynamics of Moving Bodies", (1905) Annalen der Physik, vol.17, 891.
2) Attempts at performing MM's experiment with a star light as source are vitiated by the fact that
once the light enters the lens of the apparatus it is re-radiated internally, hence, becoming again an
inmediate "proper" source, just like a terrestrial one.
3) Panofsky, W and Phillips, M "Classical Electricity and Magnetism", Addison-Wesley, Reading,
Mass., 1962, pg. 291.
4) Panofsky and Phillips, Ibid. pg. 292.
5) Lorentz, H A, "Electromagnetic Phenomena in a System Moving with any velocity less than that of
Light," Proc. Acad. Sc. Amsterdam, vol. 6, 809 (1904).
----Francisco J. Müller is the actual President of the Natural Philosophy Alliance
(see the section "Alternative Physics On Line" in this same volume of Episteme),
and is known for a criticism of relativity grounded even on original
experimental results (see point 16 in the second list of the quoted section).
Varela Academy of Science and Philosophy
8025 SW 15 St.
Miami, Florida 33144
U.S.A.
[email protected]
168
On the Impossibility to Describe the Fields of the System of
Uniformly Moving Charges in the Frame of Special Relativity
(Vladimir Onoochin)
1. Introduction.
In this article, we intend to discuss one point of foundation of the relativistic theory,
i.e. the transformational properties of the scalar potential of the uniformly moving charges.
The relativistic theory has the pretension to play a role of an absolutely true theory and this
fact seems to be undisputable to such extent that some questions laying in the basis of this
theory are treated as postulates or as direct consequences of the postulates. However, the
special relativity is based on some experimental facts which cannot be derived from the
postulates of the theory. The subject of this article is the analysis of the consistency of the
relativistic transformations of the potentials with the experimental facts.
Development of the classical electrodynamics at the end of XIX and beginning of XX
century went in a way when the main attention was focused on seeking the transformations
for the EM field while going from a frame at a rest to the moving frame. However, the
expressions for transformed EM fields have not been studied with necessary thoroughness,
namely, only the expressions for the fields created by single point charge were analyzed. But
even while analysing these simple expressions some points are overlooked; by the way, these
points form the basis of the special relativity. We will show that these 'holes' in basement of
the special relativity make the latter to be incorrect. We start from well known Lorentz
transformations.
It is known from the special relativity that the coordinates in the laboratory frame and
uniformly moving frame are connected by the Lorentz transformations:
x′ =
x − vt
1− v2 c2
y′ = y z′ = z t′ =
t − vx / c 2
;
1 − v2 c2
(1)
and, correspondingly, the charge density and the scalar potential must transform as:
ρ =
ϕ =
ρ′
1− v2 c2
ϕ′
1− v2 c2
;
(2a)
.
(2b)
In Eqs. (2), the quantities ρ ' and ϕ ' are defined in co-moving frame where the charge
is at rest so the quantities j x′ and Ax′ are equal to zero.
If the above equations are fulfilled, then the electrodynamical quantities provide
invariance of the physical laws in both frames. We emphasize that, despite of widespread
belief, these equations are not postulates1, but they either must be proven or derived from the
experimental data.
169
The first of equations (2) can be easily proven. Since the charge density of the
elementary charge is described by the Dirac delta function, for uniformly moving charge the
proof goes as follows:
ρ ( x, y , z, t ) = δ ( r , t ) = δ ( x − vt )δ ( y )δ ( z ) = δ
=
δ ( x ′ )δ ( y ′ )δ ( z ′ )
1− v c
2
2
(
)
1 − v 2 c 2 ⋅ x ′ δ ( y ′ )δ ( z ′ ) =
ρ ( r′ )
=
1 − v2 c2
;
(3)
.
(4)
which agrees with the law of conservation of the total charge:
∫ ρ ( x, y, z )dxdydz = ∫
ρ ( x′, y′, z′ )
1− v c
2
2
1 − v 2 c 2 dx ′ dy ′dz ′ = q
Validity of Eq. (2b) has been proven by Lorentz who solved the wave equation for the
ϕ potential with its rhs describing uniformly moving elementary charge:
 1 ∂2
∂2
∂2
∂2 
 2 2 −
 ϕ ( x, y , z, t ) = 4π ρ ( x − vt )
−
−
∂ x 2 ∂ y 2 ∂ z 2 
 c ∂t
(5)
in relativistic approach (here, ρ(x – vt) is the density of the uniformly moving charge).
Finally, we must show that solution of Eq. (5) has the following properties:
- It transforms according to Eq. (2b);
- It describes the Liénard-Wiechert and Coulomb potentials of the uniformly moving
charge in co-moving frame and the laboratory frame respectively.
2. Relativistic solution of the wave equation.
Before starting the procedure of resolution, it must be noted that the wave equation
with the extended source in its rhs cannot be treated as a well defined partial differential
equation, because some physics is hidden there. This physics is that one cannot calculate the
total potential created by the source as the integral of the potentials created by every moving
infinitesimal element of the source. The reason of such a limitation in calculating the sum is
that calculating the sum means collecting some information at the only point. But the speed of
propagation of information is limited by the speed of light c. So during the process of
collection of the whole information about the source, this source displaces itself and actually
we cannot determine from what element of the source information comes at a given instant of
time.
This problem does not exist in pre-relativistic theories because according to them, the
characteristics of the source do not change while going to another frame. But in special
relativity all characteristics of the source, except for the value of the charge, do change.
Formally we could make some suggestions regarding the changes of the parameters, however,
when verifying the foundation of the special relativity, we have to use only quantities which
can be measured directly. Taking into account the problem caused by the finiteness of the
speed of propagation of information, we conclude that we must use the only way to find the
solution in relativistic approach, i.e. we must go to co-moving frame where the source is at
rest. In this frame, collecting information from all elements of the source becomes
170
independent on the speed of propagation of information, because the problem reduces to the
electrostatic task of finding the ϕ potential created by some extended charge. Then one returns
to the original frame so expression for the ϕ potential is transformed too. This expression
must describe the ϕ potential in the original frame. We should expect that all transformations
during this procedure must satisfy to the requirements of relativistic invariance (covariance).
Below we realize this procedure.
According to the arguments given above, we go from the laboratory frame to the comoving frame for the charge where the charge is at rest, so:
 1 ∂2
∂2
∂2
∂2 
4π ρ ′ ( x ′ , y ′ , z ′ )
 2
 ϕ ′ ( x′, y′, z′, t ′ ) =
−
−
−
. (6)
2
2
2
2 
2
2
∂ x′
∂ y′
∂ z′ 
1 − v c  c ∂ t′
1 − v2 c2
1
In opposition to most papers on transformation properties of the electrodynamical
)
(
quantities, we keep the factor
−1
1 − v 2 c 2 in both sides of Eq. (6), in order to show that the
wave equations in two inertial frames differ one from another only by the constant factor. So
the "principle of invariance" is fulfilled for Eqs. (5) and (6).
Because the rhs of Eq. (6) does not depend on the time variable, the lhs should not
depend on t' variable too so this equation reduces to Poisson-like equation (we now omit the
factor
(
1 − v2 c2
)
−1
):
 ∂2
∂2
∂2 

 ϕ ′ ( x ′ , y ′ , z ′ ) = − 4π ρ ( x ′ , y ′ , z ′ )
+
+
2
2
2 
′
′
′
∂
x
∂
y
∂
z


.
(7)
Solution of Eq. (7) is known. It is the Coulomb potential created by the charge being at
rest:
ϕ ′ ( x′ , y ′ , z ′ ) =
∫
ρ ′ ( x1′ , y1′ , z1′ )
dx1′ dy1′ dz1′
r' − r'1
.
(8)
The final step is to return to the laboratory frame. By means of Eq. (2b), the scalar
potential takes the form:
ϕ ( x, y , z , t ) =
ϕ'
1− v c
2
2
=
1
1− v c
2
2
∫
ρ ′ ( x1′ , y1′ , z1′ )
r' − r'1
;
(9)
where the rhs of Eq. (9) should be expressed via the original variables x, y , z, t after
calculating the integral.
But if we analyze the above procedure for the resolution of the wave equation, we find
one strange point. For better understanding, we write step by step the above procedure in
symbolic form. So these steps from Eq. (5) to Eq. (7) can be written as (we re-write Eqs. (2a)
and (2b) as ρ = γ ρ ′ and ϕ = γ ϕ ′ ):
Wϕ = ρ  W ′γ ϕ ′ = γ ρ ′  Wϕ ′ = ρ ′
;
(10)
171
where W is the operator of the wave equation, sign  means "the Lorentz transformations of
the variables (and functions of these variables)" and sign ⇔ means "which is equivalent to".
The second equation in this chain is equivalent to the third equation, since the "wave
1 ∂2
operator" 2 2 − ∇ 2 is invariant under the Lorentz transformations, i.e. W' = W .
c ∂t
The inverse procedure, i.e. transformation of the solution, to the original frame, should
be written in symbolic form as:
ϕ ′ = (W − 1 ) ' ρ ′  γ − 1ϕ = (W − 1 )γ
−1
ρ ⇔ ϕ = (W − 1 ) ' ρ
;
(11)
where W-1 is the inverse wave operator. The chain (11) is correct if the "inverse wave
operator" is transformed, under the inverse Lorentz transformations of the coordinates, as:
(W ) ' = W
−1
−1
.
(12)
;
(13)
But Eq. (12) is incorrect because the integral operator:
W −1 =
1
dxdydz
R− r
∫
is not Lorentz-invariant. So we obtain a strange result, i.e. if one makes inverse Lorentz
transformations of Eq. (8), in analogy with the transformations of Eq. (5), one finds that the
solution for the ϕ potential via the charge density ρ does not maintain its original form when
transforming from one frame to the other. In different words, despite the form of the wave
equation, which is covariant, the solution of this wave equation is not covariant.
The problem can be stated in another way. One is able to calculate the value of the
scalar potential in the laboratory frame by two methods. First, by treating the rhs of Eq. (8) as
some mathematical expression, one can make the inverse Lorentz transformations of both
integrand, taking into account transformation (2) , and the element of volume dV' , and then
calculate the integral. The second way is to calculate the integral in the rhs of Eq. (8), i.e. to
calculate ϕ as a function of x ′ , y ′ , z ′ , and then to make inverse Lorentz transformation to the
variables x, y , z , taking into account that the quantity ϕ transforms according to Eq. (2b) too.
The final results obtained by these two methods are different and this difference is
caused by difference in sequence of mathematical operations used while calculating the
potential. But because the final result cannot depend on the sequence of mathematical
operations (namely, transformation of variables and calculation of the integral), some error
must be hidden in the proof of the covariance of the scalar potential.
This difference actually exists. For example, it is known that the Coulomb potential
ϕ ′ = q ′ R ′ cannot be transformed into the Liénard-Wiechert potential by using the first
method, because, when transforming the charge q', which is invariant (q' = q), and
denominator, one obtains:
ϕ′=
q′
x′ 2 + y′ 2 + z′ 2
ϕ =
q
( x − vt ) 2
1− v c
2
2
+ y2 + z2
;
(14)
172
and the potential given by Eq. (14) is no the Liénard-Wiechert potential of the uniformly
moving charge2.
So, as we have seen above, there is some problem when trying to prove the covariance
of the scalar potential of the single uniformly moving charge. But Lorentz used another
method in proving the covariance of the ϕ potential3. He compared the relativistic solution
(Eq. (9)) with the solution of the wave equation (5) obtained by the method of directly solving
the wave equation [3] (Ch. 18.3), and he showed identity of both expressions. Below we
analyze the method of Lorentz, and prove why these expressions are not identical.
3. Direct solution of the wave equation.
In this Chapter, we consider why Lorentz obtained the relativistic properties for the
Liénard-Wiechert and Coulomb potentials. The solution of Eq. (9), for a charge with spherical
shape in a frame where the charge is at rest, is given by the formula:
ϕ ' ( x' , y ' z ') =
q
r'
.
(15)
This solution is derived by expansion of the denominator in a series of spherical
harmonic functions (Eq. (3.70) of [1]) in a region r > r0 , where r0 is effective radius of the
charge. Since the charge has spherical shape, then all terms of the expansion, except the zero
term, are equal to zero, and so we obtain (15). Inverse transformation of the potential (Eq. (2))
gives:
ϕ ( x, y , z, t ) =
ϕ ' ( x′, y ′, z′ )
1 − v2 c2
=
1
[
q
1 − v 2 c 2 x′ 2 + y′ 2 + z′ 2
]
1/ 2
;
(16)
and after the Lorentz transformation of the coordinates we have:
ϕ ( x, y , z, t ) =
q
1
1
1/ 2
2
2
4π ε 0 1 − v c  ( x − vt ) 2
2
2
+ y + z 

2
2
 1− v c

;
(17)
ϕ ( x, y , z, t ) =
q
4π ε 0
.
(18)
or
1
( x − vt ) 2 +
(1 − v
2
c 2 )( y 2 + z 2 )
The above expression is the well known expression for the LW potential of the
uniformly moving charge. Thus, at least in one case, the relativistic approach gives the correct
result, despite of the breakdown of the Lorentz invariance of the operator (13). Below we
analyze why this is possible. In order to do it, we consider derivation of Eq. (5) by a method
of "direct solution of the wave equations" ([3], Ch. 18.3). In this method, one does not use
Lorentz transformation of the coordinates, but one introduces some physically reasonable
assumptions while solving the wave equation with the source corresponding to uniformly
moving charge. Obviously, the field created by such a source must follow this charge.
173
Therefore, the partial spatial and time derivative are not independent one of another, but they
are linked by the relation:
∂
= − v⋅ ∇
∂t
.
(19)
This relation means that any parameter of the field changes, during the time interval
dt, at the same value as while displacing to the distance –vdt along the direction of motion of
the charge. Taking into account Eq. (19), we are able to transform the wave equation (5) to:

v2  ∂ 2
∂2
∂2 
  1 − 2  2 +
 ϕ ( x, y , z, t ) = − ρ ( x, y , z )
+
2
2 

c
∂
x
∂
y
∂
z



.
(20)
One can see that dependence of the potential on the time disappears in the rhs of Eq.
(20) so actually Eq. (19) corresponds to the Galilean transformation of the coordinates:
x → x − vt ;
y→ y ; z→ z ;
t→ t
.
(21)
;
(22)
By change of variables:
x′ =

1 − v c 
y′ = y


z′ = z


x
2
2
Eq. (20) can be reduced to the ordinary electrostatic Poisson equation:
∇ ′ 2ϕ = − ρ
(
1 − v 2 c 2 x′, y′, z′
)
;
(23)
.
(24)
whose solution is:
ϕ ( x′, y′, z′ ) =
1
4π
∫
ρ ( 1 − v 2 c 2 x1′ , y1′ , z1′ )
r' − r'1
We have in the lhs of Eq. (24) the scalar potential in the laboratory frame which,
however, is still expressed via quantities defined in the co-moving frame. Inverse transition is
made by changing the variables:
1 − v 2 c 2 ( x − vt ) = x ′ 

y = y′


z = z′

.
(25)
So finally, we have for the scalar potential in the laboratory frame two solutions
obtained in relativistic approach and by direct solving the wave equation. For better
understanding, we re-write Eqs. (9) and (24):
174
ϕ =
ϕ =
ρ ′ ( x1′ , y1′ , z1′ )
r' − r'1
;
(26a)
ρ ( 1 − v 2 c 2 x1′ , y1′ , z1′ )
r' − r'1
.
(26b)
1
4π 1 − v 2 c 2
1
4π
∫
∫
Because both the above equations are written for the same potential, we must have:
1
∫
1 − v2 c2
ρ ′ ( x1′ , y1′ , z1′ )
dx1′ dy1′ dz1′ =
r' − r'1
∫
ρ ( 1 − v 2 c 2 x1′ , y1′ , z1′ )
dx1′ dy1′ dz1′ .
r' − r'1
(27)
This will be the basic equation of our further analysis.
4. Analysis of the function describing the charge density.
This equation can be treated as some integral equation for the functions ρ and ρ ′ .
Unfortunately, because these functions belong to different frames we are not able to compare
them4. However, we can get some information about these functions. Since ρ ′ describes a
single charge being at rest, it must be represented by some function with spherical symmetry.
By the way, the function ρ has not such a symmetry5. But in order to satisfy Eq. (27) for any
r ′ , i.e. in such a way that the method of direct solution gives the same results as the
relativistic approach, then it is necessary that the function ρ can be transformed to the form
which has spherical symmetry. This can be easily proven by simple consideration. Actually,
in order to satisfy Eq. (27), one can evaluate only the values of the function ρ defined in a
limited region of the space, i.e. where the charge is located. Formally, the function ρ is
defined in the whole space, however, for calculation of the integrals, only values of this
function defined in limited region are essential. In opposition to this region of internal
variables, the region where r ′ is defined, and it is essential for the calculation of the integral,
is much greater, since it must be the whole space. So the only possibility to choose the true
form of the function ρ is to assume that this function can be transformed (in the integrand of
Eq. (27)) into a symmetric one on the variables x ′ , y ′ , z ′ . Since when v = 0 the function ρ
must degenerate into the function having spherical symmetry for the variables x, y , z , finally
we have the functional equation for this function (we omit the signs "prime"):
[
]
ρ (1 − v 2 c 2 ) x 2 + y 2 + z 2 =
[
Cρ x 2 + y 2 + z 2
1− v c
2
2
]
.
(28)
It can be shown that this functional equation has two only solutions, i.e.:
[
 ρ = C1 exp − ( x 2 + y 2 + z 2 ) σ 2

