Cite as: doi:10.26081/K6SH05

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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. In anti-de Sitter
JT gravity, we define and analyze the quantum stochastic process induced
by the boundary, and show Einsteinâ€™s equations arise from the evolution
of probability under the non-Markovian process. In particular, the area
of compactified space in the gravitational theory can be identified as a
probability distribution evolving under the quantum process.
Extrapolating these and analogous results in flat JT gravity, we
conjecture that general relativity arises in the semi-classical limit of
the evolution of probability with respect to quantum stochastic
processes.
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