Must Quantum Spacetimes Be Euclidean?

TL;DR

This paper explores the effects of quantum mechanics on spacetime structure using the Bohm-de Broglie interpretation, revealing that quantum effects primarily induce a signature change from Lorentzian to Euclidean, affecting the geometry of the universe.

Contribution

It introduces a Bohm-de Broglie framework for quantum geometrodynamics, highlighting the unique quantum effect of signature change and proposing new boundary conditions for Wheeler-DeWitt solutions.

Findings

Quantum effects do not break spacetime but change its signature to Euclidean.

Real solutions of Wheeler-DeWitt equations are compatible with strong gravity limits.

New boundary conditions are needed for consistent quantum geometrodynamics.

Abstract

The Bohm-de Broglie interpretation of quantum mechanics is applied to canonical quantum cosmology. It is shown that, irrespective of any regularization or choice of factor ordering of the Wheeler-DeWitt equation, the unique relevant quantum effect which does not break spacetime is the change of its signature from lorentzian to euclidean. The other quantum effects are either trivial or break the four-geometry of spacetime. A Bohm-de Broglie picture of a quantum geometrodynamics is constructed, which allows the investigation of these latter structures. For instance, it is shown that any real solution of the Wheeler-De Witt equation yields a generate four-geometry compatible with the strong gravity limit of General Relativity and the Carroll group. Due to the more detailed description of quantum geometrodynamics given by the Bohm-de Broglie interpretation, some new boundary conditions on solutions of the Wheeler-DeWitt equation must be imposed in order to preserve consistency of this finer view.