We review seven models which consistently couple quantum matter and (Newtonian) gravity in a nonstandard way. For each of them, we present the underlying motivations, the main equations, and, when available, a comparison with experimental data.

1.
C.
Rovelli
,
Living Rev. Relativ.
11
,
5
(
2008
).
2.
M. B.
Green
,
J. H.
Schwarz
, and
E.
Witten
,
Superstring Theory: Loop Amplitudes, Anomalies and Phenomenology
(
Cambridge University Press
,
2012
), Vol. 2.
4.
E.
Schrödinger
,
Naturwissenschaften
23
,
807
(
1935
).
5.
A. J.
Leggett
,
Prog. Theor. Phys. Suppl.
69
,
80
(
1980
).
6.
7.
J. S.
Bell
,
Speakable and Unspeakable in Quantum Mechanics: Collected Papers on Quantum Philosophy
(
Cambridge University Press
,
2004
).
8.
G. C.
Ghirardi
,
A.
Rimini
, and
T.
Weber
,
Phys. Rev. D
34
,
470
(
1986
).
9.
F.
Karolyhazy
,
Il Nuovo Cimento A
42
,
390
(
1966
).
10.
F.
Károlyházy
,
A.
Frenkel
, and
B.
Lukács
, “
On the possibility of observing the eventual breakdown of the superposition principle
,” in
Physics as Natural Philosophy
, edited by
A.
Simony
and
H.
Feschbach
(
MIT Press
,
Cambridge, MA
,
1982
), p.
204
.
11.
F.
Károlyházy
,
A.
Frenkel
, and
B.
Lukács
, “
On the possible role of gravity in the reduction of the wave function
,” in
Quantum Concepts in Space and Time
, edited by
R.
Penrose
and
C. J.
Isham
(
Oxford University Press
,
1986
), pp.
109
128
.
12.
S.
Bera
,
S.
Donadi
,
K.
Lochan
, and
T. P.
Singh
,
Found. Phys.
45
,
1537
(
2015
).
14.
S. L.
Adler
and
F. M.
Ramazanoğlu
,
J. Phys. A
40
,
13395
(
2007
);
S. L.
Adler
and
F. M.
Ramazanoğlu
,
J. Phys. A
42
,
109801
(
2009
). https://iopscience.iop.org/article/10.1088/1751-8121/42/10/109801/meta
15.
S. L.
Adler
,
A.
Bassi
, and
S.
Donadi
,
J. Phys. A
46
,
245304
(
2013
).
16.
S.
Donadi
and
A.
Bassi
,
J. Phys. A
48
,
035305
(
2015
).
17.
L.
Diósi
and
B.
Lukács
,
Phys. Lett. A
181
,
366
(
1993
).
19.
L.
Diósi
and
B.
Lukács
,
Ann. Phys.
499
,
488
(
1987
).
20.
21.
G.
Ghirardi
,
R.
Grassi
, and
A.
Rimini
,
Phys. Rev. A
42
,
1057
(
1990
).
22.
M.
Bahrami
,
A.
Smirne
, and
A.
Bassi
,
Phys. Rev. A
90
,
062105
(
2014
).
23.
A.
Smirne
and
A.
Bassi
,
Sci. Rep.
5
,
12518
(
2015
).
24.
B.
Helou
,
B.
Slagmolen
,
D. E.
McClelland
, and
Y.
Chen
,
Phys. Rev. D
95
,
084054
(
2017
).
25.
A.
Tilloy
and
T. M.
Stace
,
Phys. Rev. Lett.
123
,
080402
(
2019
).
26.
S.
Donadi
,
K.
Piscicchia
,
C.
Curceanu
,
L.
Diósi
,
M.
Laubenstein
, and
A.
Bassi
,
Nat. Phys.
17
,
74
(
2021
).
27.
A.
Vinante
and
H.
Ulbricht
,
AVS Quantum Sci.
3
,
045602
(
2021
).
28.
R.
Penrose
,
Gen. Relativ. Gravitation
28
,
581
(
1996
).
29.
W.
Marshall
,
C.
Simon
,
R.
Penrose
, and
D.
Bouwmeester
,
Phys. Rev. Lett.
91
,
130401
(
2003
).
30.
R.
Howl
,
R.
Penrose
, and
I.
Fuentes
,
New J. Phys.
21
,
043047
(
2019
).
31.
S. L.
Adler
,
Quantum Theory as an Emergent Phenomenon: The Statistical Mechanics of Matrix Models as the Precursor of Quantum Field Theory
(
Cambridge University Press
,
2004
).
32.
S.
Adler
, “
Gravitation and the noise needed in objective reduction models
,” in
Quantum Nonlocality and Reality: 50 Years of Bell's Theorem
, edited by
Mary
Bell
and
Shan
Gao
(
Cambridge University Press
,
2016
).
