General Relativity as Geometro-Hydrodynamics

TL;DR

This paper explores the analogy between general relativity and hydrodynamics, focusing on how quantum gravitational effects and quantum field excitations influence the emergence and classical behavior of spacetime.

Contribution

It introduces a bottom-up perspective on the emergence of general relativity from semiclassical gravity, highlighting stochastic behavior, quantum decoherence, and the hydrodynamic analogy of spacetime.

Findings

Emergence of stochastic spacetime behavior via Einstein-Langevin equation

Quantum field fluctuations induce detectable Planckian effects below Planck scale

Decoherence of correlation histories supports classical spacetime emergence

Abstract

In the spirit of Sakharov's `metric elasticity' proposal, we draw a loose analogy between general relativity and the hydrodynamic state of a quantum gas. In the `top-down' approach, we examine the various conditions which underlie the transition from some candidate theory of quantum gravity to general relativity. Our emphasis here is more on the `bottom-up' approach, where one starts with the semiclassical theory of gravity and examines how it is modified by graviton and quantum field excitations near and above the Planck scale. We mention three aspects based on our recent findings: 1) Emergence of stochastic behavior of spacetime and matter fields depicted by an Einstein-Langevin equation. The backreaction of quantum fields on the classical background spacetime manifests as a fluctuation-dissipation relation. 2) Manifestation of stochastic behavior in effective theories below the threshold arising from excitations above. The implication for general relativity is that such Planckian effects, though exponentially suppressed, is in principle detectable at sub-Planckian energies. 3) Decoherence of correlation histories and quantum to classical transition. From Gell-Mann and Hartle's observation that the hydrodynamic variables which obey conservation laws are most readily decohered, one can, in the spirit of Wheeler, view the conserved Bianchi identity obeyed by the Einstein tensor as an indication that general relativity is a hydrodynamic theory of geometry. Many outstanding issues surrounding the transition to general relativity are of a nature similar to hydrodynamics and mesoscopic physics.