A Kinetic Theory Approach to Quantum Gravity

Abstract

We describe a kinetic theory approach to quantum gravity -- by which we mean a theory of the microscopic structure of spacetime, not a theory obtained by quantizing general relativity. A figurative conception of this program is like building a ladder with two knotted poles: quantum matter field on the right and spacetime on the left. Each rung connecting the corresponding knots represent a distinct level of structure. The lowest rung is hydrodynamics and general relativity; the next rung is semiclassical gravity, with the expectation value of quantum fields acting as source in the semiclassical Einstein equation. We recall how ideas from the statistical mechanics of interacting quantum fields helped us identify the existence of noise in the matter field and its effect on metric fluctuations, leading to the establishment of the third rung: stochastic gravity, described by the Einstein-Langevin equation. Our pathway from stochastic to quantum gravity is via the correlation hierarchy of noise and induced metric fluctuations. Three essential tasks beckon: 1) Deduce the correlations of metric fluctuations from correlation noise in the matter field; 2) Reconstituting quantum coherence -- this is the reverse of decoherence -- from these correlation functions 3) Use the Boltzmann-Langevin equations to identify distinct collective variables depicting recognizable metastable structures in the kinetic and hydrodynamic regimes of quantum matter fields and how they demand of their corresponding spacetime counterparts. This will give us a hierarchy of generalized stochastic equations -- call them the Boltzmann-Einstein hierarchy of quantum gravity -- for each level of spacetime structure, from the macroscopic (general relativity) through the mesoscopic (stochastic gravity) to the microscopic (quantum gravity).

Latex 19 pages. Invited talk given at the 6th Peyresq Meeting, France, June, 2001. To appear in Int. J. Theor. Phys. 2002

References in corpus (3)

• Classical aspects of quantum fields far from equilibrium
• Stochastic Theory of Relativistic Particles Moving in a Quantum Field: II. Scalar Abraham-Lorentz-Dirac-Langevin Equation, Radiation Reaction and Vacuum Fluctuations
• Coarse-Grained Effective Action and Renormalization Group Theory in Semiclassical Gravity and Cosmology

Cited by in corpus (11)

• Quantum Spacetime Phenomenology
• Stochastic Gravity: Theory and Applications
• Stochastic Gravity: Theory and Applications
• Probing a Gravitational Cat State
• Induced quantum metric fluctuations and the validity of semiclassical gravity
• Conservative entropic forces
• Uniformly Accelerated Charge in a Quantum Field: From Radiation Reaction to Unruh Effect
• Noise kernel for a quantum field in Schwarzschild spacetime under the Gaussian approximation
• Fractal Spacetimes in Stochastic Gravity? -- Views from Anomalous Diffusion and the Correlation Hierarchy
• Noise Kernel for Self-similar Tolman Bondi Metric: Fluctuations on Cauchy Horizon
• Quantum Noise and Fluctuations in Gravitation and Cosmology