33.
K.
Krasnov
,
J. High Energy Phys.
2015
,
37
.
34.
G.
Gasbarri
,
M.
Toroš
,
S.
Donadi
, and
A.
Bassi
,
Phys. Rev. D
96
,
104013
(
2017
).
35.
G. C.
Ghirardi
,
P.
Pearle
, and
A.
Rimini
,
Phys. Rev. A
42
,
78
(
1990
).
36.
M.
Carlesso
and
S.
Donadi
, “
Collapse models: main properties and the state of art of the experimental tests
,” in
Advances in Open Systems and Fundamental Tests of Quantum Mechanics
, edited by
B.
Vacchini
,
H.-P.
Breuer
, and
A.
Bassi
(
Springer
,
2019
), pp.
1
13
.
37.
M.
Carlesso
,
S.
Donadi
,
L.
Ferialdi
,
M.
Paternostro
,
H.
Ulbricht
, and
A.
Bassi
,
Nat. Phys.
18
,
243
(
2022
).
39.
C.
Møller
,
Colloq. Int. C. N. R. S.
91
,
15
(
1962
).
41.
M.
Bahrami
,
A.
Großardt
,
S.
Donadi
, and
A.
Bassi
,
New J. Phys.
16
,
115007
(
2014
).
42.
S.
Carlip
,
Classical Quantum Gravity
25
,
154010
(
2008
).
43.
N.
Gisin
,
Helv. Phys. Acta
62
,
363
(
1989
).
44.
A.
Großardt
,
J.
Bateman
,
H.
Ulbricht
, and
A.
Bassi
,
Phys. Rev. D
93
,
096003
(
2016
).
45.
H.
Yang
,
H.
Miao
,
D.-S.
Lee
,
B.
Helou
, and
Y.
Chen
,
Phys. Rev. Lett.
110
,
170401
(
2013
).
46.
D.
Kafri
,
J.
Taylor
, and
G.
Milburn
,
New J. Phys.
16
,
065020
(
2014
).
47.
K.
Jacobs
and
D. A.
Steck
,
Contemp. Phys.
47
,
279
(
2006
).
48.
J. L.
Gaona-Reyes
,
M.
Carlesso
, and
A.
Bassi
,
Phys. Rev. D
103
,
056011
(
2021
).
49.
N.
Altamirano
,
P.
Corona-Ugalde
,
R. B.
Mann
, and
M.
Zych
,
Classical Quantum Gravity
35
,
145005
(
2018
).
50.
G. D.
Bartolomeo
,
M.
Carlesso
, and
A.
Bassi
,
Phys. Rev. D
104
,
104027
(
2021
).
51.
A.
Tilloy
and
L.
Diósi
,
Phys. Rev. D
93
,
024026
(
2016
).
52.
S.
Nimmrichter
and
K.
Hornberger
,
Phys. Rev. D
91
,
024016
(
2015
).
53.
J.
Sanchez Gomez
,
Decoherence Through Stochastic Fluctuations of the Gravitational Field
edited by
L.
Diosi
and
B.
Lukacs
(
World Scientific
,
Singapore
,
1992
), Vol. 456, pp.
88
93
54.
W.
Power
and
I.
Percival
,
Proc. R. Soc. London, Ser. A
456
,
955
(
2000
).
55.
H.-P.
Breuer
,
E.
Göklü
, and
C.
Lämmerzahl
,
Classical Quantum Gravity
26
,
105012
(
2009
).
56.
57.
C.
Anastopoulos
and
B.
Hu
,
Classical Quantum Gravity
30
,
165007
(
2013
).
58.
I.
Pikovski
,
M.
Zych
,
F.
Costa
, and
Č.
Brukner
,
Nat. Phys.
11
,
668
(
2015
).
59.
A.
Bassi
,
A.
Großardt
, and
H.
Ulbricht
,
Classical Quantum Gravity
34
,
193002
(
2017
).
60.
L.
Asprea
,
G.
Gasbarri
, and
A.
Bassi
,
Phys. Rev. D
103
,
104041
(
2021
).
61.
S.
Bose
,
A.
Mazumdar
,
G. W.
Morley
,
H.
Ulbricht
,
M.
Toroš
,
M.
Paternostro
,
A. A.
Geraci
,
P. F.
Barker
,
M.
Kim
 et al., 
Phys. Rev. Lett.
119
,
240401
(
2017
).
62.
C.
Marletto
and
V.
Vedral
,
Phys. Rev. Lett.
119
,
240402
(
2017
).
63.
Due to their smaller mass, the contribution from the electrons can be negligible compared to that of the atomic nuclei. Here, nucleons are taken as a fundamental constituent because the model is formulated in the non-relativistic regime; therefore, the energies are not high enough to resolve their structure.
You do not currently have access to this content.