Classical Spacetime from Quantum Gravity

TL;DR

This paper demonstrates how classical spacetime can emerge from quantum gravity by analyzing a quantum cosmological model and showing the correspondence between quantum states and classical Einstein equations.

Contribution

It introduces a new asymptotic expansion method for the Wheeler-DeWitt equation and links quantum states to classical spacetime dynamics.

Findings

Coherent states produce quantum back reaction proportional to classical energy

Generalized invariant basis leads to Einstein-Hamilton-Jacobi equivalence

Classical Einstein equations emerge from quantum cosmological model

Abstract

We show how classical spacetime emerges from quantum gravity through the study of a quantum FRW cosmological model coupled to a free massive scalar field using a new asymptotic expansion method of the Wheeler-DeWitt equation. It is shown that the coherent states of the nonadiabatic basis of a particular generalized invariant give rise to the quantum back reaction of matter field proportional to classical energy and the Einstein-Hamilton-Jacobi with matter becomes equivalent to the classical Einstein equation.