The status of geometry and matter in re-interpreted WdW equation

TL;DR

This paper reinterprets the Wheeler-DeWitt equation, showing it describes a unified geometry-matter field where geometry is fundamental, and demonstrates how quantum effects can resolve singularities and induce local geometry creation.

Contribution

It introduces a new interpretation of the Wheeler-DeWitt equation as a unified geometry-matter field with implications for singularity resolution and quantum geometry creation.

Findings

Quantum theory exhibits gravitational decoherence at signature change.

Singularities are dynamically resolved in the quantum framework.

Local geometries are created during quantum evolution in cosmological models.

Abstract

I have shown that the field defined by the Wheeler-DeWitt equation for \textit{pure gravity} is neither a standard gravitational field nor the field representing a particular universe. The theory offers a unified description of geometry and matter, with geometry being fundamental. The quantum theory possesses gravitational decoherence when the signature of $R^{(3)}$ changes. The quantum theory resolves singularities dynamically. Application to the FLRW $\kappa=0$ shows the creation of local geometries during quantum evolution. The 3-metric gets modified near the classical singularity in the case of the Schwarzschild geometry.