Models of spontaneous wave func9on collapse and optomechanics

Models of spontaneous wave func1on collapse and optomechanics Quantum Interfaces with Nano-­‐opto-­‐
electro-­‐mechanical devices: Applica1ons and Fundamental Physics Erice, 1st – 5th August 2016 (Angelo Bassi – University of Trieste & INFN) Quantum Mechanics Linearity è Superposi1on Principle è Schrödinger's cat è Measurement Problem
Modify the Schrödinger equa1on J.S.Bell Speakable and Unspeakable in Quantum Mechanics E.P. Wigner in: Quantum Op1cs, Experimental gravity and Measurement theory, Plenum, NY (1983) A.J. Legge^ Supplement Progr. Theor. Phys. 69, 80 (1980) H.P. Stapp In: Quantum Implica1ons: Essay in Honor of David Bohm, Routledge & Kegan Paul, London (1987) S. Weinberg Phys. Rev. Le6. 62, 486 (1989). R. Penrose In: Quantum Concepts of Space and Time, Oxford U.P. (1985) S.L. Adler Quantum Theory as an emergent phenomenon, CUP (2009) G.C. Ghirardi, A. Rimini, T. Weber Phys. Rev. D 34, 470 (1986) P. Pearle Phys. Rev. A 39, 2277 (1989) L. Diosi L. Diosi, Phys. Rev. A 40, 1165 (1989)
How to modify the Schrödinger equa1on? The no-­‐faster-­‐than-­‐light condi1on heavily constraints the possible ways to modify the Schrödinger equa1on. In par1cular, it requires that nonlinear terms must always be accompanied by appropriate stochas1c terms. N. Gisin, Hel. Phys. Acta 62, 363 (1989). Phys. Le6. A 143, 1 (1990) N. Gisin and M. Rigo, Journ. Phys. A 28, 7375 (1995) J. Polcinski, Phys. Rev. Le6. 66, 397 (1991) H.M. Wiseman and L. Diosi, Chem. Phys. 268, 91 (2001) S.L. Adler, “Quantum Theory as an Emergent Phenomenon”, C.U.P. (2004) A. Bassi, D. Dürr and G. Hinrichs, Phys. Rev. Le6. 111, 210401 (2013). L. Diosi, Phys. Rev. Le6. 112, 108901 (2014) M. Caiaffa, A. Smirne and A. Bassi, in prepara1on The con1nuous dynamics (simplified) d|⇥⇤t =

⌅
i
Hdt +
(A
~
⇥A⇤t )dWt
quantum A⇥t =
t |A| t ⇥
2
(A
⇥A⇤t )2 dt |⇥⇤t
collapse nonlinear The wave func1on is dynamically and stochas1cally driven by the noise Wt towards one of the eigenstates of the operator A This equa1on describes microscopic physics, macroscopic physics, and what happens in quantum experiments (Born rule, collapse …) (Mass-­‐propor1onal) CSL model P. Pearle, Phys. Rev. A 39, 2277 (1989). G.C. Ghirardi, P. Pearle and A. Rimini, Phys. Rev. A 42, 78 (1990) d
|
dt
ti =

p Z
i
H+
d3 x (M (x) hM (x)it ) dWt (x)
~
m0
Z Z
3
3
d
xd
y G(x y) (M (x) hM (x)it ) (M (y)
2
2m0
M (x) = ma† (x)a(x)
G(x) =
hM (y)it ) |
1
2
2
exp[
(x)
/4r
C]
3/2
(4⇡rC )
The operators are func1on of the space coordinate. The collapse occurs in space. Two parameters = collapse strength
rC = localization resolution
2 3/2
= /(4⇡rC
)
= collapse rate
ti
The collapse rate Small superpositions
Large superpositions
+
+
⌧ rC
Collapse NOT effective
Amplification
mechanics
rC
Collapse effective
Few particles
no collapse
quantum
behavior
Γ = λn2N
Fast collapse
n = number of particles
within rC
N = number of such
clusters
Many particles
+
classical
behavior
CSL Parameters ⇠ 10
8±2
1
s
QUANTUM – CLASSICAL TRANSITION (Adler -­‐ 2007) Mesoscopic world: Latent image forma1on + percep1on in the eye (~ 104 -­‐ 105 par1cles) S.L. Adler, JPA 40, 2935 (2007) A. Bassi, D.A. Deckert & L. Ferialdi, EPL 92, 50006 (2010) ⇠ 10
