Quantum gravity as the way from spacetime to space quantum states thermodynamics

TL;DR

This paper develops a quantum gravity framework derived from thermodynamics of quantum states, utilizing a 3+1 Dirac-ADM approach to formulate a Wheeler-DeWitt theory and explore space quantum states thermodynamics.

Contribution

It introduces a novel realization of quantum gravity through a canonical 3+1 approach, deriving a Wheeler-DeWitt theory without superspace metric and formulating space quantum states thermodynamics.

Findings

Derived Wheeler-DeWitt theory as a classical field theory of Bose fields.

Constructed quantum theory via second quantization and Bogoliubov transformation.

Identified a static space quantum state space with a stable vacuum.

Abstract

Physical spacetime geometry follows from some effective thermodynamics of quantum states of all fields and particles described in frames of General Relativity. In the sense of pure field theoretical Einstein's point of view on gravitation the thermodynamic information is actually quantum gravity. We propose new realization of this old idea by studying the canonical 3+1 Dirac-ADM approach to pseudo-Riemannian (Lorentzian) manifold of General Relativity. We derive the Wheeler-DeWitt theory as the Global One-Dimensional classical field theory of the Bose field associated with embedded 3-space, where Wheeler's superspace metric is absent. The classical theory is discussed, some deductions on tachyon state, Dark Energy density and cosmological constant are included. Reduction to 1st order evolution is carried out, and quantum theory by the second quantization in the Fock space of creators and annihilators is constructed by employing the Heisenberg equation and the bosonic Bogoliubov transformation for diagonalization. In result we find the static reper with stable vacuum, where quantum states of 3-space can be considered, and finally space quantum states thermodynamics is formulated.