2
2
2
2
 ρ = C 2 (V ) θ ( x + y + z ) − r0
[
]
]
.
(29)
In the previous formulae C and C1 are some constants, the constant C2(V) does depend
on the volume V of the charge, r0 is the radius of the charge, and θ is the Heaviside step
function. A parameter σ in the first solution of (29) corresponds to some "effective radius" of
the charge. The second solution in Eq. (29) does describe the model of the electron used by
Lorentz, where the charge is represented as a particle with the radius r0 and a uniform charge
175
distribution inside. When this charge moves, its size does contract in the direction of the
motion, and, since the volume of the charge contracts too, the value of the charge density
arises proportionally. After integration over internal variables, this solution yields Eq. (15).
But it is a well established point in classical electrodynamics [3] (Ch. 18.1) that the
only known parameter of the electron is its total charge equal to e, and any calculation of the
EM fields and potentials based on some specific charge distribution inside the electron cannot
be physically meaningful. So one of the fundamental points of the special relativity, i.e. the
proof of the covariance of the scalar potential, is derived by using questionable assumptions.
Actually, both charge distributions (29), necessary for the covariance of the scalar potential,
are forbidden by quantum mechanics. As a matter of fact, quantum mechanics does not allow
the existence of singular distributions (second distribution in Eq. (29) is singular on the
boundary of the electron). But the first distribution in Eq. (29) must be caused by some
potential of oscillatory type. However, it is not physically sound to suggest that the internal
force (Poincaré tension) arises proportionally with the distance (in this case, the internal force
would yield the potential of oscillatory type).
We should remark at last that in classical electrodynamics, the elementary charge is
described by some singular distribution, i.e. by the Dirac δ-function. It is known that this
distribution has some representation, and despite the multitude of these representations, the
final result cannot depend on the specific representation chosen to describe the elementary
charge. However, we have that only the two specific representations (29) do satisfy the
condition which is required on the shape of the charge in order that the scalar potential created
by the charge of a given shape is relativistically covariant. So the existence of only two
specific representations for the δ-function, instead of the existence of the whole multiplicity
of them, in order to provide for the covariance of the expression for the scalar potential, must
be mathematically incorrect.
In conclusion, we obtain that the only relativistically correct method of establishing
the connection between the LW and Coulomb potentials is relativistically non-invariant itself.
Therefore, the relativistic connection (2b) between these potentials derived by Lorentz looks
like an artefact, which is conditioned by applying the point like approximation (29b) of the
elementary charge. But if we consider the connection between the LW and Coulomb
potentials in a strictly mathematical way, and at very small distance, we obtain that Eq. (2b) is
wrong. Therefore, the scalar potential cannot be treated as the zero-component of a relativistic
four-vector.
Notes
1
Despite of this, in most textbooks on classical electrodynamics, relativistic covariance of the scalar
potential is treated as a fact which does not need any proof. For example, in [1] (Ch. 11.9) it is noted
that covariance of the vector and scalar potential follows from the covariance (invariance)
requirements to all electrodynamical quantities. In [2] (Sec. 16), it is written without any explanations
that the vector and scalar potentials form relativistic four-vector.
2
The derivation of the LW potential from the Coulomb potential given in [2] (Sec. 63) is incorrect.
Actually, while applying the Lorentz transformation to the lhs of chain (14), it is illegal to change the
spatial quantity R' by c(t' - t1'). As a matter of fact, R' = c(t' - t1') is some equation, but not an identity.
3
Actually, Lorentz operated with the fields but not with the potentials, however, the method is the
same.
176
4
It is the main trouble of the special relativity that it is impossible to compare quantities which belong
to different frames.
5
This function must describe the charge contracted in the direction of the motion.
References
[1] - J. D. Jackson, Classical Electrodynamics, 2nd edn (New York: Wiley, 1975).
[2] - L.D. Landau and E.M. Lifshitz, The Classical Theory of Field, (Pergamon, Oxford,
1975).
[3] - W. K. H. Panofsky and M. Phillips, Classical Electricity and Magnetism, (NY, 1955).
----Vladimir Onoochin was born in Gorgii region, Russia, in 1953. In 1990 he
took a PhD degree in Physics at Ioffe insititue, St. Petersburg. He is actually the
manager of radiophysics (spectrometers) project at Sirius Ltd, Moscow. His
main areas of interest are: Electrodynamics of short ultrawideband (UWB)
current and EM pulses; Development of the measurement equipment and
measurement of the powerful EM pulses in 1 to 150 GHz frequency range;
Pulsed power devices. Special points of interest are even some problems in
classical electrodynamics usually omitted by mainstream physics, such as
penetration of the EM fields through metallic shields, longitudinal EM waves
and properties of the EM potentials in different gauges, etc.. To these topics the
author has dedicated many research papers.
"Vladimir Onoochin" <[email protected]>
177
Simmetrizzazione delle equazioni di Maxwell
con l'introduzione del campo gravitazionale,
un'idea bizzarra?
(Sabato Scala)
Introduzione
Sono passati circa 15 anni da quando, con un carissimo amico oltre che compagno di studi,
affrontammo la preparazione dell'esame di Campi Elettromagnetici con il simpaticissimo oltre
che preparatissimo prof. Giorgio Franceschetti.
Fu proprio da una accattivante introduzione al suo libro dedicato a questa affascinante e
complessa materia, che, un po' per gioco, nacque l'idea bizzarra che voglio proporre al
paziente lettore.
Il tempo passato e la ruggine accumulatasi per effetto della mia attuale professione
interamente centrata sullo sviluppo software ben distante dai miei passati interessi, potrà farmi
compiere più di un errore per i quali chiedo venia tenendo soprattutto conto che quanto
propongo vuole essere semplicemente ciò che fu allora: un complesso gioco di fantasia.
Onestà vuole, anche per inquadrare nella corretta luce il presente articolo, che narri anche del
piccolo retroscena che ispirò l'idea di fondo del nostro "gioco" fisico-matematico.
Era appena uscito un volumetto di fanta-storia estremamente affascinante dedicato al famoso
"Esperimento Philadelphia". La storia mai confermata dai vertici militari americani, narra di
un esperimento svoltosi alla fine del 1945 che, nelle intenzioni degli studiosi che vi presero
parte, avrebbe dovuto consentire la "deviazione" della luce con la conseguente
mimetizzazione di un qualsiasi oggetto consentendo, in pratica, di vedere ciò che si trovava
dietro di esso e quindi rendendo invisibile l'oggetto frapposto.
Il libretto, estremamente ben congegnato con tanto di "soffiate", di "scienziati dissociati",
interviste, esperimenti preparatori, ecc., non sembrava affatto scritto da un semplice
giornalista ma da qualcuno che aveva una conoscenza notevole di fenomeni elettromagnetici.
Eppure qualcosa non quadrava: nel libro c'era praticamente tutto ciò che serviva per una
succosa ricetta di fanta-fisica, ma senza la necessaria conclusione.
L'idea di fondo, del testo, era basata sulla adozione di un campo elettromagnetico prodotto in
una apparato contenuto in una misteriosa sfera, collegato ad un alternatore ed impiantato sulla
nave che nel libro aveva il nome di Eldridge.
Il nome, che nel libro si dice sia stato attribuito all'esperimento dagli allora vertici militari
americani, è "Rainbow Experiment".
La cosa che ci affascinò non fu tanto lo straordinario esito dell'esperimento - che provocò, a
detta dell'autore, la reale sparizione della nave - ma i sub-effetti di quell'esperimento, narrati
dall'autore con chiaro sensazionalismo e gusto dell'orrido.
La nave sparisce, ma compare in un porto a vari chilometri di distanza e in pochi istanti,
ritorna al suo posto. Alla sua riapparizione i marinai sono, in parte impazziti, in parte fusi con
la materia del vascello, in parte scomparsi del tutto.
Altra cosa interessante è la narrazione puntigliosa degli esperimenti che precedono quello
definitivo, fatta utilizzando condensatori con dimensioni dell'ordine del metro, bobine giganti,
e alternatori appositamente realizzati, il tutto condito con segnalazione delle frequenze di
alimentazione, della capacità dei condensatori, della entità delle correnti impiegate, ecc.
Tra gli effetti segnalati c'è il sollevamento degli apparati, la loro vibrazione e oscillazione con
frequenza pari a quella dell'alternatore ecc.
178
Insomma il tutto, anche se mai in alcuna parte del testo viene riportato, sembra chiaramente
dovuto alla generazione di un campo gravitazionale collegato ai campi elettrici e magnetici ad
alta frequenza utilizzati per alimentare gli apparati.
La variazioni nello spazio-tempo, anche se mai viene detto nel libro, sembrano dovute proprio
agli effetti di un gigantesco campo gravitazionale tale da provocare la deviazione delle onde
elettromagnetiche luminose intorno alla nave.
Per dirla in sintesi, sebbene il testo non ne faccia mai riferimento, esso descrive gli effetti del
sogno dei fisici di quegli anni (1945): l'unificazione dei campi.
La simmetrizzazione
Da qui veniamo a questa bislacca idea e alla ispirazione venutaci dal libro del prof.
Franceschetti, che nulla mai seppe di questo nostro "gioco", visto il motivato timore di
"saltare" la seduta d'esami per eccesso di "stupidità".
Prima di tutto andiamo all'oggetto del contendere: le equazioni di Maxwell, vediamole nella
forma differenziale:
1) ∇ . D = ρ
2) ∇ . B = 0
3) ∇ × E = -
∂B
∂t
4) ∇ × H = J +
∂D
.
∂t
Franceschetti faceva notare nel suo libro l'anomalia costituita dalla mancanza di simmetria del
sistema di equazioni, evidente nell'assenza nella equazione 2) di un equivalente della densità
di carica elettrica ρ che si trova nella equazione 1) , e nella equazione 3) di un equivalente
della densità di corrente J che si trova nella 4) , per non dire dei segni con cui appaiono le
due derivate temporali, una volta meno e una volta più.
L'asimmetria ha un effetto fisico evidente che si rileva integrando la 1) e la 2):
∫∫∫
(∇ . D)dV = Q
∫∫∫
(∇ . B)dV = 0 .
In pratica, mentre esiste in natura una entità chiamata "carica elettrica" (Q) , in grado di
generare un campo le cui linee partono a raggiera da essa, lo stesso non si può dire per il
campo magnetico, poiché non sembra esistere in natura la "carica magnetica".
Nel libro si ipotizza esistente la carica magnetica ρm e si perviene alle seguenti equazioni:
1') ∇ . D = ρ
2') ∇ . B = ρm
3') ∇ × E = Jm -
∂B
∂t
179
4') ∇ × H = J +
∂D
.
∂t
In esse è stata introdotta, come dicevamo, una ipotetica densità di carica magnetica ρm e la
corrispondente densità di corrente magnetica Jm . Non esistendo il primo dei due termini (o
quantomeno non essendo mai stata trovata la carica magnetica) risulta inesistente e quindi
inessenziale anche il secondo.
Unica anomalia nella simmetria, resta il segno meno nella derivata parziale rispetto al tempo
per il vettore B.
Da questa e da altre scarne osservazioni, tra cui l'einsteiniana "Dio non gioca a dadi!", ci
ponemmo il problema di un possibile intervento di simmetrizzazione sulle equazioni che,
però, includesse anche il campo gravitazionale.
Cominciamo a far osservare le analogie tra il campo elettrico e gravitazionale partendo dalla
legge di Coulomb che descrive l'intensità dell'interazione tra due cariche elettriche:
Fq =
1
4π ε
0
Q1 Q2
r2
ove ε0 = 8,854188 x 10–12 Kg–1m–3s2C2 .
Questa espressione, formalmente, è simile all'intensità della forza di gravità che agisce tra due
masse:
Fg = G
M1 M 2
.
r2
Dalla equazione della forza di Coulomb si ricava quella del campo elettrico (scalare):
Eq =
1
4π ε
0
Q
,
r2
mentre da quella della forza di gravità si ricava l'analoga espressione per il campo
gravitazionale (scalare):
X = G
M
.
r2
A questo punto, supponendo di voler creare un campo elettrico equivalente a quello
gravitazionale, introducendo una carica "equivalente" alla massa, uguagliando le forze
dovremmo far uso di un'equazione del tipo seguente:
Qmequiv = κ0 M ,
ove κ0 sarà una costante tale che κ02 = 4πε0 G .
Ricordando che G = 6,670 x 10-11 Nm2Kg-2 , si ottiene:
κ0 = 4,306 x 10-10 CKg-1 .
Introduciamo quindi una densità di carica equivalente ρmequiv definita come:
180
ρmequiv = κ0 ρk ,
ove ρk = densità di massa per unità di volume.
Per esprimere un'equazione formalmente analoga a quella del campo prodotto da una carica
elettrica anche per il campo gravitazionale è necessario introdurre anche un termine omologo
all'ε0 , che chiameremo ζ0 , definito ovviamente dalla:
ζ0 = κ0 / 4πG .
La precedente equazione del campo gravitazionale (scalare) assume, quindi, la seguente forma
(dove abbiamo abbreviato mequiv in meq):
X =
1
4π ζ
Qmeq
0
r2
.
Ricordando la relazione tra il vettore D e il vettore E , campo elettrico nel vuoto (all'interno
di altri materiali è necessario moltiplicare per una costante ε tipica dello specifico materiale):
D = ε0 E ,
per analogia definiamo un omologo vettore
gravitazionale:
R
associato al vettore
X
del campo
R = ζ0 X .
A questo punto possiamo scrivere le equazioni del campo gravitazionale in forma
differenziale, indicando, come detto dianzi, con ρk la densità di massa:
5) ∇ . R = κ0 ρk = ρmeq
6) ∇ × X = 0 .
La seconda equazione si ricava ricordando che il campo gravitazionale è irrotazionale
(conservativo), in pratica il lavoro che si compie muovendosi lungo un percorso chiuso è
nullo (il lavoro lo si ottiene integrando la 6) ).
Fin qui nulla di nuovo, salvo una forma diversa per le equazioni del campo gravitazionale.
Ora supponiamo per un attimo che le equazioni di Maxwell possano essere messe insieme a
queste aggiungendo qualche termine di collegamento. Supponiamo anche che la forma delle
equazioni di Maxwell contenga già la "forma" in cui appariranno tutti i termini di
collegamento. Intendiamo con ciò dire che ci dovranno essere dei termini omologhi dei
∂D
termini J ,
che appaiono nelle predette equazioni. Questo vuol dire che dovremo
∂t
introdurre, ove manca, un termine Jk omologo della densità di corrente elettrica J , ed un
altro termine gravitazionale omologo del termine (differenziale) corrispondente al contributo
del vettore D . Il tutto andrà fatto supponendo che il termine differenziale per il vettore R
dovrà comparire con segni alternati + e – , in modo che il complesso delle equazioni presenti
una certa simmetria matematica. Fermi mantenendo i termini ρm e Jm già introdotti da
Franceschetti e comunque inessenziali (a valore nullo), a causa della inesistenza della carica
181
magnetica, non resta che introdurre una densità di corrente di massa Jk che si affiancherà alle
densità di corrente J e Jm . In buona sostanza i termini nuovi che affiancheremo a quelli già
presenti a destra del segno di uguaglianza nelle equazioni di Maxwell - nella forma con gli
∂R
apici - saranno Jk e una sorta di densità di corrente di massa di spostamento
. Bisogna
∂t
anche tenere ovviamente conto della necessaria omogeneità dimensionale delle quantità
fisiche che si sommeranno tra loro, per il che sarà necessario introdurre, oltre alla costante
κ0 , anche un'altra costante λ0 , che ragioni di "simmetria fisica" fanno presumere di poter
definire come:
λ0 =
1
µ
= 0 c ~ 30 Kg m2C-2s-1 ,
4π ε 0 c
4π
ove c =
1
ε0µ0
è la velocità della luce nel vuoto ( µ0 indica, come usuale, la permeabilità
magnetica).
In definitiva, ecco come si presenterebbero le equazioni unificate ottenute per estensionesimmetrizzazione di quelle di Maxwell con l'introduzione del campo gravitazionale:
7) ∇ . D = ρ
8) ∇ . B = ρm
9) ∇ . R = ρmeq
10) ∇ × E = λ0(Jk +
11) ∇ × H = J +
∂R
∂B
) - Jm ∂t
∂t
∂D
∂R
- Jk ∂t
∂t
12) ∇ × X = κ0(Jm +
∂B
∂D
) - κ0λ0(J ).
∂t
∂t
Dalle equazioni si vede come i tre termini di corrente, uno per ciascuno dei 3 campi,
compaiono alternativamente nelle 10), 11) e 12) insieme ai termini differenziali dei tre campi
R , D , B (che appaiono sotto forma di derivate parziali rispetto al tempo), con i segni più e
meno in forma ciclica. Questa ipotesi di simmetrizzazione spiegherebbe anche l'anomala
presenza del segno meno nelle equazioni già ampliate da Franceschetti con l'introduzione dei
termini magnetici.
Non resta che verificare se:
a) le equazioni producono effetti che non hanno a quel che si sa un equivalente fisico,
nel qual caso il nostro discorso cadrebbe senz'altro;
b) le equazioni generano effetti che hanno qualche rispondenza in fenomeni noti ma
non ancora spiegati, o ne prevedono di ancora non noti che potrebbero però essere reali.
182
In pratica non resta che verificare la "sostenibilità" del precedente sistema di equazioni nel
mondo reale, dopo di che "divertirsi" a dedurne eventuali effetti pratici ancora sconosciuti.
Coerenza delle equazioni con fenomeni fisici osservati
Cominciamo con considerazioni di carattere generale.
In assenza di correnti di massa e di variazioni del campo gravitazionale le equazioni classiche
∂R
di Maxwell restano invariate poiché: Jk = 0 e
=0.
∂t
Ferma restando la costanza della massa nelle normali situazioni sperimentali, le variazioni
possono esser dovute unicamente ad azioni dinamiche e quindi a movimenti di masse (flussi
di massa).
Quali sono le masse in movimento, coinvolte nei fenomeni elettromagnetici?
Sappiamo che la corrente elettrica è dovuta ad un flusso di elettroni all'interno di campi
elettromagnetici, di conseguenza un flusso di elettroni produce sia una corrente elettrica
grazie alla carica dell'elettrone, sia una "corrente di massa", grazie alla massa dello stesso
elettrone. Calcolando la divergenza della 11) , e ricordando che la divergenza di un rotore è
sempre uguale a zero, si ha:
∂D
∂R
) - (∇ . Jk) - (∇ .
) =
∂t
∂t
∂ (∇ . R)
∂ (∇ . D )
= (∇ . J) +
- (∇ . Jk) = 0,
∂t
∂t
∇ . (∇ × H) = (∇ . J) +(∇ .
la quale diventa, in virtù delle equazioni 7) e 9) :
(∇ . J) +
∂ ρ meq
∂ρ
- (∇ . Jk) = 0.
∂t
∂t
Passando all'integrale di superficie si ottiene:
I+
∂ Qmeq
∂Q
- Ik = 0.
∂t
∂t
In questo caso sembrerebbe negata la legge di conservazione della carica elettrica, che si
esprime nella seguente formula:
I = -
∂Q
,
∂t
ma si ottiene una sorta di conservazione di "carica totale":
13)
I - Ik = -
∂ Q ∂ Qmeq
+
.
∂t
∂t
Ricordiamo inoltre che, essendo la massa dell'elettrone pari a: me = 9,1091 x 10-31 Kg , e il
termine moltiplicativo 4πε0G pari a: 1,8544 x 10 -21 Kg–3m-1s2C2N , per la quantità totale di
massa di elettroni che attraversano la sezione del conduttore nell'unità di tempo si ottiene un
termine moltiplicativo dell'ordine di grandezza di un 10 -51 che, per quanto numerosi siano gli
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atomi all'interno di detta sezione, rende totalmente irrilevante da un punto di vista quantitativo
il termine correttivo nella precedente legge di conservazione della carica totale.
Poniamoci, ora, nella ipotesi di assenza di cariche coulombiane in movimento (corrente
elettrica), e di presenza di un campo magnetostatico. L'equazione di conservazione della
carica totale prende adesso questa forma:
14)
Ik = -
∂ Qmeq
∂t
.
Ricordando ancora una volta il valore numerico della costante moltiplicativa 4πε0G , quando
una massa di 1 Kg attraversa una superficie unitaria in 1 secondo, si otterrebbe una corrente di
"massa equivalente" pari a 6,18 10-21 A, praticamente non misurabile. Questo conferma
l'applicabilità del principio di conservazione della carica coulombiana come ottima
approssimazione della equazione generale della conservazione della carica totale anche in
presenza di masse in movimento.
Altra legge che parrebbe violata è quella della irrotazionalità del campo elettrico in un campo
magnetostatico che si ricava integrando la 10) :
∫
E . ds = λ0Ik .
In buona sostanza si otterrebbe la previsione che una massa in movimento produce un campo
elettrico perpendicolare alla direzione del movimento, e disposto con simmetria circolare
intorno alla massa. Ovvero, che mettendo una massa in movimento attraverso una spira chiusa
si produce un campo elettrico nella spira, e quindi una corrente.
L'osservazione fatta in precedenza, però, ci porta ad affermare che la irrotazionalità del campo
elettrico in un campo magnetico statico resta sostanzialmente valida, cioè con buona
approssimazione, fintantoché non entrano in gioco masse in movimento dell'ordine di 10 12
tonnellate, in grado di produrre, correnti di 1 micro Ampere.
In altre parole, ammettendo per un attimo che le equazioni siano valide, non si può ottenere
corrente apprezzabile semplicemente facendo passare per esempio dell'acqua all'interno di un
tubo.
Un problema serio è invece posto dalla 12) , che nega la irrotazionalità del campo
gravitazionale (vedi 6) ) in presenza di campi elettrici e magnetici non statici, ferma restando
la inesistenza di correnti magnetiche create da un monopolo magnetico, e quindi l'identità J m
= 0 . La 12) prevede nuovi inattesi fenomeni fisici, perché, se è vero, come abbiamo appena
visto, che gli effetti dei moti di masse su campi elettrici e magnetici sono sostanzialmente
inapprezzabili, viceversa per quelli dei campi elettromagnetici sui moti delle masse (sul
campo gravitazionale) sarebbe vero esattamente il contrario.
Effetti delle equazioni unificate sulla possibilità di creare un campo gravitazionale a
partire da campi elettromagnetici
Vediamo come si trasforma la 12) scrivendola in forma integrale:
15)
∫
X . ds = - κ0λ0 I + κ0
∂
∂
(flusso di B) - κ0λ0
(flusso di D) .
∂t
∂t
184
Supponiamo di voler realizzare un apparato elettromagnetico che sfrutti la 15) per generare un
campo gravitazionale opposto a quello terrestre, in pratica un apparato elettromagnetico per la
levitazione gravitazionale.
Considerando i termini al secondo membro, ci vengono offerte due possibili vie:
1 - Sfruttare il termine di corrente e quindi adoperare una corrente continua.
2 - Sfruttare i termini di flusso elettromagnetico e quindi adoperare generatori di corrente
alternata in grado di generare campi elettromagnetici tempovarianti.
La prima soluzione parrebbe quella più abbordabile anche per la semplicità degli apparati
composti da un generatore di corrente continua ed una bobina.
Sarebbe, infatti, sufficiente far circolare una corrente opportuna, in una spira circolare per
produrre un campo gravitazionale orientato perpendicolarmente al campo della spira e, quindi,
in grado di farla sollevare.
La presenza del termine moltiplicativo κ0λ0 , purtroppo, rende impraticabile questa soluzione.
Supponendo, infatti, di essere in presenza di campi elettrostatici, e considerando il campo X
prodotto costante in intensità e direzione lungo il piano della spira (questa è in realtà solo una
approssimazione, in quanto il campo gravitazionale è perfettamente verticale al piano della
spira solo al centro di essa, mentre tende a ruotare intorno al conduttore quando ci si allontana
dal centro) la 15) può essere scritta come segue:
X
∫
ds = X 2πR = κ0λ0 I ,
da cui:
X = κ0λ0 I/2πR .
A questo punto, ricordando che g = 9,8 m s -2 (ovvero N/Kg) è l'accelerazione di gravità media
sulla terra, e supponendo di disporre di una spira di raggio R = 1 m , se ne ricava che la
corrente necessaria per produrre il sollevamento sarebbe pari a:
I = 6,28 x 9,8 / (30 x·4,306 x 10-10) = 4,76 109 Ampere ,
che è purtroppo un valore del tutto incompatibile con la dissipazione per effetto Joule che
affligge i tradizionali conduttori, oltre che una corrente difficilmente generabile.
Il problema potrebbe forse essere risolto nell'ambito della tecnologia dei superconduttori, ma
vogliamo vagliare alternative differenti e tecnologicamente più agevoli. Ripieghiamo, quindi,
sull'uso di campi elettrici e magnetici tempovarianti, soffermando la nostra attenzione sul
termine legato alle variazioni nel tempo del flusso magnetico. Anche in questo caso, per poter
generare un campo X opposto alla direzione della attrazione gravitazionale terrestre, si può
pensare di ricorrere ad una spira "magnetica" circolare di raggio r , e nuovamente
supporremo X costante (indipendente cioè da ds , pur consci del fatto che questa
approssimazione è valida solo nei pressi del centro della spira). Nell'attuale ipotesi il campo
X ha una direzione ortogonale al piano della spira e dipende unicamente dal tempo, essendo
indotto dal flusso dei campi elettromagnetici tempovarianti. Estraendo X(t) dall'integrale a
sinistra della 15), tale termine diviene pari a: 2πr X(t) . A questo punto non resta che
progettare la spira magnetica in grado di produrre le variazioni di campo che appaiono a
destra della equazione 15).
Per generare un campo siffatto possiamo pensare di adoperare un solenoide toroidale avvolto
su ferro. Questo accorgimento ci consente di "amplificare" l'effetto del termine µ0
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(permeabilità magnetica nel vuoto, che vale 1,2566 x 10 -6 m Kg C-2), che nel nostro caso va
moltiplicato per un termine aggiuntivo µr , una costante pura che per il ferro ha un valore di
circa 800. Indicheremo con µferr = µ0 µr il termine che sostituisce la permeabilità magnetica
nel vuoto, per avvolgimenti su ferro. Vediamo subito perché un simile dispositivo potrebbe
rispondere, in linea di principio, alle nostre esigenze. Ogni spira dell'avvolgimento genera,
percorsa da corrente, un campo magnetico ortogonale alla spira. Possiamo avvolgere le spire
seguendo il "cerchio magnetico" che desideriamo realizzare. Ciò che si ottiene è, appunto, una
bobina a forma di toro circolare. Indichiamo con N s il numero di spire che formano la
bobina, con R il raggio del toro e con r il raggio di ciascuna delle spire minori che avvolte
formano il toro, e passiamo a calcolare il campo magnetico indotto dalla corrente I(t) .
Partendo dall'integrale della 11) , calcolato nella ipotesi che D ed ed R siano costanti, si ha:
∫
H . ds = I(t) .
Questa equazione è applicabile a ciascuna delle spire circolari che formano l'avvolgimento.
Le linee del campo H divengono, per simmetria, circolari e coassiali e quindi il campo
scalare H complessivo indotto è pari a:
H(t) = Ns I(t) / 2πr ,
da cui:
B(t) = µferr H = µferr Ns I(t) / 2πr .
Se utilizziamo un generatore di corrente alternata con pulsazione ϖ0 si ottiene per la I(t)
l'espressione sinusoidale: I(t) = I0 sin(ϖ0t) , e quindi:
B(t) = µferr H = µferr Ns I0 sin(ϖ0t) / 2πr .
A questo punto torniamo alla 15). Sappiamo che con correnti ordinarie il primo termine di
corrente, a sinistra, può essere trascurato; inoltre trascuriamo, per ora, anche la derivata
parziale di D rispetto al tempo, che andrà comunque riportata in conto alla fine del calcolo,
poiché questa componente nasce per induzione ogni qual volta si generano campi magnetici
tempovarianti, ed è inseparabile da essi (con la conseguenza che il rendimento complessivo
del nostro "motore antigravitazionale" cala considerevolmente, tenuto conto del fatto che il
lavoro associato al generatore del campo gravitazionale verrà in parte dissipato dalla
resistenza del conduttore ed in parte impiegato per la generazione del campo indotto ma
indesiderato D ). Ecco la forma che prende l'equazione, ferma restando l'ipotesi di
indipendenza di X(t) da ds :
2πR X(t) = κ0
∂
(flusso di B) .
∂t
Applicando ad essa il valore (scalare) di B(t) prodotto dal toro circolare si ottiene:
2πR X(t) = [κ0 µferr Ns I0
∂
sin(ϖ0t)] / 2πr .
∂t
Da qui si ottiene:
4π2 rR X(t) = κ0 µferr Ns I0 ϖ0 cos(ϖ0t) ,
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e quindi in definitiva:
16)
X(t) = κ0 µferr Ns I0 ϖ0 cos(ϖ0t) / 4π2 rR .
Per avere un'idea di come vanno quantitativamente le cose, supponiamo di utilizzare un toro
di raggio R = 6 m , avente sezione circolare di raggio r = 0,005 m , e conduttori a sezione s
= 0,001 m (sicché il numero di spire massimo ottenibile con un solo avvolgimento sarà: N s =
2πR / s = 37700 ). Un siffatto toro avrà un volume pari a:
V = πr2 x 2πR = 2 π2 r2 R = 2,95 x 10-3 m3 ,
e una massa che si deduce dal valore precedente moltiplicandolo per la densità del materiale
di composizione. Sebbene l'avvolgimento sia su ferro, mentre il materiale di conduzione
sarebbe, in generale, di rame, supporremo per semplicità che tutta la struttura toroidale sia in
ferro, sicché, indicata con Dferr la densità volumetrica di questo materiale, che considereremo
pari a 9,7 103 Kg/m3 , la massa complessiva risulterà pari a M = Dferr V = 28,7 Kg .
Tornando al nostro punto, per sollevare il toro sarà necessario produrre un valore massimo di
X(t) (che si ottiene considerando la condizione di picco del coseno, cioè quando questo
raggiunge il suo valore massimo pari ad 1) pari al richiamato valore "critico" 9,8 N/Kg .
Possiamo ricavare quindi la necessaria frequenza di alimentazione partendo dall'espressione
del campo prodotto:
X = κ0 µferr Ns I0 ϖ0 / 4π2rR = 9,8 ,
la quale implica:
ϖ0 = 2πf = 4π2rRX / κ0 µferr Ns I0 (f = frequenza) ,
ovvero:
f = 2πrRX/κ0 µferr Ns I0 .
Ricorrendo ad una corrente di 1 Ampere si ottiene, per il generatore di corrente, che la
frequenza di alimentazione necessaria per il sollevamento è di circa 110 Mhz.
Ci sarebbe però un altro problema da risolvere. Essendo la corrente alternata di tipo
sinusoidale, più che sollevarsi, il nostro veicolo sarebbe soggetto ad una vibrazione verticale
di altissima frequenza, quale quella precedentemente stimata. L'alimentatore del sistema non
può essere quindi puramente sinusoidale, ma andrebbe adoperata, semmai, una sinusoide
raddrizzata con le "gobbe" troncate al primo quarto. L'operazione di "raddrizzamento" della
sinusoide si può ottenere con l'uso di un ponte di raddrizzamento e di un filtro opportuno.
Ecco una immagine dell'apparato proposto:
187
Si porrebbe, a questo punto, pure la questione dello spostamento dell'eventuale macchina
volante nelle diverse direzioni. Una possibile soluzione sarebbe quella di costruire una cupola
tale che le linee di forza del campo gravitazionale prodotto siano, punto per punto, ortogonali
ad essa. Sulla cupola, poi, andrebbero alloggiati gli apparati per produrre il campo
gravitazionale di compensazione. Un'idea potrebbe essere quella di ricoprire la cupola con
una serie di solenoidi toroidali compositi di piccole dimensioni, ma si potrebbe anche tentare
di utilizzare il campo elettrico, e quindi l'ultima componente della 15), approfittando inoltre
del "piccolo" vantaggio offerto dal fattore moltiplicativo λ0 . La soluzione proposta consente
di creare da un lato lo spostamento dell'apparato in qualunque direzione, dall'altro consente di
riutilizzare i piccoli solenoidi toroidali per ridurre le vibrazioni del "velivolo", alimentandoli,
magari, con una corrente sfasata di 90 gradi rispetto a quella che alimenta il solenoide
toroidale principale. Ecco un'immagine dell'apparato proposto in sezione:
Non è difficile riconoscere, nella macchina, la classica forma a sfera schiacciata di un UFO, e
non può, sempre rimanendo nel fantastico, non tornare alla mente l'apparizione dei primi di
questi oggetti intorno agli anni 50. Il vero problema è che la frequenza di alimentazione
sembra difficilmente compatibile con la tecnologia dell'epoca, quindi il mistero resta, anche
se è interessante notare che questo tipo di apparecchio potrebbe produrre effetti molto simili a
quelli che solitamente vengono associati agli avvistamenti di UFO, vediamone alcuni.
L'elevata frequenza genera correnti indotte, e quindi può provocare bruciature o carbonizzare
188
composti biologici (piante, animali, etc.) che si avvicinino all'apparato in funzione,
esattamente come accade in un forno a microonde. La gravità inversa prodotta dall'oggetto
provocherebbe una forza repulsiva gravitazionale nella parte inferiore di esso, e quindi lo
schiacciamento di superfici (ad esempio manto erboso) pur senza che il sistema vi si sia
fisicamente poggiato. La parte superiore della sfera, invece, presenterebbe una forza
gravitazionale attrattiva che produce una compressione dell'aria con conseguente
riscaldamento, rendendo possibili anche fenomeni di luminescenza. La compressione dell'aria
indotta nella parte superiore potrebbe a sua volta provocare fenomeni di diffrazione, rendendo
vaghi i contorni dell'ipotetico veicolo.
Infine, il sistema può interferire con sistemi elettronici, provocando disturbi radio o inducendo
correnti tali da distruggere gli strumenti, o bloccarne temporaneamente il funzionamento.
Possono, in questo caso, venire in mente i blocchi dei motori di normali autoveicoli, spesso
segnalati nel corso di avvistamenti, a causa della interferenza per induzione elettromagnetica
con le bobine degli spinterogeni.
L'esperimento Rainbow: possibile?
Visto che ci siamo già "screditati" abbastanza agli occhi del paziente lettore, arrivando a dare
una "spiegazione" razionale alle fantasticherie ufologiche, perché non ritornare alla fantasia
primitiva da cui eravamo partiti?
Veniamo, quindi, all'esperimento Rainbow che ci ispirò, quasi oltre 15 anni fa, le bizzarrie
che abbiamo esposto. Da un punto di vista puramente teorico, disponendo i solenoidi su una
sfera, anziché su una cupola, come per il famoso esperimento, si potrebbe generare un campo
antigravitazionale centrato sul centro della sfera. Se, in linea di principio, i solenoidi sono
alimentati ad alta frequenza e con intensità di corrente elevate, il campo antigravitazionale
potrebbe provocare una deviazione della luce verso l'esterno del campo, e non verso l'interno
come accade, ad esempio, nei pressi di un campo gravitazionale tradizionale ed attrattivo
intenso quale quello di un buco nero.
Inutile dire che, proseguendo sulla via di speculazioni quasi fantasiose, ci sarebbero effetti
anche sullo spazio-tempo. Sempre in teoria, mentre nei pressi di un campo gravitazionale
attrattivo di notevoli dimensioni il tempo scorre più lentamente, in un campo
antigravitazionale artificiale il tempo scorrerebbe più velocemente, facendo apparire "il
mondo esterno" praticamente fermo. La stravaganza considerata consentirebbe lo spostamento
della nave a velocità che per il mondo esterno sarebbero pressoché istantanee! Esisterebbero
anche delle ulteriori particolari anomalie, dovute alla distanza dal centro della sfera che
produce il campo. Infatti, il tempo, evidentemente, scorrerebbe più veloce man mano che ci si
avvicina al centro della sfera, come dire in buona sostanza che l'interno della sfera
viaggerebbe più velocemente della parte esterna della nave, con conseguenze difficili da
immaginare.
Altro, straordinario, risultato sarebbe la possibilità di costruire una macchina del tempo che,
vista la possibilità di generare campi gravitazionali inversi, potrebbe scorrere al contrario
consentendo viaggi nel passato, e non solo quelli nel futuro già contemplati dalla relatività
einsteniana!!
Soltanto un'idea bizzarra?
E' con mia somma meraviglia che, solo pochi giorni or sono, durante una delle mie
peregrinazioni attraverso le autostrade telematiche, mi sono imbattuto in una sconcertante
teoria, peraltro estremamente ben congegnata, e con basi logiche che vanno assai oltre la mia
semplice idea di simmetrizzazione. Ebbene, la teoria espone risultati ed equazioni non molto
dissimili da quelle illustrate in questo lavoro. Essa porta il nome del fisico tedesco Burkhard
189
Heim (scomparso, purtroppo, il 14 gennaio del 2001), ed è reperibile in linea al seguente
indirizzo:
http://www.mufon-ces.org/docs/heimphysics.pdf ,
relativo al documento: The Physics of Burkhard Heim and its Applications to Space
Propulsion, by Illobrand von Ludwiger, M.Sc., realizzato per la presentazione al primo
Workshop Europeo sulla Field Propulsion, 20-22, Gennaio 2001, University of Sussex,
Brighton, GB.
Sintetizzarla in maniera corretta è pressoché impossibile, ma possiamo delineare le linee di
fondo ed il percorso logico seguito da Heim. L'obiettivo che si è posto lo scienziato è stato
quello di comprendere se le equazioni della Relatività Generale di Einstein potessero essere
combinate e rese compatibili con quelle della fisica quantistica, adottando opportuni
accorgimenti matematici ed in particolare una apposita matematica che fosse in grado di far
transitare dallo spazio dei tensori della fisica dei sistemi macroscopici a quello della
quantizzazione dello spazio-tempo, e quindi a ciò che Heim chiama spazio dei "selettori" per
la fisica quantistica. Il tutto senza interruzioni o rotture, ma con un unico sistema di equazioni.
Ebbene, Heim non solo riesce nel suo intento, ma lo fa introducendo uno spazio ad 8
dimensioni ove, alle 4 tradizionali (3 per lo spazio ed una per il tempo) se ne aggiungono altre
4 virtuali. Uno spazio che potremmo definire "spazio delle configurazioni", ove sono allocate
tutte le possibili forme della realtà, le dimensioni aggiuntive facendo riferimento al piano che
descrive la probabilità dei cambiamenti di stato. Le equazioni spiegherebbero non solo la
possibilità di considerare la Relatività e la Meccanica Quantistica come applicazioni
particolari di esse, ma anche di desumere in maniera automatica, quali loro soluzioni,
l'esistenza di 4 tipologie di particelle: fotoni, neutroni, cariche elettriche e gravitoni, di cui
Heim calcola, sempre in base alle sue equazioni, il valore esatto delle rispettive costanti.
Ma non finisce qui. Le equazioni applicate allo cosmologia consentono di interpretare ciò che
appare come espansione dell'universo quale effetto della espansione del metrone (quanto di
spazio) e del cronone (quanto di tempo), e quindi di calcolare il momento iniziale
corrispondente alla nascita dell'Universo (la teoria non prevede alcun Big-Bang).
Quello che, però, è più rilevante ai nostri fini, è la applicazione di questa teoria alla fisica
dell'elettromagnetismo, che porta alle equazioni di seguito riportate:
Ove:
Γ = campo gravitazionale
µ = mesofield
α = permettività gravitazionale nel vuoto (1/4πγ = 1.19 × 109 s²kg/m³)
γ = costante di gravitazione universale ( γ = 6.67422 × 10-11 m³/s² kg)
ß = 1/αc² (9.34 × 10-27 m/kg)
c = velocità della luce (3 × 108 ms)
je = densità di corrente elettrica
jm = densità di corrente di massa .
Heim aveva lavorato, fino al 1954, presso il Max-Planck-Institut di Goettingen, che
abbandonò a causa di un grave handicap che lo privò dell'uso degli occhi e delle mani. Tra il
190
1979 e il 1984 pose mano ad una voluminosa opera (699 pagine) in cui espose l'intera teoria.
Quando uscì il volume praticamente nessuno ricordava che Heim già nel 1959 era divenuto
famoso proponendo un nuovo sistema di propulsione astronautico.
----[Per una presentazione dell'autore si rimanda al suo articolo pubblicato nella
prima parte di questo stesso numero di Episteme]
[email protected]
191
Recent Developments in the Relativistic Electrodynamics
Controversy
(Gianfranco Spavieri, Miguel Rodríguez and Edgar Moreno)
Abstract
In this paper we consider the controversial facets of two tests that are supposed to show
experimental evidence against the accepted standard electrodynamics based on special
relativity. The first refers to the detection of longitudinal electromagnetic forces in current
carrying conductors, and the second represents a modified version of the Trouton-Noble
experiment for which a non-null result has been found. Although the first test is inconclusive,
the positive result of the second, if it is really such, is surprisingly in agreement with standard
electrodynamics.
*****
1 - Introduction
Classical electrodynamics is in a slow but continuous evolution and some of the recent
advances are the results of discussions that have been going on for decades. In recent times
many papers have been published on themes related to the so called "electrodynamics
controversy." This is a scientific controversy between physicists in favor of the standard
relativistic interpretation of classical electrodynamics and physicists that favor an approach to
electrodynamics based on coordinate transformations different from the Lorentz
transformations and, thus, negate the validity of special relativity.
In this paper we consider, both from a theoretical and experimental point of view, two aspects
of this ongoing controversy, namely: the detection of longitudinal forces on current elements
[1-8] and an experiment of the Trouton-Noble type [10-16] which, supposedly, leads to a nonnull result, in contrast to the traditional view exposed in many textbooks.
Before going into the details, we would like to make a general comment on the reliability of
the papers that deal with this type of conflicting aspects of fundaments of physics. As it has
been remarked by several epistemologists and experts in the philosophy of science, most
physicists assume spontaneously a partial position in these discussions. The remark is that
some experimentalists are tempted to, and in fact do, try to arrange the experimental set up in
such a way that the data are trimmed or slightly modified in favor of expected or desired
results, which would corroborate their own visions or theories. Moreover, it is not uncommon
to find out that theoreticians may have selected from the existing theory formulas or partial
approaches that lead to a theoretical result in agreement with their vision, most of the times
neglecting "unintentionally" other formulas or approaches that would lead to opposite or
different results.
We believe that the majority of physicists deal with controversial issues with serious and
frank attitude, so that the effects of "unintentional" modification of experimental data and
manipulation of theoretical models is probably limited and, hopefully, do not alter
significantly the objective physical results. Nevertheless, some of these controversies, which
generally imply the waste of a lot of time, would not subsist if physicists were a little more
scrupulous in their research. Moreover, some physicists, either in favor the official, standard
view of accepted theories or not, assume generally a rigid and dogmatic attitude that often
prevents discussion and advances. Sometimes this attitude prevents the research of issues that
later are recognized as real fundamental unsolved problems of modern physics.
192
With this in mind, we try to address in an objective way the two experimental topics
mentioned above, being our impartiality somewhat assured because, although the predictions
of opposing theories are clear, we are not completely in favor of the expected standard
prediction.
Two groups of researchers performed recent experiments on these topics. The novelties of the
experiments, which make them interesting from a theoretical point of view, are:
- In the case of detection of longitudinal forces, a time varying current has been used
[3], unlike other previous experiments where the current was steady-state [1-2, 4-6].
- In the case of the Trouton-Noble experiment, the parallel plate capacitor was not
shielded from external electric fields [13], unlike previous experiments of this type
[10-12].
2 - Advances in the Controversy of the Longitudinal Forces on Current Elements
This is an old discussion that sets as opposing theories or formulas, describing the force acting
a current element, the Ampere law and the Biot-Savart law.
The Ampere law reads
∆ Fm, n = − k
imin dmdn
,
( rm, n ) 2
(1)
where im and i n are the currents flowing in the current elements of length dm and dn
respectively, r is the distance between the two elements, and k is a dimensionless geometrical
function that takes into account the direction of current in each element.
An important feature of this law is that the action and reaction principle holds for the
interaction between two current elements. Moreover, besides the usual forces perpendicular to
the current elements, this law predicts also the existence of longitudinal forces, i.e. forces
acting on a current element in the direction of the current.
The Biot-Savart law reads
∆ Fm , n = im dm × B n ,
(2)
where Bm is the magnetic field due to current element dn , given by the Laplace formula
dB n =
rn , m
µ
(i n dn) ×
.
4π
(rn ,m ) 3
(3)
For this law, the forces are always perpendicular to the current element. However, this law
does not comply with the action and reaction principle between two current elements.
Nevertheless, both laws give the same result when the interaction is extended to the complete
circuit and the action and reaction principle is not violated.
Several of the experiments that try to discriminate the two laws experimentally have been
discussed in Ref. 4-5, 7. It has been remarked that the theoretical advantage of the Ampere
law is that it complies with the action and reaction principle. Although some more refined
discussion should be in order on this theoretical aspect, the final impression we have, from an
experimental point of view, is that a point in favor of the Ampere law has not yet been made.
In this article we consider the results of a recent experiment by Graneau et al. [3] who claim
to have proven the existence of electromagnetic longitudinal forces. Their experimental set up
193
consists of a closed circuit where a high intensity time-dependent current I is induced, as
shown in schematically in Fig. 1. In this experiment, a capacitor is charged at a very high
voltage and then discharged when connected to the electric circuit where a current I = I(t) is
induced. A small section R of the circuit is isolated from the rest of the circuit by two air
gaps, Gu and Gd, so that the rod R can move up and down if a net force acts on it in the
longitudinal direction.
Graneau et al. observed that the rod moves, during their tests, and it reaches a height h that
depends on the maximum intensity of the current and also on the difference between the
lengths of the up and down gaps, Gu and Gd. Their data indicate that the net force, which
makes the rod reach the height h, is zero for a symmetric set up, when Gu = Gd, while the
force and the height h increases progressively up to a maximum value when, progressively,
one sets Gd < Gu.
Thus, Graneau et al. conclude that their experiment proves the existence of electromagnetic
longitudinal forces and favor Ampere's law. An extended article refuting their conclusions has
been recently submitted for publication [8]. Here we give some of the arguments used for the
rebuttal and use this occasion to make some other comments about this controversy with the
aim to provide suggestions for other tests of electrodynamics where time-dependent fields are
used.
Qualitatively, our explanation of the results of Graneau et al. is the following. The net force
exists but it is not of electromagnetic nature. When the current I of very high intensity is
induced in the circuit, most of the power P = RcI 2 is dissipated via the Joule effect in the air
gaps where the electrical resistance Rc is higher than in the rest of the circuit. The air in the
gaps reaches a high temperature and pressure, generating a gas expansion, like a small
explosion that acts on the inner surface of the mobile rod R.
However, the air in the smaller gap Gd is relatively more confined than the air in the upper
gap Gu. Molecules, radiation energy, electrons, etc., of the expanding ionized air, will bounce
back and forth many more times between the inner walls of the gap Gd than of Gu, before
they leave the gap. Thus the pressure exerted in the smaller gap is more effective than that in
the larger gap. It is this pressure difference that generates the net upward force that pushes the
rod at a height h.
The details and a quantitative description of this mechanism are given in Ref. 8 where it is
shown that the dependence of h with the length Gd is in good agreement with the
experimental data and in better agreement with the the experimental results than the
predictions of the Ampere law, as calculated by these authors. Thus, we believe that the
experiment here considered is not conclusive and cannot be taken as an experimental proof of
Ampere's law.
Some considerations are in order here that can help to address the controversy on what are the
real forces acting on charges or current elements.
The novelty of this experiment is that it is conducted in non steady-state conditions, since the
current varies with time. In this circumstance, the vector potential A(t), associated with the
time varying current, also varies with time. Since A(t) can be in the direction of a current
element, the force –q dA/dt = qE, where E is the induction electric field and q the charge
associated to a current element, may also be in the direction of current elements.
Generally, the circuit is neutral so that besides the moving charge q there is also a stationary
charge –q in the current element, and there should be no net force. But, if the rod R
accumulates a net charge during the extreme conditions of the test, a longitudinal force could
be acting on R, even though it is probably small in this set up.
However, the interesting point in the case of time-dependent fields is that one realizes that,
contrary to the usual steady-state conditions where the Biot-Savart law is generally
confirmed, there is no mention in the literature of experiments dedicated to the detection of
forces acting on charges or current elements due to time-dependent induction fields.
194
When the phenomenon of induction is applied to a closed loop we have many direct
verifications of the law of induction, or Faraday's law, in terms of the emf,
emf =
∫E
⋅ d ,
induced in the loop, which has an integral form. In this common case, there are forces acting
in the direction of the current but only the resultant on the closed loop is being tested in terms
of the induced current or voltage difference. The differential force acting on a current element
or a part of a loop is not being tested in the usual induction experiments.
Thus, what has not been tested experimentally is not only if these induction forces are the
same for charges at rest or in motion (as the moving charges in a current element), but if the
induction forces act at all in an isolated stationary charge that is not part of a closed circuit.
One reason why the experimental results for the last mentioned case are not obvious, even for
standard relativistic electrodynamics, is that the action and reaction principle does not hold for
the interaction between a coil producing a time varying magnetic field and an isolated charge
(this is the so called Shockley-James paradox, solved in Ref. 9). Theoretically, there should be
a force –q dA/dt acting on the isolated charge. However, the existence of a possible reaction
force on the coil has been the source of controversial discussions [9].
There is a pragmatic reason why these problems related to time-varying fields are mentioned
here. From an operational point of view, it may be easier experimentally to detect possible
discrepancies with classical electrodynamics for isolated static charges than current elements.
In fact, a current element is mainly a theoretical concept that is difficult to realize
experimentally, as all the objections and drawbacks of the experiments on longitudinal forces
performed so far has shown. While an isolated charge is a theoretical concept realized
experimentally in many set ups, such as the experimental proof of Coulomb law, and it should
be easier to handle without ambiguities.
Thus, our suggestion and belief is that the electrodynamics controversy may achieve more
interesting and definite results if it shifts its attention to the possible tests of electromagnetic
interactions with time-dependent fields of the type mentioned above.
3 - A New Experiment of the Trouton-Noble Type
With the same spirit that motivated the mentioned papers [4] and [5], we believe that it is
worth reconsidering here one of the tests of classical electrodynamics, the Trouton-Noble
(TN) experiment, that has been recently discussed in the literature.
The outcome of the TN experiment has been considered a null result for decades. Trouton and
Noble wanted to verify that a charge moving with respect to the ether frame where the
Maxwell equations were valid, would create a magnetic field. In order to check this
hypothesis, they suspended a charged capacitor to a thin thread. Since the Earth (and the
capacitor) was supposed to be moving with respect to the frame of the ether, the magnetic
field produced by one of the charges of the capacitor in motion would act, via the Lorentz
force, on the other charge producing a torque and an observable rotation of the apparatus.
The experiment was first performed by TN [10] and later by Chase [11], and more recently
and with a high sensitivity by Hayden [12]. The results of all these experiments indicate so far
that the effect sought by TN does not exist.
However, recently Cornille [13] has claimed that he performed a TN experiment with positive
result and gives a number of reasons why the previous experiments failed while his
succeeded. This result is surprising because it seems to defy the generally accepted
interpretation of the TN experiment and of the standard, relativistic interpretation of classical
electrodynamics.
195
In the present section we show that a test of the Faraday law in differential form can be
related to an experiment of the TN type. Furthermore, we clarify the experimental limits of
the original TN experiment and of that performed by Cornille. In a future paper we consider
another test of the Faraday law in differential form and point out an interesting and unique
experimental consequence of the validity of the conservation laws in electrodynamics.
Without considering here Cornille's theoretical arguments in detail, we have noticed that
Cornille's experimental set up differs from the others because he did not shield the suspended
condenser from external electric fields. He also mentions that the magnetic field of the Earth
cannot produce a torque because the charges of the capacitor are at rest in the laboratory
frame of the Earth.
We show that, theoretically and contrarily to the current belief, in specific experimental
conditions an experiment of the TN type, consisting of a suspended charged capacitor, may
succeed. In fact, according to the standard interpretation of Faraday's law of induction, a
positive result is theoretically possible if the effect of the small magnetic field of the Earth on
the capacitor is taken into account.
However, the foreseen non-null result refers to the action of the external magnetic field of the
Earth on the TN capacitor, which is actually rotating about the Earth axis in its diurnal
rotational motion. It does not refer to the effect originally sought by TN and other theoretical
effects considered by Cornille.
Furthermore, the experiment of the TN type here considered, may provide a definitive
quantitative test of the old theory of magnetic field lines ''cutting,'' which supposedly has been
disproved qualitatively by the Kennard [14] experiment.
In the final part of the paper we indicate the experimental conditions that lead to a positive
result for an experiment of the TN type and comment on the experimental result of Cornille.
4 - The Standard Description of the Faraday Disk
The Faraday disk, as shown in Fig. 2, consists of a conducting disk rotating about its
symmetry axis and connected to an electric circuit AECR with one end (A) on the axis at the
center of the disk and the other end (R) in the form of a sliding contact touching the external
circumference. When a magnet is placed near the rotating disk with its magnetic pole aligned
along the disk axis, an induction current flows in the circuit.
If the magnetic field B is uniform near the disk of radius R rotating with angular frequency ω,
the electromotive force is given by
1
emf = ∫ E ⋅ d l = ∫ ( v × B) ⋅ dl = wR 2 B
i
2
(4)
In many textbooks, result (4) is deduced from the integral form of Faraday's law taking into
account the change of the magnetic flux as the material segment AR rotates in the presence of
the field B. The integral form of Faraday's law cannot tell where, along AECR, the emf is
induced.
However, considering Faraday's law in differential form, the expression v×B represents the
induction, effective field Ei seen by the charges co-moving with the disk along the segment
AR. It is a consequence of the validity of the Lorentz force F=E+q v×B, written in a reference
frame S, that indicates that the charge moving with velocity v in the presence of B and with
E=0, experiences the field Ei=F/q= v×B.
According to the transformations of the electromagnetic fields of special relativity, an
observer in a reference frame S' instantaneously co-moving with a point of the disk
experiences the fields B´≈B and E´≈ v×B.
The observers of both frames S and S' agree that the emf is induced in the radial path of the
disk and the description of the effect is essentially the same for S and S'. The same result is
196
obtained if the magnet is rotating with the disk or if a rotating conducting magnet alone is
used as a Faraday disk. In fact, according to the standard relativistic interpretation of
electrodynamics a cylindrical magnet can be thought of as made of a cylindrical current
distribution, and the current and field produced by the current is the same even if the current
loops rotate about the symmetry axis.
Historically, the field lines of B were considered to have a precise physical reality. The
potential difference generated across the radius AR was interpreted as due to the cutting of the
magnetic field lines by the rotating metal. In the term qv×B, the velocity was interpreted as
that of the charge with respect to the field lines, and not as the velocity of the charge relative
to the reference frame where the magnetic field is measured.
In the case of a Faraday disk formed by a rotating magnet, in the pre-relativistic
interpretation, Faraday's hypothesis of 1851 -- in which he visualized the magnetic lines as
fixed to the magnet and rotating with it -- was assumed. In this case, the lines will thus be cut
by the external branch ECR and the emf is not induced in the disk but instead in the stationary
part ECR of the electric circuit. In this interpretation v represents the velocity of the ''cutting''
field lines at the position of the ECR.
Measurements of the induced voltage and/or current cannot discriminate between one theory
or the other since in both cases the generated intensities are the same. In 1917 Kennard [14]
achieved a breakthrough when he suppressed the ECR branch and was capable of measuring
an induced potential difference along AR when the whole system rotated as a unit. Kennard's
experiment consisted of a cylindrical capacitor and a coaxial solenoid. The induced
electrostatic charge separation was measured by inserting an electrometer by means of two
leads located along the axis. One of the lead was connected to the inner part of the capacitor,
the other was connected to a radial wire reaching the outer part of the capacitor. When Tate
[15] in 1922 reviewed the whole problem, he acknowledged Kennard's result and the implied
disproof of the theory of rotating lines of force.
Without negating the validity of Kennard's experiment, we point out some of its limitations.
First of all the apparatus consisted, as in the case of the Faraday disk, of two parts in relative
motion: the measuring device, or electrometer, at rest; and the rotating capacitor in motion.
What is being measured is always a potential difference between the two parts and not the
local field. The inner part of the capacitor had finite dimensions and one cannot exclude that,
if the flux lines are rotating, they may induce a potential difference in the stationary part of
the electrometer. Furthermore, the results are necessarily qualitative because of the difficulties
of graduating the electrometer and eliminating additional electrostatic effect due to the air
drag produced by the rotating parts.
In an ideal experiment the measuring device should be co-moving with the rotating apparatus
(magnet or solenoid) and measure the local electric field intensity, so that these objections no
longer apply. This ideal situation is achieved with the set up of an experiment of the TN type
that exploits the Earth rotation, as described in the sections below.
5 - The Effect of the Magnetic Field of the Earth
The magnetic field of the Earth (Fig. 3) is usually approximated by the equivalent field
produced by a magnetic dipole placed at the center of the Earth of intensity m o=8.1×1025
gauss⋅cm3. Correspondingly, the magnetic field on the surface of the Earth varies from 0.3 to
0.6 gauss depending on the latitude.
The magnetic dipole is not aligned with the axis of rotation with which it forms an angle
α≈14°, corresponding to a distance of about 1000 miles between the geographic and the
magnetic pole. The radial component mosinα is quite smaller than the axial component
mocosα, being sinα/cosα ≈ 0.22. In the following we consider first the effect of axial
component and then show that, for our purposes, the radial component has no effect and can
be neglected.
197
Let us consider the component aligned with the Earth axis with a dipole moment intensity of
m=mocosα. To all respects, the Earth can be considered equivalent to a rotating magnet so
that the results of Sec. 2 valid for the Faraday disk can be applied here.
What is of interest here are the perpendicular and tangential components of B to the Earth
surface. Taking the z-axis of frame S aligned with m, the components of the field B at a given
latitude and longitude of the vector r are given by
B=
3 r ( r⋅ m )
r
5
−
m
r
3
(5)
By means of Eq. (5), one can find the field components that, because of the symmetry, do not
depend on the longitudinal or azimuthal angle φ, but depend on the latitude θ . In analogy
with the interpretation of the Faraday disk, a charge fixed on the Earth and rotating with it in
the presence of the field B will feel the effective electric field Ei.=F/q=v×B.
We consider now the effect of the small radial component m r=mosinα of the magnetic dipole.
In the rest frame S, the radial component mr rotates with angular velocity ω. At a point r in
space the magnetic field due to mr is a time-varying field and, by Maxwell's equations there
must be also an induction electric field. In order to find this electric field, one can consider a
moving inertial reference frame S' instantaneously at rest with a point rotating with the same
angular velocity ω. We use special relativity but neglect retardation effects and relativistic
corrections of order higher than v/c. In S' the magnetic field Br´≈ Br produced by mr is
constant and there is no electric field. Transforming the fields one finds that the electric field
in S is given by -v×Br. The Lorentz force due to mr acting on a charge fixed on the rotating
Earth, is F=qE+qv×Br =q(-v×Br+ v ×Br)=0. Thus, the radial component mr does not have a
net effect on a charge at rest on the Earth.
The main difference between the effect of m and mr, is that m generates a constant magnetic
field in S, while mr generates a constant magnetic field in S'.
In conclusion, a charge fixed on the rotating Earth feels only the effect of the field B due to
m, i.e. it experiments a field Ei.=F/q=v×B.
6 - An Experiment of the Trouton-Noble Type in the Magnetic Field of the Earth
Let us consider now a charged capacitor suspended by a thin elastic thread of torsion constant
k as in the case of the Trouton-Noble experiment. The capacitor is generally described as two
charges of opposite value q placed at the ends of an insulating rod and separated by a distance
d, as shown in Fig. 4.
In the following we assume the standard interpretation of electrodynamics which foresees a
null result for the effect sought originally by Trouton and Noble. This was supposed to be a
torque due to the self-action of the charges moving in the ether and generating a magnetic
field with their motion.
What we look for in the present experiment is the effect of the external magnetic field of the
Earth on the moving charges. As discussed in the section on the Faraday disk, in the frame S
the sought effect is due to the Lorentz force qv×B, in the frame co-moving with the charge the
effect is due to the existence of the electric field qv×B. In order to detect this electric field,
shielding screens around the capacitor must be avoided, as in the case of Cornille's
experimental set up.
With respect to frame S, the velocity v of the charges is in the West to East direction. The
only torque on the capacitor about the axis of suspension is due to the component Bp of the
magnetic field perpendicular to the Earth surface that produces a force F=qvBp lying on the
plane of v and d, tangent to the Earth. The resulting torque is
198
[ (
)]
τ = r× q v× B p = qvB p dcosϕ
,
where ϕ is the angle formed by the vectors v and d.
This torque generates a rotation of the capacitor that tends to set d perpendicular to v. At the
position of equilibrium the capacitor has rotated by an angle ε such that τ=kε. In order to
verify that this angle is detectable with an apparatus of the Trouton-Noble type, we express
the charge on the capacitor, for a parallel-plate capacitor, as q=CV and C=εoS/d. The result is
that, when cosϕ = 1,
ε =
ε o SV ( vB p )
k
.
(6)
In order to estimate ε, we consider a location near the equator where the tangential velocity is
greater, for example in Venezuela at 8° above the equator corresponding to θ=82° in Eq. (5´).
In this case, with the radius of the Earth given by r=6.37×106m and a velocity of
v=ωrsinθ=445m/sec near the Equator, the perpendicular field component turns out to be
Bp=0.17gauss directed toward the centre of the Earth and Ei=v×B≈ 7.5×10-3V/m. With a
potential difference of V=2×104Volt, a plate surface S=1m2 and a torsion constant k=108
kg⋅m2/s2, the torsion angle turns out to be of the order of ε≈0.13 radians≈7.5°, which is easily
observable.
7 - Conclusions
We have considered two aspects of the electrodynamics controversy.
The first aspect refers to the detection of longitudinal forces acting on current elements. We
discuss the experiments by Graneau et al. and point out some weakness in the experimental
set up that make it unreliable for this test.
However, an interesting feature of the experiment performed by Graneau et al. is that timedependent fields have been used. This feature reminds us that there are no tests of the
elementary laws on charges and current elements and that Faraday's law of induction has been
tested with great accuracy but only in its integral form, on closed loops.
Consequently, our suggestion is that the electrodynamics controversy should be directed
toward testing the elementary forces relevant to the discussions on the Shockley and James
paradox.
The second aspect refers again to the test of the Faraday law in differential form. We have
shown that the effects of the magnetization produced by the rotating Earth can be described in
analogy with those produced by a rotating magnet. Thus, an apparatus of the TN type should
lead to a non-null result and can be used to detect the small induction electric field Ei=v×B
seen by an observer at rest on the Earth surface and co-moving with it in its diurnal rotational
motion with a tangential velocity v=ω×r.
This induction electric field is analogous to the local field supposed to be generating the emf
observed in a closed electrical circuit in the Faraday disk. Therefore, this experiment can be
used as a test of the Faraday law in differential form and as a quantitative test for the
localization of the emf, which has been already qualitatively verified by Kennard.
The non-null result reported by Cornille for his TN experiment -- with a high voltage of
40×103V -- seems to corroborate the existence of the small induction electric field Ei
However, there are still some difficulties.
First of all, Cornille's result is qualitative, as he observed a rotation of the apparatus tending to
align along the velocity v, but did not measure the torque. He also states that the rotation is
199
unchanged by reversing the potential difference and concludes that the TN effect exists. If we
discard the existence of the effect originally sought by Trouton and Noble, an explanation of
the effect observed by Cornille can be attributed to an electrostatic induction of objects near
the capacitor, which does not depend on the sign of the potential difference.
In conclusion the experimental evidence for the localization of the emf is still uncertain and at
most qualitative. However, the experiment described in this paper represents a theoretical
improvement and its realization should be able to settle the question of localization -- and the
questions raised by Cornille's experiment -- in a quantitative and definite way.
Acknowledgments
This research was made possible by a grant from the CDCHT (C-1015-00-05-B, ULA,
Mérida, Venezuela).
References
1.
P. Graneau, Phys. Lett. A 97, 253 (1983)
2.
T.E. Phipps and T.E. Phipps Jr., Phys. Lett. A 146, 6 (1990).
3.
N. Graneau, T. Phipps Jr., and D. Roscoe, Eur. Phys. J. D 15, 87 (2001).
4.
G. Cavalleri, G. Spavieri, and G. Spinelli, Eur. J. Phys. 17, 205 (1996).
5.
G. Cavalleri, G. Bettoni, E. Tonni, and G. Spavieri, Phys. Rev. E, 57, 1 (1998).
6.
P. T. Pappas, Nuovo Cimento B 76, 189 (1983).
7.
Cavalleri G., Spavieri G. and Tonni E., Hadronic J. 21, 459 (1998).
8. G. Cavalleri and G. Spavieri, submitted to Eur. Phys. J. (2001).
9.
Y. Aharonov, P. Pearle, and P. Vaidman, Phys. Rev. A 37, 4052 (1988); G. Spavieri,
Nuovo Cimento B 109, 45 (1994).
10.
Trouton F.T. and Noble H.R., Proc. Royal Soc., 72, 132 (1903).
11.
Chase C.T., Phys. Rev., 28, (1926).
12.
Hayden H.C., Rev. Sci. Instruments., 65, 788 (1994).
13.
Cornille P., Galilean Electrodynamics, 9, 33 (1998).
14.
Kennard E., Phil. Mag. 33, 179 (1917).
15.
Tate J., Bull. Nat. Res. Council, 4, 6 (1922).
16.
L. Nieves, M. Rodriguez, G. Spavieri, and E. Tonni, Nuovo Cimento B 116, 585
(2001).
Figure Captions
Fig. 1. Scheme of the electrical circuit used by Graneau et al. for the detection of longitudinal
electromagnetic forces. The mobile part of the circuit R moves up when a strong, impulsive
electric current flows.
Fig. 2. Scheme of the Faraday disk picturing the magnetic flux lines generated by the magnet.
In the Faraday disk the emf is induced along the rotating material segment AR of the circuit.
Fig. 3. Scheme of the magnetic field lines of the Earth. The Earth magnetization can be
represented by a magnetic dipole placed at the centre of the Earth.
200
Fig. 4. A Trouton-Noble apparatus is suspended to a thin elastic thread. Due to the rotational
motion of the Earth, the charged condenser moves with velocity v in the presence of the
external magnetic field B. The Lorentz force F=qv×B acts on the charges ±q and tends to
rotate the condenser until d is perpendicular to v.
----FIG. 1
201
FIG. 2
202
FIG. 3
FIG. 4
----Centro de Astrofísica Teórica, Facultad de Ciencias, Universidad de Los Andes
Mérida, 5101 - Venezuela
[email protected]
[A presentation of the first two authors can be found in Episteme N. 3]
203
Dynamic Space Converts Relativity
Into Absolute Time And Distance
(Tuomo Suntola)
Abstract
A confusing feature in the theory of relativity is the use of time and distance as parameters in
explaining the constancy of the velocity of light and the reduced frequencies of atomic clocks
in fast motion and in high gravitational field. It is well known that a radio signal passing a
mass center is delayed compared to a signal from same distance through free space. Instead of
stating that the velocity of the signal were reduced the theory of relativity explains that time
close to mass centers flows slower thus saving the basic assumption of the theory, the
constancy of the velocity of light. Same is true for atomic oscillators and the characteristic
absorption and emission frequencies of atoms, an atomic clock loosing time when in fast
motion is not considered as running slower but as experienced slower flow of time.
A key demand of a physical theory is its capability to create an understandable picture of the
reality we observe. Instead of just introducing mathematical expressions for observations, a
physical theory should explain the logic behind the phenomena observed. The old Ptolemy
astronomy worked well for calendar and eclipses but failed in serving as a basis for a physical
view of celestial motions. A key in Copernicus' findings was the realization of the observer's
state in the system - instead of defining the observer's state as the origin at rest Copernicus
identified the Sun as the origin of the planetary system with Earth orbiting and rotating like
any other planet. Such a structure gave basis for a physical approach of motions in the system
thus opening a new era for the understanding of the celestial mechanics and the laws of
nature.
The Dynamic Universe approach takes a further step in reorienting the observer. The
observable three-dimensional space as whole is considered as a closed spherical structure with
its dynamics determined by a zero energy balance between gravitation and motion in the
structure. Such approach links local phenomena to the state and motion of whole space and
gives physical explanations to several postulates like the velocity of light, the rest energy of
matter and the Mach's principle. It also explains the dependence of the velocity of light on the
gravitational environment and the dependence of the ticking frequencies of atomic clocks on
the state of local motion and gravitation - not by distorting time and distance coordinates but
in absolute time and distance.
*****
1 - Space as the surface of a 4-sphere
Many physicists have noticed the striking equivalence between the total rest energy of all
mass in space and the gravitational energy of space estimated from Newton's gravitational
energy as E ≈ GMΣ2/R where R = c/H is the Hubble radius. For further analysis of the total
gravitational energy we need to assume certain geometry of space. A natural solution is a
three-dimensional surface of a four-dimensional sphere. Following the ideas of Ludwig
Schläfli, Georg Riemann and Ernst Mach, Einstein, Ref. [1] proposed such geometry in 1917.
Einstein was looking for static space, which lead to the need of the cosmology constant to
prevent shrinkage of the structure. Further, the fourth dimension was already reserved for
time in the theory of relativity just completed. As the result, the spherical space was rejected.
204
Combining the idea of space as the surface of a 4-sphere to the mystery of the equality
between the gravitational energy and the rest energy of mass in space suggests that space as
the surface of a 4-sphere is in motion at velocity c in the direction of the radius of the 4sphere so that the energy of motion related to mass in space moving at velocity c along the 4radius is written like the energy of light as E = cp = c⋅MΣ c = MΣ c2 (see Figure 1).
E”(m)
F’(g),t
−
R4
m
R"
M" −
F”(g)
R4
E”(g)
MΣ
= 2ρ
π
R4
2
3
Figure 1. The tangential shrinking force, F'(g),t, due to the gravitation of uniformly
distributed mass in spherical space is equivalent to the gravitational effect, F"(g), of
mass equivalence M" at distance R" from mass m along the 4-radius of the structure.
The sum of the total energies of motion and gravitation in space is zero.
A detailed mathematical analysis taking into account the four-dimensional geometry in the
expression for the gravitational energy allows the zero-energy balance between motion and
gravitation to written in form
M Σ c02 −
GGE M Σ2
= 0
R4
(1)
where GE = 0.776 is a geometrical factor resulting from the integration of the gravitational
energy throughout the three-dimensional surface of the 4-sphere, Ref. [2].
When solved for the velocity of space, c0, in the direction of the radius of the structure we get
c0 = ±
GGE M Σ
GM "
= ±
R4
R"
(2)
which means that for maintaining the zero energy balance in space the velocity of expansion
or contraction along the 4-radius is linked to the gravitational constant, total mass in space
and the actual length of the 4-radius. For a mass density 5 ⋅10−27 [kg/m3], which is 0.55 times
the Friedmann critical mass, and the 4-radius of space R4 = 14⋅109 light years, the numerical
value of c0 in equation (2) is equal to c0 = c = 300 000 km/s. The latter form of equation (2)
applies the mass equivalence M" of space at distance R" in the fourth dimension, in the
direction of the 4-radius of three-dimensional space (see Figure 2). When applied to mass
object m equation (1) means that the rest energy of matter can be explained as the energy of
motion due to the expansion of space along the 4-radius.
The buildup and release of the energy of matter in space can be described as a zero-energy
process from infinity in the past through singularity to infinity in the future. In the contraction
phase mass obtains its velocity against the release of gravitational energy like in free fall and
in the expansion phase the energy of motion obtained in the contraction is converted back to
the gravitational energy.
205
dM
R"
M"
D
x,y,z
m
Im
Figure 2. The integrated gravitational effect of all
the mass in space on a mass object m can be
described as the gravitational effect of mass M" at
distance R" along the imaginary axis inside closed
space.
In the expansion phase, the radial motion of space works against the gravitation of the
structure, which means that the radial expansion velocity is gradually diminishing. The
relative reduction of the expansion velocity in the present state of the Universe is about
∆c0/c0 = 4⋅10−11 /year. It turns out that the frequencies of atomic clocks and the characteristic
wave numbers of the spectral lines of atoms are directly proportional to the internal
momentum due to the motion of space at velocity c0. Accordingly, the reduction of the
velocity of light is not detectable in measurements based on the readings of atomic clocks.
Energy of motion
∞
time
−∞
contraction
∞
expansion
−∞
Energy of gravitation
Figure 3. Contraction and expansion of space and the
corresponding evolution of the energies of motion and
gravitation. In the contraction phase, the 4-radius of space goes
from infinity to zero. In the expansion phase, after singularity, the
radius increases from zero back to infinity. Zero total energy is
preserved through the entire process.
206
2 - The fourth dimension
The shocking message of equations (1) and (2) is that the velocity light appears as the velocity
of all mass in the fourth dimension. Same message is hidden in the line element in Lorentz
coordinates or Minkowski metrics which in local homogeneous space can be expressed as
( ds )
2
= − ( cdt ) + ( dx ) + ( dy ) + ( dz )
2
2
2
2
(3)
or in vector form as
ds = i cdt + dx + dy + dz
(4)
where c instead of dt is expressed as a vector in the fourth dimension, mathematically shown
as the imaginary direction. Following the concept of space as the three dimensional surface of
a 4-sphere, c in equation (4) does not mean motion in space but motion of space, i.e. motion
that all matter at rest in space is subject to according to equation (2). Accordingly, the rest
momentum of a mass object in space is
p 4 = i mc 4
(5)
i.e. momentum in the fourth dimension which, when summarized to a momentum p in a space
direction gives the total momentum ptot relevant with the total energy of an object moving in
space
Etot = c4 ptot = c4 pr2 + ( mc4 )
2
(6)
Equation (6) shows the total energy of an object in the same format as given by the theory of
special relativity, however, without the use of the Lorentz transformation as a correction of
the coordinates. Equation (6) describes the total energy as the result of the orthogonal sum of
momenta due to the motion of space and the motion in space.
In fact, motion of space at the velocity of light along the radius of curvature is implicitly
given in the Hubble law and the uniform expansion of space, which were not known at the
time the theory of relativity was formulated.
3 - Motion in spherical space
Observing that any motion in spherically closed space is central motion relative to the mass
equivalence of space in the fourth dimension, the gravitational acceleration in the fourth
dimension is reduced due to central acceleration (Figure 4). The effect can be expressed as a
reduction of work done by the object against the gravitation of the mass equivalence of space
in the fourth dimension. The effect can be expressed in terms of a reduction of the internal
mass mI responding to the gravitational interaction with the total mass in space
mI = meff ( 1 − β
2
)= m
1− β
2
(7)
The reduction of the internal mass reduces the momentum of the object in the fourth
dimension and, accordingly the "excitation" of the energies of motion and gravitation. It can
be shown that such situation results in a reduction of the characteristic frequencies of atomic
oscillators, i.e. the frequency of atomic oscillators moving at velocity β = v/c is reduced by
factor 1 − β 2 as
fI = f0 1− β
2
(8)
where f0 is the frequency of the oscillator at rest in the local energy frame. Equations (7) and
(8) give direct physical meanings to the Lorentz factor - not as a correction of time coordinate
but a factor reducing the internal energetic response of a moving object to the gravitation of
207
the total mass in space on the object. In terms of inertia this means that the buildup of kinetic
energy when accelerating an object to a velocity in space involves the work done in reducing
the gravitational energy due to all mass in space.
Im
2
FC=mv /R”
v
F"i(a) = χmradc /R”
2
v=c
Fg =−GmM”/R”
=−Eg/R”
2
R"
R”
F"g = −χmradc /R”
2
M”
Figure 4. (a) As central motion relative
to the center in the fourth dimension,
motion in space reduces the gravitational effect of the total mass described
by mass equivalence M" in the fourth
dimension.
Figure 4. (b) For an object moving at a
velocity equal to the velocity of space
in the fourth dimension the gravitational effect of the total mass in space
is fully counterbalanced by the centrifugal acceleration.
4 - The effect of mass centers on the local velocity of light
The idealized picture of completely symmetric spherical space assumes that mass is uniformly
distributed all over the space. When mass is cumulated into mass centers in space the
conservation of total gravitational energy demands that the "smooth" surface of an ideal fourdimensional sphere is tilted to form dents in the fourth dimension around mass centers in
space. In tilted space also the direction of the fourth dimension is turned relative to the
direction of the expansion, accordingly, locally the velocity of space in the fourth dimension
is reduced in proportion to the tilting (see Figure 5).
In a local gravitational frame the famous equation E = mc2 shall written in form
Eδ = c0δ mc
homogeneous space
c φ
c0
dr
M
φ
dr0
c0
(9)
Figure 5. In the vicinity of a mass center
local space is tilted by angle φ relative to
homogeneous space moving at velocity c0.
Accordingly, the velocity of space, c, in the
local fourth dimension is c = c0 cosφ .
208
where c is the local velocity of light in the gravitational state denoted by the gravitational
factor δ and c0δ is the velocity of light outside the local gravitational frame, in the apparent
homogeneous space of the local frame. The local velocity of light can be expressed in terms
of the local gravitational state as