17
s
1
QUANTUM – CLASSICAL TRANSITION (GRW -­‐ 1986) p
rC = 1/ ↵ ⇠ 10
Macroscopic world (> 1013 par1cles) G.C. Ghirardi, A. Rimini and T. Weber, PRD 34, 470 (1986) 5
cm
Increasing size of the system Microscopic world (few par1cles) Experimental tests The obvious way to test collapse models is with ma^er-­‐
wave interferometry Predic1on of quantum mechanics (no environmental noise) Predic1on of collapse models (no environmental noise) Interferometric Experiments PERSPECTIVES
Atom Interferometry photon, it could have come A
B
from either of the diamond Pump pulse
Scattered photon
Mirror
crystals in which one phoPump pulse
non was excited. The indistinguishability of these two
Phonon
possibilities during detection means that the two dia- Making quantum connections. The method
mond samples coherently used by Lee et al. to generate entanglement
between two macroscopic diamonds is illusshared one phonon, which trated. (A) A pumping laser pulse generates a
Beam splitter
Detector
is the hallmark of a quan- correlated pair of a phonon inside the diamond
tum-entangled state.
as well as a scattered photon. (B) The scattered photons from two diamonds are brought together for interference and detection.
T h e e n t a n g l e m e n t When one photon is detected, the two diamonds coherently share a phonon. Thus, the quantum state created has the hallmarks
between the two diamond of quantum entanglement.
Adlersamples was confirmed in
experiments in which a second laser pulse need to be a macroscopic device in which could be done within the coherence time of
de-excited the shared phonon and re-emitted entanglement is preserved and used over long the solids, even at room temperature.
a photon that was subsequently detected. By times and distances. The lifetime of entangleReferences and Notes
this method, Lee et al. demonstrate that the ment in the experiment by Lee et al. is still too
1. K. C. Lee et al., Science 334, 1253 (2011).
two diamonds share entanglement at a 98% short for many quantum information applica2. L.-M. Duan, Nature 414, 413 (2001).
C. W. Chou et al.,
Nature 438,
828 (2005).
K. room-temperature
C. Lee et al., S3.4.cience. 334, 1253 (2011). confidence level. These results provide a tions, in part because of the
T. Chanelière et al., Nature 438, 833 (2005).
striking example that entanglement is not par- environment and the strong coupling of pho5. N.9Sangouard,
C. Simon, H. (
de2016) Riedmatten, N.
S. B
elli e
t a
l., P
RA 4, 0
12108 Gisin, Rev.
ticular to microscopic particles but can mani- non modes in solids. However, the experiment
Mod. Phys. 83, 33 (2011).
6. D. L. Moehring et al., Nature 449, 68 (2007).
fest itself in the macroscopic world, where it emphasizes an important
point,
that
ultrafast
7. S. Olmschenk et al., Science 323, 486 (2009).
could be used in future studies that make fun- optical technology can alleviate the require8. E. Togan et al., Nature 466, 730 (2010).
damental tests of quantum mechanics.
ment on quantum coherence time. In future,
9. C. Clausen et al., Nature 469, 508 (2011).
10.
