We consider a global quantum system (the “Universe”) satisfying a double constraint, both on total energy and total momentum. Generalizing the Page and Wootters quantum clock formalism, we provide a model of 3 + 1 dimensional, non-relativistic, quantum spacetime emerging from entanglement among different subsystems in a globally “timeless” and “positionless” Universe.
References
1.
D. N.
Page
and W. K.
Wootters
, Phys. Rev. D
27
, 2885
(1983
).2.
W. K.
Wootters
, Int. J. Theor. Phys.
23
, 701
(1984
).3.
D. N.
Page
, “Clock time and entropy
,” in Physical Origins of Time Asymmetry
, edited by J. J.
Halliwell
, J.
Perez-Mercader
, and W. H.
Zurek
(Cambridge University
, Cambridge
, 1993
).4.
B. S.
DeWitt
, Phys. Rev.
160
, 1113
(1967
).5.
C. J.
Isham
, “Canonical quantum gravity and the problem of time
,” in Integrable Systems, Quantum Groups, and Quantum Field Theories
, edited by L. A.
Ibort
and M. A.
Rodríguez
(Springer
, New York
, 1993
), p. 157
.6.
H.
Everett
, “The theory of the universal wave function
,” in The Many Worlds Interpretation of Quantum Mechanics
(Princeton University, Department of Physics
, 1957
), pp. 1
–140
.7.
V.
Giovannetti
, S.
Lloyd
, and L.
Maccone
, Phys. Rev. D
92
, 045033
(2015
).8.
E.
Moreva
, M.
Gramegna
, G.
Brida
, L.
Maccone
, and M.
Genovese
, Phys. Rev. D
96
, 102005
(2017
).9.
C.
Marletto
and V.
Vedral
, Phys. Rev. D
95
, 043510
(2017
).10.
V.
Vedral
, “Time (inverse) temperature and cosmological inflation as entanglement
,” in Time in Physics
, edited by R.
Renner
and S.
Stupar
(Springer
, New York
, 2017
), pp. 27
–42
.11.
L.
Maccone
and K.
Sacha
, Phys. Rev. Lett.
124
, 110402
(2020
).12.
A. R. H.
Smith
and M.
Ahmadi
, Quantum
3
, 160
(2019
).13.
A.
Boette
and R.
Rossignoli
, Phys. Rev. A
98
, 032108
(2018
).14.
A.
Boette
, R.
Rossignoli
, N.
Gigena
, and M.
Cerezo
, Phys. Rev. A
93
, 062127
(2016
).15.
J.
Leon
and L.
Maccone
, Found. Phys.
47
, 1597
(2017
).16.
P. A.
Hoehn
, A. R. H.
Smith
, and M. P. E.
Lock
, Phys. Rev. D
104
, 066001
(2021
).17.
P. A.
Hoehn
, A. R. H.
Smith
, and M. P. E.
Lock
, Front. Phys.
9
, 587083
(2021
).18.
T.
Favalli
and A.
Smerzi
, Quantum
4
, 354
(2020
).19.
T.
Favalli
and A.
Smerzi
, Phys. Rev. D
105
, 023525
(2022
).20.
A. R. H.
Smith
and M.
Ahmadi
, Nat. Commun.
11
, 5360
(2020
).21.
N. L.
Diaz
, J. M.
Matera
, and R.
Rossignoli
, Phys. Rev. D
100
, 125020
(2019
).22.
N. L.
Diaz
and R.
Rossignoli
, Phys. Rev. D
99
, 045008
(2019
).23.
C.
Foti
, A.
Coppo
, G.
Barni
, A.
Cuccoli
, and P.
Verrucchi
, Nat. Commun.
12
, 1787
(2021
).24.
E.
Castro-Ruiz
, F.
Giacomini
, A.
Belenchia
, and Č.
Brukner
, Nat. Commun.
11
, 2672
(2020
).25.
V.
Baumann
, F.
Del Santo
, A. R. H.
Smith
, F.
Giacomini
, E.
Castro-Ruiz
, and C.
Brukner
, Quantum
5
, 524
(2021
).26.
V.
Baumann
, M.
Krumm
, P. A.
Guérin
, and Č.
Brukner
, Phys. Rev. Res.
4
, 013180
(2022
).27.
28.
L. R. S.
Mendes
and D. O.
Soares-Pinto
, Proc. R. Soc. A
475
, 20190470
(2019
).29.
30.
E.
Moreva
, G.
Brida
, M.
Gramegna
, V.
Giovannetti
, L.
Maccone
, and M.
Genovese
, Phys. Rev. A
89
, 052122
(2014
).31.
A. V.
Rau
, J. A.
Dunningham
, and K.
Burnett
, Science
301
, 1081
(2003
).32.
Y.
Aharonov
and L.
Susskind
, Phys. Rev.
155
, 1428
(1967
).33.
Y.
Aharonov
and L.
Susskind
, Phys. Rev.
158
, 1237
(1967
).34.