GM 
GM 

c = c0δ cos φ = c0δ ( 1 − δ ) = c0δ  1 −
 ≈ c0δ  1 − rc 2 
rc
c
0 0δ 

(10)
where φ is the tilting angle of local space and δ the gravitational factor as expressed in terms
of the gravitational constant G, M the mass of the central mass of the gravitational frame at
distance r from the location of the object studied.
Factor mc in equation (9) has the meaning of momentum in the local fourth dimension. The
kinetic energy of free fall in a local gravitational frame is gained against a release of the rest
energy of the falling object through the reduction of the local velocity of light.
As a consequence of the reduction of the momentum in the fourth dimension the locally
obtainable maximum velocity in space, the local velocity of light, and the frequencies of
internal atomic processes are reduced. Motion in space reduces the frequencies of internal
atomic processes through the reduction of internal mass, mass centers in space reduce the
frequencies through a reduced velocity of light in tilted space. Combining effects of motion
on the internal mass of an object and the effect of reduction of local velocity of light, the
characteristic frequencies of an atomic oscillator moving at velocity β in gravitational state δ
in a local gravitational frame can be expressed as
fδ , β = f 0δ ,0 ( 1 − δ
)
1− β
2
(11)
where frequency f0δ,β is the frequency of the oscillator at rest in the apparent homogeneous
space of the local gravitational frame.
Local tilting of space and the reduction of the velocity of light near mass centers have several
interesting consequences. Light or radio signal passing a mass center is delayed due to the
lengthened path and reduced velocity. Also, the path is bent due to the local deformation of
space. A further consequence of the local deformation of space is that the main axis of
elliptical planetary orbits is subject to a rotation observed as a shift in the perihelion of the
orbit.
5 - The system of cascaded gravitational frames
Real space consists of cascaded gravitational systems such as our planetary system in the
solar system, the solar system in the Galaxy, and the Galaxy in the local galaxy group.
Following the zero energy principle, in cascaded gravitational systems the local velocity of
light can be related to the velocity of light in apparent homogeneous space around the local
dent and, finally, to the expansion velocity of hypothetical homogeneous space in the fourth
dimension (see Figure 6). This also means that in a gravitational frame like the Earth
gravitational frame the zero reference for the local velocity of light is locked to the shape of
the local dent, the zero reference follows the orbital motion of the Earth around the Sun, i.e.
the reference at rest "the local ether" for the propagation of light in the Earth gravitational
frame is the Earth centered non-rotating frame (or Earth Centered Inertial frame in the
language of the general theory of relativity). Based on the present knowledge of the
gravitational systems Earth is bound to (the Solar system, Milky way and the local galaxy
group), the local velocity of light on the Earth is about 1/10 6 (one per million) lower than the
velocity of light in hypothetical homogeneous space where all mass were uniformly
distributed.
209
Im0δB
the apparent homogeneous space
of the MB frame
Re0δB
ImδB=Im0δA
Re0δA
ImδA
m
MA
MB
the apparent
homogeneous
space of the MA frame
Figure 6. Apparent homogeneous space of the MA frame around
mass center MA follows the direction of space in the MB frame as
it were without the MA center.
The assumption we made of space as a closed surface of a four dimensional sphere
contracting and expanding by maintaining zero total energy leads to a number of phenomena
we are used to know as relativistic effects. As a major difference to the theory of relativity we
do not need to use the coordinate quantities, distance and time as parameters to explain the
phenomena.
In dynamic space, the effects of motion and local gravitation on internal atomic processes like
the ticking frequencies of atomic clocks can be understood as consequences of the motion and
local gravitation on the energetic state of the objects. More than that, we can understand why
the velocity of light is the maximum velocity obtainable in space and how the inertia of mass
linked to the total mass in space.
We do not need to assume that time were different due to gravitational field to understand the
delay and bending of light near mass centers or the gravitational red- and blueshift of atomic
clocks and electromagnetic radiation. We can honor the coordinate quantities as constant
measures in all observations. The velocity of light is not a constant but a function of the local
gravitational state.
In a complete form, taking into account the cascaded gravitational frames the equation for the
rest energy of an object shall be written as
Eδ = mc02 ( 1 − δ
n
) ∏  ( 1 − δ i )
i= 0
1 − β i2 

(12)
where m is the mass of the object, c0 is the expansion velocity of space. Gravitational factors
δi describe the effects of the gravitational states of each gravitational frame in its parent frame
and factors βi = vi /ci the motions of the local frame in the parent frames. On the Earth, the
local velocity of light can be estimated to be c ≈ 0.999999 c0. Taking into account the effects
of the cascaded system of gravitational frames the frequency of atomic oscillators can be
expressed as
n
fδ , β = f 0 Π  ( 1 − δ i ) 1 − β i2 
i= 0 

