Could gauge gravitational degrees of freedom play the role of environment in "extended phase space" version of quantum geometrodynamics?

TL;DR

This paper explores how gauge gravitational degrees of freedom in extended phase space quantum geometrodynamics could act as an environment, leading to classical behavior of the Universe through decoherence effects.

Contribution

It introduces a framework where gauge degrees of freedom are quantized alongside physical ones, proposing they can induce classicality in the Universe's quantum state.

Findings

Gauge degrees of freedom can serve as an environment causing decoherence.

The density matrix of the Universe can develop a Gaussian form under certain gauge fixings.

The classical behavior of the Universe may break down near boundaries of different spacetime regions.

Abstract

In the context of the recently proposed formulation of quantum geometrodynamics in extended phase space we discuss the problem how the behavior of the Universe, initially managed by quantum laws, has become classical. In this version of quantum geometrodynamics we quantize gauge gravitational degrees of freedom on an equal basis with physical degrees of freedom. As a consequence of this approach, a wave function of the Universe depends not only on physical fields but also on gauge degrees of freedom. From this viewpoint, one should regard the physical Universe as a subsystem whose properties are formed in interaction with the subsystem of gauge degrees of freedom. We argue that the subsystem of gauge degrees of freedom may play the role of environment, which, being taken into account, causes the density matrix to be diagonal. We show that under physically reasonable fixing of gauge condition the density matrix describing the physical subsystem of the Universe may have a Gaussian peak in some variable, but it could take the Gaussian form only within a spacetime region where a certain gauge condition is imposed. If spacetime manifold consists of regions covered by different coordinate charts the Universe cannot behave in a classical manner nearby borders of these regions. Moreover, in this case the Universe could not stay in the same quantum state, but its state would change in some irreversible way.