Supported by the National Basic Research Program of
GRW
The demonstration of entanglement in with improvement of the ultrafast technology,
China (973 Program) 2011CBA00300 (2011CBA00302),
macroscopic systems also has important or by using more isolated degrees of freedom
Army Research Office, and Air Force Office of Scientific
Research MURI program.
implications for the ongoing efforts to realize in solids—such as as the nuclear spins (8) or
quantum computation and communication. A the dopant rare-earth ions (9)—for quantum
full-size quantum computer eventually will memory, many more quantum operations
10.1126/science.1215444
T. Kovachy et al., Nature 528, 530 (2015) 10-2
M = 87 amu d = 0.54 m T = 1 s 10-4
10-6
10-8
Entangling Diamonds CSL
10-10
10-12
Molecular Interferometry 10-14
M = 104 amu d = 10-­‐7 m T = 10-­‐3 s 10-18
S. Eibenberger et al. PCCP 15, 14696 (2013) 10-16
M. Toros et al., ArXiv 1601.03672 10-20
-22
10
M = 1016 amu d = 10-­‐11 m T = 10-­‐12 s Lower bound: Collapse effec1ve at the macroscopic level Graphene disk: N =Mathematical
1011 amu, d = 10-­‐5 m, Dances
T = 10-­‐2 s with Wolves
ECOLOGY
10-10
-6
10-8 Sebastian10
J. Schreiber
10-4
10-2
100
c
n the movierDances
with Wolves, a lone
The 280 radio-collared wolves studied by
wolf facilitates Lieutenant John Dunbar’s Coulson et al. are direct descendants of 41
immersion into the complex culture of gray wolves reintroduced into Yellowstone
the Sioux Indians. This immersion required National Park between 1995 and 1997 (4).
overcoming multiple cultural barriers. Ecol- This reintroduction was part of a larger effort
ogists and evolutionary biologists face an involving a simultaneous reintroduction in
equally daunting challenge of understanding Idaho and a naturally colonized population
how environmental change affects ecological in Montana. It was extremely successful; by
and evolutionary dynamics (1). Historically, 2010, the Northern Rocky Mountain wolf
. h^p://www.cost.eu/COST_Ac1ons/ca/CA15220 researchers examined these impacts in isola- population had expanded to 1651 individuals
tion. However, these dynamics can occur on (5). Individuals within this expanding popula-
I
Data and modeling of Yellowstone wolf
populations illustrate the complex interrelated
ecological and evolutionary responses to
environmental change.
to environmental change, Coulson et al. fuse
integral projection models (IPMs) with classical population genetics. Unlike their matrix
model counterparts (7), IPMs describe the
dynamics of populations with traits that vary
continuously, such as body size (8), as well
as discrete traits, such as coat color (9). Traditional IPMs track how the number of individuals with a particular body size changes
due to births, deaths, and individual growth.
The rules underlying these changes are deter-
To improve interferometric tests, it will be necessary to go to micro-­‐gravity environment in outer space. COST Ac1on QTSpace
Non interferometric tests M. Bahrami, M. Paternostro, A. Bassi, H. Ulbricht, Phys. Rev. Le6. 112, 210404 (2014). S. Nimmrichter, K. Hornberger, K. Hammerer, Phys. Rev. Le6. 113, 020405 (2014). L. Diósi, Phys. Rev. Le6. 114, 050403 (2015) The collapse induces a Brownian mo1on on the system Charged free par1cle 1. Quantum mechanics Nano-­‐par1cle in a op1cal cavity 2. Collapse models Spontaneous photon emission Extra shi\ and broadening Due to its excellent sensitivity, optical interferometry is
the most widely used technique to detect the motion of ultrasensitive mechanical resonators, for applications which
range from magnetic resonance force microscopy !MRFM",1
investigation of quantum effects in mechanical systems,2 and
fundamental physics experiments.3 Unfortunately, optical detection becomes hard to implement when the size of the resonator is pushed to the nanoscale, because of the diffraction
limit, and when low or ultralow temperatures are required to
reduce the thermal force noise, as for single spin MRFM. In
the latter case, resonator heating due to light absorption is
found to limit the effective cooling of the resonator.4 This
problem can be partially circumvented only by substantially
reducing the input light power, at the price of reducing the
displacement sensitivity. Other techniques have been recently demonstrated to be more compatible with ultralow
temperatures. In particular, both single electron transistors5
and microwave cavities6–8 have demonstrated outstanding
displacement sensitivity for the detection of nanomechanical
resonators at temperatures below 100 mK. So far, however,
their implementation has been limited to systems where detector and resonator are tightly integrated, which is not practical for scanning probe applications. Moreover, for microwave techniques the direct photon absorption still remains an
issue at millikelvin temperatures, which again can only be
mitigated by reducing the input power. Displacement sensors
based on quantum point contacts have also been demonstrated in an off-board setup9 but so far their use has been
limited to liquid helium temperature.
