The author reviews the arguments most often raised against a fundamental coupling of classical spacetime to quantum matter. The author shows that an experiment by Page and Geilker does not exclude such a semiclassical theory but mandates an inclusion of an objective mechanism for wave function collapse. In this regard, the author presents a classification of semiclassical models defined by the way in which the wave function collapse is introduced. Two related types of paradoxes that have been discussed in the context of the necessity to quantize the gravitational field can be shown to not constrain the possibility of a semiclassical coupling. A third paradox, the possibility to signal faster than light via semiclassical gravity, is demonstrably avoided if certain conditions are met by the associated wave function collapse mechanism. In conclusion, all currently discussed models of semiclassical gravity can be made consistent with observation. Their internal theoretical consistency remains an open question.
References
1.
The Role of Gravitation in Physics: Report from the 1957 Chapel Hill Conference
, edited by C. M.
DeWitt
and D.
Rickles
(Max Planck Research Library
, Berlin
, 1957
).2.
K.
Eppley
and E.
Hannah
, Found. Phys.
7
, 51
(1977
).3.
T. W. B.
Kibble
, “Is a semi-classical theory of gravity viable?
” in Quantum Gravity 2. A Second Oxford Symposium
, edited by C. J.
Isham
, R.
Penrose
, and D. W.
Sciama
(Oxford University
, New York
, 1981
), pp. 63
–80
.4.
D. N.
Page
and C. D.
Geilker
, Phys. Rev. Lett.
47
, 979
(1981
).5.
G.
Baym
and T.
Ozawa
, Proc. Natl. Acad. Sci.
106
, 3035
(2009
).6.
A.
Belenchia
, R.
Wald
, F.
Giacomini
, E.
Castro-Ruiz
, Č.
Brukner
, and M.
Aspelmeyer
, Phys. Rev. D
98
, 126009
(2018
).7.
N.
Huggett
and C.
Callender
, Philos. Sci.
68
, S382
(2001
).8.
J.
Mattingly
, “Is quantum gravity necessary
?” in Einstein Studies Volume 11. The Universe of General Relativity, Einstein Studies
, edited by A. J.
Kox
and J.
Eisenstaedt
(Birkhäuser
, Boston
, 2005
), pp. 327
–338
.9.
J.
Mattingly
, Phys. Rev. D
73
, 064025
(2006
).10.
C.
Kiefer
, Quantum Gravity
, 2nd ed., International Series of Monographs on Physics (Clarendon, Oxford
, 2007
), Vol. 124
.11.
M.
Albers
, C.
Kiefer
, and M.
Reginatto
, Phys. Rev. D
78
, 064051
(2008
).12.
A.
Kent
, Classical Quantum Gravity
35
, 245008
(2018
).13.
E.
Rydving
, E.
Aurell
, and I.
Pikovski
, Phys. Rev. D
104
, 086024
(2021
).14.
With the greatest appreciation, I welcome any clues regarding the mode of operation of the mysterious “Chicago machine” transforming hogs into sausages.
15.
L.
Rosenfeld
, Nucl. Phys.
40
, 353
–356
(1963
).16.
C.
Møller
, “Les Théories Relativistes de la Gravitation
,” in Colloques Internationaux CNRS
, edited by A.
Lichnerowicz
and M.-A.
Tonnelat
(CNRS
, Paris
, 1962
), Vol. 91
.17.
R. M.
Wald
, “Quantum field theory in curved spacetime and black hole thermodynamics
,” in Chicago Lectures in Physics
, edited by R. M.
Wald
, H. J.
Frisch
, G. F.
Mazenko
, and S. R.
Nagel
(The University of Chicago
, Chicago
, 1994
).18.
R.
Penrose
, Gen. Relativ. Gravitation
28
, 581
–600
(1996
).19.
20.
A.
Bassi
, K.
Lochan
, S.
Satin
, T. P.
Singh
, and H.
Ulbricht
, Rev. Mod. Phys.
85
, 471
(2013
).21.
S.
Bose
et al, Phys. Rev. Lett.
119
, 240401
(2017
).22.
C.
Marletto
and V.
Vedral
, Phys. Rev. Lett.
119
, 240402
(2017
).23.
M.
Reginatto
and M. J. W.
Hall
, J. Phys.
1275
, 012039
(2019
).24.
S.
Pal
, P.
Batra
, T.
Krisnanda
, T.
Paterek
, and T. S.
Mahesh
, Quantum
5
, 478
(2021
).25.
26.
M. K.
Döner
and A.
Großardt
, “Is gravitational entanglement evidence for the quantization of spacetime?
” (unpublished).27.
L.
Diósi
, Phys. Lett. A
105
, 199
(1984
).28.
R.
Penrose
, Philos. Trans. R. Soc. London, Ser. A
356
, 1927
–1939
(1998
).29.
D.
Giulini
and A.
Großardt
, Classical Quantum Gravity
28
, 195026
(2011
).30.
H.
Yang
, H.
Miao
, D.-S.
Lee
, B.
Helou
, and Y.
Chen
, Phys. Rev. Lett.
