On Pilot Wave Quantum Cosmology

TL;DR

This paper explores the de~Broglie--Bohm pilot wave formulation of quantum theory, its extension to quantum gravity, and the implications of foliation dependence and non-locality for a realistic universe model.

Contribution

It analyzes the extension of pilot wave quantum theory to gravity and reveals foliation dependence and inherent non-locality in the framework.

Findings

Quantum equilibrium issues are discussed within pilot wave theory.

Foliation of spacetime becomes distinguished in quantum gravity.

Quantum non-locality is inherent in the pilot wave formulation.

Abstract

The de~Broglie--Bohm (pilot wave) formulation of quantum theory appears to be free from the conceptual problems specific to quantum mechanics (problem of measurement) and to quantum cosmology (problem of time). We discuss the issue of quantum equilibrium which arises within its context. We then study the extension of this formulation to the case of gravity and demonstrate that the foliation of spacetime by space-like hypersurfaces obtained during the solution of the quantum problem turns out to be distinguished in general. This means that quantum pilot wave dynamics is not invariant with respect to arbitrary change of foliation, or, in other terms, that quantum non-locality takes place. We also discuss general structure of a realistic pilot wave theory which could describe the universe.