In this letter, we demonstrate a rather simple alternative
detection technique, based on the use of a dc superconducting quantum interference device !SQUID", which in principle does not require any power to be directly dissipated in
the mechanical resonator. Our method involves attaching a
ferromagnetic particle to the end of the resonator $Fig. 1!a"%
which, whenever the resonator moves, causes a change in
magnetic flux in a superconducting detection coil, positioned
close to the resonator $Fig. 1!b"%. A cantilever displacement x
is thus converted into a coil flux ! = "x, where the constant "
is proportional to the magnetic moment # of the ferromag-
netic particle and depends in a complex way on the coil
geometry and the relative position and orientation of magnetic moment and coil. The flux change in the detection coil
is measured by the dc SQUID amplifier via a superconducting flux transformer of total inductance Lt, which includes a
calibration transformer and the SQUID input coil.
In our experiment, we use a silicon resonator consisting
of a 100 nm thick single crystal beam, 5 #m wide and
Non-­‐Interferometric Experiments Cold Atom Gas F. Laloë et al. Phys. Rev. A 90, 052119 (2014) Can1lever M = 87 amu T = 30 s A. Vinante et al., Phys. Rev. Le^. 116, 090402 (2016) M = 1014 amu T = ∞ Cold Atom Gas M. Bilardello et al., ArXiv 1605.01891 a"
Electronic mail: [email protected].
0003-6951/2011/98"13!/133105/3/$30.00
98,is133105-1
© 2011 American InstituteDownloaded
of Physics to IP:
This article
is copyrighted as indicated in the article. Reuse of AIP content
subject to the terms at: http://scitation.aip.org/termsconditions.
140.105.16.64 On: Thu, 03 Dec 2015 09:34:06
M = 87 amu T = 1 s X-­‐Ray FIG. 1. !a" An electron microscopy image of the silicon resonator with a
magnetic sphere attached to its end. The single crystal beam is 100 nm thick,
5 #m wide, and 100 nm long. The 4.5 #m diameter magnetic sphere is
made of a neodymium based alloy with remanence Br = 0.75 T. The frequency of the lowest flexural mode of the resonator is 3084 Hz, with a
quality factor of 3.8$ 104. !b" Circuit diagram illustrating the detection
scheme. The motion x of the resonator induces a flux ! = "x in the detection
coil and a current I = −! / Lt in the superconducting detection loop, which is
measured by the dc SQUID.
Lower bound: Collapse effec1ve at the macroscopic level Graphene disk: N = 1011 amu, d = 10-­‐5 m, T = 10-­‐2 s C. Curceanu et al., J. Adv. Phys. 4, 263 (2015). M = 1 Kg T = days / months Gravita1onal wave detectors M. Carlesso et al., ArXiv 1606.04581 M = 1030 amu T = ∞ Updated version of: S.L. Adler and A. Bassi:, Science 325, 275 (2009) Beyond CSL The collapse is driven by a random noise. In the CSL model, the noise is white and no dissipa1ve effects are included. This makes the model rela1vely easy to work with, but not physically realis1c. Progress has been made in generalizing CSL, both with a colored spectrum, as well as with dissipa1on. Collapse models in space REVIEW: A. Bassi and G.C.