110
, 170401
(2013
).31.
A.
Großardt
, J.
Bateman
, H.
Ulbricht
, and A.
Bassi
, Phys. Rev. D
93
, 096003
(2016
).32.
A.
Großardt
, Classical Quantum Gravity
38
, 245009
(2021
).33.
W.
Struyve
, Int. J. Mod. Phys. A
35
, 2050070
(2020
).34.
35.
A.
Tilloy
and L.
Diósi
, Phys. Rev. D
93
, 024026
(2016
).36.
D. J.
Bedingham
, “Collapse models, relativity, and discrete spacetime
,” in Do Wave Functions Jump?: Perspectives of the Work of GianCarlo Ghirardi, Fundamental Theories of Physics
, edited by V.
Allori
, A.
Bassi
, D.
Dürr
, and N.
Zanghi
(Springer International Publishing
, Cham
, 2020
), pp. 191
–203
.37.
D.
Kafri
, J. M.
Taylor
, and G. J.
Milburn
, New J. Phys.
16
, 065020
(2014
).38.
An insightful discussion of the issue of energy conservation in semiclassical gravity is presented by Maudlin et al. (Ref. 40), as was kindly revealed to me in a prudent referee report.
39.
E.
Okon
and D.
Sudarsky
, “The weight of collapse: Dynamical reduction models in general relativistic contexts
,” in Collapse of the Wave Function: Models, Ontology, Origin, and Implications
, edited by S.
Gao
(Cambridge University
, Cambridge
, 2018
), pp. 312
–345
.40.
T.
Maudlin
, E.
Okon
, and D.
Sudarsky
, Stud. History Philos. Sci. Part B
69
, 67
(2020
).41.
C. W.
Misner
, K. S.
Thorne
, and J. A.
Wheeler
, Gravitation
(W. H. Freeman and Company
, San Francisco
, 1973
).42.
S. W.
Hawking
, Commun. Math. Phys.
43
, 199
(1975
).43.
44.
Z.-W.
Wang
and S. L.
Braunstein
, Nat. Commun.
9
, 2977
(2018
).45.
N.
Bohr
and L.
Rosenfeld
, Mat. Fys. Medd. K. Dan. Vidensk. Selsk.
12
, 3
(1933
).46.
Belenchia et al. (Ref. 6) point out that, due to conservation of the center of mass, there is no dipole moment if one considers the entire system of Alice's mass and the surrounding lab. In the symmetric situation considered here, there is also no contribution to from the quadrupole, Ref. 13. For the further discussion, we assume that Alice and Bob are both located within a sufficiently large laboratory together, such that there is a dipole contribution. The generalization to situations where the leading order contributions stem from the quadrupole or octopole moments is straightforward.
47.
A.
Mari
, G. D.
Palma
, and V.
Giovannetti
, Sci. Rep.
6
, 22777
(2016
).48.
A.
Stefanov
, H.
Zbinden
, N.
Gisin
, and A.
Suarez
, Phys. Rev. Lett.
88
, 120404
(2002
).49.
S. J.
Clark
and R. W.
Tucker
, Classical Quantum Gravity
17
, 4125
–4157
(2000
).50.
J. D.
Bekenstein
, Phys. Rev. D
86
, 124040
(2012
).51.
Of course, one can simply. postulate the Planck length as a fundamental limit for position measurements, Ref. 13.
52.
53.
M.
Bahrami
, A.
Großardt
, S.
Donadi
, and A.
Bassi
, New J. Phys.
16
, 115007
(2014
).54.
A.
Kent
, Phys. Rev. A
72
, 012108
(2005
).55.
A.
Kent
, Phys. Rev. D
103
, 064038
(2021
).56.
57.
U.
Delić
, M.
Reisenbauer
, K.
Dare
, D.
Grass
, V.
Vuletić
, N.
Kiesel
, and M.
Aspelmeyer
, Science
367
, 892
(2020
).58.
A.
Sugarbaker
, S. M.
Dickerson
, J. M.
Hogan
, D. M. S.
Johnson
, and M. A.
Kasevich
, Phys. Rev. Lett.
111
, 113002
(2013
).59.
S.
Eibenberger
, S.
Gerlich
, M.
Arndt
, M.
Mayor
, and J.
Tüxen
, Phys. Chem. Chem. Phys.
15
, 14696
(2013
).60.
A. D.
O'Connell
et al, Nature
464
, 697
(2010
).61.
R.
Colella
, A. W.
Overhauser
, and S. A.
Werner
, Phys. Rev. Lett.
34
, 1472
(1975
).62.
S.
Donadi
, K.
Piscicchia
, C.
Curceanu
, L.
Diósi
, M.
Laubenstein
, and A.
Bassi
, Nat. Phys.
17
, 74
(2021
).63.
We choose osmium because it is the densest known element. Note that the effect of the density on the result is marginal, as long as one does not consider densities many orders of magnitude above those naturally occurring in solid bodies.
© 2022 Author(s). Published under an exclusive license by AIP Publishing.
2022
Author(s)
You do not currently have access to this content.