Probabilistic deconstruction of a theory of gravity, Part II: curved space

TL;DR

This paper explores a probabilistic framework for understanding gravity, proposing that spacetime volume measures are constrained by quantum dynamics, and shows how Einstein's equations emerge from quantum stochastic processes in holographic models.

Contribution

It introduces a novel probabilistic approach to gravity, linking quantum stochastic processes to Einstein's equations in holographic and JT gravity models.

Findings

Einstein's equations emerge from quantum stochastic evolution in AdS JT gravity.

Spacetime volume measure is interpreted as a probability density.

Conjecture that general relativity arises from semi-classical quantum probability evolution.

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.