Probabilistic deconstruction of a theory of gravity, Part I: flat space

TL;DR

This paper explores a stochastic process in flat space Jackiw-Teitelboim gravity, revealing how Einstein's equations emerge from quantum boundary dynamics and identifying the space's area as a probability density in the semi-classical limit.

Contribution

It introduces a probabilistic framework for flat space JT gravity and demonstrates the emergence of Einstein's equations from quantum boundary dynamics in the semi-classical limit.

Findings

Quantum boundary dynamics induce a Markov process in flat space

Einstein's equations emerge from the semi-classical limit of the quantum process

The space's area acts as a probability density evolving under the Markov process

Abstract

We define and analyze a stochastic process in anti-de Sitter Jackiw-Teitelboim gravity, induced by the quantum dynamics of the boundary and whose random variable takes values in $AdS_2$. With the boundary in a thermal state and for appropriate parameters, we take the asymptotic limit of the quantum process at short time scales and flat space, and show associated classical joint distributions have the Markov property. We find that Einstein's equations of the theory, sans the cosmological constant term, arise in the semi-classical limit of the quantum evolution of probability under the asymptotic process. In particular, in flat Jackiw-Teitelboim gravity, the area of compactified space solved for by Einstein's equations can be identified as a probability density evolving under the Markovian process.