Ghirardi, Phys. Rept. 379, 257
(2003)
White noise models
Colored noise models
REVIEW: A. Bassi, K. Lochan,
S. Satin, T.P. Singh and H.
Ulbricht, Rev. Mod. Phys. 85,
471 (2013)
All frequencies appear
with the same weight
The noise can have an
arbitrary spectrum
GRW / CSL
Infinite temperature
models
No dissipative effects
G.C. Ghirardi, A. Rimini, T. Weber , Phys.
Rev. D 34, 470 (1986)
G.C. Ghirardi, P. Pearle, A. Rimini, Phis.
Rev. A 42, 78 (1990)
QMUPL
L. Diosi, Phys. Rev. A 40, 1165 (1989)
DP
L. Diosi, Phys. Rev. A 40, 1165 (1989)
Non-Markovian CSL
P. Pearle, in Perspective in Quantum Reality
(1996)
S.L. Adler & A. Bassi, Journ. Phys. A 41,
395308 (2008). arXiv: 0807.2846
Non-Markovian QMUPL
A. Bassi & L. Ferialdi, Phys. Rev. Lett. 103,
050403 (2009)
Dissipative QMUPL
Finite temperature
models
Dissipation and
thermalization
A.  Bassi, E. Ippoliti and B. Vacchini,
J. Phys. A 38, 8017 (2005).
Dissipative GRW & CSL
A. Smirne, B. Vacchini & A. Bassi
Phys. Rev. A 90, 062135 (2014)
A. Smirne & A. Bassi
Nat. Sci. Rept. 5, 12518 (2015)
Non-Markovian &
dissipative QMUPL
L. Ferialdi, A. Bassi
Phys. Rev. Lett. 108, 170404 (2012)
Interferometric experiments and the new models PERSPECTIVES
Atom Interferometry photon, it could have come A
B
from either of the diamond Pump pulse
Scattered photon
Mirror
crystals in which one phoPump pulse
non was excited. The indistinguishability of these two
Phonon
possibilities during detection means that the two dia- Making quantum connections. The method
mond samples coherently used by Lee et al. to generate entanglement
between two macroscopic diamonds is illusshared one phonon, which trated. (A) A pumping laser pulse generates a
Beam splitter
Detector
is the hallmark of a quan- correlated pair of a phonon inside the diamond
tum-entangled state.
as well as a scattered photon. (B) The scattered photons from two diamonds are brought together for interference and detection.
T h e e n t a n g l e m e n t When one photon is detected, the two diamonds coherently share a phonon. Thus, the quantum state created has the hallmarks
between the two diamond of quantum entanglement.
Adlersamples was confirmed in
experiments in which a second laser pulse need to be a macroscopic device in which could be done within the coherence time of
de-excited the shared phonon and re-emitted entanglement is preserved and used over long the solids, even at room temperature.
a photon that was subsequently detected. By times and distances. The lifetime of entangleReferences and Notes
this method, Lee et al. demonstrate that the ment in the experiment by Lee et al. is still too
1. K. C. Lee et al., Science 334, 1253 (2011).
two diamonds share entanglement at a 98% short for many quantum information applica2. L.-M. Duan, Nature 414, 413 (2001).
C. W. Chou et al.,
Nature 438,
828 (2005).
K. room-temperature
C. Lee et al., S3.4.cience. 334, 1253 (2011). confidence level. These results provide a tions, in part because of the
T. Chanelière et al., Nature 438, 833 (2005).
striking example that entanglement is not par- environment and the strong coupling of pho5. N. Sangouard, C. Simon, H. de Riedmatten, N. Gisin, Rev.
ticular to microscopic particles but can mani- non modes in solids. However, the experiment
Mod. Phys. 83, 33 (2011).
