General Relativity as Classical Limit of Evolutionary Quantum Gravity

TL;DR

This paper explores how classical general relativity emerges as a limit of quantum gravity by analyzing the dynamics in a synchronous gauge, revealing a non-zero Hamiltonian interpreted as a dust fluid, and examining quantum cosmology and Schrödinger dynamics.

Contribution

It introduces an evolutionary quantum gravity framework with a non-vanishing Hamiltonian and connects it to classical limits, quantum cosmology, and Schrödinger dynamics.

Findings

Non-zero Hamiltonian interpreted as dust fluid

Quantum cosmology overlaps with Wheeler-DeWitt picture

Time dependence linked to WKB correction in quantum spectrum

Abstract

We analyze the dynamics of the gravitational field when the covariance is restricted to a synchronous gauge. In the spirit of the Noether theorem, we determine the conservation law associated to the Lagrangian invariance and we outline that a non-vanishing behavior of the Hamiltonian comes out. We then interpret such resulting non-zero ``energy'' of the gravitational field in terms of a dust fluid. This new matter contribution is co-moving to the slicing and it accounts for the ``materialization'' of a synchronous reference from the corresponding gauge condition. Further, we analyze the quantum dynamics of a generic inhomogeneous Universe as described by this evolutionary scheme, asymptotically to the singularity. We show how the phenomenology of such a model overlaps the corresponding Wheeler-DeWitt picture. Finally, we study the possibility of a Schr\"odinger dynamics of the gravitational field as a consequence of the correspondence inferred between the ensemble dynamics of stochastic systems and the WKB limit of their quantum evolution. We demonstrate that the time dependence of the ensemble distribution is associated with the first order correction in $\hbar$ to the WKB expansion of the energy spectrum.