(13)
where f 0 is the frequency of the oscillator in hypothetical homogeneous [see equation (11) as
reference].
210
6 - Expansion of space occurs everywhere
By linking the energies of motion and gravitation through the zero energy principle, the
spherically expanding space allows (or demands) the expansion of space also to occur within
local gravitational systems. In the Earth − Moon system this means that out of the 3.8 cm
annual increase in the Earth to Moon distance 2.8 cm is due to the expansion of space and
only 1 cm due to the tidal interaction.
In cosmological scale the propagation of light follows a spiral path, characterized by equal
velocities in the fourth dimension with the expansion of space and the propagation observed
in space (see Figure 6).
Figure 6. At cosmic distances the propagation
path of light appears as a spiral in four
dimensions.
p=h0/λ ⋅c
R4=R4(t)
The precise geometry of space and the defined propagation path of light in spherical space
allows the derivation of the Hubble law and the redshift versus magnitude dependence
without arbitrary parameters needed in the standard cosmology model. The Hubble law
obtains the forms
z=
D R4
1 − D R4
and v =
D
c
R4 0
(14)
where the optical distance of the object, D, is the integrated tangential component of the light
path from the object to the observer, which is the distance traveled by light in space.
Inherently, equation (14) is consistent with the definition of the redshift in the general theory
of relativity.
The energy flux of an object with redshift z can be expressed as
F( obs )
F( e)
=
1
z ( z + 1)
2
(15)
corresponding to magnitude versus redshift relationship
m = m0 + 5log z + 2.5log ( z + 1)
(16)
Equation (16) gives a perfect match to the observed redshift − magnitude dependence of
supernovas as shown in Figure 7. Accordingly, recent confusion regarding the redshift versus
magnitude observations becomes solved without any new assumption or parameter, the
prediction derived from the dynamic spherical space is shown as the solid curve in Figure 7,
also showing recently published observations on supernovas.
211
apparent magnitude
26
Figure 7. Apparent magnitude as a
function of redshift in the range
z = 0.01 to 1. The dots show
observations reported by Perlmutter
et al. , Ref. [5].
22
2
F/F0 = 1/[z (1+z)]
18
14
0.01
0.1
redshift (z)
1
7 - Doppler effect and gravitational redshift of electromagnetic radiation
The combined gravitational shift of atomic oscillators and the Doppler effect of
electromagnetic radiation in a particular gravitational frame has the form
f A( B ) = f B
( 1 − GM
( 1 − GM
rA c 2 ) 1 − β
( 1 − β B vˆ B ⋅ rˆ )
rB c 2 ) 1 − β B2 ( 1 − β A vˆ A ⋅ rˆ )
2
A
(17)
Equation (17) can be derived from the classical Doppler effect by taking into account the
effects of gravitation and motion on the frequencies of oscillators.
In the general theory of relativity the Doppler equation corresponding to equation (17) has the
form, Ref [3],
f A( B ) = f B
( 1 − β B vˆ B ⋅ rˆ )
rB c 2 − β B2 ( 1 − β A vˆ A ⋅ rˆ )
1 − 2 GM rAc 2 − β
1 − 2 GM
2
A
(18)
In the Earth gravitational frame the difference between equations (17) and (18) is too small to
be detected (for example, in the famous Scout D experiment, Ref. [4], the difference between
equations (17) and (18) is of the order 10−18.
When related to the frequency of the transmitter, fA, equations (17) obtain the form of the
classical Doppler equation
f A( B ) = f A
( 1 − β B vˆ B ⋅ rˆ )
( 1 − β A vˆ A ⋅ rˆ )
(19)
where the effect of the velocities of the transmitter and receiver βA and βB are velocities in the
local rest frame.
8 - Discussion
The Dynamic Universe approach is an "energy based" description of observable reality
instead of the "metrics based" description given by the theory of relativity. Unlike the theory
of relativity, the Dynamic Universe is derived starting from structure and zero energy balance
of whole space and then, by conserving the energy balance in the system, derived into local
phenomena. Such approach relates all local phenomena to the energetic state of whole space,
which can be found to result in the effects generally referred to as "relativistic effects". The
DU approach re-establishes the classical meanings of time and distance, which as coordinate
212
quantities, are not used as parameters in explaining observations. The DU approach gives
precise predictions to phenomena covered by the theory of relativity and the standard
cosmology model. In addition, the DU approach explains the origin of inertia and the Mach's
principle, the nature of mass as the substance for the expression of energy, and the physical
mechanisms of the effects of motion and gravitation on the frequencies of atomic oscillators.
It also describes the buildup and release of the rest energy of matter in the contraction and
expansion of space in the zero-energy process of spherical space from infinity in the past to
infinity in the future, Ref. [2].
References
[1] Einstein, A., Kosmologische Betrachtungen zur allgemeinen Relativitätstheorie,
Sitzungsberichte der Preussischen Akad. d. Wissenschaften (1917)
[2] Suntola, T., The Dynamic Universe, A New Perspective on Space and Relativity, Suntola
Consulting Ltd., ISBN 951-97938-6-0 (2002), www.sci.fi/~suntola
[3] Baker, M.L., Jr., Astrodynamics, Academic, New York (1967) 218
[4] Vessot, R.F.C., Levine, M.W. et al., Phys. Rev. Letters, 45, 26 (1980) 2081
[5] Perlmutter, S. et al., 1998 AAS Meeting Jan 1998, Washington DC
----Tuomo Suntola, Dr. Tech.
Senior Scientific Advisor
Fortum Corporation
POB 100, 00048 FORTUM, Finland
http://www.sci.fi/~suntola
[email protected]
Tuomo Suntola was born in Finland in 1943. Helsinki University of
Technology, M. Sc. (1967), Ph. D. (1971), Scientist at State Research Centre,
VTT, (1971-1973). Development of humidity sensor for Vaisala Oy (Humidity
measuring instruments based on Humicapã sensors are still world market
leaders in humidity sensing and monitoring). Chief Scientist Instrumentarium
Oy/Lohja Corporation (1974-1987). Development of Atomic Layer Epitaxy,
ALE, for manufacturing of electroluminescent thin films. Development of flat
panel display product and production machinery, implementation of the
technology into commercial activity. Managing director of Microchemistry Ltd,
a research company in Neste Group (1987-1997). Development of solar cell
technologies, extension of the use of Atomic Layer Epitaxy to the manufacturing
of heterogeneous catalysts and a research tool for surface chemistry. Direction
of the ALE technology and machinery to semiconductor applications, start up of
business activity on Atomic Layer Deposition ALD for semiconductor
manufacturers. Microchemistry Ltd's ALD business was merged into ASM
213
(Holland) in 1998. ALD technology has become a main stream technology for
nanoscale semiconductor devices, (e.g. Applied Materials, Veeco, IPS, Genus).
Senior Scientific Advisor and R&D Fellow, Fortum Corporation since 1997.
Docent at Physics Department of Tampere University of Technology since 1975.
Lectures on semiconductor physics 1972-78. Member of the Finnish Academy of
Technology, TTA since 1983, board member 1988-93. Board member of the
Mentor Program since 1999. Deputy board member in the Foundation of
Technology in Finland since 1991. He holds patents and has published widely
in the fields of material science, thin film technology, and surface chemistry.
[See even the presentation of Dr. Suntola's book which is published in the first
Section of this same number of Episteme]
214
Nature of Energy, Light, and Einstein's
Light-Principle in Special Theory of Relativity
(Paramahamsa Tewari, B. Sc. Engg.)*
Introduction
With the discovery of positron (1932), a unique phenomenon of annihilation of matter
(electron and positron) was observed. In this process, both the particles lose their mass,
charge, and existence, producing annihilation-radiation, that is, light. An essential fact
revealed through annihilation is that light is the last phenomenon of energy-effect before
electron and positron lose their basic properties. Therefore, in order to understand the nature
of light produced, an exact knowledge on the nature of charge and mass, and their distribution
in the structure of the particles is essential, so as to gain deeper insight of the physical process
of conversion of mass and charge into light, and to avoid any erroneous conclusion in the
interpretation of this phenomenon. Further, light produced by thermal radiation is also
considered emitted by orbital electrons in atoms, though, the structure of the electrons is not
affected in this process. Light is some form of energy; and energy, from mass-energy
equation, is expected to have proportionate mass. Therefore, understanding the origin of mass
and charge in the electron structure is the first crucial step in determining the real nature of
energy and the annihilation-light.
Apart from the basic properties of light, that is energy-content, wavelength and frequency, the
process of its transmission in absolute vacuum is equally important. In post relativity era,
space medium, when considered without electromagnetic fields, is believed an empty
extension (void) and, yet, light is supposed to be somehow transmitted in this void of
nothingness. Such an assumption presupposes that the properties of mass, inertia, charge, and
energy, possessed by matter, are independent of spatial reality, that is, the energy constituting
matter is not derived from space. But, a comprehensive theory that explains creation of mass,
inertia, charge and energy, say, in electron-structure; and that pinpoints the very source of
universal energy and its fundamental nature, is nonexistent in contemporary physics.
In this article, creation of electron from space, postulated to be fluid and nonmaterial in my
earlier works [1,2,3] has been first described; mass, charge, energy and basic fields in the
electron structure and the medium of space are briefly analyzed and defined; and from the
observed conversion of mass and charge in the annihilation process, nature of the
annihilation-light has been determined. With the new physical picture of the annihilationlight, shown here to be the most fundamental light-effect in the universe, conceptual errors in
the current understanding of the nature of light have been pinpointed. Einstein's lightprinciple in special theory of relativity has been examined for its correctness.
Mass and Charge of Electron
The property of mass of electron has been shown [1,2,3] to originate from the medium of
space - postulated to be a nonmaterial medium with fluidity, incompressibility, continuity,
homogeneity, mass-less ness, and zero-viscosity. That is, none of the properties, except
fluidity, possessed by matter, exists in space. The only property of the fluid-medium of space
(hereafter, referred as "space") is a limit to its velocity of flow and also to the angular velocity
of rotation (ω) when circulating in a vortex. Fig.1 shows an irrotational vortex of space which
has opened up at the center into a dynamically stable spherical void due to the postulated
limiting ω, which is also the maximum velocity gradient, c/r e, where "c" is the limiting flow
215
of space (maximum velocity-field), and "re" is the radius of the spherical interface enclosing
the void.
A diametrical cross section of the vortex (Fig.2) shows an inward maximum accelerationfield c2/re; this inward radial acceleration of space prevents dilation of the vortex and results in
dynamic stability. The vortex described above is the electron structure.
216
The mass of electron is defined as volume-integral of space-velocity within the interface, just
prior to the creation of electron; and can be derived (Fig. 1) considering a differential element
of volume: dV = (π re2 sin2 θ) re dθ, since, space, equivalent to this volume, is forced out at
velocity ω re sin θ during the creation of void when the speed of space in circulation reaches
c, and angular velocity becomes ω. Mass of the elemental volume from above definition: dM
= dV (ω re sin θ). Integral over the spherical volume within the interface gives, θ varying from
0 to π
me = (4π/3) re3 c.
(1)
Mass has the dimension of [L4/ T], and in CGS unit, it has been derived3:
gram = 8.6 x 106 cm4/s.
(2)
Charge of electron is defined as the surface integral of space velocity on the spherical
interface. Considering the elemental surface: dA= (2π re sinθ) re dθ, and charge on it: dQ =
[(2π re sin θ) re dθ] ω re sin θ. Integrating over the whole interface, θ varying from 0 to π
qe = (π/4) 4π re2 c.
(3)
The charge has the dimension of [L3/T], and in CGS unit,
CGSE = cm3 /s.
(4)
With the use of (1), inward gravitational field (g) due to mass of electron at a radial distance r
from the electron center has been derived1,2,3
217
g = (k/4πc) me / r2
(5)
2
where k is 1/s .
With the use of (4), inward electric field (E) due to charge of electron at a radial distance r
from the electron center has been derived1,2,3
E = -c2 re2 sin2 θ / 2 r2.
(6)
Basic constants derived [1,2,3] are: Coulomb's constant, with electron as the unit of charge, is
c/4π; dialectic constant of vacuum: ∈ = π / 2c; permeability-constant: µ0 = 2 / πc; electron's
intrinsic angular momentum: L= (4/5) me c re; magnetic moment of electron: µ = (3/4) qe c re;
Planck constant1 for electron: h = (4/5) me c re. All these constants show proportionality to c,
which quantitatively proves the postulated universality of c.
Energy in Electron Structure
Qualitatively, most basic state of universal energy is defined as "dynamic space in linear,
accelerating, or circulating motion".
The central void at the electron center is field-less and hence energy-less (Fig. 3a), whereas,
as per the modern concept of electron - a point-mass and a point-charge - energy is distributed
all the way up to the center (3b).
The latter leads to the following serious problems:
218
(a) energy in the electrostatic field of an electron becomes infinite at r = 0;
(b) electron can emit and absorb energy.
With the central void at the electron center, minimum value of r is r e, and not 0; thus avoiding
the integration of energy to reach an infinite value. Also, the energy-less center of electron
cannot emit energy (photons); neither can it absorb energy, because, the interface of the
electron with space-circulation at limiting speed, is impervious to all external interactions.
The distribution of energy in the structure of a stationary electron starts from its interface and
spreads throughout the universal space as gravity and electrostatic fields. During motion,
acceleration, or rotation of electron around a center, relative to space, the gravitational and the
electrostatic energy is seen [1,2,3] as electromagnetic energy or light (discussed later).
Energy of Electron Creation
Refer to Fig. 1. As explained earlier, a differential element of disc with volume: dV= π re2 sin2
θ re dθ, has mass: dM = dV (ω re sinθ) = c π re3 sin3 θ dθ. The area at the interface of the
elemental disc, 2π re sin θ re dθ, is subjected at each point to an inward radial acceleration
field: af = (ω re sin θ) 2 / re sinθ = c2sin θ / re, where c = ω re. Supposing, the elemental disc
collapses under the above inward acceleration-field to zero radius. The work done in this
process will be:
dE = dM af (re sin θ)
= (c π re3 sin3 θ dθ) (c2 sin θ / re) (re sinθ) = π re3 c3 sin5θ dθ.
Integrating over the whole interface where θ varies from 0 to π
E = (4/5) [(4π/3) re3 c] c2,
which, from mass-equation (1), becomes
E = (4/5) me c2.
(7)
The 'work done' is the energy produced due to the displacement of the inward acceleration
field from the interface to its center; this energy fills up the void, and should be equal to the
energy required to create the void at the electron center. Thus, the energy required for the
creation of electron from (7) is (4/5) me c2.
Medium of Space, and its States
Fig. 4(a) shows the most basic state of space-a static non-viscous fluid, incompressible,
continuous and mass less. This is the most basic substratum of the universe, existing eternally.
In Fig. 4(b) dynamic space is depicted. The flow-velocity of space is termed as velocity-fieldthe most fundamental field, which produces all energy fields (Fig. 4c), that is, gravity,
electrostatic, magnetic, nuclear, and electromagnetic. The solar system exists in the universal
dynamic space with fields and matter (Fig. 4c) created by the galaxy.
219
Creation of Electron
The process of creation2 of electron is shown in Fig. 5.
220
In a space vortex (irrotational) when the angular velocity of rotation reaches the limiting ω,
space breaks down into a spherical void due to being subject to the highest velocity gradient
c/re, as discussed before. The radial outward flow of space, creating the interface, takes place
at the limiting speed c, and halted after a time interval r e /c, because that is the maximum
volume of the spherical void possible for dynamical stability. Since the fluid space is
incompressible, a spherical shell of radial width re, with outward pressure3 in it, is created
concentric with the interface (void), and is transmitted in the universal space at the limiting
speed c, thus energizing the universe gravitationally. Due to the incompressibility of space, at
a sphere of radius r, there will be actual displacement (radial) of space points (Fig. 6), which
will create gravitational potential there proportionately. This potential will exist as long as the
void exists at the electron center.
221
Annihilation Process
There can be two electron vortices, with their velocity fields (in between them), opposite in
direction, or in the same direction (Fig. 7a,b).
There is only one fundamental particle [1,2,3], electron, which, looked from the other end of
its axis, is a positron. Positive and negative charges are relative concepts. Electrical attraction
222
between an electron and a positron can be determined from (6) from which Coulomb's
equation has been derived [1,2,3]. Qualitatively, the unidirectional velocity fields between an
electron and a positron (Fig.7a) cause attractive electrical force drawing the particles together.
In this process, the spherical interfaces of the particles can be imagined to finally superpose
each other (Fig. 7c); thus stopping the oppositely directed space-circulations around their
interfaces, and leading to the collapse of their central voids and annihilation of the particles.
Consequently, as experimentally observed, light is produced.
Fundamental Nature of Light
It is evident that the void-interiors of the electron and positron, being energy-less, cannot emit
any kind of energy (photon). The energy (velocity and acceleration fields) in the vortex
structure of these particles pervades the whole universal space before annihilation; and
following annihilation, the process of dying (reducing to zero) of the electromagnetic and
gravitational potentials of the particles, initiating from their superposed interfaces, is seen as a
pulse, or a single shell of light (Fig.8).
When the interfaces of the particles superpose, there is only one spherical-void common to
both; space flows radially at its maximum speed c into the void (Fig. 8); the duration of
collapse, ∆t = re / c. During this time interval, a shell of radial width, ∆t c, that is, (re/c) c = re,
is formed, and transmitted outward at speed c relative to space. The transmission of the shell
is a process that de-energizes the space medium, erasing for all the time the gravitational and
electrostatic potentials that were created at the time of creation of the (now non existent)
electron and positron. The spherical shell produced due to dying of potentials-a process of deenergizing of space substratum consequent to the electron/positron annihilation-is the
fundamental light.
The gravitational field of electron is radial and uniformly distributed on its interface (Fig.9).
223
Therefore, the effect of light due to dying-gravitational-potential will have spherical
symmetry. Whereas, the maximum electrostatic fields of these particles, is confined mostly to
the diametrical plane at right angles to the axis of rotation (Fig.1); hence, maximum effect of
light produced due to dying-electrostatic-potential will be confined within this plane.
Wavelength and Frequency
The wavelength of annihilation light (Fig.8) is equal to the electron radius. This light, with a
single shell, cannot have the concept of frequency applicable to it. In case there are several
annihilations taking place at a point, one after the other, without absolutely any time gap
between the successive annihilations, then the frequency can be defined as the nos. of shells
formed in unit time. Also, if the time for the formation of a single shell is ∆t, then frequency f
can be defined as: f = 1/∆t, keeping in mind, however, that this mathematical operation does
not mean that the single light-shell has the property of frequency as per the conventional
definition of frequency mentioned above. When light is produced due to atomic vibration
(Fig.10), the frequency of light is determined by the nos. of atomic oscillations in unit time,
assuming that the oscillations are continuous [2,3].
224
Fig. 10
The shell of light produced in annihilation, as well as a light -shell produced in atomic
vibration have their centers fixed with the source (assumed stationary relative to space), while
the wave front with a fixed wavelength (radial) is transmitted at speed c relative to space. In
225
the modern concept of light, the photon, postulated as a "packet of energy", is understood to
have its center moving at speed of light relative to the source. It is not clear as to how the
concept of frequency is related with a photon; though, physical picture is not possible,
perhaps, a photon wobbles transverse to its line of motion, a number of times say, f, in a unit
time, while traversing at speed c relative to the source. And, if that is the possible physical
picture, then, "f" will have meaning for a photon (with indivisible energy quantum, hf) only
after it has traveled for a unit time having wobbled f times! Again, the specific characteristic
of a photon that determines its wavelength remains obscure. Though, it is well known that the
classical concepts of wavelength and frequency are inapplicable for a photon in quantum
physics, in the absence of a physical picture, there occurs a serious conceptual error, leading
to a mathematical discrepancy in the very basic relationship between energy and frequency in
the Planck energy equation as pointed out below.
Planck Energy Equation
Based on the concepts of Maxwell-Hertz, that electromagnetic (light) energy is given off from
electrical oscillators, Planck believed that the orbiting electrons inside the atoms of a glowing
solid-emitter radiated electromagnetic waves in different quantities, the frequency being
determined by the vibration of the oscillator. The classical picture was revised by Planck
based on his observed experimental fact when he assumed that an oscillator, at any instant,
could have its total energy (potential, kinetic) only as an integral multiple of the energy
quantity hf, where h is a universal constant (experimentally determined) and f is the frequency
of vibration of the oscillator. Thus, the light energy can be absorbed or emitted in an
indivisible quantum of magnitude hf. Planck energy equation is:
E = h f.
(8)
It can be also written as
E / f = h.
(9)
It is seen from (9) that "h" is the energy associated with one oscillation of the vibrator, on the
following basis.
It has been shown elsewhere [2,3] that a time varying gravitational potential at the surface of
an atom produces light (Fig. 10); and that one shell of light produced due to atomic vibration
has energy close to the experimentally determined value of h. Though Planck believed that the
oscillator emits its own energy (kinetic, potential) possessed by it structurally, by deriving h
from the varying gravitational potential in space external to the oscillating atom (Fig.10), a
new fact has been brought to light: that the "least energy" produced (in each shell of light) is "
E / f". Therefore, the quantity "h f" is, actually, the energy contained in f-numbers of
successive light- shells produced by the oscillator in unit time, and cannot be an "indivisible
quantum" of light-energy available at an instant, which Planck assumed.
Further, as stated earlier, the structures of the oscillators, either electrons or atoms, are not
suited to absorb or emit energy-a serious misconception continuing since Maxwell's
theoretical conclusion that oscillations of electric current leads to a loss of energy from the
system in the form of electromagnetic waves. The modern concept that heat and light energy
get detached from the oscillating atoms is corroborated in the following: "4…the collisions
between atoms and molecules in a gas are said to be perfectly elastic. Although this is an
excellent approximation, even such collisions are not perfectly elastic; otherwise one could
not understand how energy in the form of light or heat radiation could come out of gas." But
such a concept of energy absorption and emission is basically wrong with the vortex structure
226
of electron and atom. Even in 'oscillating electric current', the electrons cannot part with their
structural energy (the velocity field in the vortex).
The intrinsic angular momentum of electron derived from its vortex structure: L = (4/5) m e c
re; substituting the values of me and re, it is found [2,3] to be 7.5 times less than the Planck
constant. However, for an average atom, Planck constant computed is close to the
experimentally determined value [2,3].
The dimensions of h are that of angular momentum-same as the angular momentum of
electron given above. Though, the angular momentum of electron is 7.5 times smaller than the
accepted value of the Planck constant, the nearness of the two values may lead to a guess that
the orbital electrons in the atoms are indeed the electric oscillators that produce light, as
imagined by Planck and others, and as is also the prevalent concept. In this conjecture,
however, following difficulty arises.
An atom shows overall electrical neutrality in the region beyond the orbital electrons, where
only the gravitational field of the atom should exist. On account of this, h has been computed
theoretically with the considerations of the time-varying potential of gravitation alone [2,3].
This is not to say that a charged atom will not produce light; rather the value of h obtained
from an assembly of charged oscillating atoms should be different, and so also the nature of
light (frequency, wavelength) produced.
Since the structure of light is shown to consist of successive shells, it can be said that light
energy exists in quanta, where quanta is defined as "energy in each shell"; whereas, the
kinetic energy of a moving body, which is proportional to the velocity of the body that can
continuously vary, can not have quanta of energy. Any generalization coming out of Planck
energy equation, and leading to the concept that all forms of energy occur in quanta, is
therefore erroneous.
Black Body Radiation
In a hollow cavity, the equilibrium distribution of electromagnetic radiation energy,
experimentally obtained, shows that at low frequency the energy is proportional to f 2, while at
high frequency there is an exponential drop. Whereas, the theoretical energy distribution as
per Rayleigh-Jeans law gives excessive energy for higher frequency, such that if integrated
over all frequencies the total energy becomes infinite. Though, classical mechanics places no
limit to the frequency of the mechanical oscillators (atoms), a limit to the oscillator's
frequency is imposed by the motion of the fluid-space submerging the atomic vortices
(oscillators). The displacement of the atoms from their mean positions displaces space, which
has a limiting speed c. If an average radius of atoms is taken as taken as 1.5 x 10 -8cm, the
displacement of an atom on either side of its mean position up to a length equal to the radius
will involve total displacement relative to space as 3x10 -8cm. Time required for the fluid
space to move up to this length at its maximum speed is: 3x10 -8cm/(3x1010cm/s) = 10-8s. The
nos. of light shells produced in one second due to this atomic oscillation will be 10 18/s, which
is the frequency of the light produced. Thus, maximum frequency of the oscillators in thermal
radiation, excluding X-rays and gamma, should be limited to about 10 18/s. It can therefore be
inferred that the exponential fall of energy distribution in cavity at higher frequencies is due
to the reaction from space at higher oscillation frequencies. The classical concept that to
determine the total energy within a cavity (black body radiation), integral has to extend over
all the frequencies is based on a misconception that atoms oscillate in the void ness (reaction
less) of space and hence there can be no limit to their frequency of oscillation.
Explaining Photoelectric Effect - Einstein's Error
In the vortex structure of atom (Fig.11), the vortices of the orbital electrons, interlocked with
the velocity fields of the atomic vortex, are carried round the nucleus as explained earlier.
227
As is well known, the outer orbital electrons, if interacted with light of appropriate
wavelength, are released in photoelectric effect. It is now believed that the photoelectrons
absorb energy from the incident light for their release, and also for the kinetic energy that
they possess. On this phenomenon, the following new aspects are to be taken into account.
As stated before, absorption of energy by an electron is, structurally, impossible. The orbital
electron, already in circulating motion, possesses kinetic energy due to the velocity field of
the atomic vortex. This energy is computed: The nuclear radius of an average atom is, r n =
2.37 x 10-9 cm. Like an electron, the nucleus too has its axis of rotation and, hence, the
maximum electrostatic field is confined in a circular vortex in a plane (more or less), at right
angles to the axis of rotation. In the irrotational vortex, space-circulation velocity falls
inversely as the radius of rotation. In the electron vortex, in the diametrical plane transverse to
the axis of rotation, c re = constant. Applying this relationship also on the nuclear surface,
c r e = u n rn
(10)
where un is the maximum tangential velocity of space on the nuclear surface in the
diametrical plane at right angles to the axis of rotation. Substituting in (10) the known values
of c, re, and rn = 2.37 x 10-9 cm, we have
un = (3x1010) 4x10-11 / 2.37x10-9 = 5x108 cm/s.
(11)
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This velocity, as stated above, falls in the atomic vortex (around the nucleus) inversely as the
radius of space rotation. Assuming the radius of rotation of the outermost orbital electron to
be 10-8cm, the space circulation-speed, which is also the tangential-velocity of the orbital
electron, will be
v = un (2.37x10-9cm) / 10-8cm =(5x108cm/s) 2.37x10-1 =1.2x108cm/s.
(12)
The kinetic energy of the orbital electron is
E kin = (1/2) me v2 = (1/2) 10-27 (1.2x108) 2 = 7.2X10-12 erg.
(13)
The experiments show that the kinetic energy of the photoelectrons is about 8x10 -12 ergs,
which is so very close to the value obtained above (13). It is thus seen that Einstein mistook
the source of the kinetic energy of the photoelectron, thinking that it came from the incident
light; whereas, the reality is that the velocity field in the atomic vortex projects the electron
after the incident light has triggered its release, as explained below.
Production of light due to oscillation of an atom has been mentioned before (Fig.10). We shall
analyze here the displacement of an atom during its oscillation, and the radial flow of the
surrounding space. An atomic nucleus, composed of independent electronic voids, closely
packed, approximates to a "spherical hole" in space, central with the atom. The atom, during
displacement equal to its diameter, leaves a "hole" in its previous location. This "hole" is
filled due to radial flow of space at speed c, through the light's first wavelength λ, which gets
formed. The time taken for this flow across the wavelength is λ/c; and the acceleration of
space is c / (λ/c), which is c2/ λ. Each successive wavelength, formed due to the oscillations of
the atom, possesses the above inward acceleration-field across it (radial). Now suppose that
the spherical wave front of one of these shells, during its transmission, meets an orbital
electron of an atom. The orbital velocity v of this electron, is derived from the atomic vortex
which subjects it to an inward acceleration v 2 / r, where r is the radius of its rotation. The
electron is held by electrical force, created by the above inward acceleration towards the
nuclear center. The acceleration field c 2/λ, within the wavelength of the light shell that meets
the orbital electron of the atom, is also inward, that is, towards the light source. For the
electron to be released from the atomic vortex, the above two acceleration fields must be
equal and opposite. Thus,
c 2 / λ = v2 / r
Or
λ = c2 r / v2.
(14)
(15)
Substituting the values: v = 1.2 x 10 8 cm/s obtained above (12); r = 10-8 cm; c = 3x1010 cm,
the value of λ comes to, 6.25x10-4 cm, which corresponds to the cutoff frequency of, 3 x 10 10 /
6.25x10-4, that is, 0.48 x 1014 cycles/s. (For metallic sodium, the threshold frequency is about
5x1014 sec-1). Considering the approximate nature of the assumptions on the orbital radius of
electron, and the radius of an average size of nucleus, with which the space-circulation
velocity around the nucleus and the orbital velocity of the electron were calculated; any better
result from (15) to conform to the experimentally obtained value of threshold frequency is
unlikely. For, the orbital radius of the electron, if supposed to be 10 -9cm, rather than 10-8cm,
the thresh hold frequency calculated from (15) will be closer to the experimental value.
The additional information given by (15) is as follows. In atomic vortex, the velocity field
falls inversely from the nucleus center; and therefore, the inner orbital electrons will have
higher speed of rotation. On release by the incident light shell, these electrons will possess
higher kinetic energy. It is seen from (15) that for higher value of the electron's speed v, the
wavelength λ is smaller. It is thus concluded that with higher frequency of the incident light,
229
the photoelectrons released will show higher kinetic energy. This is an experimentally
observed fact.
The above analysis shows that the concept of the photon-nature of light, with an indivisible
quanta of energy possessed by each photon, is a case of the most serious misconception,
which led Einstein (who was a believer in the emptiness of space, as evident from the
formulation of special theory of relativity) to wrongly treat light-energy, hf, as the
instantaneous value (when in reality, this energy is produced and accumulated in unit time);
because this way, the kinetic energy of the photoelectrons, as observed experimentally, could
be explained without going deeper into the structure of the atom (that became known later
about 1912 through Rutherford's experiments) to determine whether the photoelectrons have
any other source in the atomic structure that imparts kinetic energy to them at the time of their
ejection from the atoms.
Though, Planck integrated together the energy of f nos. of shells erroneously, he still believed
that light energy is distributed uniformly over an expanding set of wave fronts. In contrast,
Einstein conceptualized that the energy of light is not distributed evenly over the whole wave
front, as the classical picture demanded; rather it is concentrated or localized in discrete small
regions. With the help of both these energy integration and concentration operations, the right
order of magnitude of the kinetic energy of the photoelectrons, as observed experimentally,
could be achieved at an instant in the quantity hf .
For better understanding of the physical significance of the "indivisible quanta", we take the
following example: Consider the case of a light source producing successive spherical wave
pulses or spherical shells of light with frequency f, say 10 15/s and wavelength 3x10-5cm. In
one second, the energy produced by f nos. of shells will be hf, that is 6.62x10 -27 erg s x 1015/s
= 6.62x10-12erg. Now, if it is desired to make the energy "hf" indivisible, then the independent
shells produced successively in one second become indistinguishable, and the new imaginary
wavelength of this light will become: λf = (3x10-5) cm x 1015 = 3x1010cm; while the
frequency will be one, that is, only one wavelength of this large width of 3x10 10cm will be
produced in one second. The quantum physics will accept the energy of this new shell of light
as calculated above, but not the new wavelength and frequency. It will accept the energy
content of this new shell of light for explaining the photoelectric effect; and will reject the
wavelength and frequency because the hidden inconsistencies in the photon model will come
to the fore.
Without any physical picture, clarity and meaningful explanations, some of these ambiguous
conceptions on the fundamental nature of light laid foundation to quantum physics.
Shortest Wavelength of Light
As is known, in positronium, the electron and positron circle each other, till annihilation; this
happens due to interaction of their vortices. At the final instant preceding annihilation, the
rotation of the particles will reach the limiting speed c, because this is the speed that space has
on the interfaces of the particles. In (15) the value of v will be equal to c. Also the distance
between the centers of the particles being 2re, the value of r in (15) will be 2re. Substituting
these values in (15), the shortest possible wavelength of light is
λs = c2 (2re) / c2 = 2 re = 2 (4 x 10-11 cm)= 8 x 10-11 cm.
(16)
The shortest wavelength of light in the universe is produced consequent to the annihilation of
electron and positron.
230
Interaction of X-rays with Atoms
High-speed electrons, projected inside a vacuum tube and stopped by its walls produce Xrays. Here, each electron on impact and almost instantaneous-rebound leaves a "spherical
hole" of the size of electron-void at the point of its contact with the wall, to be filled in with
the space flowing nearly at speed c. This process is somewhat similar to the light produced
during annihilation because, here too, the potentials in space associated with the electron at
the instant of impact, die away, producing (which is seen as) X-rays. From each point of
electron's contact with the wall, a spherical shell of light expanding at speed c will arise.
Though the energy distribution on the wave front of the shell will fall inversely as the square
of the radius of the expanding shell; yet, this shell after transmitting for some distance and
with depleted energy-density on its wave front, on meeting an atom of a metal, releases an
electron possessing kinetic energy almost equal to the kinetic energy of the first electron that
produced the X-ray pulse. Indeed, the principle of energy conservation cannot explain this
phenomenon because the same is not relevant here. Recognizing that light has the nature of
successive shells, and in each shell, across the wavelength, exists an "acceleration field" of
constant magnitude independent of the energy density in the wave front; the release of the
electron, as discussed earlier in the case of the photoelectric effect, is attributable to this
acceleration field, rather than to the energy density in the X-ray's wave front. If however, the
explanation is sought with the idea of energy exchange between the X-ray and the ejected
electron, this effect is most puzzling. In the words of Sir William Bragg: 'It is as if one
dropped a plank into the sea from a height of 100 feet, and found that the spreading ripple was
able, after traveling 1000 miles and becoming infinitesimal in comparison with the original
amount, to act upon a wooden ship in such a way that a plank of that ship flew out of its place
to a height of 100 feet.' Yet this effect was not utilized to support the wave nature of light. It
was argued that the X-rays when passed through a gas, ionize only few molecules, and had
the rays had the wave-property many more molecules should be ionized since the wave will
meet all the molecules. This argument does not hold good with the shell nature of light;
because, the acceleration-field in the X-ray shell has to be in opposition to the acceleration
field of the orbital electron, that is, both the opposing acceleration fields must be in line for
effective nullification of the electron's bond in the atomic vortex; which requires that the
orbital electron, at the instant when it meets the light-shell (wave front), should be moving
tangential to it. Obviously, such a disposition of the light shell and the electron can be only in
rare encounters and, hence, the numbers of the ionized molecules with one shell of light are
expected to be limited. Thus it is seen that wave nature (or more precisely shell nature) of
light can explain the ionization of gases by the X-rays satisfactorily.
Bohr's Theory of Atomic Radiation
As per classical electromagnetism, electric charges in acceleration will radiate energy, and
hence the orbital electrons in the atom will lose energy due to which the emitted radiation
should continuously change. However, the existence of sharp spectrum lines, are not in accord
with the above prediction of the classical theory. As a solution to this problem, Bohr
postulated different 'energy states' for an atom, such that when it falls from a higher to the
lower energy state, it emits a photon with energy hf as per Planck's energy equation.
As discussed before, in the space vortex structure of the atom and electron, the orbital
electrons have already their fixed orbits. These electrons, carried by the vortex around the
nucleus, can neither lose any energy (structural, potential or kinetic) due to orbital motion, nor
change their orbits due to strong bond created by the velocity fields in between the nucleus
and the electrons; because 'losing energy' by an electron signifies 'losing part of its vortex
structure'. Further, these electrons make negligible contribution to the gravitational potential
231
of the atom that, as seen before, produces light due to its time variation [2,3]. Moreover, the
basic error of Bohr lies in the application of the concept of Planck's indivisible energy quanta
hf, in equating the same with the differential energy between the two energy states, composed
of the sum of the kinetic energy of the orbital electron and the electrical potential energy of
the proton-electron system; this is because, as mentioned before, the energy 'hf' is the quantity
produced in a unit time, whereas, the energy released due to difference between two energy
states of Bohr (even if the energy states are supposed to exist) is instantaneous.
The Compton Effect
Compton's experiments are said to confirm that photon is a concentrated bundle of energy.
The experiment consisted of a beam of X-rays of known wavelength falling on graphite
block. He measured the intensity of the scattered X-rays with respect to their wavelength. His
conclusion is that the X-rays are not waves but several photons each with energy, "h f". A
photon, in his experiment, collides with a "free" electron in the graphite block, like the
collision of billiard balls. He treats in his mathematical analysis the "free electron" as the one,
which is not bound with the atom of the graphite block, and is at rest. The collision of photon,
assumed with a free electron, has the following implication.
As is well known, X-rays can damage molecules and ionize gases; and like in photoelectric
effect, will extract electrons bound in atoms. In the latter case, even if the outermost orbital
electron is released, its own kinetic energy in the atomic vortex, as discussed before, will be
about 10-11erg. By assuming the collision of the X-ray with a "stationary" electron, the initial
kinetic energy of the electron prior to its release from the atom has been neglected. In any
case, one cannot assume that the X-ray interacts only with a "free and motionless" electron.
This kinetic energy of about 10-11erg will be larger for the inner orbital electrons, which rotate
at greater speed. For, an inner orbital electron, with an average speed of three times the speed
of the outermost electron, will increase the above kinetic energy to about 10 -10erg. The
quantity of energy, accounted in Compton's experiment against the kinetic energy of the recoil
electron, is about the same order of magnitude; the concept behind is that the electron's recoil
energy comes from the energy of the incident X-ray photon. If an X-ray of frequency 10 17 is
used during the experiment, its energy as per Planck energy equation will be; hf = 6.6x10 -27x
1017 = 6.62x 10-10erg, which is not far from the above figure of the kinetic energy of the
ejected electron that it would have had in the vortex of the atom due to its rotation prior to the
release. On account of neglecting the initial kinetic energy of the released electron, and
matching this figure with the indivisible energy quanta, Compton's conclusions on the photon
nature of X-rays become erroneous. The misinterpretation of Compton experiment - that Xrays is not of wave but photon-nature - led to a misleading picture of photon, both
qualitatively and quantitatively.
Another misconception in the above experiment is to believe that a bullet-like photon after
striking an electron rebounds with a reduced frequency. Evidently Compton believed that a
single photon has a frequency; that it oscillates, perhaps, across its line of motion. As stated
earlier, frequency for light would be meaningful only if it is defined as the numbers of waves,
photons or shells, produced per unit time. But, in case of a single photon, its wavelength is not
known in a physical way except for the mathematical expression c / f, which leads to an
imaginary large wavelength of 3 x1010cm, and a single frequency, described earlier.
Compton's interpretation of his experiment together with the basic concept of relativity that
all kinds of energy should have mass, made photon to possess hypothetical mass, momentum
and inertia, while the most fundamental cause for its observed uniform motion at the constant
speed of light remained unknown.
From the relevant literature, it is seen that Compton's arguments to assign momentum to a
photon run as follows: As per the classical wave theory of light, if a body fully absorbs the
energy E from a parallel beam of light, then a linear momentum E/c is transferred to the body.
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Based on this Compton, using Planck Energy equation E= h f, derives momentum, p, for an
individual photon
p = E / c = h f / c = h / λ.
(17)
But the "radiation pressure" on a body is otherwise explainable by the interaction of light shell
with the gravity field of atom without absorption of light energy [4]. The classical physics is
equally wrong in the concept of absorption and emission of light energy. Further, the use of
Planck Energy equation makes a single photon to possess enormous energy, that is, 10 16 times
the actual energy, if we use light of frequency 10 16/s, because in reality, the energy of a single
shell of light is, 6.62x10-27erg, as determined by Planck Constant.
It is seen that the concept of "energy quanta" misguided Compton too (after Einstein and
Bohr) in the interpretation of his experimental results.
Constancy of the Speed of Light in Special Theory of Relativity
Einstein postulated that different observers, moving at uniform velocities relative to each
other and to a source of light, should find their measurements of the speed of light to be the
same, provided they use a defined reflection procedure. Let us suppose that light consists of
several particles of energy (energy-as conventionally interpreted today, such that there is little
difference at quantum level between matter and energy) say, electrons with properties of mass
and momentum, being projected from a light source at random in all directions so as to form a
uniform spherical distribution. The observers can choose any one of these particles for the
test. A particular observer, moving in the same direction as his chosen particle, will find its
speed different from the measurement of the other observer who is moving against the motion
of the particle, as per classical relativity. Similarly, if light is imagined as a swarm of photons,
each with mass, momentum and kinetic energy (as believed to day), being emitted from the
source at random without any constant interval between the two successive photons from the
same atom, the Galilean relativity will indeed be applicable, similar to the above-cited
example of the shower of electrons; and the two observers will measure different velocity for
the same photon. But, as shown before, the structure of light is that of successive shells of
mass-less energy with a constant time-interval between the fronts of the adjoining shells
emitted from each atom, as determined by the atom's vibration. It's the time-interval of
emission between the successive shells that determines the frequency of light; whereas, in the
earlier example of the photon-model of light, the frequency of light is a mere mathematical
quantity, E/h, having no relationship with the timings of emission of the two successive
photons from the same atom. It is this haziness on the physical picture of the frequency and
wavelength of a photon that leads to misinterpretations of the results of several experiments
devised to check the above postulate of special relativity. The following simple analysis,
almost trivial, supports constancy of light-speed measurements by different observers in
relative uniform motion postulated by Einstein.
In Fig.12 a source of light S (stationary with respect to space) from which a single spherical
shell of light, produced consequent to the annihilation of an electron and a positron located in
S, is transmitted at a constant speed c relative to the medium of space.
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When the wave front of this shell meets the eye of an observer O, who is also stationary
relative to the static space, let him record this instant assuming that his time is the same as that
of any other observer (universal time) who may even be in motion relative to space. Let him
also record the instant when the tail end of the shell passes away from him. If λ is the radial
width of this light-shell (wave length of this shell of light is r e, equal to the electron radius),
then, from the ratio of λ and the time difference between the above two instants, say t 1, the
observer can calculate the speed of light from the relation
c = λ (1/ t1) = λ / t1
(18)
because, light-effect is postulated to be transmitted within the wavelength at constant speed c
relative to the stationary space. Let S produce similar shells in succession such that the tail
end of a shell coincides with the front of the following shell. If the nos. of shells received by
O in unit time is f, he will calculate the distance covered by f nos. of shells in unit time as fλ,
and time duration as ft1. With the ratio of these two quantities he will get the value of c, same
as before. It is seen that the measurement of the light velocity across one wavelength is the
same as across any of the successive wavelengths, provided the successive shells are similar
with no interruptions in between. Now let O move with a uniform velocity v relative to the
static space towards S, and record his timings across one shell. Because his velocity relative to
the light shell now is v + c, time elapsed across one shell will be
234
t2 = λ / (c + v)
(19)
which is shorter than t1 measured earlier. The moving observer's eye interacts with the lighteffect within the approaching shell for a shorter duration now and, hence, he sees the
wavelength as:
λm = length through which the light effect is transmitted in time t2
= c t2 = c λ/ (c + v).
(20)
The nos. of shells meeting the eye of the observer in unit time from (19) will be
fm = 1 / t2 = 1 / [λ / (c + v)] = (c + v) / λ.
(21)
The moving observer can now determine the light speed from (20) and (21) as:
Speed of light = λm fm = [c λ / (c + v)] (c + v) / λ = c.
(22)
From (18) and (22) it is seen that the observer, in moving as well as stationary states, finds
that the speed of light is constant; and he reaches this conclusion without sacrificing the
traditional concept of time.
In the well-known experiment of Sagnac, a beam of light is split into two halves that travel
around closed identical paths (reflected through mirrors) in opposite directions, and combined
again in a detector to examine their interference pattern. The rotation of the apparatus
produces shift in interference fringes as a function of the angular velocity. From (20) and (21)
the reflecting mirrors along one path, rotating opposite to the light beam, will 'see' shorter
wavelength and, proportionately, more of light-shells in unit time (frequency); while the
mirrors rotating in the same direction as the light beam in the other path, will see longer
wavelength and lesser nos. of the light-shells in the same time interval. On account of this, the
wavelength as well as the frequency of the two beams reaching the detector will be different
and, consequently, a shift in the interference fringes will occur. The product of the
wavelength and the corresponding frequency for each path of the beam remaining the same,
the mirrors placed in the two paths (observers) will find the same value of the velocity of
light. Therefore, on rotation of the apparatus, appearance of the shift in the interference
fringes in Sagnac's experiment should not be taken to mean that the light has different speeds
(relative to space) along the two paths.
The above interpretation of Sagnac experiment can be confirmed by increasing the nos. of the
reflecting mirrors in each path; in which case the shift in the interference pattern should
increase.
The effect of light at a space point involves creation of light shell there from the already
existing gravitational potential at that point, and its further transmission. This process repeats
continuously as the light shell traverses each point in space. In the various experiments, set up
to determine the light speed, only transmission aspect of light is taken into account, neglecting
the process of the formation of the wavelength-the radial spread of light. That is why a "ray"
of light, supposed to be continuously issuing forth from the source, is erroneously supposed to
have instantaneous reflection from a mirror, and also instantaneous interaction with the eye of
the observer; as if the wavelength is zero. Due to this misconception, it does not become
apparent that a moving mirror reflects light of wavelength different from what it receives; and
a moving observer too sees light of wavelength different from what he sees the same light to
be, when stationary relative to space.
Considering Einstein's treatment of special relativity, in the moving frame of reference (with
respect to the stationary one) the reflecting mirror for the light signal located at the X- axis,
235
should also be moving at uniform velocity like the observer; the ray of light (replaced by
annihilation light source, sending out light-shells one after the other) from the origin of the
axes towards the +X axis in this frame of reference will be reflected by the moving mirror at
an increased wavelength and decreased frequency, as shown above; and the observer, because
of his motion opposite to the reflected ray, will find the wavelength of this light decreased
and the frequency increased proportionately. In the stationary frame of reference, the
stationary observer receives the reflected ray of the same wavelength as that of the ongoing
ray. Thus, the observers in both the reference frames find the reflected ray having the same
wavelength. Since their time is the same as the universal time, the nos. of shells per unit time,
that is the frequency of the light ray, will be equal for both of them; hence, they get the same
velocity of light irrespective of the motion of the moving observer.
Fresenel, around 1820, postulated ether-drag in a moving material medium and increase in
light velocity on account of this. His ether-drag is close to the velocity-field that gets
associated with the moving molecules of matter-responsible for momentum [2,3].
Transmission of light along the motion of the medium will increase the wavelength, whereas,
it's opposite direction will decrease it. As the respective frequencies also will proportionality
change, the velocity of light in both the directions of light will remain the same. This subtle
aspect, that despite changes in wavelengths the speed of light will be the same, had not been
taken note of. Fizeau's experiment to measure speed of light in flowing water detected
changes in speed because he based his conclusion on fringe-shift that will occur when unequal
wavelengths are superposed.
In the assumed void-ness in space of 20 th century physics, which provides no explanation to
the creation of matter and fields, speed of light too has no medium, either for its creation or
for transmission; in fact in a medium of nothing ness, matter and light cannot exist. Therefore,
if the velocity of light measured by different observers in uniform relative motion with respect
to each other has to be the same as postulated in special theory of relativity, the spatial-reality
and shell-nature of light require recognition. With this proposed conceptual shift on the basic
nature of the absolute vacuum and the nature of light, the relativistic concepts involving
changes in length and time dependent on the motion of the observers will become redundant.
Light speed is Independent of the Motion of the Source
Consider an electron with its vortex structure. At any point in space, the velocity field and its
radial distance from the vortex center will determine the magnitudes of its gravitational and
electrostatic potentials [1,2.3]. As discussed earlier, a displacement of the electron's center
will produce changes in the potentials; such changes will occur during electron's motion,
either uniform are accelerating. The equalization of potentials due to self-action of space takes
place at speed c with respect to space. Therefore, considering motion of electron at ordinary
velocity, it can be assumed that the field structure of electron retains its original symmetry of
