Emergence of General Relativity from Loop Quantum Gravity

TL;DR

This paper presents a model showing how classical general relativity can emerge from loop quantum gravity using matter-based relational coordinates, with results aligning with general relativity at large scales.

Contribution

It introduces a relational model demonstrating the emergence of classical gravity from loop quantum gravity, including the recovery of diffeomorphism algebra and dynamics.

Findings

Recovery of four-dimensional diffeomorphism algebra

Emergence of large-scale gravitational dynamics

Conformance with general relativity near singularities

Abstract

A model is proposed to demonstrate that classical general relativity can emerge from loop quantum gravity, in a relational description of gravitational field in terms of coordinates given by matter. Local Dirac observables and coherent states are defined to explore physical content of the model. Expectation values of commutators between the observables for the coherent states recover the four-dimensional diffeomorphism algebra and the large-scale dynamics of the gravitational field relative to the matter coordinates. Both results conform with general relativity up to calculable corrections near singularities.