Y.
Aharonov
and T.
Kaufherr
, Phys. Rev. D
30
, 368
(1984
).35.
S. D.
Bartlett
, T.
Rudolph
, and R. W.
Spekkens
, Rev. Mod. Phys.
79
, 555
(2007
).36.
S. D.
Bartlett
, T.
Rudolph
, R. W.
Spekkens
, and P. S.
Turner
, New J. Phys.
11
, 063013
(2009
).37.
G.
Gour
and R. W.
Spekkens
, New J. Phys.
10
, 033023
(2008
).38.
A.
Kitaev
, D.
Mayers
, and J.
Preskill
, Phys. Rev. A
69
, 052326
(2004
).39.
M. C.
Palmer
, F.
Girelli
, and S. D.
Bartlett
, Phys. Rev. A
89
, 052121
(2014
).40.
S. D.
Bartlett
, T.
Rudolph
, R. W.
Spekkens
, and P. S.
Turner
, New J. Phys.
8
, 58
(2006
).41.
A. R. H.
Smith
, M.
Piani
, and R. B.
Mann
, Phys. Rev. A
94
, 012333
(2016
).42.
D.
Poulin
and J.
Yard
, New J. Phys.
9
, 156
(2007
).43.
F.
Girelli
and D.
Poulin
, Phys. Rev. D
77
, 104012
(2008
).44.
M.
Skotiniotis
, B.
Toloui
, I. T.
Durham
, and B. C.
Sanders
, Phys. Rev. Lett.
111
, 020504
(2013
).45.
D.
Poulin
, Int. J. Theor. Phys.
45
, 1189
–1215
(2006
).46.
T.
Miyadera
, L.
Loveridge
, and P.
Busch
, J. Phys. A
49
, 185301
(2016
).47.
L.
Loveridge
, P.
Busch
, and T.
Miyadera
, Europhys. Lett.
117
, 40004
(2017
).48.
L.
Loveridge
, T.
Miyadera
, and P.
Busch
, Found. Phys.
48
, 135
–198
(2018
).49.
50.
R. M.
Angelo
, N.
Brunner
, S.
Popescu
, A. J.
Short
, and P.
Skrzypczyk
, J. Phys. A
44
, 145304
(2011
).51.
R. M.
Angelo
and A. D.
Ribeiro
, J. Phys. A
45
, 465306
(2012
).52.
S. T.
Pereira
and R. M.
Angelo
, Phys. Rev. A
91
, 022107
(2015
).53.
L.
Maccone
, Found. Phys.
49
, 1394
–1403
(2019
).54.
C.
Rovelli
, Classical Quantum Gravity
8
, 317
(1991
).55.
C.
Rovelli
, Int. J. Theor. Phys.
35
, 1637
–1678
(1996
).56.
F.
Giacomini
, E.
Castro-Ruiz
, and Č.
Brukner
, Nat. Commun.
10
, 494
(2019
).57.
A.
Vanrietvelde
, P. A.
Hoehn
, F.
Giacomini
, and E.
Castro-Ruiz
, Quantum
4
, 225
(2020
).58.
59.
60.
F.
Giacomini
, E.
Castro-Ruiz
, and Č.
Brukner
, Phys. Rev. Lett.
123
, 090404
(2019
).61.
L. F.
Streiter
, F.
Giacomini
, and Č.
Brukner
, Phys. Rev. Lett.
126
, 230403
(2021
).62.
A. C.
de la Hamette
and T. D.
Galley
, Quantum
4
, 367
(2020
).63.
64.
A.
Ballesteros
, F.
Giacomini
, and G.
Gubitosi
, Quantum
5
, 470
(2021
).65.
66.
A. C.
de la Hamette
, T. D.
Galley
, P. A.
Hoehn
, L.
Loveridge
, and M. P.
Mueller
, arXiv:2110.13824 (2021
).67.
S. A.
Ahmad
, T. D.
Galley
, P. A.
Hoehn
, M. P. E.
Lock
, and A. R. H.
Smith
, Phys. Rev. Lett.
128
, 170401
(2022
).68.
69.
D. T.
Pegg
, Phys. Rev. A
58
, 4307
(1998
).70.
D. T.
Pegg
and S. M.
Barnett
, Phys. Rev. A
39
, 1665
(1989
).71.
V.
Giovannetti
, S.
Lloyd
, and L.
Maccone
, Phys. Rev. A
67
, 052109
(2003
).72.
N.
Margolus
and L. B.
Levitin
, Physica D
120
, 188
(1998
).73.
K. V.
Kuchar
, Int. J. Mod. Phys. D
20
, 3
(2011
).74.
R.
Gambini
, R. A.
Porto
, J.
Pullin
, and S.
Torterolo
, Phys. Rev. D
79
, 041501(R)
(2009
).75.
J.
von Neumann
, Mathematical Foundations of Quantum Mechanics
(Princeton University
, Princeton
, 1955
).76.
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