distribution as before in static state.
Let an electron and a positron, moving together at ordinary speed, under go annihilation.
After collapse of the electron-void during annihilation, it loses mass, charge, and its existence;
but, since the entire field distribution can not die instantly, the light shell produced continues
its transmission relative to space with the point of annihilation as its center, independent of
the speed of the particles prior to the instant of their annihilation. The point of annihilation
and the surrounding field structure get fixed relative to space subsequent to the annihilation.
On similar arguments it will be seen that light produced during atomic vibration is transmitted
at speed c relative to space due to self-action of space to equalize the potential gradients.
Further, since light shells are mass less entities, not emitted from within the electron or atom
in the light source, they cannot carry the momentum of the source (light-producing particles,
atoms and electrons in the constitution of the moving source of light).
236
Time Dilation
The traditional concept of time was revised in special relativity. Though it has been shown
above that with the shell-nature of light, the postulate of relativity on invariance of the speed
of light in different frames of reference is supported, the following thought experiment reveals
the fallacy of the often-quoted arguments5 in support of time dilation.
Fig.13 shows a platform in uniform motion with two observers A and B on it, and another
stationary observer C on the ground.
The relativist's view is that 'if the observer A lights a match-stick creating a flash, the observer
B sitting opposite to him will think that the flash has directly come to him along the route PQ,
whereas, the observer C will see the path along PQ 1, since, during the time the flash has
reached him, the platform has reached to a new location P1 Q1 R1 S1. The path of the flash
does not look the same to the two observers B and C. Since the flash is moving with A, it
seems to B taking a longer path; and if the speed of light is to remain the same, the longer
path must seem to take longer time: time must pass faster for C'. The misconception on the
nature of light in the above statement is the presupposition that "the flash is moving with A".
But is the flash really moving with the observer A? It has been shown above that the speed of
light is independent of the motion of the source. Hence, the uniform motion of A cannot be
imparted to the flash of light that he creates by striking a match. To further pinpoint the
relativistic misconception on the motion of the flash along with A, let us suppose that A has
with him an electron and a positron that undergo at some instant annihilation. As explained in
the earlier section, the point of annihilation along with the field structure of the particles will
237
get fixed in space, while the observers A and B will move on. Supposing, B can see the point
of annihilation P even prior to the instant when the light shell consequent to annihilation
reaches him, he will see that P is shifting to his left due to his own motion (relative to space)
to the right along with the platform; and by the time B reaches Q1, he will see that the light
shell has taken the route PQ1 to reach him; PQ1 is the same length as seen by C. Therefore, the
assumption of the relativist that the flash of light is moving with A is erroneous. Further, if the
stationary observer C stands at D, where PQ1 = PD, the light shell will reach both B and C at
the same instant.
It has been shown that the new concepts of 'time dilation' and 'simultaneity' are clearly
superfluous in special theory of relativity, since, the invariance of the speed of light in
different frames of reference in relative uniform motion follows otherwise from its very basic
nature.
Conclusion
The ether was declared superfluous in special relativity without identifying and providing a
substitute for a universal entity, which could create cosmic energy and matter. And in the
absence of a basic theory of matter that alone can reveal the genesis of material properties
(mass, inertia, charge), and the associated energy-fields including electromagnetic, any
generalization that the laws of nature are invariant in respect of all inertial systems will
certainly lead to a highly complex theorization, just as special relativity has come to be. But,
despite that, discarding photon model of light, and with a nonmaterial fluid space, Einstein's
Light-Principle-that the velocity of light is invariant in respect of all inertial system, is
vindicated with the shell-nature of light, which light in reality is.
Notes
*
Former Executive Director (Nuclear Projects), Nuclear Power Corporation, India.
1
It has been shown that Planck constant is not a universal constant; and, theoretically, each atom has a
Planck constant with slight difference in magnitude. Electron too has a Planck constant.
2
Creation of electrons and positrons take place in the interiors of the stars and the galactic center,
where space circulations reach the limiting speed.
3
The word "pressure" is used in material fluid; for fluid-space another appropriate word is to be
coined.
4
The Feynman Lectures on physics, Feynman,Leighton, Sands; Vol. 1, page 10-9.
5
"The Clock Paradox", Dr. J. Bronowski, Scientific American, February 1963, Vol. 208, No.2. pp.
134-144.
References
1. P. Tewari, (1982), "Space is the Absolute Reality", Proceedings of ICSTA, International
Publishers, East-West , Niederschocklstr, 62, 8044 Graz, Austria.
2. P. Tewari, (1995), Beyond Matter - A Comprehensive Theory of the Material Universe,
Editor: Wolfram Bahmann, Feyermuhler Str, 12, D-53894 Mechernich.
3. P. Tewari, (1984, 1996), Beyond Matter, Crest Publishing House, G-2, Ansari Road, Darya
Ganj, New Delhi - 110 002.
238
4. P.Tewari, (2000), "Conceptual Error on the Fundamental Nature of Light-Phenomenon in
classical electrodynamics, led to the Complexities in Quantum Physics", Journal of New
Energy, Vol.5, No. 1.3084 E.3300 South, Salt Lake City, Utah 84109-2154.
----Paramahamsa Tewari was born on January 6, 1937, and graduated in
Electrical Engineering in 1958 from Banaras Engineering College, India, and
held responsible positions in large engineering construction organizations,
mostly in Nuclear Projects of the Department of Atomic Energy, India. He was
also deputed abroad for a year at Douglas Point Nuclear Project, Canada. He
retired in 1997 from his position as Executive Nuclear Director, Nuclear Power
Corporation, Department of Atomic Energy, India, and is the former Project
Director of the Kaiga Atomic Power Project. Fundamentals of physics attracted
Tewari's imaginations right from the early school and college days. Over the
last two decades his new ideas on the basic nature of space, energy, and matter
have concretized into definite shape from which a new theory (Space Vortex
Theory) has emerged. The theory reveals the most basic issue of relationship
between space and matter precisely pinpointing that space is a more
fundamental entity than matter. The physical significance of mass, inertia,
gravitation, charge and light are revealed by extending the analysis in the
theory beyond material properties and into the substratum of space, which
again is broken down into fieldless voids, thus showing the limit to which a
physical theory can possibly reach. The real universe is shown to be opposite to
the current concepts of concrete-matter and empty space. The books that he has
authored on Space Vortex Theory are: The Substantial Space and Void Nature
of Elementary Material Particles (1977); Space Vortices of Energy and Matter
(1978); The Origin of Electron's Mass, Charge Gravitational and
Electromagnetic Fields from "Empty Space" (1982); Beyond Matter (1984). He
has lectured as invited speaker in international conferences in Germany, USA,
and Italy on the newly discovered phenomenon of Space Power Generation. For
the practical demonstration of generation of electrical power from the medium
of space, Tewari has built Space Power Generators that operate at over-unity
efficiency, thereby showing that space medium indeed is the source of
generation of basic forms of energy.
http://www.tewari.org/
[email protected]
[See even the presentation of Dr. Tewari's book which is published in the first
Section of this same number of Episteme]
239
On the Space-Vortex Structure of Cosmic Bodies
(Paramahamsa Tewari, B. Sc. Engg.)
1. As per the recent recorded data on the solar wind close to the surface of the sun, the wind
velocity varied from a minimum of about 380 km/s to the maximum of about 500 km/s,
giving an average of 440 km/s [ http://soho.nascom.nasa.gov/ ; 48 hours of solar wind data on
10 July 2002]. While the sun rotates axially at a peripheral speed of about 2 km/s at the
equator in the plane at right angles to its axis, the reason for so high a wind velocity is briefly
explained with the principles of space vortex theory.
René Descartes, the great French philosopher and mathematician, in his Vortex Theory,
postulated around the middle of the 17th century that the solar system is a large vortex of ether
(space) that he defined to be a "property less" fluid. And in this vortex, the planets were
carried along their orbits with no relative motion between them and the surrounding ether.
"He firmly denied that the earth moved (relative to the neighboring space medium), and
asserted that it was carried along with its water and air in one of those larger motions of the
celestial ether which produce the diurnal and annual revolutions of the solar system"
[Pioneers of Science; Sir Oliver Lodge; Dover Publications, INC.]. His above concept was
powerful enough to protect him against any possible persecution by the church which, unlike
Galileo, did not occur. That Descartes was right in his principles is clear from the fact that in
addition to the explanation and derivation of the most basic phenomenon of surface gravity of
the sun and the planets, the genesis of the solar wind close to the sun's surface can also be
computed with the principles of Space Vortex Theory (SVT) which has postulates very
similar to the Cartesian Philosophy.
In my paper "On Planetary Motion caused by Solar Space Vortex" [Journal of New Energy,
Vol. 3, No. 2/3, August 1998], Kepler's third law was derived, showing that the orbital speed
of a planet is inversely proportional to the square root of the distance from the sun's center. If
v is the orbital velocity of a planet whose orbit is at a distance r from the sun
v = k / (r)1/2
(1)
where k is a constant of the solar space vortex.
Substituting the known value of the orbital speed of the planet Mercury (it can be any other
planet also) and its distance from the sun in (1), k is determined. Now, using this value of k,
and substituting in (1) the sun's radius for r, it is calculated in the paper referred above that: v
= 436.7 km / s. This shows that in the near hood of the sun's surface, its gaseous matter will
be subjected to a maximum average velocity of 436.7 km / s, due to fluid-space circulation
around the sun in the solar space vortex. The above computed value is so very close to the
recorded data (440 km / s) mentioned above.
The existence of the solar space vortex and the reality of the space-circulation gets proved (in
the earlier paper) by deriving the surface gravity of the sun as: g s = v2 / Rs, where v is the
space velocity calculated above, Rs is the radius of the sun and gs is its surface gravity. The
value of 274 m / s2 obtained through the above calculations is exactly the same as accepted to
day.
240
It is most unlikely that through any other contemporary physical theories so accurate
quantitative results and physical explanations revealing the genesis of the solar wind can be
had.
2. The Space Vortex Theory deals with the fundamental structural relationship between the
universal matter and the space of the universe.
Postulating the medium of space as a nonmaterial fluid, with a limiting flow and rotation
when in vortex motion, it is shown that the universal matter cannot exist, or be created, in the
absence of a dynamically real (energetic) space, as the only source of primordial energy. A
circulating fluid-space creates energy and matter as its own vortices. The following are some
essential aspects of this theory.
- The most fundamental state of energy is an accelerating volume of the fluid-space.
- The electron is identified as the only fundamental particle of matter - an irrotational vortex
of space with a limiting speed (speed of light relative to the absolute vacuum) of rotation.
- The property of "mass" (introduced in the Newton's laws of motion) of electron is shown to
be due to a discontinuity in the energy distribution (field-less-void) in its vortex-structure at
the center, rather than due to some kind of densification and continuous distribution of energy
at the electron's center, as generally supposed currently. The property of inertia exhibited by
matter follows from an "inward acceleration field" from the circulating-space acting towards
the electron-center due to the existence of the central void in its structure.
- The most fundamental field is "velocity field" defined as the velocity of a fluid-space-point,
when space is in linear or circulating motion. The "charge" and "mass" of electron are shown
proportional to the limiting value of this velocity field. The direction of spin in the electron's
space-vortex determines the nature of electric charge; positive are negative.
- A "gravitational potential" in space is created with the breakdown of the fluid-space in the
electron's vortex-structure during its creation. Thermal radiation (light) from a vibrating atom
is caused in space by a time-varying gravitational potential of the atom-only remotely
connected with the orbital electrons in the atom as believed today.
- All the universal constants, presently known, have been derived with a single universal
constant (speed of light) and the electron radius.
241
- Surface gravity of the Earth, the Sun and the other planets, has been theoretically derived
with a hitherto unknown formula in celestial mechanics.
- A new electrical repulsive force operating between the Sun and the planets that maintains
stability of the planets in the solar system has been found. The orbital radii of the planets have
been accurately determined with a new equation that uses this electrical repulsive force.
- The constancy of speed of light as measured by different observers in relative motion is
supported (special relativity), while time dilation is concluded to be superfluous.
- A serious misconception on the basic nature of light and, consequently, inappropriate use of
Planck constant in photoelectric effect and atomic structure, are shown to be the cause that led
to the present complexity and incomprehensibility of the quantum physics.
- An unambiguous proof of the operation of the electrical forces of repulsion and attraction
among cosmic bodies has been provided recently with the observation of the colliding
galaxies; It was predicted that if two galaxies are drawing closer and closer, then this would
be due to an electrical attractive force, and for that to exist, the galaxies in question must have
opposite directions of their spin.
- A decisive proof of generation of output electrical power more than the input has been
achieved in a new system of power generation, thus showing a clear cut violation of the
Lenz's law (law of conservation of energy).
If indeed this pair of galaxies are drawing closer, then their spin directions
will be opposite; the attractive force will be electrical (in addition to gravity).
It would be of interest to know precisely the spin directions,
as this will prove the existence of electrical forces too between cosmic bodies.
3. This last comment is concerning the recent press news from NASA on the picture of
colliding galaxies (NGC 4676) sent back by the Hubble Space Telescope's new camera.
242
You can see above a picture enlarged from the NASA website (from
http://antwrp.gsfc.nasa.gov/apod/ap990722.html). They are spinning in opposite directions in
support of the predictions contained in my article "On Planetary Motion caused by Solar
Space Vortex" [Journal of New Energy, Vol.3, No.2/3, Summer/Fall,1998].
[See http://antwrp.gsfc.nasa.gov/apod/colliding_galaxies.html for more pictures.]
It was brought out in this article that the planets and the sun, due to their axial spin, will
possess electrical charge, and will therefore be subjected to electrical repulsive forces between
them. The stability of the planets in the solar system was analyzed taking this new electrical
repulsive force into consideration.It was also generalized that all cosmic bodies, includig
galaxies, possessing axial spin will have electrical charge. Cosmic bodies with similar
direction of spin will repel; whereas, with opposite directions of their spin, will attract
electrically. The formula for the quantitative determination of the electrical forces was also
given in the article.
It thus follows that the force of attraction between the pair of galaxies reported by NASA, if
these are drawing closer and closer, is an electrical attractive force, and the galaxies must
necessarily have opposite directions of their spin.
It is added that the modern celestial mechanics takes no account of the electrical forces
between the cosmic bodies.
It would be of interest to know if the spins of these galaxies are indeed opposite; that will
prove the existence of the new electrical force discussed in my above article.
----[A presentation of the author can be found at the end of his previously published
paper]
243
Louis T. More: Prophet of the 20th Century
(Theo Theocharis)
Strange Rapprochment
"Belatedly ... a strange rapprochement is under way between the forces of religion and
science." (Peter Stanford, "Science meets God half way", The Sunday Times News Review, p.
3.9, 27 October 1996.)
As I have been pointing out since 1977, and as I shall show below, this rapprochement is a
debut-de-siècle [beginning-of-century] matter, not a fin-de-siècle [end-of-century] affair.
<<The Chief Rabbi [of the UK] Dr Jonathan Sacks [has said]: "I don't think there would have
been a single social observer in the year 1900 who would have predicted that religion and
religions would be as strong in the world today and, indeed, even in the liberal West, as they
are.">> (John Tusa, "They said God was dead - why won't he lie down?", Church Times
(UK), 8 November 1996, pp. 12-13.)
Prophet
But at least one "social observer", Louis Trenchard More, who of course had to be
knowledgeable in all the subjects that matter, came very close to making this prediction not
much later than 1900 - specifically in 1912. The understanding shown in 1912 by L. T. More,
("The Theory of Relativity", The Nation (USA), Vol. XCIV, pp. 370-371, 1912) is so deep,
the insight so visionary, and the prescience so profound, that the following relevant passage
deserves to be quoted in full:
<<Both Einstein's theory of Relativity and Planck's theory of the Quanta are proclaimed
somewhat noisily to be the greatest revolutions in scientific method since the time of Newton.
That they are revolutionary there can be no doubt, in so far as they substitute mathematical
symbols as the basis of science and deny that any concrete experience underlies these
symbols, thus replacing an objective by a subjective universe. The question remains whether
this change is a step forward or backward, into light or into obscurity. It is held, and
apparently rightly, that the revolution effected by Galileo and Newton was to replace the
metaphysical methods of the schoolman by the experimental methods of the scientist. Now
the new methods might seem to be just the reversal of that step, so that, if there is any
revolution in thought, it is in reality a return to the scholastic methods of the Middle Ages.>>
(Louis Trenchard More, "The Theory of Relativity", The Nation (USA), Vol. XCIV, pp. 370371, 1912.)
Mysterianism
In his regular column "Hard drive" in the London Daily Telegraph weekly supplement
Connected, Peter Cochrane is described thus: "Peter Cochrane holds the Collier Chair for the
Public Understanding of Science and Technology at the University of Bristol." In the opening
paragraph of his "Bricks in an unreal city" (Hard drive, 10 February 2000), Peter Cochrane
wrote with evident admiration: <<Richard Feynman was ... a founding father of our most
244
fundamental atomic understanding. One of my favourite Feynman key pronouncements is the
shrewd:
'I think we can safely assume that no one understands quantum mechanics.'>>
In fact Richard Feynman was the best known living scientist in the world from the 1960s until
he died in the 1980s. Moreover, the curious "no one understands quantum mechanics"
viewpoint articulated in the very last year of the 20th century by a Professor for the Public
Understanding of Science and Technology at a leading University has been the standard
viewpoint of establishment science and philosophy throughout the 20th century. I recognised
the stark and gross inconsistency pointed out here from the very beginning of my scientific
studies in the 1970s when I also devised my standard rebuttal:
"A theory that no one understands is not scientific but hopelessly mystic." (Theo Theocharis
"Men of [Surreal] Ideas", The Listener, 4 May 1978.)
Science Re-Enslaved by Religion
"The 17th century is better remembered as the time that science liberated itself from
theology." (Malcolm Povey, "In need of perspective", Financial Times, 20 June 1994, p. 26.)
Prediction: The 20th century will be better remembered as the time that science
re-enslaved itself to theology.
[email protected]
245
Ultimate Creative Ignorance
(Theo Theocharis)
I supply here independent support to the important argument involved in the title of Foster
Lindley's ([email protected]) "Creative Ignorance" (Human and Ecological Risk Assessment,
Vol. 7, No. 6, pp. 1593-1601, November 2001). It is useful to quote these passages that
explicate the label "Creative Ignorance":
"The probabilist converts cognitive uncertainty into physical uncertainty. … As the
probabilist presents his failure to differentiate as a discovery about the nature of reality, it is
a creative use of ignorance."
It is not only the probabilist who "converts cognitive uncertainty into physical uncertainty".
Every professor of physics everywhere does the same, and more (ie worse). The so-called
Heisenberg's Uncertainty Principle was devised (in the 1920s) in order to codify a certain
measumental inaccuracy. It was converted right away into physical uncertainty. Not much
later, it was converted again - this time into some new convoluted combination of
physical/cognitive certainty/uncertainty: the physicist knows (with certainty?) that the
physical entities featuring in Heisenberg's inequality really fluctuate, but (at least for the time
being) within the restricted bounds permitted by Heisenberg's inequality.
This last conversion is best debunked as follows:
Creation of the Universe: According to current cosmological thinking, a(n already existing)
quantum of energy (obeying the again already existing law of Heisenberg's Uncertainty
Principle) transformed itself into matter which somehow inflated itself to the presently known
Universe. One is bound to ask:
Which proposition is more believable?:
(i) The Universe was created by an all-mighty God;
(ii) The Universe was created by a tiny quantum fluctuation.
On careful reflection, the latter does not give sufficient credit to Heisenberg, so it must be rephrased thus:
(ii)' The Universe was created (some 15 billion years before Heisenberg's birth) by an
uncertainty in Heisenberg's knowledge.
There have been debates in physics and philosophy forums as to whether the act of observing
creates the observed entity, but is there one professor of physics anywhere who has ever
repudiated these other (now seventy year old) moronic abuses of elementary Aristotelian
logic?
[email protected]
246
What the Global Positioning System
Tells Us about the Twin's Paradox
(Tom Van Flandern)
Abstract. In the GPS, all atomic clocks in all reference frames (in orbit and on the ground) are
set once and stay synchronized. We can use this same trick to place a GPS-type clock aboard
the spacecraft of a traveling twin. That clock will stay synchronized with Earth clocks,
allowing a clear resolution of the twin's paradox in special relativity - why the traveler expects
to come back younger, and why the stay-at-home twin is not entitled to the same expectation.
Background
In a previous article [1], I described how the Global Positioning System (GPS) is a marvelous
laboratory for testing relativity because the orbiting and ground atomic clocks have differing
gravitational potentials and high relative speeds. Their precision is such that the predicted
relativistic clock corrections are confirmed to within a fraction of a percent. However, initial
expectations based on special relativity were that clocks in different reference frames should
have different readings and rates. Yet the Global Positioning System is designed in such a
way that, after the individual clock rates are adjusted once pre-launch for the predicted
relativity effects, all satellite clocks in all orbits remain in synchronization with one another
and with all ground clocks without need for further consideration of relativity corrections,
with the exception of one small correction needed for the slight non-circularity of the orbits.
The previous article concluded with a discussion of what this means for Einstein's special
relativity (SR), and for the competing Lorentzian relativity (LR) theory. The comparison
favors LR as the simpler theory describing the relativity of motion.
As history buffs may know, the Lorentz Ether Theory (LET) [ 2] appeared a year before
Einstein's 1905 publication of SR. Of course, LET incorporated both the relativity principle
(taken from Poincare, but it was first formulated about a generation earlier) and the Lorentz
transformations that bear his name. The essential new element introduced by Einstein the
following year was the equivalence of all inertial frames, thereby eliminating the need for the
luminiferous ether. This first postulate of SR makes the Lorentz transformations reciprocal;
i.e., they work equally well from any inertial frame to any other, then back again; so it has no
meaning to ask which of two identical clocks in different frames is ticking slower in any
absolute sense. The second postulate of SR makes the speed of light independent of not only
the speed of the source (which is also true generally for waves in any medium, including
luminiferous ether), but also independent of the speed of the observer (which is a feature
unique to SR).
Today, many physicists and students of physics have acquired the impression that
these two postulates have been confirmed by observations. However, that is not the case. In
fact, none of the eleven independent experiments verifying some aspect of SR [1] is able to
verify either postulate. It is now widely believed that no experiment is capable of verifying
these postulates even in principle [3], because they become automatically true by convention if
one adopts the Einstein clock-synchronization method, and they become just as automatically
false if one adopts a different synchronization convention such as the "universal time"
postulate of Lorentz. Of interest here is the point that the GPS uses the latter synchronization
convention for pragmatic reasons, as I will shortly explain.
247
So is the difference between SR and LET then purely cosmetic? No, it is not cosmetic
at all. It is true that both SR and LET explain all existing electromagnetic-based experiments
and, in that sense, would remain viable theories of the relativity of motion. But the difference
between them is much more than aesthetic. In addition to a great difference in practicality for
use in systems such as the GPS (in favor of LET), the two theories differ about whether or not
material bodies can exceed the speed of light in forward time. In SR, that is proved impossible
because time ceases to advance for any entity traveling at the speed of light. By contrast, in
LR, no speed limit for material bodies exists. It is true that speed relative to the preferred
frame causes electromagnetic-type clocks (which include all ordinary mechanical, biological,
and atomic clocks) to slow, meter sticks to contract, and the momentum of bodies to be
increased by the relativistic factor γ = 1 1 − v 2 c 2 just as in SR. But in LR, time, space,
and the matter content themselves are not affected. (Here, v is the speed of the body and c is
the speed of light.) So the question of which theory better represents nature is of major
importance to the future of physics, which is presently invested in the belief that speeds faster
than light in forward time are not possible.
Today, our concepts of the "luminiferous ether" are considerably different than they
were in Lorentz's day. It is now widely recognized that the local gravity field serves as the
"preferred frame" of LET. With this alteration from Lorentz's original concept but without
any change in the math or structure of the theory, LET has now become known simply as
"Lorentzian relativity" (LR). Although LR has no intrinsic speed limit, it recognizes the innate
difficulty of material bodies composed in part of electrons, while propagating in luminiferous
ether, being able to exceed the wave speed of that ether, the speed of light. LR treats this as
analogous to a propeller-driven aircraft exceeding the speed of sound without any outside
assists, such as from gravity. A force that cannot itself propagate faster than light cannot
propel material bodies faster than light.
Of critical importance to choosing the model that best represents nature, none of the
eleven independent experiments testing SR verify frame reciprocity or distinguish SR from
LR. In fact, historically, de Sitter, Sagnac, Michelson, and Ives concluded from their
respective experiments that SR was falsified in favor of the Lorentz theory. 1 Indeed, the GPS
itself is a practical realization of Lorentz's "universal time", wherein all clocks remain
synchronized despite being in many different frames with high relative speeds. However,
subsequent re-interpretation of SR allowed that theory to survive these objections.
This "magic" is envisioned to happen by virtue of each clock in the system being
synchronized to an imaginary clock in the Earth-centered inertial (ECI) frame,
instantaneously co-located with the moving clock, and assumed to be in a gravitational
potential equal to that at sea level at Earth's poles. (Note the "coincidence" that the magic
makes use of the Lorentzian preferred frame, the local gravity field.) This trick makes the
clock rates all the same as they would have been if they were at rest in the ECI frame and in a
constant potential field. This is all very nice, but hardly what Einstein envisioned when
speaking of two clocks in relative motion, one at a station and one on a passing train. How
simple special relativity would have become all these years if physicists had realized that all
they had to do was reset the clock rates so they all ticked at the same rate as the reference
clock in the local gravity field!
The converse is also true. Suppose we did not change the clock rates before launch,
but instead let them tick at their design rates in accord with whatever speed and potential they
experienced in orbit. Now, suppose we tried to Einstein-synchronize the system of clocks.
Satellite and ground clocks would tick at different rates. And if we tried to work in any local,
248
instantaneously co-moving inertial frame, the corrections needed to synchronize with each
orbiting clock would be unique to that observer's frame and different from moment to moment
because both clocks are accelerating. The practical difficulties of operating the system would
be virtually insurmountable. What we would gain by doing that is constancy of the measured
speed of light in all inertial frames. But because all clocks are now re-synchronized to just the
ECI frame in the GPS, the speed of light is constant in that one frame, and the invariance of
the speed of light in other inertial frames is of no practical value.
In a recent article, Ashby [4] claimed that the clock-epoch correction term (also called
"time slippage" term) in the Lorentz transformations, vX c 2 (see Eq. below), can be dropped
even when its value is large, but he is very vague about why. However, this particular term is
the only difference of consequence between Einstein synchronization of clocks in different
inertial frames and Lorentz synchronization of clocks to an underlying "universal time". And
the GPS system has been designed to use Lorentz synchronization, for which one frame, the
local gravity field or ECI, is special; not Einstein synchronization, wherein clocks tick at their
natural rates and all inertial frames are equivalent. By itself, this does not prove LR "right" or
SR "wrong". But the practical difficulties for GPS of not changing the natural rates of clocks
pre-launch, or with the use of SR for any frame but the Lorentzian preferred frame, are very
great. If a ring of satellites (A, B, C, …, Y, Z) circled the Earth in a common orbit, and each
satellite tried to Einstein synchronize with the next in sequence, then when Z tried to complete
the circuit by Einstein-synchronizing with A, the corrections required would lead to time
readings for A different from the starting readings, making closure impossible.
Introducing the twins
The "twin's paradox" is an illustration of the complexity of SR's interpretations of nature.
Suppose two identical twins start out at some common instant. One remains on Earth. The
other (the "traveler") is on a spacecraft headed for Alpha Centauri (AC) four light-years away
at 99% of the speed of light, for which speed the time dilation factor is γ ≈ 7 . (We choose a
large value of γ so that the effects of the relativity of motion will be large and obvious, not
subtle.) Upon arrival at AC, the traveler turns back to Earth at the same speed (or is replaced
by a traveler already headed toward Earth of identical biological age at the moment they pass,
to avoid need for an acceleration). The round trip requires slightly over 8 years Earth time;
let's say 98 months to be specific. This is path 1 in Figure 1. When the twins are reunited, the
Earth-bound twin is 98 months old, and the traveler is 14 months old (a factor of 7 less).
Figure 2.
The traveling twin's journey to Alpha Centauri (AC) begins at Earth (E).
Upon arrival, the traveler can return to Earth by any path (1),
continue on to Beta Centauri (2), or circle Alpha Centauri (3).
That much is a clear prediction of SR. Note especially that no accelerations need
actually occur at the beginning or end of the journey, nor even in the middle if we do the
"twin replacement" trick. That is consistent with cyclotron experiments showing that
249
accelerations as such, even as great as 1019 g (where g is the acceleration of gravity at sea
level), have no effect on clocks [5]. At each stage of the journey where an event occurs,
comparisons can be made without ambiguity between adjacent points, one in each of the
inertial frames containing the clocks or twins to be compared. Despite the fact that many
textbooks discussing the twin's paradox treat accelerations as essential, that is illusory.
Accelerations are unbounded in size, and in principle can be done in an instant, allowing no
local time to elapse in any relevant frame. Accelerations (as distinct from velocities) and
forces (as distinct from potentials) do not change local clocks, clock rates, or biological aging.
Now we come to the paradox part: Why isn't the traveler entitled to claim that the
spacecraft remained at rest and the Earth traveled away at 99% of the speed of light, then
turned around and came back? From that perspective, the original traveler would argue that
the Earth-bound twin should be the younger one. We will examine the rather different
answers to that question offered by SR and by LR.
The traveler takes along a GPS clock
Let's more closely follow what is happening to our two twins. Imagine that the inertial frame
of reference containing Earth and AC is filled everywhere with synchronized clocks at rest, so
that any traveler can always look out a window and read what time Earth-frame people think
it is. See Figure 2. And let the traveler take a "GPS clock" along on his journey, along with an
unadjusted "normal" clock. The GPS clock is preset in rate before the journey so that, once
placed aboard the spacecraft, it will remain synchronized in epoch and rate with clocks on
Earth, just as real GPS clocks do. Then the on-board GPS clock will always give readings
identical to the nearest Earth-frame clock visible outside the spacecraft window. This instant
ability to compare traveler's time in his own frame with time everywhere in the Earth-AC
frame will prevent paradoxes from arising.
Figure 2.
From the Earth-frame, all stationary clocks are synchronized, and all clocks moving with the
spacecraft are not. From the spacecraft, the situation is reciprocal. However, the on-board GPS clock
always agrees with the Earth-frame clock immediately outside the spacecraft window. ©
Now let's examine the journey details. When the traveler's journey begins, the onboard native clock ticks slower than the GPS clock by a factor of seven. But isn't that already
an asymmetry present at a stage where there is simply a relative motion, and no way to decide
which twin should be aging slower? LR answers simply "yes" because the frame of the local
gravity field is the preferred frame in which clocks tick fastest, and time in all other relatively
250
moving frames passes more slowly. But SR offers the opposite answer. And understanding
that answer is the key to understanding SR.
SR is a mathematical theory built around the Lorentz transformations. Let the time T
be the reading on a clock fixed in the Earth frame; and let X be the relative location in the
Earth frame of a clock fixed in the spacecraft frame moving at speed v relative to the Earth
frame. Let t be the time reading on the natural clock in the traveling spacecraft, and x be the
relative location of Earth in the spacecraft's frame. In that frame, Earth passes the spacecraft
with a speed − v . As before, the Lorentz time dilation/length contraction parameter is γ ,
having a value of 7 when v = 0.99c . So in general, the relation between the Earth-frame
clock and the spacecraft-frame clock is:
t = γ ( T − vX c 2 )
x = γ ( X − vT )
Because the relationships are reciprocal (all inertial frames are equivalent in SR), the
inverse relations (with v → − v ) must also hold:
T = γ ( t − vx c 2 )
X = γ ( x − vt )
Now let's compare time in the two frames. First, let an observer at a clock fixed on
Earth watch time on the spacecraft clock. Then the observer is looking at a point X = vT .
Substituting that into eq. , we get the unsurprising result that x = 0 , meaning that the
spacecraft clock remains fixed at the origin of its own coordinate system. And from the time
transformation, using the definition of γ , we get t = T γ , which restates the well-known
prediction of SR we cited above that the spacecraft clock will appear to the Earth observer to
be ticking γ = 7 times slower than the Earth-fixed clock.
That much is routine. But before we leave the Earth frame, let's do one more
calculation. Suppose the spacecraft frame is likewise filled with clocks everywhere, Einsteinsynchronized with each other. Because all such clocks are at rest relative to one another, they
can simply exchange light signals and assume that the light takes equal time for the uplink
and downlink portions of its round trip. Then the average of the transmission and reception
times on one clock must agree with the signal reflection time on the other clock by definition
of "Einstein synchronization". Now, from the Earth frame, let's peer into the spacecraft frame
at the point X = 0 , the fixed location of the Earth observer. From Eq. , we now have t = γ T .
The meaning of this relation is that the Earth observer sees a succession of spacecraft-frame
clocks parading by, and time on the succession of clocks goes by γ = 7 times faster than
Earth time.
You read that right. According to SR, at the same time that each and every clock in the
spacecraft frame is seen by the Earth frame to tick γ = 7 times slower, time in the spacecraft
frame on a succession of passing clocks is passing by γ = 7 times faster than Earth time. To
repeat this essential point, in any inertial frame with a relative motion, all individual clocks
tick slower but overall frame time moves forward at a faster rate. Such is the effect of the
vX c 2 term in the transformation. The time difference between clocks in different frames is a
function of the different rates they tick at and of the "time slippage" effect, whereby time is a
function of location in any relatively moving frame. In SR, this would remain true even if we
used the GPS trick and eliminated the rate differences between clocks. In general, the time
slippage effect dominates the effect of a changed clock rate for any clock in a frame with
251
relative motion. (N.B. Time is everywhere the same when viewed from within an inertial
frame. But it is everywhere different in that same frame from the perspective of any other
frame with a relative motion because of time slippage.)
It is worth studying the points in the preceding two paragraphs because, while
mathematically permissible, they defy our intuitions and are what makes relativity such an
unintuitive theory.
The traveler looks back at the Earth twin
Now let's switch to the spacecraft frame and look back at the Earth-frame clock at x = vt
using Eq. . Then we get X = 0 and T = t γ . So the spacecraft clock sees the Earth clock
ticking γ = 7 times slower than itself. Substituting x = 0 , we get T = γ t : the spacecraft twin
sees Earth-frame clocks streaming by outside his window with time elapsing on a succession
of them at γ = 7 time faster. So both effects, relative clock rates and frame time from time
slippage, are reciprocal and symmetric between the two frames.
And that is SR's answer to the symmetry challenge we posed at the outset of the
spacecraft's journey. Both LR and SR predict that the spacecraft's clocks will appear to tick
slower than all Earth-frame clocks as viewed by Earth-frame observers. But SR (only)
predicts that the situation looks reciprocal and symmetric for observers in the spacecraft frame
looking at clocks in the Earth frame. The traveler is therefore not surprised by the behavior of
the GPS clock on board, which correctly records a combination slower clock rate plus a fast
time slippage for the Earth frame, and stays in agreement with the Earth-frame clocks passing
by just outside the spacecraft window.
Now consider the traveler's arrival at AC, when the spacecraft turns around or is
replaced by a spacecraft heading Earthward at the same speed. Neither the natural clock nor
the on-board GPS clock changes rate or reading significantly during the turn-around.
However, before the turn-around, the Earth-frame clocks say four years (actually, 49 months)
of Earth time have elapsed since the journey began, and the spacecraft natural clock says
seven months of spacecraft time have elapsed. But the spacecraft infers that only a single
month has elapsed back on Earth because a single clock in another frame is affected only by
clock slowing, not time slippage; whereas the spacecraft agrees that 49 total months have
elapsed at AC because the journey began with a 48-month time slippage for AC and added
one more month during the journey. As usual, time slippage corrections (where applicable)
dominate clock readings in other frames.
We now come to the crux of the resolution of the paradox, which seems paradoxical
only in SR. The traveler has inferred that only one month has elapsed back on Earth since his
journey began, so by spacecraft-frame reckoning, Earth time is just one month later than the
actual departure time. For example, if the journey commenced in 2000 January, when the
traveler arrives at AC, the on-board GPS clock reads 2004 February; but the traveler infers
that Earth clocks still read 2000 February. Because of the finite speed of light, the traveler can
see Earth only as it was, not as it is now, and therefore cannot check this inference by direct
observation. According to SR, all these clock-reading inferences are not just illusions, but
reflect the real, physical time for each frame involved. So at the same time and place that an
AC resident infers that Earth time is 2004 February, the spacecraft traveler infers it is 2000
February - a four-year difference; and both are correct for their respective frames.
Then the spacecraft turns around. Nothing changes locally. But inferences about
remote time change greatly because of time slippage, which now has the opposite sign. Now
252
the traveler infers that Earth time is 2008 February - four years into the future instead of the
past. As a consequence, the traveler will again infer that only one month of Earth time will
elapse during the return journey, and all participants agree that Earth time upon the traveler's
return will be 2008 March. The traveler arrives back younger (14 months old) than the stayat-home twin (98 months - over 8 years old). According to LR, this is because the traveler had
a high speed relative to the preferred frame, the local gravity field; and there never was any
symmetry between the two frames. But according to SR, the elapsed time is a combination of
slowed aging and time slippage effects, the latter changing discontinuously when the direction
of the traveler changes.2
The Earth twin thinks the traveler should naturally age slower because his clocks run
slower. And the traveler thinks the Earth twin should naturally age faster because the time
slippage effect dominated the slowed aging effect when that twin turned around. Note that the
traveler could have taken any path whatever as long as the spacecraft speed relative to the
Earth frame remained 0.99 c . Then at every instant along the journey, the traveler's
biological age will be a factor γ = 7 less than the elapsed time on the on-board GPS clock,
which will agree with the Earth clocks upon return.
Indeed, the spacecraft could have simply continued in a straight line past AC and on to
Beta Centauri (BC), say (for purposes of this example only), 8 light-years from Earth. Then
there was no turn-around event, but the traveler is still just 14 months old on arrival, and
twins born on BC at the same time the Earth twin was born (according to Earth-frame clocks)
will still be 98 months old. And the traveler will infer that the BC twins started out 96 months
old at the journey's beginning, and aged just two months during the journey. So clearly,
neither the turn-around event nor any acceleration is essential to the result; and the SR
resolution of the paradox retains its symmetry and the equivalence of all frames.
Hence, from the traveler's perspective, wherever the spacecraft goes in any direction
without changing speed relative to the Earth frame, it will encounter Earth frame clocks with
more elapsed time than on the natural clock aboard the spacecraft (but with the same elapsed
time as for the on-board GPS clock). But the traveler will infer that all clocks in the Earth
frame are always ticking slower than the natural spacecraft clock, and beings in the Earth
frame are always aging more slowly than the traveler. Everything encountered can be
explained by a combination of clock rate changes and time slippage. The traveler cannot infer
that the Earth-bound twin will be the younger one upon the spacecraft's return because Earth
experienced a time slippage event (whether sudden or gradual), rapidly aging everyone on
Earth during the traveler's journey. That time slippage event is no different in character than
the one that a hypothetical twin on Beta Centauri would experience if the traveler continued
on past AC without a turn-around event.
The traveler takes different paths
What we have just described are careful and correct inferences of SR as applied to the twin's
paradox. This also shows the essentially mathematical nature of the theory, because it does
violence to what we fondly call "common sense". The most important point to note carefully
is that the theory is internally consistent, and no mathematical contradictions can be found no
matter how the transformation equations are manipulated, or how many frames or twins are
introduced. The next important point to note is that SR makes demands on our credulity that
LR does not. Let's examine why.
At the point of turn-around on the original journey from Earth to AC, the traveler's
inferences about time on Earth changed suddenly. Instead of the physically unrealistic instant
253
turn-around, let's assume the spacecraft "orbits" around AC to perform the turn-around. (To
stay at a safe distance from the star at the same speed, this would require propulsion, not just
gravity.) This can still take a time short enough to be neglected, especially at such a high
relative speed. So the traveler's spacecraft changes from headed away from Earth and
inferring the Earth year is 2000, to traveling toward Earth and inferring the Earth year is 2008.
Again, SR says this is real, physical time, and not an illusion.
So before commencing a journey back to Earth, let's suppose the traveler orbits AC
several times. Then each time the traveler heads away from Earth in that orbit, Earth time
drops back to 2000; and each time the traveler heads toward Earth, inferred Earth time
becomes 2008. The Earth-year is intermediate for intermediate orbital positions. Now the
significance of repeating this situation several times is that, as Earth time goes to 2008, many
people will have died and others will be born. And on each occasion that Earth time reverts to
2000, some of the dead will be resurrected and some living young children in 2008 will cease
to exist in 2000. Note that while all this is happening according to SR, the on-board GPS
clock representing LR's "universal time" continues to insist that Earth time is the same as
spacecraft time and AC time: 2004 everywhere. In SR, effects of this type are never
observable because they "lie outside the observer's light cone", hidden from direct view by the
finite speed of light. Nonetheless, SR insists that such changes affect real, physical time and
are not mere illusions, because the viewpoint of each inertial frame is just as valid as that
from any other frame.
Conclusions
In LR, one reference frame (the local gravity field) is preferred; and speed cannot affect time,
but only the rate of ticking of mechanical, electromagnetic, or biological clocks. However,
just as we do not assume that time has been affected when the temperature rises and causes a
pendulum clock to slow down, LR says that changes in clock rates are changes in the rates of
physical processes, and do not affect space or time. So by carrying an on-board GPS clock on
the spacecraft, we are offered a clear choice between models: Earth time can be what SR
infers it is, or it can be what the GPS clock says it is. In the former case, SR works, but leads
to heavy-duty complexities and fantastic inferences about the nature of time at remote
locations. Moreover, the proof that nothing can travel faster than light in forward time stands
intact. In the latter case, LR works with great simplicity and in full accord with our intuitions
about the universality of the instant "now". And the speed of light is no longer a universal
speed limit because time itself is never affected either by motion or by gravity.
Aside from these practical difficulties with the use of SR in the GPS, Einstein's special
relativity is also under challenge in a more serious way from the "speed of gravity" issue,
because the proven existence of anything propagating faster than light in forward time (as all
experiments indicate is the case for gravity) would falsify SR outright [ 6, 7]. So it is entirely
possible that reality is Lorentzian, not Einsteinian, with respect to the relativity of motion. In
that case, physics may have no speed limit when the driving forces are gravitational or
electrodynamic rather than electromagnetic in nature. And that may be the most important
thing that the GPS has helped us to appreciate.
Notes
[1] T. Van Flandern, "What the Global Positioning System tells us about relativity", in Open
Questions in Relativistic Physics, F. Selleri, ed., Apeiron, Montreal, 81-90 (1998). Also available online at <http://metaresearch.org>, "cosmology" tab, "gravity" sub-tab.
254
[2] H.A. Lorentz, Lectures on Theoretical Physics, Vol. III, "The principle of relativity for uniform
translations", Macmillan & Co., London, 208-211 (1931). Contains summary of and citation to
original 1904 paper.
[3] H. Erlichson, "The rod contraction-clock retardation ether theory and the special theory of
relativity", AJP 41, 1068-1077 (1973).
[4] N. Ashby, "Relativity and the Global Positioning System", Phys.Today May, 41-47 (2002).
[5] Bailey, J., Borer, K., Combley, F., et al., "Measurements of relativistic time dilation for positive
and negative muons in a circular orbit", Nature 268, 301-305 (1997).
[6] T. Van Flandern, "The speed of gravity - What the experiments say", Phys.Lett. A 250, 1-11
(1998).
[7] T. Van Flandern and J.P. Vigier, "Experimental repeal of the speed limit for gravitational,
electrodynamic, and quantum field interactions", Found.Phys. 32(#7), 1031-1068 (2002).
1
De Sitter argued that the forward displacement of starlight (aberration) depended on absolute, not
relative, speeds because both components of a double star, each with some unique velocity, had the
same aberration. Sagnac argued that the fringe shifts expected but not seen in the Michelson-Morley
experiment are seen if the experiment is done on a rotating platform. Michelson argued in the 1925
Michelson-Gale experiment that the Earth was just such a rotating platform. Ives argued that ions
radiated at frequencies determined by absolute, not relative, motion because they had to pick a specific
frequency to radiate at. In each case, a complex-but-now-familiar SR explanation could account for
the same observed results.
2
We note in passing that the effect that SR expects accelerations or frame changes to have on remote
clocks would constitute an instantaneous action at a distance, a violation of the causality principle.
Acknowledgments
The author thanks the Meta Research Board and members for financial support, with a special
thanks to Tim Seward. The artwork in Figure 2 is Copyright (2002) by Boris Starosta,
<http://starosta.com>.
----Tom Van Flandern received his Ph.D. degree in Astronomy, specializing in
celestial mechanics, from Yale University in 1969. He spent 20 years at the U.S.
Naval Observatory, where he became the Chief of the Celestial Mechanics
Branch. In 1991, Tom formed a Washington, DC-based organization, Meta
Research, to foster research into ideas not otherwise supported solely because
they conflict with mainstream theories in Astronomy. Tom is editor of the Meta
Research Bulletin, which specializes in reporting anomalies and evidence that
does not fit with standard theories in the field. During the past few years, he has
also been a Research Associate at the University of Maryland Physics
Department in College Park, MD, and a consultant to the Army Research
Laboratory in Adelphi, MD, working on improving the accuracy of the Global
Positioning System (GPS). North Atlantic Books is the publisher of Tom's 1993
book, Dark Matter, Missing Planets and New Comets. A second edition was
published in 1999. As with his research papers, the book is critical of many
255
standard models in astronomy, such as the Oort Cloud, the Dirty Snowball, and
the Big Bang theory. Tom also organizes the Eclipse Edge Expeditions to
optimal solar eclipse viewing sites. During his career as a professional research
astronomer, Tom has been honored by a prize from the Gravity Research
Foundation; served on the Council of American Astronomical Society's Division
on Dynamical Astronomy; taught astronomy at the University of South Florida
and to Navy Department employees; been a consultant to NASA's Jet Propulsion
Lab; and done several spots for the "Project Universe" series that continues to
air occasionally on public TV.
Meta Research <[email protected]>
http://metaresearch.org/
256
REPRINTS
257
Sulle attrazioni newtoniane di origine idrodinamica
(Emilio Almansi)
1. In un liquido omogeneo, indefinito (praticamente abbastanza esteso in tutte le direzioni), si
abbia un numero qualunque di corpi C , C' , C'' , ... , i quali subiscano rapide variazioni di
forma, od anche solo di posizione, tali che il fenomeno presenti, nel suo insieme, un periodo
θ piccolissimo.
Quando siano verificate certe condizioni che accenno più avanti, avviene che, per ogni
corpo, la forza risultante delle pressioni che il liquido esercita sugli elementi della sua
superficie ha, in un intervallo di tempo multiplo di θ , un valor medio corrispondente
all'attrazione che su quel corpo eserciterebbero gli altri, se i corpi del sistema possedessero
certe masse m , m' , m'', le quali si attraessero secondo la legge di Newton.
Questo interessante fenomeno, ed altri analoghi, furono per la prima volta studiati, in casi
particolari, sia dal lato matematico, sia sperimentalmente, dal prof. C.A. Bjerknes.
L'argomento è stato poi ripreso, ed ampiamente svolto in un suo corso di lezioni, dal figlio
prof. V. Bjerknes(1).
I procedimenti analitici da me seguiti in altra Nota(2), permettono di arrivare al risultato nel
modo più semplice e generale.
2. Supporremo che nel movimento indotto nel liquido la velocità sia ovunque continua, derivi
da un potenziale ϕ , e si annulli all' infinito; che i pesi delle particelle liquide siano
trascurabili; che la densità sia uguale ad 1 .
Denotiamo con (F) la forza che al tempo t agisce sopra un corpo C del sistema. Essa può
decomporsi (Nota preced.) in due forze (F0) ed (F) . Le proiezioni X0 , Y0 , Z0 sopra gli assi
coordinati della forza (F0) sono derivate esatte rispetto al tempo di funzioni periodiche col
periodo θ : onde il valore medio (in un intervallo multiplo di θ ) della forza stessa - vale a
dire la forza che ha per proiezioni i valori medii di X 0 , Y0 , Z0 - è nullo. Noi trascureremo
questa forza (F0) .
Le proiezioni della forza (F) sono
X=
∫
σ
 1  ∂ϕ 2  ∂ϕ 2  ∂ϕ 2
∂ϕ ∂ϕ ∂ϕ ∂ϕ 
 
