Abstract
Einstein’s theory of general relativity is based on the premise that the physical laws take the same form in all coordinate systems. However, it still presumes a preferred decomposition of the total kinematic Hilbert space into local kinematic Hilbert spaces. In this paper, we consider a theory of quantum gravity that does not come with a preferred partitioning of the kinematic Hilbert space. It is pointed out that, in such a theory, dimension, signature, topology and geometry of spacetime depend on how a collection of local clocks is chosen within the kinematic Hilbert space.
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References
B.S. DeWitt, Quantum Theory of Gravity. 1. The Canonical Theory, Phys. Rev. 160 (1967) 1113 [INSPIRE].
C.J. Isham, Canonical quantum gravity and the problem of time, NATO Sci. Ser. C 409 (1993) 157 [gr-qc/9210011] [INSPIRE].
K.V. Kuchar, Time and interpretations of quantum gravity, Int. J. Mod. Phys. D 20 (2011) 3 [INSPIRE].
E. Anderson, Problem of time in quantum gravity, Annalen Phys. 524 (2012) 757.
C. Rovelli, Partial observables, Phys. Rev. D 65 (2002) 124013 [gr-qc/0110035] [INSPIRE].
B. Dittrich, Partial and complete observables for Hamiltonian constrained systems, Gen. Rel. Grav. 39 (2007) 1891 [gr-qc/0411013] [INSPIRE].
R. Gambini, R.A. Porto and J. Pullin, A relational solution to the problem of time in quantum mechanics and quantum gravity: a fundamental mechanism for quantum decoherence, New J. Phys. 6 (2004) 45.
S.-S. Lee, A model of quantum gravity with emergent spacetime, JHEP 06 (2020) 070 [arXiv:1912.12291] [INSPIRE].
J.M. Maldacena, The Large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].
R.L. Arnowitt, S. Deser and C.W. Misner, Dynamical Structure and Definition of Energy in General Relativity, Phys. Rev. 116 (1959) 1322 [INSPIRE].
C. Teitelboim, How commutators of constraints reflect the space-time structure, Annals Phys. 79 (1973) 542 [INSPIRE].
S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96 (2006) 181602 [hep-th/0603001] [INSPIRE].
V.E. Hubeny, M. Rangamani and T. Takayanagi, A Covariant holographic entanglement entropy proposal, JHEP 07 (2007) 062 [arXiv:0705.0016] [INSPIRE].
M. Van Raamsdonk, Building up spacetime with quantum entanglement, Int. J. Mod. Phys. D 19 (2010) 2429 [Gen. Rel. Grav. 42 (2010) 2323] [arXiv:1005.3035] [INSPIRE].
A. Lewkowycz and J. Maldacena, Generalized gravitational entropy, JHEP 08 (2013) 090 [arXiv:1304.4926] [INSPIRE].
M. Headrick, V.E. Hubeny, A. Lawrence and M. Rangamani, Causality & holographic entanglement entropy, JHEP 12 (2014) 162 [arXiv:1408.6300] [INSPIRE].
T. Faulkner, A. Lewkowycz and J. Maldacena, Quantum corrections to holographic entanglement entropy, JHEP 11 (2013) 074 [arXiv:1307.2892] [INSPIRE].
N. Lashkari, M.B. McDermott and M. Van Raamsdonk, Gravitational dynamics from entanglement ‘thermodynamics’, JHEP 04 (2014) 195 [arXiv:1308.3716] [INSPIRE].
X.-L. Qi, Exact holographic mapping and emergent space-time geometry, arXiv:1309.6282 [INSPIRE].
T. Faulkner, M. Guica, T. Hartman, R.C. Myers and M. Van Raamsdonk, Gravitation from Entanglement in Holographic CFTs, JHEP 03 (2014) 051 [arXiv:1312.7856] [INSPIRE].
C. Cao, S.M. Carroll and S. Michalakis, Space from Hilbert Space: Recovering Geometry from Bulk Entanglement, Phys. Rev. D 95 (2017) 024031 [arXiv:1606.08444] [INSPIRE].
J. Maldacena and L. Susskind, Cool horizons for entangled black holes, Fortsch. Phys. 61 (2013) 781 [arXiv:1306.0533] [INSPIRE].
S.-S. Lee, Emergent gravity from relatively local Hamiltonians and a possible resolution of the black hole information puzzle, JHEP 10 (2018) 043 [arXiv:1803.00556] [INSPIRE].
S.-S. Lee, State dependent spread of entanglement in relatively local Hamiltonians, JHEP 05 (2019) 215 [arXiv:1811.07241] [INSPIRE].
S.-S. Lee, Horizon as Critical Phenomenon, JHEP 09 (2016) 044 [arXiv:1603.08509] [INSPIRE].
D.N. Page and W.K. Wootters, Evolution without evolution: dynamics described by stationary observables, Phys. Rev. D 27 (1983) 2885 [INSPIRE].
I. Bars, Survey of two time physics, Class. Quant. Grav. 18 (2001) 3113 [hep-th/0008164] [INSPIRE].
G. Amelino-Camelia, L. Freidel, J. Kowalski-Glikman and L. Smolin, The principle of relative locality, Phys. Rev. D 84 (2011) 084010 [arXiv:1101.0931] [INSPIRE].
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ArXiv ePrint: 2012.14416
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Lee, SS. Clock-dependent spacetime. J. High Energ. Phys. 2021, 204 (2021). https://doi.org/10.1007/JHEP04(2021)204
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DOI: https://doi.org/10.1007/JHEP04(2021)204