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Probabilistic deconstruction of a theory of gravity, Part II: curved space
by Sunok Josephine Suh
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Submission summary
| Authors (as registered SciPost users): | Josephine Suh |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2208.12204v3 (pdf) |
| Date accepted: | 2023-12-28 |
| Date submitted: | 2023-11-14 04:06 |
| Submitted by: | Suh, Josephine |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We propose that the underlying context of holographic duality and the Ryu-Takayanagi formula is that the volume measure of spacetime is a probability measure constrained by quantum dynamics. We define quantum stochastic processes using joint quantum distributions which are realized in a quantum system as expectation values of products of projectors. In anti-de Sitter JT gravity, we show that Einstein's equations arise from the evolution of probability under the quantum stochastic process induced by the boundary, with the area of compactified space in the gravitational theory identified as a probability density evolving under the quantum process. Extrapolating these and related results in flat JT gravity found in arXiv:2108.10916, we conjecture that general relativity arises in the semi-classical limit of the evolution of probability with respect to quantum stochastic processes.
Author comments upon resubmission
We have revised the manuscript to take into account the referee's feedback and suggestions.
Best regards,
Josephine
List of changes
1. We have rewritten parts of the introduction, in particular the last three paragraphs on p. 2, to clarify the logic and explain the analogy to chaos better. We have also tried to shorten sentences when appropriate.
2. On top of p. 17, we have added a paragraph about the relation of our work to known aspects of AdS/CFT including the Ryu-Takayanagi formula.
3. We have made other small changes requested by referees, clarifying notation and adding definitions.
Published as SciPost Phys. 16, 012 (2024)