 dσ
 + 
+
+
 + 
 α −
∂x ∂y ∂z ∂x
 2  ∂ x 
 ∂z 
 ∂y 

,
ecc., rappresentando σ la superficie del corpo, ed α , β , γ i coseni della normale esterna(3).
Il potenziale di velocità ϕ presenta, in ogni istante, tutti i caratteri del potenziale
newtoniano di masse µ , µ' , µ'' , ... distribuite negli spazi S , S' , S'' , ... occupati dai corpi.
Infinite distribuzioni dànno luogo, nello spazio esterno, allo stesso potenziale ϕ : noi
supporremo di fissarne una. Verremo così a definire la funzione ϕ anche negli spaz! S , S',
S'' , ... Supporremo che essa risulti, in ciascuno di questi spazi, finita e continua insieme alle
sue derivate prime e seconde. Attraversando le superficie dei corpi, la funzione ϕ e le sue
derivate prime non dovranno subire discontinuità. La densità ρ relativa a questa
distribuzione di masse ideali sarà:
ρ=
− 1  ∂ 2 ϕ ∂ 2ϕ ∂ 2 ϕ 
+
+

 .
4π  ∂ x 2 ∂ y 2 ∂ z 2 
258
Ciò posto, trasformiamo, nella espressione di X , l'integrale esteso a σ in un integrale
esteso allo spazio S limitato da σ . Otterremo:
 ∂ 2ϕ ∂ 2ϕ ∂ 2ϕ  ∂ ϕ
+
dS .
X = -∫ S  2 +

