General Relativity as Geometro-Hydrodynamics

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.

Latex 18 pages. Expanded version of an invited talk given at the Second Sakharov International Symposium, Lebedev Physical Institute, Moscow, May 20-24, 1996

References in corpus (3)

• Quantization of Point Particles in 2+1 Dimensional Gravity and Space-Time Discreteness
• Stochastic Behavior of Effective Field Theories Across Threshold
• Cosmology as `Condensed Matter' Physics

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• Noether Current, Horizon Virasoro Algebra and Entropy
• The Structure of the Gravitational Action and its relation with Horizon Thermodynamics and Emergent Gravity Paradigm
• Action principle for the Fluid-Gravity correspondence and emergent gravity
• Uniformly Accelerated Charge in a Quantum Field: From Radiation Reaction to Unruh Effect
• Two Aspects of Black hole entropy in Lanczos-Lovelock models of gravity
• Decoherence in Quantum Gravity: Issues and Critiques
• Fractal Spacetimes in Stochastic Gravity? -- Views from Anomalous Diffusion and the Correlation Hierarchy
• Gravity as an emergent phenomenon: a GFT perspective
• Black Hole Thermodynamics, Casimir Effect and Induced Gravity
• Black Hole Thermodynamics in Semi-Classical and Superstring Theory
• Quantum Noise and Fluctuations in Gravitation and Cosmology