General Relativity as GeometroHydrodynamics
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 `topdown' 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 `bottomup' 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 EinsteinLangevin equation. The backreaction of quantum fields on the classical background spacetime manifests as a fluctuationdissipation 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 subPlanckian energies. 3) Decoherence of correlation histories and quantum to classical transition. From GellMann 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.
 Publication:

arXiv eprints
 Pub Date:
 July 1996
 arXiv:
 arXiv:grqc/9607070
 Bibcode:
 1996gr.qc.....7070H
 Keywords:

 General Relativity and Quantum Cosmology
 EPrint:
 Latex 18 pages. Expanded version of an invited talk given at the Second Sakharov International Symposium, Lebedev Physical Institute, Moscow, May 2024, 1996