∂ y2 ∂ z2  ∂ x
 ∂x
Poniamo
X1 =
∂ϕ
∂ϕ
∂ϕ
, Y1 =
, Z1 =
,
∂y
∂x
∂z
e teniamo conto della espressione di ρ . Avremo:
X = 4π
∫
S
X 1 ρ dS
e, analogamente,
Y = 4π
∫
S
Y1 ρ dS , Z = 4π
∫
S
Z 1 ρ dS .
Queste formule possiamo interpretarle dicendo che la forza (F) relativa al corpo C è, in
ogni istante, quella stessa che si avrebbe se le masse ρdS si attraessero secondo la legge di
Newton, e la costante dell'attrazione fosse uguale a 4π .
Parimente si potrebbe dimostrare che i momenti rispetto agli assi coordinati delle pressioni
esercitate dal liquido sugli elementi di σ sono uguali ai momenti delle forze 4πX1ρdS , ecc.
3. Supponiamo, ora, che le mutue distanze fra i corpi C , C' , C'' , ... siano grandissime
rispetto alle loro dimensioni lineari. Denoti P un punto fisso, che si trovi costantemente nello
spazio S occupato da C . Così per gli altri corpi C' , C'' , ... , consideriamo i punti fissi P' ,
P'' , ...
Nelle formule precedenti noi possiamo ritenere che X1 , Y1 , Z1 siano le derivate del
potenziale ϕ , dovuto alle sole masse esterne µ' , µ'' , ... (la resultante delle mutue azioni che
si esercitano tra le masse elementari ρdS di uno stesso corpo essendo identicamente nulla).
Invece di X1 , Y1 , Z1 scriviamo X1 + δX1 , Y1 + δY1 , Z1 + δZ1 , intendendo ora che X1 , Y1 ,
Z1 siano le derivate, nel punto P , del potenziale ϕ , calcolato come se le masse µ' , µ'' , ...
fossero concentrate nei punti P', P'' , ... Ponendo
δX = 4π
∫
S
δ X 1 ρ dS , ecc.,
avremo: X = 4πX1µ + δX , ecc. Ammettiamo che la forza di componenti δX , δY , δZ sia
trascurabile rispetto alla forza di componenti 4πX1µ , 4πY1µ , 4πZ1µ (ciò che potrà non
avvenire; per es., se µ= 0). Potremo allora ritenere X = 4πX1µ , ecc. Onde, detta r la
distanza costante PP' , e posto
f = 4π
µµ '
r2
la forza (F) risu1terà, in ogni istante, dall'attrazione (f) dovuta al corpo C' , e delle altre
analoghe dovute agli altri corpi.
259
Le masse µ , µ' , ... si possono esprimere molto semplicemente mediante i volumi S , S' , ...
dei corpi corrispondenti. Si ha infatti:
−1
4π ∫
µ =
σ
∂ϕ
dσ
∂n
.
∂ϕ
è uguale alla componente, secondo la normale esterna, della velocità di un
∂n
punto di σ , se diciamo ora dS l'incremento che subisce, nel tempo dt , il volume S , sarà
E poichè
ds = dt
∫
σ
∂ϕ
dσ
∂n
,
e, perciò,
µ =
− 1 dS
.
4π dt
Analogamente sarà µ' =
− 1 dS'
. Onde, ponendo
4π dt
1 dS dS '
,
4π dt dt
q=
avremo
f =
q
:
r2
dalle quali formule vediamo che se in un certo istante i volumi S , S' sono ambedue crescenti
od ambedue decrescenti, e quindi q > 0 , la forza (f) è realmente un'attrazione; altrimenti, è
una ripulsione.
4. Il valor medio (F') della forza (F) , quindi ancora della forza (F) , in un intervallo
multiplo di θ , o uguale a θ , sarà la risultante della forza (f') di grandezza
f' =
q'
,
r2
ove q' è il valore medio di q , e delle analoghe relative agli altri corpi. Avremo dunque:
θ
1
1
qdt =
q' =
∫
θ 0
4π
θ
dS dS ' dt
.
dt dt θ
0
∫
Facciamo ora un'ipotesi più particolare intorno al modo di variare dei volumi S , S' , ecc.:
supponiamo cioè che si abbia
S = S0(1+hε) , ecc.,
260
ove S0 ed h rappresentano due quantità costanti per il corpo C , ε una funzione del tempo,
periodica con periodo θ , uguale per tutti i corpi. Se poniamo
m = hS0 , m' = hS' , sarà:
dS
dε
dS'
dε
= m
,
= m'
. E, perciò,
dt
dt
dt
dt
θ
mm' dε 2 dt
( )
q' =
;
4π ∫0 dt θ
quindi
f' = k
mm'
,
r2
essendo
1
k =
4π
θ
dε
∫ ( dt )
0
2
dt
.
θ
In questo caso, dunque, attribuito alla costante dell'attrazione il valore dato dall'ultima
formula, si ha una perfetta analogia tra la forza (F') e le attrazioni newtoniane delle masse
ideali (costanti) m , m' , ...
5. Nella formula S = S 0(1+hε) , noi possiamo sostituire ad ε una funzione lineare di ε , con
che verranno solo a variare le costanti S 0 ed h . Potremo allora fare in modo che il massimo
e il minimo valore della funzione periodica ε siano +1 e -1 . Diciamo S 1 ed S2 i valori
corrispondenti di S (notando che, se la costante h è negativa, S 1 rappresenterà il valor
minimo di S ). Si avrà S1 - S2 = 2hS0 = 2m ; quindi
1
(S1 - S2) .
2
m =
Le masse m vengono così ad essere le semi-differenze fra i valori estremi dei volumi dei
corpi.
t
Quanto alla costante k , osserviamo che, se s'introduce la variabile τ =
, si ha
θ
1 dε
dt dε
dτ =
,
=
,
θ
dt
θ dτ
k =
1
θ
2
1
4π
θ
dε
∫ ( dτ )
2
dτ .
0
Di qui vediamo che per una determinata funzione ε(τ) (per esempio, se
t
ε = sen 2πτ = sen 2π ) la costante dell'attrazione è inversamente proporzionale al
θ
quadrato del periodo.
261
(1) Fields of force, Columbia University Press. New-York, 1906. Vedasi anche la Memoria di
W. Voigt, Beiträge zur Hydrodynamik, Gött. Nachr., a. 1891.
[NdR - A proposito della relazione tra i Bjerknes qui citati, e il C.J. Bjerknes autore sia di due
articoli in questa sezione di Episteme, sia del libro presentato nell'apposita rubrica della I
Parte, si veda appunto la detta recensione.]
(2) Sopra le azioni le quali si esercitano fra corpi che si muovono o si deformano entro una
massa liquida, Rendiconti della R. Accad. dei Lincei, dicembre 1913. [Riporteremo tra breve
qui di seguito il paragrafo introduttivo di questo lavoro.]
(3) Nella Nota preced. le X ed X 0 di questa Nota sono chiamate X1 ed X2 ; la quantità
sotto il segno d'integrazione nella espressione di X ( X 1 ) è denotata con -H . La espressione
di H è data a pag. 537.
-----Questo lavoro è stato pubblicato nei Rendiconti della Reale Accademia dei Lincei, 1914, Vol.
XXIII, 1° Sem., pp. 287-291.
*****
Riteniamo al solito di fare cosa utile ai lettori offrendo loro il paragrafo introduttivo
dell'articolo di cui alla precedente Nota 2, che apparve sempre sui Rendiconti della Reale
Accademia dei Lincei, 1913, Vol. XXII, 2° Sem., pp. 533-544.
Meccanica. - Sopra le azioni le quali si esercitano fra corpi che si muovono o si
deformano entro una massa liquida. Nota del Corrisp. E. ALMANSI.
1. È noto che due sfere immerse in una massa liquida sufficientemente estesa in tutte le
direzioni, aventi i loro centri in due punti fissi dello spazio, e raggi periodicamente variabili
intorno ad un valor medio, al quale si conservino sempre vicinissimi, esercitano una su l'altra
un'azione attrattiva o repulsiva, secondochè le loro pulsazioni hanno la medesima fase, o fase
opposta.
Parimente, se, restando costanti i raggi delle sfere, i centri si spostano sopra una retta,
oscillando intorno a due punti fissi, le due sfere si attraggono o si respingono a seconda che i
loro centri hanno, in ogni istante, velocità rivolte in senso contrario, o nello stesso senso.
La trattazione analitica dei problemi di questo tipo, pur supponendo, come io supporrò,
irrotazionale il movimento del liquido, e trascurabili le forze di massa, incontra difficoltà le
quali, fatta eccezione per un numero limitatissimo di casi (tra cui quelli accennati), sono da
ritersi insormontabili.
Se però ci si contenta di determinare i caratteri generali del fenomeno, di stabilire, per
esempio, se fra due corpi, in date condizioni di movimento, si esercitano azioni attrattive o
repulsive, rinunziando alla loro valutazione quantitativa, si arriva con facilità, in tutti quei casi
che più interessano, allo scopo prefisso.
È appunto la trattazione del problema così ridotto quella che io qui mi propongo(1). [...]
(1) Sul problema delle sfere pulsanti o oscillanti, ved. W. Voigt, Beiträge zur Hydrodynamik,
Gött. Nachr., a. 1891.
262
Unforgettable, unforgivable, Stefan...
(Si veda anche la foto con cui si apre il Reprint di Omero Speri e Piero Zorzi nella I Parte di questo
stesso numero/See also the photograph which appears in the Reprint by Omero Speri and Piero Zorzi
in the first Part of this same number)
Marinov: Annus Horribilis
(The Story of) A Payed Advertisement Published by Nature
(Stefan Marinov)
The year l996 will be an earthquake year for conventional physics: many formulas in the
textbooks will be changed, many century-old dogmas will be renounced and many saints will
be de-sainted. This radical change had to begin tens of years ago but the lack of glasnost in
physics all over the world has delayed it and instead to have evolutional step-by-step
reformations and several lighter earthquakes, now there will be a tremendous one. Vous l'avez
voulu, Georges Dandins!
By my half-a-century experimental and theoretical work I showed the following (see
references in my 16 books, 60 refereed papers, 8 paid advertisements and numerous papers
and editor's comments in the journal DEUTSCHE PHYSIK edited by me):
1. The principle of relativity is wrong. Indeed, I rneasured three times optico-mechanically
and once electromagnetically the Earth's absolute velocity. Its magnitude is 350 km sec -1 wlth
equatorial coordinates of its apex δ = -20° , α = 12h (approx.).
2. The principle of equivalence is wrong. Indeed, my interferometric "coupled mirrors"
experiment which was carried out during a year showed that when the laboratory's
acceleration was kinematic (acceleration with respect to distant stars), the laboratory's
velocity changed, while when it was dynamic (gravitational attraction by the Earth) there was
no change.
3. The energy conservation law is wrong. My machines MAMIN COLIU and VENETIN
COLIU which work with zero, or near to zero, Lenz effect, and SIBERIAN COLIU which
263
works with anti-Lenz effect violated this law. Only because of lack of money I could not
close the energetic cycle in the first two, but the third one was not expensive and I could run it
as a perpetuum mobile. The day when I shall present this machine at a press-conference will
be the start-day for the earthquake.
4. The Lorentz equation is wrong. If there are two electric charges q , q' moving with
velocities v , v' and the vector-distance from q' to q is r , according to the Lorentz
equation the force with which q'v' acts on qv is given by the following Grassmann formula
fG = (µ0qq'/4πr3){(v.r)v' - (v.v')r}.
(1)
Numerous experiments done by other authors (Hering's experiments are from the beginning
of the century!) and by me showed that the force acting on qv can be not only transverse to
its velocity, as required by (1), but also longitudinal. Any rational man when seeing at least
one falsifying experiment rejects the respective formula (Popper), however for thousands and
thousands of Betonköpfe [heads made with ferro-concrete!] even hundred experiments were
not enough. In the photograph [not included in the original] there is one such falsifying
experiment which (as well as the other) can be carried out by children: A cylindrical magnet
is cut along one of its axial planes and the one half is turned up-down (the magnetic forces
themselves do the rotation). Around this magnet, there is à trough filled with mercury in
which the copper ring which can be seen at right swims (the children take salt solution and
suspend the ring on threads). After sending current of some tens of amperes from the battery
at left, which is regulated by the rheostat, the ring begins to rotate. That's all!
5. The Lorentz-Marinov equation is the right one. As according to (1) f'G is not equal and
oppositely directed to fG , I obtained Marinov formula by the most simple and natural
symmetrization of (1) (take into account that r = -r')
fM = (fG - f'G)/2 = (µ0qq'/8πr3){(v'.r)v + (v.r)v' - 2(v.v')r} .
(2)
Proceeding from (2), and assuming Φ ≠ 0 , ∂A/∂t ≠ 0 , I obtained by the most simple
calculations that the force with which an electric system acts on a test charge q moving with
velocity v is
f/q = -gradΦ - ∂A/∂t + v×B + vS = Elor + v×B + vS ,
(3)
where Φ, A are the electric and magnetic potentials generated by the system at the point of
the charges location, Blor = rotA is the Lorentz magnetic intensity, Swhit = -divA/2 is the
Whittaker magnetic intensity and
Bmar = -(µ0/8π) ∫
q'(v×v')(r.v)/v2r3 ,
Smar = -(µ0/8π) ∫
q'(v.v')(r.v)/v2r3 ,
(4)
are the Marinov vector and scalar magnetic intensities. B = Blor + Bmar is called vector
magnetic intensity and S = Swhitt + Smar is called scalar magnetic intensity. (3) is called the
Lorentz-Marinov equation. If neglecting the last term and under B we understand Blor we
obtain the Lorentz equation which I call the Lorentz-Grassmann equation. That's the whole
theory!
264
6. The angular momentum conservation law is wrong. My Bul-Cub machine with interrupted
current and rotating Ampere bridge with interrupted current rotated under the action of
internal forces only. Marinov's formula allows violation of the angular momentum
conservation law as the magnetic forces with which two charges interact are equal and
oppositely directed but may not lie on the line connecting them.
7. It is impossible to violate the momentum conservation law in electromagnetism. Obvious
conclusion from Marinov's formula.
8. Displacement current does not exist. For closed circuits both Grassmann and Marinov
formulas do not allow violation of the momentum and angular momentum conservation laws
as the first terms in (1) and (2) contain total differentials. As conventional physics believes in
the displacement current of Maxwell, it accepts that all currents always are closed. I showed
by numerous experiments that there is no displacement current (neither in vacuum nor in
dielectrics) and one can interrupt the circuits by the help of condensers. At the age of 15 I
understood that displacement current is a phantasmagoria and presented to my teacher in
Sofia the following objection: "If the displacement current between the plates of a condenser
acts with magnetic forces on other currents, then according to Newton's third law the other
currents must act with magnetic forces on the displacement current and set it in motion. But
how, comrade teacher, can vacuum be set in motion?" Teacher's answer was: "Shut up,
child!"
9. The gauge transformations are illegitimate. According to conventional physics not the
potentials but the intensities determine the motion of the test charge (exactly the opposite is
true), and thus any change of the potentials which leaves the intensities the same is allowable,
i.e. one can calibrate the potentials. It is easy to see that the calibration divA = 0 is allowable.
Thus conventional physics believes that a really existing force, the Whittaker force fw =
-qvdivA/2 = qvSwhitt can be put equal to zero. Monstrosity! To see the action of fw take two
metal spheres the one charged positively and the other negatively. Put around one of the
spheres a circular wire along which current flows, so that it is perpendicular to the line
connecting the spheres. When connecting the spheres by a wire and current begins to flow, the
circular wire begins to rotate. The only force which acts on the circular wire is fw .
10. There is no propagation of interaction. As only mass can move from one point to another,
"interaction" can be only a ghost. But a rational man does not believe in ghosts. on the other
hand, the mathematical expressions of Bmar and Smar show that the "fields" cannot propagate
in space with a certain velocity, as Bmar and Smar depend on the direction of motion of the
test charge. To these people who may object that one is not sure whether the Lorentz-Marinov
equation is the right one, my answer is: Until the day when some falsifying experiment should
be presented (ths day will never come!) the world is impelled to accept it as true.
11. Potential, radiation and radiation reaction electric intensities. These three kinds of
intensities can be obtained if putting in the expression for the Lorentz electric intensity Elor
(see (3)) the observation electric and magnetic potentials
Φ= q/4πε0r , A = µ0qv/4πr
with r = r' - v'.r'/c , v = v' + u'r'/c,
(5)
where r , v , u are distance, velocity and acceleration at the observation moment t and r' ,
v' , u' at the advanced mornent t' = t - r/c (conventional physics wrongly calls t' "retarded
moment"). Conventional physics, following Liénard and Wiechert, wrongly writes A with
265
v' . For this reason conventional physics obtains only the potential and radiation intensities,
Epot , Erad , and artificially introduces the radiation reaction intensity Erea coming to
phantasmagoric "self-accelerations". Proceeding from (5) I (and any child who can
differentiate!) obtained also the radiation reaction intensity Erea = -µ0qw/6πc , where w = w'
is the charge's super-acceleration. Erad = µ0qr'×{(r' - v'r'/c)×u'}/4π(r' - v'.r'/c) is due to
moving mass (radiated energy), as charges moving with acceleration lose energy, while Erea
acts on the radiating charge itself. To obtain all radiation effects one has simply to integrate
the obtained formulas for a single charge. That's nearly all about radiation of electromagnetic
waves!
12. There are no "fields". According to the "field-marshals" the "fields" exist physically. One
can move them and a moving magnetic field produces electric field, etc. When I hear all these
stupidities, I get diarrhea. After repeating the Rowland experiment (a magnetic needle near a
charged disk deviates when the disk is set in rotation), I carried out the inverse one (the disk
at rest, the needle rotates) and the co-moving one (disk and needle rotate), taking instead of a
needle a Hall detector. According te the "field-marshals" the inverse experiment must give the
same effect as the direct one (I observed no effect), while the co-moving experiment must
give null result (I observed the same effect as the direct experiment). The inertial experiments
can be done charging a conveyer belt.
13. Current conducting wires become charged positively. Conventional physics asserts that
they remain neutral (Clausius postulate). Meanwhile always after measurements, the rheostat
in the photograph [included in the original but not here, due to its poor quality] remained
charged and touching it by hand there was a spark. The positive sign was established by the
method known to ancient Greeks. Every child explains the effect taking into account that the
positive electrode of the battery "sucks" electrons from the wire while the negative electrode
"spits" electrons and the former effect is primary.
14. B-machines and S-machines. The electromagnetic machines working on B are called Bmachines and these ones working on S are called S-machines. By the help of the first three
fingers of his right hand any child older than 15 can show when looking at the third term in
(3) that the B-generators brake. Meanwhile by the help of only one finger any child younger
than 15 can show when looking at the fourth term in (3) that the S-generators accelerate.
15. The perpetuum mobile SIBERIAN COLIU. Swhitt produced by the first term in (2) and for
a complete circuit is null. For this reason can be observed only at interrupted circuits (see item
9). However Smar can be different from zero also for a complete circuit. Why then has
nobody observed it? - Because all people have worked with cylindrical or quasi-cylindrical
magnets for which Smar = 0 . Who has cut a cylindrical rnagnet in two pieces rotating the one
half up-down? - NOBODY!!! The first man who has done this is called Gennadi Nicolaev and
lives in Tomsk [... - Russian words follow]. For this reason I called this magnet the
SIBERIAN COLIU magnet and the perpetuum mobile which I constructed with it is the
SIBERIAN COLIU machine. The machine shown in the photograph [once again not included
in the original] is a SIBERIAN COLIU machine. It will work as a perpetuum mobile if the
driving torque produced by the current induced in the ring when it will be set in rotation with
a certain velocity will be larger than the friction torque. I constructed this machine in the
photograph in 1993 and the last three years I did nothing else than to try to increase its driving
torque and decrease its friction torque. The driving torque was produced only by the S (i.e.,
Smar ) currents. Smar is very strong near the cutting plane, from the one side positive, from the
other negative. The dozens of my SIBERIAN COLIU machines are presented with
photographs in DEUTSCHE PHYSIK.
266
16. All conventional theories for the origin of Earth's magnetization are wrong. If rotating a
cylindrical piece of any metal by a boring machine, one sees that it becomes magnetized.
Conventional physics believes first that only ferromagnetics become magnetized and second
that the magnetization is proportional to the angular rotational velocity, as this was
promulgated by Barnett. My friend C. Monstein demonstrated that the magnetization is
proportional to the linear rotational velocity and I called this the Monstein-Barnett effect.
Proceeding from the Monstein-Barnett effect I calculated the magnetization of the Earth, the
Sun and the planets, obtaining excellent coincidences with the measured values. As Venus is
the only planet whose nucleus is liquid, it is not magnetized. The most cherished conventional
theory for Earth's magnetization is the "unipolar dynamo theory" of Elsasser. It is ridiculous,
as a unipolar machine can work only at the existence of sliding contacts and moving with
respect to each other parts.
17. Magretic energy does exist. By the most elementary speculations and calculations I
showed that: a) the gravitational energy of two masses is not a negative quantitiy, as accepted
by conventional physics, but a positive quantity, b) the gravitational potential generated by all
masses of the universe is equal to c2 , c) electricity and gravity are two completely analogical
sciences from a mathematical point of view. The only difference is that the gravitational
"charges" are the proper masses m0 = m/(1 - v2/c2)1/2 and that negative masses do not exist.
There are no other differences. Thus a magretic energy, i.e., a "magnetic kind" of energy in
gravity must exist and gravity is to be called gravimagretism (this is the title of part IV of my
encyclopaedic work CLASSICAL PHYSICS). I proposed a very simple experiment which can
reveal the existence of magretic energy. This experiment, moreover, can serve for
measurement of the Earth's absolute velocity.
18. The recession hypothesis for the galaxies is wrong. I call stellar "red shift" this one which
is caused by the gravitational action of the star on the emitted by it light, galactic "red shift"
this one which is caused by the gravitational action of the respective gaIaxy and cosmic - by
all cosmic matter. Conventional physic believes that the big "red shifts" of Iight coming from
remote galaxies are due to their recession velocities. This is a phantasmagoria. The most
simple calculation, which can be carried out by any child, shows that they are due to the
gravitational action of all cosmic matter and that they are proportional not to the distance of
the emitting galaxy (or quasar) but to the square of this distance. I showed that the
experimental data fit much better to a square plot. Respectively, instead of a Hubble constant,
a Hubble-Marinov constant is te be introduced, for which the children obtain the strictly
defined value HM2 = 2πγµ/3c2 , where γ is the gravitationa constant and µ is the average
mass density in the Universe.
NOTE. On the 5 March 1996 I submitted to NATURE my paper AFTER 500 YEARS
COLUMBUS-EGG-PROBLEM HAS FINALLY BEEN SOLVED, in which I show how a body
can be maintained in a state of UNSTABLE equilibrium (problem which, contrary to the
general opinion, Columbus has NOT solved). My "Marinov egg" is supported by magnetic
forces. If it has SPHERICAL form, it has three degrees of freedom (the Euler angles) free and
represents moreover a PERPETUUM MOBILE. If before the 1 May the paper will not appear
in the scientific columns of NATURE, I shall publish it as a paid advertisement. In the first (or
second) case 15 days after the publication I shall present my SIBERIAN COLIU perpetuun
mobile at a press conference.
Stefan Marinov
Morellenfeldgasse 16, A-8010 Graz
-----
267
[The previous pages are reproduced from pp. 34-35 of Marinov's Deutsche Physik
(International Glasnost Journal on Fundamental Physics), Vol. 5, N. 19, July-September 1996,
and appeared in Nature, Vol. 380, N. 6572, 28 March 1996, p. xiv, as a payed Advertisement,
with the attached NOTE as reported. Marinov extensively explains later on in his journal (pp.
40-45) how he tried to publish instead the following text, but that he was told that: "we are
enable to publish the advertisement unless [this note] is deleted [...] we would naturally
refund your money" (letter from Nature, 15th March 1996), so that he had to accept at last the
publication of an "amended" version.]
> In my advertisement (whose text is published on p. 34 of this issue) the following NOTE
was attached:
NOTE. In 1986 Dr. Maddox, the then-editor of NATURE, accepted for publication my big
paper "Experimental violations of the principles of relativity, equivalence, and conservation
of energy and angular momentum". During my visit in March 1987 he personaily began to
compose this paper on his computer and I stayed in his office and corrected any sheet which
he gave me. He could not compose the whole paper and I left London. However during a year
the composition of the paper remained, as Schubert's symphony, unvollendet. Thus in June
1988 I flew to London and composed the paper myself in NATURE's composition office. The
paper had to appear on the 18 August 1988 but because of the Benveniste's case ìts
publìcatiori was postponed for the 13 October. "I do not have the stomach for a second battle
in such a short tirme" wrote to me Dr. Maddox on the 29 July. This paper is still not
published. If the paper will not appear in the scientifìc columns of NATURE until the 1 May
1996, I shall publish it as a paid advertisement. In the first (or second) case 15 days after the
publicatìon of the paper I shall present my perpetuum mobile SIBERIAN COLIU at a press
conference.
As in a week or so after my 13-February-letter no answer came from Mrs. Smith, I asked her
on the phone which is the matter. She told me that there are problems with the NOTE and that
she has to consult Dr. Campbell and Dr. Maddox. Until the 26 February no answer came and I
phoned again. [...] [The conclusion of this story has already been mentioned: after Nature's
refusal of 15th March, Marinov proposed a different shortened version, which was found
acceptable: "I can confirm that your amended paragraph of today is acceptable for
publication" [loc. cit., p. 45].
----[The following one is Nature's letter of 26th January 1996 (see the quoted issue of Deutsche
Physik, p. 38) which refused a paper proposed by Marinov only a few days before, namely on
22nd January 1996. It was this circumstance which forced him to ask for the publication of
the payed advertisement above.]
268
MARINOV'S NOTE.
First I would like to note that if an editor has pricks of conscience when rejecting a paper, he
never mentions in bis rejecting letter (if he decides such a letter to write!) the title of the paper
and the date of submission. The same does Dr. Campbell in his above letter. Thus the title of
my rejected article was
EXPERIMENTAL VIOLATIONS OF THE PRINCIPLES OF RELATIVITY,
EQUIVALENCE, AND CONSERVATION OF ENERGY AND ANGULAR MOMENTUM,
and it was submitted on the 22 January 1996 by post.
This paper, as a matter of fact, was accepted for publication by Dr. Maddox in April 1986
and in final form in June 1988 but it never appeared in NATURE (see the story in detail in the
following pages). The paper, as composed by me in June in London was published in THE
THORNY WAY OF TRUTH, Part III (1988), p. 146.
But Dr. Campbell allowed to me to publish an advertisenìent in NATURE and in her fax of
the 9 February Mrs. Smith wrote me that the price for two pages will be 5290 £.
----[Furthermore, on April 1996, after a new correspondence's exchange, Dr. Campbell wrote to
Marinov the following final letter, which is published at p. 50 of the quoted issue of Deutsche
Physik, together with a comment of our poor friend Stefan*.]
269
> Only in religion and similar AUTHORITATIVE spiritual and ideological domains are there
"orthodox" and "unorthodox" views. In physics there are views confirmed or rejected by
experiments. Of course, there are views for whose verification there are no experiments, or
contradictory views which predict the same experiments. However a FORMULA can be
either right or wrong, a formula cannot be "orthodox" or "unorthodox". In my writings I
present FORMULAS. And I present EXPERIMENTS which can be calculated by these
formulas and which cannot be calculated by the formulas of "orthodox" physics.
----[* On the morning of July 15th 1997, Stefan Marinov committed suicide in Graz, the Austrian
town where he lived very poorly since many years as an exile. As far as his scientific activity
is concerned, since the times of the previous Advertisement, he had the resources to edit three
more numbers of Deutsche Physik, namely NN. 20, 21 and 22: the very last one is dated
April-June 1997...
More information about this singular figure of dissident XXth Century physicist can be found
in the article N. 13 ("In Stefan Marinov memoriam") published at the web page:
http://www.dipmat.unipg.it/~bartocci/listast.htm .]
270
Intorno alla legge di resistenza al moto
dei corpi in un mezzo pulviscolare
(N. Moisseiev)
INTRODUZIONE.
Ci proponiamo nel presente articolo di esporre la deduzione della legge di resistenza al moto
dei corpi in un mezzo pulviscolare, basandoci sugli stessi schemi che furono già posti a
fondamento di. talune sezioni di un nostro precedente lavoro(1).
Questioni relative alla teoria del moto in un mezzo resistente cominciano nuovamente a
suscitare interesse fra gli studiosi che lavorano nel campo della cosmogonia ed in campi
affini. Indichiamo ad esempio la serie dei lavori pubblicati dal prof. T. Levi-Civita (2), i quali
mirano tanto a dedurre la legge razionale di resistenza al moto, quanto a stabilire le equazioni
differenziali del moto stesso, ed altresì la serie di studi di G.N. Duboscin (Russ. Astronomical
Journal), dedicati principalmente all'analisi generale delle forme e delle proprietà del moto di
un punto in un mezzo resistente ed in campi di forze centrali.
Il problema stesso può essere trattato da due punti di vista diversi: come problema di
resistenza di un fluido compressibile o no al moto in seno di esso, oppure come problema di
resistenza al moto di un mezzo composto di punti discreti, di molecole, l'azione reciproca.
delle quali ha importanza e va presa in considerazione solamente per definire la struttura del
mezzo nel suo insieme, mentre nell'interrelazione loro col corpo che subisce resistenza al suo
moto, dette particelle reagiscono su di esso in modo affatto indipendente l'una dall'altra.
La prima questione, che rappresenta in sostanza un problema di idro od aerodinamica, può
presentare interesse per l'astronomia solamente in relazione al moto in mezzi di densità
sufficientemente grande, come per es. il passaggio di una meteora attraverso l'atmosfera di un
pianeta ecc.
Il secondo problema per altro presenta per la cosmogonia un interesse considerevolmente
maggiore, avendo esso da fare con mezzi molto rarefatti. Ed è per l'appunto questo secondo
aspetto del problema che prendiamo di mira nel presente lavoro.
§ I. - Espressioni generali per la resistenza nel caso di flusso semplice.
Rappresentiamoci un corpo sferico S , di raggio D intorno al cui centro è descritta una sfera
di raggio ρ , che divide il campo - in cui si può trascurare l'attrazione di questo corpo S - dal
campo, interno per rapporto a questa "sfera d'azione", in cui il moto di un punto isolato viene
retto unicamente dall'attrazione del corpo S . Rappresentiamo con x0 il quoziente D/ρ .
Ammettiamo poi che lo spazio esterno alla sfera d'azione sia, con densità uguale, riempito
di particelle materiali tanto piccole per dimensioni e per massa che si possa non tener conto
della loro azione reciproca. Sia n il numero di particelle per unità di volume e µ la massa di
una particella isolata. Supponiamo, che tutte le particelle abbiano masse eguali.
Supponiamo poi che il corpo S si muova rispetto al "centro di moto" (3) del complesso di
particelle con una velocità r . Esaminiamo, nel paragrafo presente, il caso in cui le particelle
non abbiano velocità proprie per rapporto al loro "centro di moto". Questo caso per l'appunto
noi chiameremo caso di flusso semplice. Chiameremo asse del flusso la direzione della
velocità del corpo per rapporto allo sciame di particelle.
La resistenza che le particelle offriranno al moto del corpo S consterà di due contributi
diversi:
271
1. Resistenza delle particelle che passano attraverso la sfera d'azione senza urtare il corpo S ;
2. Resistenza di particelle urtanti il corpo. L'uno si considererà come assolutamente
anelastico.
Applichiamoci a dedurre la formola che corrisponde alle particelle della prima specie.
Indichiamo, come si usa(4), con α l'angolo fra la velocità di una particella e il raggio vettore
nel momento d'entrata nella sfera d'azione; esso sarà anche eguale all'angolo del raggio
vettore del punto d'entrata coll'asse del flusso. Siano poi R e N le coordinate polari, per le
quali l'asse del flusso serve di asse polare, e finalmente N(ρ) l'angolo N corrispondente al
punto d'uscita dalla sfera d'azione.
Allora, la proiezione della velocità d'entrata sull'asse del flusso sarà
-r,
e la proiezione della velocità d'uscita dello stesso punto:
r cos(N(ρ) + α) .
Perciò l'aumento di quantità di moto per il corpo S in direzione dell'asse del flusso in
conseguenza dell'incontro con una particella sarà eguale a:
- µ r cos2[(N(ρ) + α)/2] .
(1)
D'altra parte l'equazione della traiettoria di una particella entro la sfera d'azione può essere
assunta sotto la forma:
(2)
r2 ρ sin2(α) +
R
R
R
(1 - r2ρ)sin(α)sin(N) + cos(α)cos(N) =0,
ρ
ρ
ρ
donde ricaviamo:
(3)
[(N(ρ) + α)/2] = arctg[(1 - r2ρ)tg(α)] .
Così l'espressione (1) si trascrive nel modo seguente:
(1.1)
-2µr
1
.
1 + (1 − r 2 ρ ) 2 tg 2 (α )
Perciò il completo aumento di quantità di moto del corpo in direzione dell'asse del flusso
nell'intervallo di tempo δt provocato dall'incontro con particelle che non vengano ad urtare il
corpo stesso sarà:
(4)
M δt = - µ n 4πρ2 δt
π
2
sin(α ) cos(α )dα
1 + (1 − r 2 ρ ) 2 tg 2 (α )
α = α ( D)
∫
dove α(D) rappresenta il valore limite di α , che corrisponde al. caso in cui la particella
viene a contatto col corpo S, cioè:
272
D 2 2D
D 1
+ 2 (1 − ) 2 ,
α(D) = arcsin
2
ρ r
ρ
ρ
e M la massa del corpo S.
E così, finalmente, per la reazione cercata abbiamo l'espressione
(5)
dr
)1 =
dt
µ n 2π ρ
(1 − r 2 ρ ) 2
(1 − r 2 ρ ) 2
ln
=
[
- 1 + sin2(α(D))] .
( 2 − r 2 ρ ) r 2 ρ ( r 2 ρ − 2) 1 + r 2 ρ ( r 2 ρ − 2) sin 2 (α ( D ))
R1 = M (
Occupiamoci ora della deduzione della seconda parte della reazione, dovuta all'urto con le
particelle per le quali
α < α(D) .
E' facile vedere che se ωR è l'angolo del raggio vettore con la velocità, alla distanza R, e r R
la velocità alla stessa distanza, la componente della quantità di moto di una particella urtante
il corpo S nel punto (N,D) lungo l'asse del flusso sarà:
(6)
-µ rD cos(N - ωD ) .
Approfittando dell'equazione della traiettoria e della legge delle aree otteniamo:
(6.1)
cos(N - ωD ) =
cos(α ) x 2 ( r 2 ρ − 2) + 2 x − r 2 ρ sin 2 (α ) − r 2 ρ (1 − r 2 ρ )[ x ( r 2 ρ − 2) + 1]sin 2 (α )
=
.
[1 + r 2 ρ ( r 2 ρ − 2) sin 2 (α )] x 2 ( r 2 ρ − 2) + 2 x
Per trovare l'espressione spettante alla variazione di velocità del corpo S nel piccolo
intervallo di tempo δt , in conseguenza dell'urto colle particelle del nostro sciame, possiamo
procedere nel modo seguente:
Immaginiamoci un certo corpo P* , la cui massa µ* sia eguale alla somma delle masse di
tutte le particelle, che verranno ad urtarsi col corpo S durante l'intervallo di tempo δt ,
mentre la componente della quantità di moto rispetto al corpo S sia eguale alla somma delle
componenti delle quantità di moto delle particelle medesime, cioè alla somma delle quantità
(6). Essendo δt abbastanza piccolo, l'effetto dell'urto con questo corpo fittizio P* e l'effetto
dell'urto con lo sciame delle particelle coincideranno fra loro. Così, l'aumento di velocità del
corpo S si esprimerà con la formola seguente, derivante dalle legge di urto di corpi
assolutamente anelastici:
(7)
δr =
(µ r) *
M+ µ *
dove M e µ* sono rispettivamente le masse dei corpi S e P* e (µr)* la componente delle
quantità di moto del corpo P* rispetto a S . La formola (7) rimane naturalmente valida
indipendentemente dalle velocità assolute dei corpi in questione, poiché in essa intervengono
solo velocità relative.
Abbiamo poi:
273
α (D)
(8)
(µr)* = -µ n 2πρ
2
∫ rr
D
cos( N − ω D ) sin(α ) cos(α )dα
.
δt
α =0
e
α (D)
(9)
µ* = µ n 2πρ
2
∫ r sin(α ) cos(α )dα
.
δt .
α =0
Perciò la reazione cercata sarà in questo caso semplicemente eguale a:
α ( D)
(10)
dr
R2 = M ( )2 = - µ n 2πρ2 r rD ∫ cos( N − ω D ) sin(α ) cos(α )dα
dt
α =0
dove a cos(N - ωD) va sostituita la sua espressione (6.1).
Per rD abbiamo la formola seguente:
(6.2)
rD =
1
2 − x + r2ρ x .
ρx
Riassumendo ciò che precede, perveniamo alla conclusione che la forza di resistenza offerta
dal nostro mezzo al moto del corpo S sarà rappresentata dalla formola:
(11)
R = R 1 + R2 .
Quest'espressione - particolarmente per il secondo addendo - riesce abbastanza complicata.
Non staremo perciò a trascrivere le espressioni complete per il caso generale, ma ci
limiteremo all'analisi della legge trovata nelle sue caratteristiche essenziali. E per questo
esamineremo in una prossima Nota i casi particolari più importanti.
(1) N. Moisseiev, Ueber einige Grundfragen der lheorie des Ursprungs der Kometen,
Meteore und des kosmischen Staubes, I., II., III. Teil, "Publications de l'Institut
Astrophysique", vol. V, fasc. I.
(2) T. Levi-Civita, Corpuscoli cosmici e distribuzione Maxwelliana, "Atti Acc. Pontificia",
Anno LXXXIII (1930), pp. 176-189; Ancora sul moto di un corpo di massa variabile, questi
"Rendiconti", vol. XI, 1930, pp. 626-632; ecc.
(3) Vedi Ueber einige Grundfragen ecc., I. Teil, $ 1.
(4) V. loc. cit.
----Questo lavoro, presentato dal Socio Tullio Levi-Civita nella seduta del 3 gennaio 1932, è stato
pubblicato nei Rendiconti della Reale Accademia dei Lincei, 1932, Vol. XV, pp. 135-139.
274
Exodus of Einstein's Special Theory in Seven Simple Steps
(Carl A. Zapffe)
Introduction.
For those who admire the orderliness of epistemology in theoretical physics, and are
committed to the requirements of logic in experimental physics, the following should be of
interest, and particularly because it knifes through the confusion of a century's wrangling over
c ± v values for the velocity of light.
The Seven Steps.
Seven steps of factual information come under present consideration, the first two of which
serve to shake loose the long-standing and generally unquestioning fixation upon Einstein's
special theory of relativity (STR) so that it can be re-examined without bias:
I.
The mass-energy relationship E = mc2 does not depend upon the STR, whereupon the
fate of the two are not inseparable.
As Lewis [1] demonstrated in 1908, and Einstein himself admitted in 1950 [2], the
fact of mass-energy equivalence has been inherent within the charge-momentum relationships
of Maxwell's field equations since long before Einstein was born.
II.
Elementary-particle phenomena in nuclear physics, which do exhibit the (1 - v2/c2)-1/2
relationship of an asymptotic c for both decay life τ and mass increase in terms of e/m , do
not necessarily confirm the Lorentz transfomation for t and x .
This traditional identity is pure surmise, following from the convenience of the
(1 - v2/c2)-1/2 term already appearing in the Lorentz transformation, and the heuristic appeal of
an argument that, since even the complex structure of the human being is composed of
elementary particles, that which measures time τ for the one measures time t for the other.
But on the one hand, these velocity-dependent changes - and specifically if velocity be proved
absolute - submit as well to the same treatment as the rate equations of chemistry and
thermodynamics, which of course support neither one transformation nor another; while on
the other hand heuristics is scarcely the dependable tool for bridging such a gap as that
between pions and hemoglobin. Metallurgists use similar τ measurements for the decay
behaviour of the positron [3,4], which is about as elementary as a particle can get; and the
changes in this case have no relationship whatever with velocity, the velocity being v = 0 .
Next we encounter these two massive criticisms of the STR epistemology,
one pinpointing the long debate over the chronometric paradoxes, the other using the steps of
logic to return the physical model from Einstein back to Lorentz:
III.
An impossible contradiction stands in the prediction of the Einstein equations that two
clocks, in motion relative to one another, can each be found running slow.
This classical controversy was spearheaded by the late Herbert J. Dingle, whose
book Science at the Crossroads [5] should be read. Despite the widely ranging imagination
of STR apologists, the only acceptable answer next follows.
IV.
Only if the velocity is absolute can this contradiction be resolved; and if velocity is
absolute so is space.
275
This was the monumental work of Ives [6], and the classical papers of Builder [7,8],
recently confirrned experimentally by studies of isotropy and anisotropy of the 3°K
background radiation [9].
V.
But if both velocity and space are absolute, then so is time.
This follows simply from v = x/t ; and the time t is presumably that d 2s/dt2 of the
cosmically unfolding "Big Bang", or its competing models. Therefore any velocity-dependent
features, and specifically those of elementary particles, are referable on the one hand to the
chronometry of this cosmic unfolding, and on the other hand to the isotropy of its radiative
framework.
There only remains to resolve certain problems with the seemingly
electromagnetic or Maxwellian substructuring of this space.
Return to Galilean-type Transformation.
VI.
An elementary principle of geophysics is that light from the aurora borealis or
australis, and indeed every other electromagnetic disturbance within the domain of the
terrestrial magnetosphere, arrives upon the surface at velocity c relative to geocentric rest
coordinates. Similarly, it is presumed in astrophysics that all radiation traversing a stellar
magnetosphere does so at velocity c relative to the coordinates of the repective
magnetosphere.
VII.
Since experimental physics has similarly proved, from the time of Arago's starlit
prisms in 1810 [10], to such recent tests as those of Brillet and Hall [11], that light from
either terrestrial or extraterrestrial sorces similarly traverses the local magnetosphere at
velocity c , .simple principles of geometry and trigonometry then require that c ± v light
velocities do obtain, though the differential is only discoverable along the magnetosheath
which separates the Maxwellian domain of one magnetosphere from that of another.
This is the main thrust of the Magnetospheric Ether-Drag Theory [12, 13], which
merely calls attention of relativists to principles already welI established in geophysics.
Conclusion.
From this progression of seven observations, one can only arrive at the following seven
conclusions:
1.
Einstein's physical model for his special theory of relativity must be abandoned in
favour of that of Lorentz.
2.
Lorentz's physical model must similarly be abandoned because of its outmoded field
features from standpoints of magnetospheric physics.
3.
The Einstein-Lorentz transformation must then be abandoned also because of these
errors in points of physical model.
4.
With abandonment of the Lorentz transformation, velocity-dependent phenomena
such as those in elementary-particle physics enter the province of mere rate equations:
dϕ/dv , d2ϕ/dt2 , dτ = f(v) = τ0 (1 - v2/c2)-1/2 , ... etc.
5.
All (1 - v2/c2)-1/2 relationships in general become interpreted merely as asymptotic
cosine or sec θ functions, identical with the linear equations for subsonic aerodynamics and
hydrodynamics, and unrelated except fortuitously to this same factor in the Lorentz-Einstein
transformation.
6.
No alteration at all attends the mass-energy equivalence E = mc2 .
276
7.
A physical model is new at hand, long known to geophysics but completely novel to
relativistic physics, in which space is structured in terms of the phenomenology of
electrodynamics, and which not only permits experimental confirmation, but promises an
entirely new navigational approach to astronautic odometry - measuring of one's position in
celestial reaches of so-called "empty" space.
Bibliography
[1] Lewis, G.N.: A Revision ol the Fundamental Laws of Matter and Energy, Phil. Mag. 16, 70517
(1908).
[2] Einstein, A.: Out of My Later Years, Philosoph. Lib., New York, viii + 282 (1950).
[3] Lynn, K. G. and Byrne, J. G.: Positron Lifetime Studies Made in Fatigue-Damaged AISA 4340
Samples, Metall. Trans. (A) 7, 604-6 (Apr. 1976).
[4] Hadnagy, T. D.; Byrne, J. G.; and Miller, G. R.: Effect of Porosity on the Mean Lifetime of
Positrons in Scintered and Hot-Pressed Alpha-Alumina, J. Am. Ceramics Soc. 60, 461-3 (Sept.Oct. 1977).
[5] Dingle, H.: Science at the Crossroads, Martin Brian and O'Keefe, London, 256 pp. (1972).
[6] Hazelett, R. and Turner, D. (ed. by): The Einstein Myth and the Ives Papers, The Devin-Adair
Co., Old Greenwich, CO. ix + 313 (1979).
[7] Builder, G.: Ether and Relativity, Australian J. of Phystcs 2, 279-97 (1958).
[8] Builder, G.: The Constancy of the Velocity of Light, Australian J. Phystcs 2, 457-80 (1958).
[9] Smoot, G. F.; Gorenstein, M. V.; and Muller, R. A.: Detection of Anisotropy in the Cosmic
Blackbody Radiation, Phys. Rev. Letts. 39, No. 14, 898-901 (3 Oct. 1977).
[10] Arago, F.: (Fr.) The Velocity of Light, Abs. Procès-verbaux des Séances de 1'Académie des
Sciences, Paris, p. 399 (l0 Dec. 1810).
[11] Brillet, A.; and Hall, J. L.: Improved Laser Test of the Isotropy of Space, Phys. Rev. Lett. 42,
549-52 (1979).
[12] Zapffe, C. A.: A Magnetospheric Ether-Drag Theory and the Reference Frames of
Relativistic Physics, SST. 2 No. 4, 439-54; disc. 455-9 (1979); 3, No. 4, 483-5 (1980).
[13] Zapffe, C. A.: The Magnetosphere in Relativistic Physics, Ind. J. Theoret. Phys. 30, No. 1
(1982).
*****
This essay first appeared in The Toth-Maatian Review, Volume 3, Number 4,
January 1985, pp. 1531-1535. By: CARL A. ZAPFFE, 6410 Murray Hill Rd., Baltimore,
MD 21212.
277
RECENSIONI/
REVIEWS
278
Albert Einstein, The Incorrigible Plagiarist
(XTX Inc., DownersGorve, Illinois, USA, 2002)
"The secret to creativity is knowing how to hide your sources"
(Albert Einstein)
Proposing again the remark which we made some time ago in the presentation of Kostro's
Einstein and the Ether (Episteme, N. 3, 21 April 2001, pp. 306-310), "common people", and
even "common scientists", will be surprised by the facts they discover in Bjerknes' book
(about 400 pages), which is quite useful, in that it establishes a realistic - and more
reasonable! - picture of one of the most propagandized scientific myths of all time, namely
Einstein's myth (see for instance: Alan J. Friedman & Carol C. Donley, Einstein as Myth and
Muse, Cambridge University Press, 1985).
As a matter of fact, reading this text should be a must for all people professionally interested
in the "history" of Physics or of Science (for these readers the book, its "polemical" thesis
notwithstanding, could become an indispensable tool, packed as it is with information,
quotations, meticulous references, etc.), but it is highly recommended even to teachers,
scientists of all kind, philosophers, epistemologists, in general to every person interested in
the evolution of human civilization and knowledge. Indeed, it would be difficult to deny that
the emergence of modern science is one of the most relevant events of all times, and that
Relativity in particular is the "theory" which had the greatest impact and influence on XXth
Century Western thought - though, in our opinion, and clearly in Bjerknes' as well, a negative
one).
The book is a successful attempt to break down some of the many commonplaces and
misconceptions which fill the typically apologetic History of Science, and the author does not
279
seem at all afraid to take on such a "giant". As a consequence, the result of his efforts is a
genuinely "rare find" and an interesting one.
In addition, we must emphasize that Christopher Jon Bjerknes is the great great grandson of
Carl Anton Bjerknes, who created the Pulsating Sphere Theory of Gravity and of
Electromagnetism, and who played an important rôle in the creation of the concept of charged
particle mass.
Vilhelm, Carl's son, also became famous for his work in Meteorology (Polar Front Theory;
see for instance Appropriating the Weather: Vilhelm Bjerknes and Construction of a Modern
Meteorology, by Robert Marc Friedman, Cornell University Press, 1993; Vilhelm Bjerknes,
MEM Volume of the American Meteorological Society, 1962), but his primary focus was
always on Physics and Hydrodynamics of Aether Models, and he was the scientist who gave
the Columbia lectures which are quoted in Almansi's paper (Fields of force, Columbia
University Press, New-York, 1906; see the section entitled Reprints in this same volume of
Episteme).
Continuing a truly fine family tradition, Vilhelm's son, Jacob, is also quite famous for his
work in Meteorology (Theory of Cyclones - El Niño), and now we can say that Christopher
Jon is carrying on following the footsteps of "aether theorists", who disliked (as we do)
Einstein's theory, and the consequent disappearance of the concept of aether from mainstream
Physics.
We must emphasize that this choice of "party" does not influence the usefulness of Bjerknes'
essay even for those not willing to admit this criticism of Relativity. As a matter of fact, the
book could even be construed to be rather more in favor of Relativity than the contrary, since
the proof that Einstein "borrowed" many ideas from others famous scientists, renders them
responsible for the dangerous nichilistic and irrational drift of modern scientific thought,
which Episteme has always aimed to fight...
We proceed with the presentation of the book presenting first its Table of Contents, and
further a few excerpts. Afterwards, we publish some additional commentary, mainly Phipps'
review (another scientist well known for his rather critical attitude against Relativity; we
thank Dr. Eugene F. Mallove, the Editor-in-Chief of Infinite Energy Magazine, for his consent
to publish it in parallel). We end this "chapter" with an Appendix written by Bjerknes himself
for the next edition of his research, honored to be able to present it to our readers in exclusive
preview.
TABLE OF CONTENTS:
1. THE PRI0RITY MYTH
2. SPACE-TIME, OR IS IT "TIME-SPACE"?
3. "THEORY OF RELATIVITY" OR "PSEUDORELATIVISM"?
4. HERO WORSHIP
5. E = mc2
6. EINSTEIN'S MODUS OPERANDI
7. HISTORY
8. MILEVA EINSTEIN-MARITY
9. P0LITICS AND ANECDOTES
NOTES
INDEX
280
[email protected]
http://www.xtxinc.com
[Two articles of the author, together with information about his life and work,
are published in this same volume of Episteme]
----Excerpts (Reprinted by permission. All rights reserved)
It is easily proven that Albert Einstein did not originate the special theory of relativity in its
entirety, or even in its majority. The historic record is readily available. Ludwig Gustav
Lange, Woldemar Voigt, George Francis FitzGerald, Joseph Larmor, Hendrik Antoon
Lorentz, Jules Henri Poincaré, Paul Drude, Paul Langevin, and many others, slowly
developed the theory, step by step, and based it on thousands of years of recorded thought and
research. Einstein may have made a few contributions to the theory, such as the relativistic
equations for aberration and the Doppler-Fizeau Effect, though he may also have rendered an
incorrect equation for the transverse mass of an electron, which, when corrected, becomes
Lorentz' equation.
Albert Einstein's first work on the theory of relativity did not appear until 1905. There is
substantial evidence that Albert Einstein did not write this 1905 paper on the "principle of
relativity" alone. His wife, Mileva Einstein-Marity, may have been co-author, or the sole
author, of the work.
If Albert Einstein did not originate the major concepts of the special theory of relativity, how
could such a historically significant fact have escaped the attention of the world for nearly a
century? The simple answer is that it did not.
----Book Description
(from an auto-review appeared in Canberra Times, an Australian newspaper, Thursday, 19
September 2002)
The name ''Einstein'' evokes images of a good-humoured genius, who revolutionised our
concepts of space, time, energy, mass and motion. Time named Albert Einstein "person of the
century". The language itself has incorporated "Einstein" into our common vocabulary as a
synonym for extraordinary brilliance. Many consider Einstein to have been the finest mind in
recorded human history.
That is the popular image, fostered by textbooks, the media, and hero worshiping physicists
and historians. However, when one reads the scientific literature written by Einstein's
contemporaries, a quite different picture emerges: one of an irrational plagiarist, who
manipulated credit for their work.
281
Einstein is perhaps most famous for the special theory of relativity, published in 1905 in the
German physics journal, Annalen der Physik. The paper was devoid of references, a fact that
Einstein's friend and Nobel prize winner for physics, Max Born, found troubling.
''The striking point is that it contains not a single reference to previous literature,'' Born stated
in 1955, before the International Relativity Conference in Bern. ''It gives you the impression
of quite a new venture. But that is, of course, as I have tried to explain, not true.''
Though Einstein's 1905 article contained no references, it was so strikingly similar to a paper
written by Hendrik Lorentz the previous year, that Walter Kaufmann and Max Planck felt a
need to publicly point out that Einstein had merely provided a metaphysical reinterpretation
and generalisation of Lorentz' scientific theory, a metaphysical reinterpretation and
generalisation Henri Poincare had already published.
As Charles Nordmann, astronomer to the Paris Observatory, pointed out: ''It is really to Henri
Poincare, the great Frenchman whose death has left a void that will never be filled, that we
must accord the merit of having first proved, with the greatest lucidity and the most prudent
audacity, that time and space, as we know them, can only be relative. A few quotations from
his works will not be out of place. They will show that the credit for most of the things which
are currently attributed to Einstein is, in reality, due to Poincare.''
Einstein acknowledged the fact, but justified his plagiarism in a cavalier fashion in Annalen
der Physik in 1907. "It appears to me that it is the nature of the business that what follows has
already been partly solved by other authors. Despite that fact, since the issues of concern are
here addressed from a new point of view, I believe I am entitled to leave out a thoroughly
pedantic survey of the literature, all the more so because it is hoped that these gaps will yet be
filled by other authors, as has already happened with my first work on the principle of
relativity through the commendable efforts of Mr. Planck and Mr. Kaufmann."
The completed field equations of the general theory of relativity were first deduced by David
Hilbert, a fact Einstein was forced to acknowledge in 1916, after he had plagiarised them
from Hilbert in late 1915. Paul Gerber solved the problem of the perihelion of Mercury in
1898. Physicist Ernst Gehrcke gave a lecture on the theory of relativity in the Berlin
Philharmonic on August 24, 1920, and publicly confronted Einstein, who was in attendance,
with Einstein's plagiarism of Lorentz' mathematical formalisms of the special theory of
relativity, Palagyi's space-time concepts, Varicak's non-Euclidean geometry and of the
plagiarism of the mathematical solution of the problem of the perihelion of Mercury first
arrived at by Gerber. Gehrcke addressed Einstein to his face and told the crowd that the
emperor had no clothes.
This was Einstein's response published in the Berliner Tageblatt und Handels-Zeitung on
August 27, 1920, translated into English in the book Albert Einstein's Theory of General
Relativity edited by Gerald E. Tauber: ". . . Gerber, who has given the correct formula for the
perihelion motion of Mercury before I did. The experts are not only in agreement that
Gerber's derivation is wrong through and through, but the formula cannot be obtained as a
consequence of the main assumption made by Gerber. Mr Gerber's work is therefore
completely useless, an unsuccessful and erroneous theoretical attempt.
"I maintain that the theory of general relativity has provided the first real explanation of the
perihelion motion of mercury. I have not mentioned the work by Gerber originally, because I
did not know it when I wrote my work on the perihelion motion of Mercury; even if I had
been aware of it, I would not have had any reason to mention it."
282
The fact that Einstein was a plagiarist is common knowledge in the physics community. What
isn't so well-known is that the sources Einstein parroted were also largely unoriginal. In 1919,
writing in the Philosophical Magazine Harry Bateman, a British mathematician and physicist
who had emigrated to the United States, unsuccessfully sought acknowledgment of his work.
"I am perhaps entitled to do this as my work on the subject of general relativity was published
before that of Einstein and Kottler, and appears to have been overlooked by recent writers."
My book is a documentation of Einstein's plagiarism of the theory of relativity. It discloses his
method for manipulating credit for the work of his contemporaries, reprints the prior works he
parroted, and demonstrates that he could not have drawn his conclusions without prior
knowledge of the works he copied but failed to reference.