6. D. L. Moehring et al., Nature 449, 68 (2007).
fest itself in the macroscopic world, where it emphasizes an important point, that ultrafast
7. S. Olmschenk et al., Science 323, 486 (2009).
could be used in future studies that make fun- optical technology can alleviate the require8. E. Togan et al., Nature 466, 730 (2010).
damental tests of quantum mechanics.
ment on quantum coherence time. In future,
9. C. Clausen et al., Nature 469, 508 (2011).
10.
Supported by the National Basic Research Program of
GRW
The demonstration of entanglement in with improvement of the ultrafast technology,
China (973 Program) 2011CBA00300 (2011CBA00302),
macroscopic systems also has important or by using more isolated degrees of freedom
Army Research Office, and Air Force Office of Scientific
Research MURI program.
implications for the ongoing efforts to realize in solids—such as as the nuclear spins (8) or
quantum computation and communication. A the dopant rare-earth ions (9)—for quantum
full-size quantum computer eventually will memory, many more quantum operations
10.1126/science.1215444
T. Kovachy et al., Nature 528, 530 (2015) 10-2
M = 87 amu d = 0.54 m T = 1 s 10-4
10-6
10-8
Entangling Diamonds CSL
10-10
Molecular Interferometry 10-12
M = 1016 amu d = 10-­‐11 m T = 10-­‐12 s 10-14
S. Eibenberger et al. PCCP 15, 14696 (2013) 10-16
M = 104 amu d = 10-­‐7 m T = 10-­‐3 s 10-18
10-20
ECOLOGY
Mathematical Dances with Wolves
-22
10
10-10
-6
10-8 Sebastian10
J. Schreiber
10-4
10-2
c
n the movierDances
with Wolves, a lone
wolf facilitates Lieutenant John Dunbar’s
immersion into the complex culture of
the Sioux Indians. This immersion required
overcoming multiple cultural barriers. Ecologists and evolutionary biologists face an
equally daunting challenge of understanding
how environmental change affects ecological
and evolutionary dynamics (1). Historically,
researchers examined these impacts in isolation. However, these dynamics can occur on
I
100
The 280 radio-collared wolves studied by
Coulson et al. are direct descendants of 41
gray wolves reintroduced into Yellowstone
National Park between 1995 and 1997 (4).
This reintroduction was part of a larger effort
involving a simultaneous reintroduction in
Idaho and a naturally colonized population
in Montana. It was extremely successful; by
2010, the Northern Rocky Mountain wolf
population had expanded to 1651 individuals
(5). Individuals within this expanding popula-
Data and modeling of Yellowstone wolf
populations illustrate the complex interrelated
ecological and evolutionary responses to
environmental change.
to environmental change, Coulson et al. fuse
integral projection models (IPMs) with classical population genetics. Unlike their matrix
model counterparts (7), IPMs describe the
dynamics of populations with traits that vary
continuously, such as body size (8), as well
as discrete traits, such as coat color (9). Traditional IPMs track how the number of individuals with a particular body size changes
due to births, deaths, and individual growth.
