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E. Witten, Light Rays, Singularities, and All That, Rev. Mod. Phys
Original
1901
Earlier work this paper cites.
A. Blommaert, T. G. Mertens and H. Verschelde, Clocks and Rods in Jackiw-Teitelboim Quantum Gravity, JHEP
Original
1902
Earlier work this paper cites.
N. Norris, Inequalities among averages, Ann. Math. Statist
1935
Earlier work this paper cites.
B. S. DeWitt and R. W. Brehme, Radiation damping in a gravitational field, Annals Phys
1960
Earlier work this paper cites.
B. S. DeWitt, The Quantization of geometry, in Gravitation: An Introduction to Current Research, John Wiley and Sons, New York. Chapter 8, pp. 266–381, 1962
1962
Earlier work this paper cites.
C. Rovelli, What Is Observable in Classical and Quantum Gravity?, Class. Quant. Grav
1991
Earlier work this paper cites.
S. W. Hawking, The Chronology protection conjecture, Phys. Rev. D
1992
Earlier work this paper cites.
M. Visser, van Vleck determinants: Geodesic focusing and defocusing in Lorentzian space-times, Phys. Rev. D
1993
Earlier work this paper cites.
J. D. Brown and K. V. Kuchar, Dust as a standard of space and time in canonical quantum gravity, Phys. Rev. D
1995
Earlier work this paper cites.
J. Louko and R. D. Sorkin, Complex actions in two-dimensional topology change, Class. Quant. Grav
1997
Earlier work this paper cites.

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2022

Piazza, Federico, Tolley, Andrew J.

A central property of a classical geometry is that the geodesic distance between two events is \emph{additive}.

When considering quantum fluctuations in the metric or a quantum or statistical superposition of different spacetimes, additivity is generically lost at the level of expectation values.
In the presence of a superposition of metrics, distances can be made diffeomorphism invariant by considering the frame of a family of free-falling observers or a pressureless fluid, provided we work at sufficiently low energies.
We propose to use the average squared distance between two events $\langle d^2(x,y)\rangle$ as a proxy for understanding the effective quantum (or statistical) geometry and the emergent causal relations among such observers.

E. Witten, Light Rays, Singularities, and All That, Rev. Mod. Phys
Original
1901
Earlier work this paper cites.
A. Blommaert, T. G. Mertens and H. Verschelde, Clocks and Rods in Jackiw-Teitelboim Quantum Gravity, JHEP
Original
1902
Earlier work this paper cites.
N. Norris, Inequalities among averages, Ann. Math. Statist
1935
Earlier work this paper cites.
B. S. DeWitt and R. W. Brehme, Radiation damping in a gravitational field, Annals Phys
1960
Earlier work this paper cites.
B. S. DeWitt, The Quantization of geometry, in Gravitation: An Introduction to Current Research, John Wiley and Sons, New York. Chapter 8, pp. 266–381, 1962
1962
Earlier work this paper cites.
C. Rovelli, What Is Observable in Classical and Quantum Gravity?, Class. Quant. Grav
1991
Earlier work this paper cites.
S. W. Hawking, The Chronology protection conjecture, Phys. Rev. D
1992
Earlier work this paper cites.
M. Visser, van Vleck determinants: Geodesic focusing and defocusing in Lorentzian space-times, Phys. Rev. D
1993
Earlier work this paper cites.
J. D. Brown and K. V. Kuchar, Dust as a standard of space and time in canonical quantum gravity, Phys. Rev. D
1995
Earlier work this paper cites.
J. Louko and R. D. Sorkin, Complex actions in two-dimensional topology change, Class. Quant. Grav
1997
Earlier work this paper cites.

L. Hardy, Probability theories with dynamic causal structure: A New framework for quantum gravity, 2005, [arXiv:gr-qc/0509120]
2005
Cited alongside, same era.
W. D. Goldberger and I. Z. Rothstein, An Effective field theory of gravity for extended objects, Phys. Rev. D
2006
Cited alongside, same era.
A. Almheiri, T. Hartman, J. Maldacena, E. Shaghoulian and A. Tajdini, The entropy of Hawking radiation, 2020, [arXiv:2006.06872 [hep-th]]
Original
2006
Cited alongside, same era.
S. Dubovsky, T. Gregoire, A. Nicolis and R. Rattazzi, Null energy condition and superluminal propagation, JHEP
2006
Cited alongside, same era.
P. Hayden and J. Preskill, Black holes as mirrors: Quantum information in random subsystems, JHEP
Original
2007
Cited alongside, same era.