Numerous republished quotations from Einstein's contemporaries prove that they were aware
of his plagiarism. Side-by-side comparisons of Einstein's words juxtaposed to those of his
predecessors prove the almost verbatim repetition. There is even substantial evidence
presented in the book that Einstein plagiarised the work of his first wife, Mileva Maric, who
had plagiarised others.
"Although generally associated with the names of Einstein and Minkowski, the really essentia physical
considerations underlying the theories are due to Larmor and Lorentz." -- Alfred Arthur Robb
"Einstein published a paper which set forth the relativity theory of Poincaré and Lorentz with some
amplifications, and which attracted much attention." -- Sir Edmund Whittaker
"The appearance of Dr. Silberstein's recent article on 'General Relativity without the Equivalence
Hypothesis' encourages me to restate my own views on the subject. I am perhaps entitled to do this as
my work on the subject of General Relativity was published before that of Einstein and Kottler, and
appears to have been overlooked by recent writers." -- Harry Bateman
"All this was maintained by Poincare and others long before the time of Einstein, and one does
injustice to truth in ascribing the discovery to him." -- Charles Nordmann
"Many of you have looked upon [Einstein's] paper 'Zur Elektrodynamik bewegter Koerper' in Annalen
der Physik ... and you will have noticed some peculiarities. The striking point is that it contains not a
single reference to previous literature. It gives you the impression of quite a new venture. But that is,
of course, as I have tried to explain, not true." -- Max Born
"In point of fact, therefore, Poincaré was not only the first to enunciate the principle, but he also
discovered in Lorentz's work the necessary mathematical formulation of the principle. All this
happened before Einstein's paper appeared." -- G. H. Keswani
"Einstein's explanation is a dimensional disguise for Lorentz's. ... Thus Einstein's theory is not a denial
of, nor an alternative for, that of Lorentz. It is only a duplicate and disguise for it. ... Einstein
continually maintains that the theory of Lorentz is right, only he disagrees with his 'interpretation.' Is it
not clear, therefore, that in this, as in other cases, Einstein's theory is merely a disguise for Lorentz's,
the apparent disagreement about 'interpretation' being a matter of words only?" -- James Mackaye
283
----Mr Bjerknes, an American historian of science, has authored six books on
Einstein and the theory of relativity. Albert Einstein: The Incorrigible Plagiarist
(ISBN 0971962987) is available at www.amazon.com.
----A reviewer, a physicist, July 18, 2002
ALBERT EINSTEIN WAS INDEED A PLAGIARIST
This book is very well documented, and, therefore, very convincing. I read the Dover reprint
of 'The Principle of Relativity' years ago, and realized then that Einstein just copied Lorentz,
because Lorentz' article appeared a before Einstein's and says essentially the same things. But
this book goes far beyond that and really shows a pattern by Einstein of plagiarism. I was
surprised to discover that Einstein's wife may have written the journal articles for him. The
number of citations and quotations in this book is really impressive and together form a
compelling argument stated in a very logical progression of facts. My only regret is that there
isn't more on the general theory of relativity, but the author hinted that more is to come, and
that this book is part of a series. I look forward to the future releases. I'm pleased with it and
would recommend it. It will change your view of Einstein and of the theory of relativity. If
you are doing research, I can tell you that I have never seen a book which provides more
information on the complete history of the theories than this book, including Whittaker's.
*****
Review of Albert Einstein The Incorrigible Plagiarist
(Thomas E. Phipps, Jr.)
(From Infinite Energy Magazine, N. 47, 6 October, 2002)
(http://www.infinite-energy.com)
Hagiophobia is defined as "a morbid dread of holy things." There is no question that the
author of this book, Christopher Jon Bjerknes, is an exemplary sufferer from this too-rare
complaint. For in our time Albert Einstein has been sanctified … perhaps even above Albert
Schweitzer, who certified the holiness of all living things, himself included. Einstein's life
having been told and retold by numerous hagiographers, Bjerknes has made it his aim to
provide the market with equally numerous anti-hagiographies - this being apparently the sixth
he has written. The publishers have burdened the latest with a disclaimer, "This book is
intended solely for entertainment purposes." However, we all know that nothing entertains
better than a good character assassination.
For this purpose the book employs the Socratic method, the asking of loaded questions - in
the style of, "Was this man ever known to stop beating his wife?" Physicists, who lead the
pack of Einstein idolaters, will dismiss Bjerknes's questions with contempt. But I think others
will be impressed, if nothing else, by the sheer doggedness of the scholarship that has gone
into the bibliography. This fills almost half the book and comprises 567 numbered endnotes,
284
some of which stretch for more than a page and include extensive references to the literature.
Among these notes will be found almost anything that has been written by or about Einstein
or his ideas, to the present date. My own limited scholarly resources noted only one omission:
Karl Popper, the philosopher who first (?) linked the names of Einstein and Parmenides, is
absent. But Parmenides is here, as he amply deserves to be.
From the start we note a deep schism: the author would like to side with feminists who see
Einstein's work as actually done by his much smarter first wife Mileva; but, since Bjerknes
also wants to paint that same work as stolen from earlier investigators, he faces an abiding
problem of whose character to assassinate. Here the Socratic method proves a life-saver:
Rather than offering a definitive choice, he provides weaponry for assassinating both Albert
and Mileva, and leaves it to the reader's political preference, an open question, which
candidate to take as the priority target.
Given all this smoke, how much fire is present? Einstein (or Einstein-Marity, the first wife)
stands accused primarily of "plagiarism" in respect to the basic ideas of the special relativity
theory. Narrowly construed, plagiarism refers to the copying of an earlier author's published
words. No such charge can be laid against Einstein. The author exhibits not a single instance
of word-copying or what the litigious would term copyright infringement. But that is not what
Bjerknes means. He is referring to the theft of ideas without acknowledgment. Here the case
is much stronger and also much fuzzier. Einstein's 1905 paper (which - amazingly - was
originally submitted to Annalen der Physik under the name Einstein-Marity, according to the
first-hand account, cited here, of Abram Joffe) contained not a single reference to earlier
work. This is frowned on in modern science, and should have been challenged by the editor
even then. For Einstein would have been a poor scholar, indeed, if he had failed to read
Poincare's prior work on relativity, which explicitly enunciated the Principle of Relativity.
One can understand omission of any reference to the much earlier work of Wilhelm Weber,
who developed the first and last relativistic formulation of electrodynamics in terms of
relative coordinates, velocities, and accelerations - since such would have directed attention to
the persistence of absolutist elements within "special relativity" theory. (The "observer" or
"frame" is such an element - a tertium quid extraneous to the intrinsic elements to be
described in nature, and wholly absent from Weber's theory. Minkowski's covariant
symmetrizing of the quid among all its quiddities alleviates, but does not eradicate, this echo
of absolutism.)
Another dilemma of the author in respect to special relativity is whether to concentrate his
attack on the theory itself or on its creator. If the theory is no good and was in fact stolen by
Einstein (or by Mileva) from predecessors, then it would seem the blame for this no-goodness
should fall most heavily on the latter. Error plagiarized is not error sanitized. Its provenance
aside, Bjerknes clearly distrusts the special theory (as does the present reviewer); but the book
makes little serious contribution to the comparatively vast (though little known and little
regarded) literature of its logical criticism.
Einstein's (or Einstein-Marity's) originality consisted in adjoining the Poincare relativity
principle to the Maxwell equations (which contain only one field propagation velocity
parameter c and thus necessitate what we now call "Einstein's second postulate") and in
showing that these stark logical ingredients suffice to imply a kinematics based on the
mathematical coordinate transformations that Lorentz had already spelled out. Clearly the
ideas pre-existed. But, as all inventors know, it is not permissible to patent ideas. If the
combining of pre-existing ideas in new patterns is to be called "plagiarism," then it would not
be an over-statement to say that all scientific progress and all invention depend on just this
kind of plagiarism … for what did Newton do but plagiarize from the giants on whose
shoulders he acknowledged standing? He neglected only to attach names to the giants. So did
Einstein. In both cases the behavior was perhaps a trifle magisterial … and also perhaps more
than a trifle forgivable. Still, unpleasant doubts persist in the Einstein case: Bjerknes shows
that Einstein's scientific publications reveal a lifetime pattern of similar magisterial behavior.
285
The absence of attributions in the 1905 paper was not a one-off occurrence. For example, I
quote from page 231 of the book: "David Hilbert, on whom Einstein went calling for help,
published the general theory of relativity before Einstein. Why after many years of failure, did
Einstein suddenly realize, within a few days after David Hilbert's work was public, the
equations which Hilbert published before him, and then submit his, Einstein's, identical
formulations?"
As you can see, this last (stripped of its Socratic question mark) constitutes a genuine charge
of plagiarism … but it is not backed by chapter and verse citation, equation number by
corresponding equation number, word by word. Lacking such substantiation, the charge
cannot stand in court. In law, equations, like ideas, cannot be copyrighted or patented. Still,
here is more smoke. It is doubtful if all such can be permanently cleared away. But one would
like to see scholarship comparable to that of Bjerknes applied to the task. Otherwise, a
polluted atmosphere and a bad odor linger.
In conclusion, I recommend the book to Einstein scholars and to sociologists of science as a
genuinely valuable bibliographical resource for further research on the man and his times and as a target for the Einstein hagiographers to shoot down if they can. Other readers, in
search of more than entertainment, must proceed with caution.
Thomas E. Phipps, Jr.
908 South Busey Avenue
Urbana, IL 61801, USA
(XTX, Inc., Downers Grove, IL 60515, 2002, Paperback $19.95, ISBN 0-9719629-8-7)
286
A Short History of the Concept of Relative Simultaneity
in the Special Theory of Relativity
Abstract. There is a common misconception enunciated in numerous histories, that Albert Einstein
was the first person to propose the relativity of simultaneity. It is often alleged that the paper, "Zur
Elektrodynamik bewegter Körper", Annalen der Physik, Series 4, Volume 17, (1905), pp. 891-921, at
892-895, contained the first proposal of a clock synchronization method employing observers and light
signals. Given the absence of references in Einstein's work, it has been further assumed by some that
the revised thought-experiment regarding a midpoint and relative simultaneity, which appeared in
Einstein's 1916 work, "Die Relativität der Gleichzeitigkeit", Über die spezielle und die allgemeine
Relativitätstheorie, Chapter 9, Friedr. Vieweg & Sohn, Braunschweig, (1917), pp. 16-19, was also an
original idea. The historic record proves otherwise.
Piecing together the Missing References in Einstein's Plagiarized Works
In 1887, Woldemar Voigt published the following relativistic transformation of space-time
coordinates [1]:
x' = x - vt , y' = y / γ , z' = z / γ , t' = t - vx / c2 , where γ = 1 / ( 1 - v2 / c2 )1/2 .
Poincaré asserted that simultaneity is relative, in 1898:
"XII. But let us pass to examples less artificial; to understand the definition implicitly supposed by the
savants, let us watch them at work and look for the rules by which they investigate simultaneity.
I will take two simple examples, the measurement of the velocity of light and the determination of
longitude.
When an astronomer tells me that some stellar phenomenon, which his telescope reveals to him at this
moment, happened nevertheless fifty years ago, I seek his meaning, and to that end I shall ask him first
how he knows it, that is, how he has measured the velocity of light.
He has begun by supposing that light has a constant velocity, and in particular that its velocity is the
same in all directions. That is a postulate without which no measurement of this velocity could be
attempted. This postulate could never be verified directly by experiment; it might be contradicted by it
if the results of different measurements were not concordant. We should think ourselves fortunate that
this contradiction has not happened and that the slight discordances which may happen can be readily
explained.
The postulate, at all events, resembling the principle of sufficient reason, has been accepted by
everybody; what I wish to emphasize is that it furnishes us with a new rule for the investigation of
simultaneity, entirely different from that which we have enunciated above.
This postulate assumed, let us see how the velocity of light has been measured. You know that
Roemer used eclipses of the satellites of Jupiter, and sought how much the event fell behind its
prediction. But how is this prediction made? It is by the aid of astronomic laws, for instance Newton's
law.
Could not the observed facts be just as well explained if we attributed to the velocity of light a little
different value from that adopted, and supposed Newton's law only approximate? Only this would lead
to replacing Newton's law by another more complicated. So for the velocity of light a value is adopted,
such that the astronomic laws compatible with this value may be as simple as possible. When
navigators or geographers determine a longitude, they have to solve just the problem we are
discussing; they must, without being at Paris, calculate Paris time. How do they accomplish it? They
carry a chronometer set for Paris. The qualitative problem of simultaneity is made to depend upon the
287
quantitative problem of the measurement of time. I need not take up the difficulties relative to this
latter problem, since above I have emphasized them at length.
Or else they observe an astronomic phenomenon, such as an eclipse of the moon, and they suppose
that this phenomenon is perceived simultaneously from all points of the earth. That is not altogether
true, since the propagation of light is not instantaneous; if absolute exactitude were desired, there
would be a correction to make according to a complicated rule.
Or else finally they use the telegraph. It is clear first that the reception of the signal at Berlin, for
instance, is after the sending of this same signal from Paris. This is the rule of cause and effect
analyzed above. But how much after? In general, the duration of the transmission is neglected and the
two events are regarded as simultaneous. But, to be rigorous, a little correction would still have to be
made by a complicated calculation; in practise it is not made, because it would be well within the
errors of observation; its theoretic necessity is none the less from our point of view, which is that of a
rigorous definition. From this discussion, I wish to emphasize two things: (1) The rules applied are
exceedingly various. (2) It is difficult to separate the qualitative problem of simultaneity from the
quantitative problem of the measurement of time; no matter whether a chronometer is used, or whether
account must be taken of a velocity of transmission, as that of light, because such a velocity could not
be measured without measuring a time.
XIII
To conclude: We have not a direct intuition of simultaneity, nor of the equality of two durations. If we
think we have this intuition, this is an illusion. We replace it by the aid of certain rules which we apply
almost always without taking count of them.[2]"
Circa 1899, Poincaré clarified the fact that he saw no distinction between "time" and "local
time":
"Allow me a couple of remarks regarding the new variable t': it is what Lorentz calls the local time. At
a given point t and t' will not defer but by a constant, t' will, therefore, always represent the time, but
the origin of the times being different for the different points serves as justification for his
designation."
"Disons deux mots sur la nouvelle variable t': c'est ce que Lorentz appelle le temps locale. En un point
donné t et t' ne différeront que par une constante, t' représentera donc toujours le temps mais l'origine
des temps étant différente aux différents points: cela justifie sa dénomination.[3]"
In 1900, Poincaré stated:
"In order for the compensation to occur, the phenomena must correspond, not to the true time t, but to
some determined local time t' defined in the following way.
I suppose that observers located at different points synchronize their watches with the aid of light
signals; which they attempt to adjust to the time of the transmission of these signals, but these
observers are unaware of their movement of translation and they consequently believe that the signals
travel at the same speed in both directions, they restrict themselves to crossing the observations,
sending a signal from A to B, then another from B to A. The local time t' is the time determined by
watches synchronized in this manner.
If in such a case
V = 1 / K0
½
is the speed of light, and v the translation of the Earth, that I imagine to be parallel to the positive x
axis, one will have:
t' = t - vx / V 2."
"Pour que la compensation se fasse, il faut rapporter les phénomènes, non pas au temps vrai t, mais à
un certain temps local 'N défini de la façon suivante.
Je suppose que des observateurs placés en différents points, règlent leurs montres à l'aide de signaux
lumineux; qu'ils cherchent à corriger ces signaux du temps de la transmission, mais qu'ignorant le
288
mouvement de translation dont ils sont animès et croyant par conséquent que les signaux se
transmettent également vite dans les deux sens, ils se bornent à croiser les observations, en envoyant
un signal de A en B, puis un autre de B en A. Le temps local tNest le temps marqué par les montres
ainsi réglées.
Si alors
V = 1 / K0
½
est la vitesse de la lumière, et v la translation de la Terre que je suppose parallèle à l'axe des x positifs,
on aura:
t' = t - vx / V 2 . [4]"
We know that Einstein had read Poincaré's paper.[5]
In 1902, Poincaré asserted, and we know, from Solovine's accounts [6], that Einstein had read
this work of Poincaré's:
"There is no absolute time. When we say that two periods are equal, the statement has no meaning,
and can only acquire a meaning by convention. Not only have we no direct intuition of the equality of
two periods, but we have not even direct intuition of the simultaneity of two events occurring in two
different places. I have explained this in an article entitled 'Mesure du Temps.' [7]"
Again, in 1904, Poincaré asserted that simultaneity is relative, and elaborated on the light
synchronization method that Mileva Einstein-Marity and Albert Einstein copied, in 1905,
without citation to Poincaré. Poincaré stated in 1904,
"We come to the principle of relativity: this not only is confirmed by daily experience, not only is it a
necessary consequence of the hypothesis of central forces, but it is imposed in an irresistible way upon
our good sense, and yet it also is battered.
Consider two electrified bodies; though they seem to us at rest, they are both carried along by the
motion of the earth; an electric charge in motion, Rowland has taught us, is equivalent to a current;
these two charged bodies are, therefore, equivalent to two parallel currents of the same sense and these
two currents should attract each other. In measuring this attraction, we measure the velocity of the
earth; not its velocity in relation to the sun or the fixed stars, but its absolute velocity.
I well know what one will say, it is not its absolute velocity that is measured, it is its velocity in
relation to the ether. How unsatisfactory that is! Is it not evident that from the principle so understood
we could no longer get anything? It could no longer tell us anything just because it would no longer
fear any contradiction.
If we succeed in measuring anything, we would always be free to say that this is not the absolute
velocity in relation to the ether, it might always be the velocity in relation to some new unknown fluid
with which we might fill space.
Indeed, experience has taken on itself to ruin this interpretation of the principle of relativity; all
attempts to measure the velocity of the earth in relation to the ether have led to negative results. This
time experimental physics has been more faithful to the principle than mathematical physics; the
theorists, to put in accord their other general views, would not have spared it; but experiment has been
stubborn in confirming it.
The means have been varied in a thousand ways and finally Michelson has pushed precision to its last
limits; nothing has come of it. It is precisely to explain this obstinacy that the mathematicians are
forced today to employ all their ingenuity.
Their task was not easy, and if Lorentz has gotten through it, it is only by accumulating hypotheses.
The most ingenious idea has been that of local time.
Imagine two observers who wish to adjust their watches by optical signals; they exchange signals, but
as they know that the transmission of light is not instantaneous, they take care to cross them.
When the station B perceives the signal from the station A, its clock should not mark the same hour as
that of the station A at the moment of sending the signal, but this hour augmented by a constant
representing the duration of the transmission. Suppose, for example, that the station A sends its signal
289
when its clock marks the hour o, and that the station B perceives it when its clock marks the hour t.
The clocks are adjusted if the slowness equal to t represents the duration of the transmission, and to
verify it, the station B sends in its turn a signal when its clock marks o; then the station A should
perceive it when its clock marks t. The timepieces are then adjusted. And in fact, they mark the same
hour at the same physical instant, but on one condition, which is that the two stations are fixed. In the
contrary case the duration of the transmission will not be the same in the two senses, since the station
A, for example, moves forward to meet the optical perturbation emanating from B, while the station B
flies away before the perturbation emanating from A. The watches adjusted in that manner do not
mark, therefore, the true time, they mark what one may call the local time, so that one of them goes
slow on the other. It matters little since we have no means of perceiving it. All the phenomena which
happen at A, for example, will be late, but all will be equally so, and the observer who ascertains them
will not perceive it since his watch is slow; so as the principle of relativity would have it, he will have
no means of knowing whether he is at rest or in absolute motion.[8]"
Mileva Einstein-Marity and Albert Einstein parroted Poincaré's clock synchronization
procedures, without acknowledging that Poincaré had stated them first. From the Einsteins'
1905 paper:
"I. KINEMATICAL PART
§ 1. Definition of Simultaneity
[Consider a system of coordinates, in which the Newtonian mechanical equations are valid. In order to
put the contradistinction from the [moving] systems of coordinates to be introduced later into words,
and for the exact definition of the conceptualization, we call this system of coordinates the 'resting
system'.]
If a material point is at rest relatively to this system of co-ordinates, its position can be defined
relatively thereto by the employment of rigid standards of measurement and the methods of Euclidean
geometry, and can be expressed in Cartesian co-ordinates.
If we wish to describe the motion of a material point, we give the values of its co-ordinates as
functions of the time. Now we must bear carefully in mind that a mathematical description of this kind
has no physical meaning unless we are quite clear as to what we understand by 'time.' We have to take
into account that all our judgments in which time plays a part are always judgments of simultaneous
events. If, for instance, I say, 'That train arrives here at 7 o'clock,' I mean something like this: 'The
pointing of the small hand of my watch to 7 and the arrival of the train are simultaneous events.'
It might appear possible to overcome all the difficulties attending the definition of 'time' by
substituting 'the position of the small hand of my watch' for 'time.' And in fact such a definition is
satisfactory when we are concerned with defining a time exclusively for the place where the watch is
located; but it is no longer satisfactory when we have to connect in time series of events occurring at
different places, or - what comes to the same thing - to evaluate the times of events occurring at places
remote from the watch.
We might, of course, content ourselves with time values determined by an observer stationed together
with the watch at the origin of the co-ordinates, and co-ordinating the corresponding positions of the
hands with light signals, given out by every event to be timed, and reaching him through empty space.
But this co-ordination has the disadvantage that it is not independent of the standpoint of the observer
with the watch or clock, as we know from experience. We arrive at a much more practical
determination along the following line of thought.
If at the point A of space there is a clock, an observer at A can determine the time values of events in
the immediate proximity of A by finding the positions of the hands which are simultaneous with these
events. If there is at the point B of space another clock in all respects resembling the one at A, it is
possible for an observer at B to determine the time values of events in the immediate neighbourhood
of B. But it is not possible without further assumption to compare, in respect of time, an event at A
with an event at B. We have so far defined only an 'A time' and a 'B time.' We have not defined a
common 'time' for A and B, for the latter cannot be defined at all unless we establish by definition that
the 'time' required by light to travel from A to B equals the 'time' it requires to travel from B to A. Let
a ray of light start at the 'A time' from A towards B, let it at the 'B time' be reflected at B in the
direction of A, and arrive again at A at the 'A time'.
In accordance with definition the two clocks synchronize if
290
tB - tA = t'A - tB.
We assume that this definition of synchronism is free from contradictions, and possible for any
number of points; and that the following relations are universally valid: 1. If the clock at B synchronizes with the clock at A, the clock at A synchronizes with the clock at B.
2. If the clock at A synchronizes with the clock at B and also with the clock at C, the clocks at B and C
also synchronize with each other.
Thus with the help of certain imaginary physical experiments we have settled what is to be understood
by synchronous resting clocks located at different places, and have evidently obtained a definition of
'simultaneous,' or 'synchronous,' and of 'time.' The 'time' of an event is that which is given
simultaneously with the event by a resting clock located at the place of the event, this clock being
synchronous, and indeed synchronous for all time determinations, with a specified stationary clock.
[We set forth, according to present experience, that the magnitude
( 2 A B ) / ( t'A - tA ) = c
is a universal constant (the velocity of light in empty space).]
It is essential to have time defined by means of resting clocks in the resting system, and the time now
defined being appropriate to the resting system we call it 'the time of the resting system.'[9]"
Albert Einstein believed he had a right to plagiarize, if he could put a new spin on an old idea.
He asserted this "privilege" in 1907:
"It appears to me that it is the nature of the business that what follows has already been partly solved
by other authors. Despite that fact, since the issues of concern are here addressed from a new point of
view, I believe I am entitled to leave out a thoroughly pedantic survey of the literature, all the more so
because it is hoped that these gaps will yet be filled by other authors, as has already happened with my
first work on the principle of relativity through the commendable efforts of Mr. Planck and Mr.
Kaufmann.[10]"
D. F. Comstock wrote, in 1910, in his popular exposition on the theory of relativity:
"The whole principle of relativity may be based on an answer to the question: When are two events
which happen at some distance from each other to be considered simultaneous? The answer, 'When
they happen at the same time,' only shifts the problem. The question is, how can we make two events
happen at the same time when there is a considerable distance between them.
Most people will, I think, agree that one of the very best practical and simple ways would be to send a
signal to each point from a point halfway between them. The velocity with which signals travel
through space is of course the characteristic 'space velocity,' the velocity of light.
Two clocks, one at A and the other at B, can therefore be set running in unison by means of a light
signal sent to each from a place midway between them.
Now suppose both clock A and clock B are on a kind of sidewalk or platform moving uniformly past
us with velocity v. In Fig. 1 (2) is the moving platform and (1) is the fixed one, on which we consider
ourselves placed. Since the observer on platform (2) is moving uniformly he can have no reason to
consider himself moving at all, and he will use just the method we have indicated to set his two clocks
A and B in unison. He will, that is,
send a light flash from C, the point midway between A and B, and when this flash reaches the two
clocks he will start them with the same reading.
291
To us on the fixed platform, however, it will of course be evident that the clock B is really a little
behind clock A, for, since the whole system is moving in the direction of the arrow, light will take
longer to go from C to B than from C to A. Thus the clock on the moving platform which leads the
other will be behind in time.
Now it is very important to see that the two clocks are in unison for the observer moving with them (in
the only sense in which the word 'unison' has any meaning for him), for if we adopt the first postulate
of relativity, there is no way in which he can know that he is moving. In other words, he has just as
much fundamental right to consider himself stationary as we have to consider ourselves stationary,
and therefore just as much right to apply the midway signal method to set his clocks in unison as we
have in the setting of our 'stationary clocks.' 'Stationary' is, therefore, a relative term and anything
which we can say about the moving system dependent on its motion, can with absolutely equal right
be said by the moving observer about our system.
We are, therefore, forced to the conclusion that, unless we discard one of the two relativity postulates,
the simultaneity of two distant events means a different thing to two different observers if they are
moving with respect to each other.
The fact that the moving observer disagrees with us as to the reading of his two clocks as well as to the
reading of two similar clocks on our 'stationary' platform, gives us a complete basis for all other
differences due to point of view.
A very simple calculation will show that the difference in time between the two moving clocks is
[The time it takes light to go from C to B is ½ / (V - v) and the time to go from C to A is ½ / (V + v).
The difference in these two times is the amount by which the clocks disagree and this difference
becomes, on simplification, the expression given above. - Notation found in the original.]
1/V β / (1 - β 2 )
where
l = distance between clocks A and B;
v = velocity of moving system;
V = velocity of light;
β = v / V.
The way in which this difference of opinion with regard to time between the moving observer and
ourselves leads to a difference of opinion with regard to length also may very easily be indicated as
follows:
Suppose the moving observer desires to let us know the distance between his clocks and says he will
have an assistant stationed at each clock and each of these, at a given instant, is to make a black line
on our platform. He will, therefore, he says, be able to leave marked on our platform an exact measure
of the length between his clocks and we can then compare it at leisure withy any standard we choose
to apply.
We, however, object to this measure left with us, on the ground that the two assistants did not make
their marks simultaneously and hence the marks left on our platform do not, we say, represent truly the
distance between his clocks. The difference is readily shown in Fig. 2, where M represents the black
mark made on our platform at a certain time by the assistant at A, and N that made by the assistant at B
at a later time. The latter assistant waited, we say, until his clock read the same as clock A, waited, that
is, until B was at B'; and then made the mark N. The moving observer declares, therefore, that the
distance MN is equal to the distance AB, while we say that MN is greater than AB.
Again it must be emphasized that, because of the first fundamental postulate, there is no universal
standard to be applied in settling such a difference of opinion. Neither the standpoint of the 'moving'
292
observer nor our standpoint is wrong. The two merely represent two different sides of reality. Any one
could ask: What is the 'true' length of a metal rod? Two observers working at different temperatures
come to different conclusions as to the 'true length.' Both are right. It depends on what is meant by
'true.' Again, asking a question which might have been asked centuries ago, is a man walking toward
the stern of an east bound ship really moving west? We must answer 'that depends' and we must have
knowledge of the questioner's view-point before we can answer yes or no.
A similar distinction emerges from the principle of relativity. What is the distance between the two
clocks? Answer: that depends. Are we to consider ourselves with the clock system when we answer, or
passing the clocks with a hundredth the velocity of light or passing the clocks with a tenth the velocity
of light? The answer in each case must be different, but in each case may be true.
It must be remembered that the results of the principle of relativity are as true and no truer than its
postulates. If future experience bears out these postulates then the length of the body, even of a
geometrical line, in fact the very meaning of 'length,' depends on the point of view, that is, on the
relative motion of the observer and the object measured. The reason this conclusion seems at first
contrary to common sense is doubtless because we, as a race, have never had occasion to observe
directly velocities high enough to make such effects sensible. The velocities which occur in some of
the newly investigated domains of physics are just as new and outside our former experience as the
fifth dimension.[11]"
Citing Comstock's above quoted work, Robert Daniel Carmichael wrote, in 1912:
"§ 9. Simultaneity of Events Happening at Different Places. - Let us now assume two systems of
reference S and S' moving with a uniform relative velocity v. Let an observer on S' undertake to adjust
two clocks at different places so that they shall simultaneously indicate the same time. We will
suppose that he does this in the following very natural manner:
[Compare Comstock, Science, N. S., 31 (1900) [sic]: 767-772. - Notation found in the original.]
Two stations A and B are chosen in the line of relative motion of S and S' and at a distance d apart. The
point C midway between these two stations is found by measurement.
The observer is himself stationed at C and has assistants at A and B. A single light signal is flashed
from C to A and to B, and as soon as the light ray reaches each station the clock there is set at an hour
agreed upon beforehand. The observer on S' now concludes that his two clocks, the one at A and the
other at B, are simultaneously marking the same hour; for, in his opinion (since he supposes his system
to be at rest), the light has taken exactly the same time to travel from C to A as to travel from C to B.
Now let us suppose that an observer on the system S has watched the work of regulating these clocks
on S'. The distances CA and CB appear to him to be
½ d (1 - β 2 )1/2
instead of ½ d. Moreover, since the velocity of light is independent of the velocity of the source, it
appears to him that the light ray proceeding from C to A has approached A at the velocity c + v, where
c is the velocity of light, while the light ray going from C to B has approached B at the velocity c - v.
Thus to him it appears that the light has taken longer to go from C to B than from C to A by the
amount
½ d (1 - β 2 )1/2 / ( c - v ) - ½ d (1 - β 2 )1/2 / ( c + v )
= vd (1 - β 2 )1/2 / ( c2 - v2 ) .
But since β = v / c the last expression is readily found to be equal to
293
( v / c2 ) [ d / (1 - β 2 )1/2 ] .
Therefore, to an observer on S the clocks on S' appear to mark different times; and the difference is
that given by the last expression above.
Thus we have the following conclusion:
THEOREM VII. Let two systems of reference S and S' have a uniform relative velocity v. Let an observer
on S' place two clocks at a distance d apart in the line of relative motion of S and S' and adjust them
so that they appear to him to mark simultaneously the same time. Then to an observer on S the clock
on S' which is forward in point of motion appears to be behind in point of time by the amount
( v / c2 ) [ d / (1 - β 2 )1/2 ] ,
where c is the velocity of light and β = v / c (MVLR).
It should be emphasized that the clocks on S' are in agreement in the only sense in which they can be
in agreement for an observer on that system who supposes (as he naturally will) that his own system is
at rest-notwithstanding the fact that to an observer on the other system there appears to be an
irreconcilable disagreement depending for its amount directly on the distance apart of the two clocks.
According to the result of the last theorem the notion of simultaneity of events happening at different
places is indefinite in meaning until some convention is adopted as to how simultaneity is to be
determined. In other words, there is no such thing as the absolute simultaneity of events happening at
different places.[12]"
Albert Einstein, who sought a "new point of view" from plagiarizing Poincaré's 1900 clock
synchronization method, plagiarized Comstock (1910) and Carmichael (1912), in Einstein's
book of 1916:
"THE RELATIVITY OF SIMULTANEITY
UP to now our considerations have been referred to a particular body of reference, which we have
styled a 'railway embankment.' We suppose a very long train travelling along the rails with the
constant velocity v and in the direction indicated in Fig. I. People travelling in this train will with
advantage use the train as a rigid reference-body (co-ordinate system); they regard all events in
reference to the train.
Then every event which takes place along the line also takes place at a particular point of the train.
Also the definition of simultaneity can be given relative to the train in exactly the same way as with
respect to the embankment. As a natural consequence, however, the following question arises:
Are two events (e.g. the two strokes of lightning A and B) which are simultaneous with reference to
the railway embankment also simultaneous relatively to the train? We shall show directly that the
answer must be in the negative.
When we say that the lightning strokes A and B are simultaneous with respect to the embankment, we
mean: the rays of light emitted at the places A and B, where the lightning occurs, meet each other at
the mid-point M of the length AB of the embankment. But the events A and B also correspond to
positions A and B on the train. Let M' be the mid-point of the distance AB on the traveling train. Just
when the flashes
[As judged from the embankment. - Notation found in the original.]
of lightning occur, this point M' naturally coincides with the point M, but it moves towards the right in
the diagram with the velocity v of the train. If an observer sitting in the position M' in the train did not
possess this velocity, then he would remain permanently at M, and the light rays emitted by the flashes
294
of lightning A and B would reach him simultaneously, i.e. they would meet just where he is situated.
Now in reality (considered with reference to the railway embankment) he is hastening towards the
beam of light coming from B, whilst he is riding on ahead of the beam of light coming from A. Hence
the observer will see the beam of light emitted from B earlier than he will see that emitted from A.
Observers who take the railway train as their reference-body must therefore come to the conclusion
that the lightning flash B took place earlier than the lightning flash A. We thus arrive at the important
result:
Events which are simultaneous with reference to the embankment are not simultaneous with respect to
the train, and vice versa (relativity of simultaneity). Every reference-body (co-ordinate system) has its
own particular time; unless we are told the reference-body to which the statement of time refers, there
is no meaning in a statement of the time of an event.
Now before the advent of the theory of relativity it had always tacitly been assumed in physics that the
statement of time had an absolute significance, i.e. that it is independent of the state of motion of the
body of reference. But we have just seen that this assumption is incompatible with the most natural
definition of simultaneity; if we discard this assumption, then the conflict between the law of the
propagation of light in vacuo and the principle of relativity (developed in Section VII) disappears.
We were led to that conflict by the considerations of Section VI, which are now no longer tenable. In
that section we concluded that the man in the carriage, who traverses the distance w per second
relative to the carriage, traverses the same distance also with respect to the embankment in each
second of time. But, according to the foregoing considerations, the time required by a particular
occurrence with respect to the carriage must not be considered equal to the duration of the same
occurrence as judged from the embankment (as reference-body). Hence it cannot be contended that the
man in walking travels the distance w relative to the railway line in a time which is equal to one
second as judged from the embankment.
Moreover, the considerations of Section VI are based on yet a second assumption, which, in the light
of a strict consideration, appears to be arbitrary, although it was always tacitly made even before the
introduction of the theory of relativity.[13]"
This chapter "by Einstein" has often been criticized as being "absolutist" and "Lorentzian".
One understands why it was written in the fashion that it was, when one reads the source
material, which Einstein plagiarized to produce it.
References and Notes
1. W. Voigt, "Ueber das Doppler'sche Princip", Nachrichten von der Königlichen Gesellschaft der
Wissenschaften und der Georg-Augusts-Universität zu Göttingen, (1887), pp. 41-51; republished
Physikalische Zeitschrift, Volume 16, Number 20, (October15, 1915), pp. 381-386; English
translation, as well as very useful commentary, are found in A. Ernst and Jong-Ping Hsu (W. Kern is
credited with assisting in the translation), "First Proposal of the Universal Speed of Light by Voigt in
1887", Chinese Journal of Physics (The Physical Society of the Republic of China), Volume 39,
Number 3, (June, 2001), pp. 211-230; URL: http://psroc.phys.ntu.edu.tw/cjp/v39/211.pdf . Lorentz
acknowledged Voigt's priority, and suggested that the "Lorentz Transformation" be called the
"Transformations of Relativity": See: H. A. Lorentz, Theory of Electrons, B. G. Teubner, Leipzig,
(1909), p. 198 footnote; and H. A. Lorentz, "Deux memoirs de Henri Poincaré", Acta Mathematica,
Volume 38, (1921), p. 295; reprinted in Œuvres de Henri Poincaré, Volume XI, Gautier-Villars,
(1956), pp. 247-261. Minkowski also acknowledged Voigt's priority: See: The Principle of Relativity,
Dover, New York, (1952), p. 81; and Physikalische Zeitschrift, Volume 9, Number 22, (November 1,
1908), p. 762. For further discussion of Voigt's relativistic transformation, see: R. Dugas, A History of
Mechanics, Dover, New York, (1988), pp. 468, 484, 494; A. Pais, Subtle is the Lord, Oxford
University Press, Oxford, New York, Toronto, Melbourne, (1982), pp. 121-122.
2. H. Poincaré, "La Mesure du Temps", Revue de Métaphysique et de Morale, Volume 6, (January,
1898) pp. 1-13; The Value of Science, The Science Press, New York, (1907), pp. 26-36.
3. H. Poincaré, Electrité et Optique, Gauthier-Villars, Paris, (1901), p. 530.
295
4. H. Poincaré, "La Théorie de Lorentz et le Principe de la Réaction", Archives Néerlandaises des
Sciences Exactes et Naturelles, Series 2, Volume 5, (1900), pp. 252-278, at 272-273.
5. A. Einstein, "Das Prinzip von der Erhaltung der Schwerpunktsbewegung und die Trägheit der
Energie", Annalen der Physik, Volume 20, (1906), pp. 627-633, at 627.
6. J. Stachel, Ed., The Collected Papers of Albert Einstein, Volume 2, Princeton University Press,
(1989), pp. xxiv-xxv.
7. H. Poincaré, Science and Hypothesis, Dover, New York, (1952), p. 90.
8. H. Poincaré's St. Louis lecture from September of 1904, La Revue des Idées, 80, (November 15,
1905); "L'État Actuel et l'Avenir de la Physique Mathématique", Bulletin des Sciences Mathématique,
Series 2, Volume 28, (1904), p. 302-324; English translation, "The Principles of Mathematical
Physics", The Monist, Volume 15, Number 1, (January, 1905), pp. 1-24.
9. The Principle of Relativity, Dover, New York, (1952), pp. 38-40. In order to maintain conformity
with the original German text, necessary corrections have been made, as indicated by bracketed text.
"Resting" has been substituted for "stationary", in conformity with the original German text.
10. A. Einstein, "Ueber die vom Relativitaetsprinzip gefordterte Traegheit der Energie", Annalen der
Physik, Series 4, Volume 23, (1907), pp. 371-384, at 373.
11. D. F. Comstock, "The Principle of Relativity", Science, New Series, Volume 31, Number 803, (20
May 1910), pp. 767-772, at 768-770.
12. R. D. Carmichael, "On the Theory of Relativity", The Physical Review, Volume 35, Number 3,
(September 1912), pp. 153-176, at 170-171; republished in "The Theory of Relativity", Mathematical
Monographs No. 12, John Wiley & Sons, New York, (1914/1920), pp. 40-41.
13. A. Einstein, "The Relativity of Simultaneity", Relativity: The Special and the General Theory,
Chapter 9, Methuen, London, (1920), pp. 30-33.
----[A presentation of the author is given at the end of the first of his previous two
papers published in this same issue of Episteme]
[email protected]
296
[Spettacolare immagine della grande galassia a spirale NGC 1232 della costellazione Eridano.
La galassia è grande circa il doppio della nostra Via Lattea e dista 100 milioni di anni luce.
La regione centrale contiene stelle vecchie rossastre mentre i bracci a spirale sono popolati di giovani
stelle blu e di regioni in cui nascono nuove stelle.
Sulla sinistra c'è anche una piccola galassia compagna. L'immagine è basata su tre fotografie in
ultravioletto, blu e rosso ed è stata realizzata nel 1998 con il VLT (Very Large Telescope) dell'ESO
(Osservatorio Europeo del Sud). Dell'ESO fanno parte dieci paesi fra cui l'Italia.]
La natura del tempo
(Propagazioni super-luminali - Paradosso dei gemelli - Teletrasporto)
(a cura di Franco Selleri)
(Edizioni Dedalo, Bari, 2002)
"I fisici di Copenhagen e di Göttingen non si limitarono ad enunciare
le loro tesi anticausali ed antirealistiche, ma crearono una
sequela impressionante di veri e propri <<teoremi di impossibilità>>"
(Franco Selleri)
Attenendosi a una formula ormai consueta, Episteme ritiene di fare cosa utile ai suoi lettori di
lingua italiana con il presentare un'opera che esce nelle librerie più o meno nello stesso
periodo di questo numero "speciale" della rivista, e che al pari di esso è testimone di quel
"discomfort towards the actual establishment's philosophy of Nature and of Science", di cui si
diceva nelle righe di introduzione al capitolo dedicato alla "fisica alternativa" on line.
Le "analogie" naturalmente non finiscono qui, e vanno dagli argomenti trattati al fatto che tra
gli autori ve ne sono di già ben noti ed apprezzati a chi frequenta la nostra pubblicazione,
senza tacere la circostanza (già lamentata nella "Lettera dell'editore..." con cui si apre il
presente volume) che talora le argomentazioni critiche contro la "relatività", e "derivazioni"
297
(siffatti sono da ritenersi invero, sia pure in maniera indiretta, taluni sviluppi della fisica
teorica del XX secolo), non appaiono interamente "cristalline" - ciò che, come si è affermato
nella citata "Lettera", nulla toglie peraltro al generale interesse, e soprattutto alle finalità, del
complesso dell'opera. Per esempio, alcune considerazioni sul paradosso dei gemelli,
sull'effetto Sagnac, etc., che "confondono" trattamento delle accelerazioni in relatività
speciale (in assenza cioè di gravitazione, vale a dire di curvatura dello spazio-tempo) e
relatività generale (il collegamento viene effettuato - secondo una procedura del resto assai
comune in simili casi - attraverso il "principio di equivalenza", che è in realtà assai più
"delicato" delle sue enunciazioni-utilizzazioni "ingenue"), oppure discutono in maniera
implicita, sebbene in un contesto relativistico, "oggetti fisici" mediante le "categorie
ordinarie" di spazio e di tempo, il che non può naturalmente non ingenerare equivociapparenti "contraddizioni interne" (tra i responsabili della poco brillante situazione descritta
bisogna annoverare per la verità gli stessi fisici "ortodossi", Einstein in primis, del quale non
sarebbe un totale autentico "paradosso" sostenere che non avesse "compreso" appieno le
"esigenze" della sua propria teoria...).
Ma lasciamo che sia direttamente il libro in oggetto a presentarsi, riportando alla fine,
secondo il nostro solito modo, l'intero suo sommario.
----La comprensibilità del tempo nei processi naturali è stata messa fortemente in dubbio dalla
fisica del Novecento, soprattutto a causa delle relazioni di indeterminazione di Heisenberg e
del relativismo filosofico che ha accompagnato l'affermarsi delle teorie di Einstein. Gli
sviluppi recenti presentati in questo libro, permettono il recupero di una descrizione
soddisfacente del tempo e del cambiamento.
In base a quanto sosteneva Popper, la realtà del tempo e del cambiamento è il punto cruciale
della scienza. Gli autori dei saggi qui raccolti concordano con lui e ognuno di essi discute un
diverso problema riguardante la natura del tempo in modo semplice e chiaro. Numerosi sono
gli argomenti trattati: la relazione di indeterminazione energia-tempo e lo scontro EinsteinBohr; il tempo medio di vita delle particelle instabili; il teletrasporto in tempo zero da Star
Trek alla meccanica quantistica; la trattazione relativistica del tempo e la questione della
simultaneità; il misterioso effetto Sagnac e le sue implicazioni sul tempo; il paradosso dei
gemelli secondo la relatività del tempo e secondo una teoria alternativa basata sulla
simultaneità assoluta; i segnali "super-luminali". Gli autori offrono inoltre risposte a tanti
interrogativi come ad esempio: un orologio su un aereo in volo segna il tempo più
lentamente? Il campo gravitazionale terrestre influenza il tempo segnato dagli orologi atomici
sui satelliti in orbita? Il tempo futuro è predeterminato come sostiene l'interpretazione
ortodossa della teoria della relatività? Se lo è, come è possibile la nostra evidente libertà di
scelta? È possibile sfruttare i segnali super-luminali per inviare messaggi verso il tempo
passato? L'opera si rivolge ad un pubblico ampio con un interesse scientifico, ma anche a
studenti e studiosi.
----Introduzione, Franco Selleri
La relazione di indeterminazione energia-tempo, Augusto Garuccio
Introduzione - Che cos'è l'azione? - Quanto è piccolo il quanto d'azione - Le relazioni di
indeterminazione e il dibattito sulla meccanica quantistica - Uno scontro tra giganti - Come
interpretare la relazione energia-tempo - Regole di indeterminazione, causalità, descrizione
298
spazio-temporale degli eventi quantistici
Il teletrasporto?, Milena D'Angelo
Reversibilità e irreversibilità del tempo in Meccanica Statistica, Giuseppe Gonnella
Il principio dell'aumento dell'entropia - Il punto di vista molecolare e la meccanica statistica Il teorema H - Le obiezioni di Loschmidt e Zermelo - L'entropia di Boltzmann - Il tempo e
l'universo
As time goes by... - Le antiparticelle e la freccia del tempo, Vincenzo Berardi
Viaggiare nel tempo - Le antiparticelle - La scoperta del positrone - L'interpretazione di
Feynman - Indietro nel tempo? - Epilogo
Ritardo degli orologi in moto, Michele Barone
Effetti al secondo ordine di v/c - Convenzione o Proprietà della Natura? - Violazioni
dell'invarianza delle trasformazioni di Lorentz
Il paradosso dei gemelli, Romano Manaresi
Il viaggio - Il paradosso - Il senso comune - TRR, Il principio di relatività - Realtà e
apparenza - La (non) soluzione di TRR - Inversione di marcia - TRG, Il principio di
equivalenza - Il potenziale gravitazionale - La soluzione di TRG - Velocità o accelerazione? Spiegazione causale e spiegazione strutturale - Effetto gemelli senza accelerazioni - La
previsione di TRR - Lo spazio-tempo di Minkowski - Nessun conflitto - Le Trasformazioni
Inerziali - L'effetto gemelli <<assoluto>> - Impossibilità di individuare lo spazio assoluto Conclusioni
Il futuro è predeterminato?, Nicola Russo
La teoria della relatività e il tempo - Einstein-Parmenide e il libero arbitrio - Le teorie
equivalenti alla relatività - Le trasformazioni inerziali - La realtà ritrovata
Gli orologi della teoria relativistica, Ludwik Kostro
La parola "orologio" nel linguaggio ordinario e in quello scientifico - La dilatazione del
tempo nei sistemi di riferimento in moto e nei campi gravitazionali - Esempi di processi
periodici che anticipano anziché ritardare - Processi naturali la cui esistenza dipende
interamente dal campo gravitazionale - Processi fisici la cui esistenza non dipende dal campo
gravitazionale - Processi fisici parzialmente influenzati dal campo gravitazionale - Gli orologi
e la teoria della gravitazione di Newton - Relatività generale e orologi a sorgente di energia
gravitazionale - Quali orologi considerava Einstein nella sua teoria? - Conclusioni
Il tempo sui satelliti del GPS e l'effetto Sagnac, Francesca Intini
La misura del tempo - Il Sistema di Posizionamcnto Globale - Il tempo del GPS - Come
funziona - Fattori di correzione - Le correzioni relativistiche - La correzione di Sagnac L'effetto Sagnac - Conclusioni
Simultaneità relativistica, Massimo Brighi
Cosa accade, adesso, su Marte? - Simultaneità classica - Sistemi di riferimento ed eventi - Lo
spazio-tempo di Minkowski - Simultaneità relativistica (la soluzione di Einstein) Simultaneità, sincronizzazione e velocità di sola andata - La velocità della luce - Trasporto di
orologi - Simultaneità non standard - Proprietà della relazione di simultaneità - Simultaneità
assoluta - Il teorema di Malament - Simultaneità in sistemi di riferimento accelerati e
relatività generale - Conclusioni
299
I FLOP nella trattazione relativistica del tempo, Rocco Vittorio Macrì
Il concetto di Falsificatore Logico Potenziale (FLOP) - La metafisica operativoverificazionista e i FLOP del Gedankenexperiment - La <<nave di Galileo>> e i FLOP nei
fondamenti relativistici - Considerazioni conclusive sui razzi vettori della TRS
Esperimenti <<super-luminali>>: una panoramica, Erasmo Recami
Introduzione - Relatività Speciale ed Estesa - La situazione sperimentale
E' possibile inviare messaggi verso il passato?, Franco Selleri
Segnali superluminali e paradosso causale - La regola reinterpretativa di Recami - Il tempo
non può essere capovolto - Trasformazioni fra sistemi inerziali - Le trasformazioni equivalenti
- La relatività della simultaneità resta esclusa - Solo la simultaneità assoluta è possibile
----[Franco Selleri insegna fisica teorica all¹Università di Bari. È autore di alcuni
libri pubblicati in una decina di lingue e di numerosi articoli scientifici che
trattano di fisica delle particelle e di fondamenti della teoria dei quanti e della
relatività.]
[email protected]
http://www.edizionidedalo.it/

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