The rules underlying these changes are deter-
The new experimental bounds are robust against changes in the noise. It comes not as a surprise, as these are direct tests of the superposi1on principle Non-­‐Interferometric Experiments and the new models Cold Atom Gas Can1lever Perhaps weakened if dissipa1on is taken into account Cold Atom Gas Weakened only for strong dissipa1on X-­‐Ray Disappears for any reasonable cutoff in the spectrum Gravita1onal wave detectors Perhaps weakened if dissipa1on is taken into account Collapse and gravity Fundamental proper1es of the collapse It occurs in space. It scales with the mass of the system. The possible role of gravity The “natural” way to describe it mathema1cally, is to couple the noise field to the energy density (the stress-­‐energy tensor, in a rela1vis1c framework). Gravity provides such a coupling. Problem The coupling is not the standard one prescribed by quantum theory (which would be linear). No one knows why gravity should couple as prescribed by collapse models Diosi – Penrose model L. Diosi, Phys. Rev. A 40, 1165 (1989) d|
ti
=

Z
i
Hdt + d3 x (M̂ (x) hM̂ (x)it )dWt (x)
~
Z
1
d3 xd3 y G(x y)(M̂ (x) hM̂ (x)it )(M̂ (y)
2
hM̂ (y)it )dt |
Same equa1on as that of the CSL model. The only difference is in the noise: G(x) =
G 1
~ |x|
Gravity. And no other free parameter. The localiza1on 1me is: 0
⌧ (x, x ) =
U (x
~
x0 )
U (0)
U (x) =
G
Z
3
3 0 M (r)M (r
d rd r
|x + r
0
)
r0 |
Penrose’s idea: quantum superposi1on è space1me superposi1on è energy uncertainty è decay in 1me (R. Penrose, Gen. Rel. Grav. 28, 581 -­‐ 1996) ti
Cri1cisms 1.  The model is not derived following some guideline. It does not explain why gravity enters the game (expect for G). 2.  G and 1/r do not appear in the coupling between ma^er and gravity, but in the correla1on func1on of the noise. There is no reason for that to be the case. (Gravity induced vs. gravity related collapse model.) 3.  The model diverges for point-­‐like par1cles. One needs to introduce a cut off. Then the model depends on a parameter, the cut-­‐off R0. Diosi’s original proposal: R0 = 10-­‐15 m = Compton wavelength of a nucleon. This is jus1fied by the requirement that the model is non-­‐rela1vis1c. However, this model pumps energy at a very high rate, contradic1ng experimental data. To avoid this, one has to introduce a large cut off, which at present has no jus1fica1on. The Schrödinger-­‐Newton equa1on d
i~
(x, t) =
dt
✓
~
r2
2m
2
2
Gm
Z
2
| (y, t)|
d y
|x y|
3
◆
(x, t)
L. Diósi. Phys. Le^. A 105, 199 (1984). R. Penrose, Gen. Relat. Gravit. 28, 581 (1996). D. Giulini and A. Grossardt, Class. Quantum Grav. 29, 215010 (2012) quantum spread gravita1onal collapse It comes from semi-­‐classical gravity if taken as a fundamental theory = ma^er is fundamentally quantum and gravity is fundamentally classical, and they couple as follows Gµ⌫
8⇡G
= 4 h |T̂µ⌫ | i
c
The term on the right is nonlinear in the wave func1on Wrong collapse It collapses the wave func1on, but not as prescribed by the Born rule + Double slit experiment according to standard QM Double slit experiment according to the Schrödinger-­‐Newton equa1on But there are smarter ways of tes1ng the equa1on H. Yang, H. Miao, D.-­‐S. Lee, B. Helou, Y. Chen, Phis. Rev. Le6. 110, 170401 (2013) A. Großardt, J. Bateman, H. Ulbricht, A. Bassi, Phys. Rev. D 93, 096003 (2016) It does faster-­‐than-­‐light Consider the usual “Alice & Bob sharing an entangled spin state” scenario. Alice first measure along the z direc1on: Then Alice measures along the x direc1on M. Bahrami, A. Grossardt, S. Donadi and A. Bassi, New J. Phys. 16, 115007 (2014) Acknowledgments The Group (www.qmts.it) •  Postdocs: S. Donadi, F. Fassioli, A. Grossardt •  Ph.D. students: G. Gasbarri, M. Toros, M. Bilardello, M. Carlesso, S. Bacchi, L. Curcuraci •  Graduate students: A. Rampichini Collabora1ons with: S.L. Adler, M. Paternostro, A. Smirne, H. Ulbricht, A. Vinante, C. Curceanu. www.units.it www.infn.it www.cost.eu