Quantum geometrodynamical description of the Universe in different reference frames

TL;DR

This paper explores how quantum geometrodynamics describes the Universe's evolution across different reference frames, highlighting the non-unitary and irreversible nature of gauge changes in a quantum gravitational context.

Contribution

It introduces a framework for understanding the Universe's evolution in different reference frames within quantum geometrodynamics, emphasizing gauge dependence and non-unitary transformations.

Findings

Gauge choice affects the measure of the physical subspace.

Changing reference frames induces non-unitary transformations.

Transitioning between gauges can be irreversible.

Abstract

Several years ago the so-called quantum geometrodynamics in extended phase space was proposed. The main role in this version of quantum geometrodynamics is given to a wave function that carries information about geometry of the Universe as well as about a reference frame in which this geometry is studied. We consider the evolution of a physical object (the Universe) in ``physical'' subspace of extended configurational space, the latter including gauge and ghost degrees of freedom. A measure of the ``physical'' subspace depends on a chosen reference frame, in particular, a small variation of a gauge-fixing function results in changing the measure. Thus, a transition to another gauge condition (another reference frame) leads to non-unitary transformation of a physical part of the wave function. From the viewpoint of the evolution of the Universe in the ``physical'' subspace a transition to another reference frame is an irreversible process that may be important when spacetime manifold has a nontrivial topology.