Dualism between Physical Frames and Time in Quantum Gravity

TL;DR

This paper explores the relationship between physical reference frames and the concept of time in quantum gravity, proposing that breaking time displacement invariance at the quantum level is equivalent to including a real reference fluid.

Contribution

It demonstrates how fixing the lapse function in quantum gravity leads to a Schrödinger evolution and links the breaking of time invariance to the presence of a physical reference fluid.

Findings

Schrödinger evolution derived from Einstein equations with dust fluid

Eigenvalues problem indicates dust fluid in classical limit

Breaking time invariance is equivalent to including a reference fluid

Abstract

In this work we present a discussion of the existing links between the procedures of endowing the quantum gravity with a real time and of including in the theory a physical reference frame. More precisely, as first step, we develop the canonical quantum dynamics, starting from the Einstein equations in presence of a dust fluid and arrive to a Schroedinger evolution. Then, by fixing the lapse function in the path integral of gravity, we get a Schroedinger quantum dynamics, of which eigenvalues problem provides the appearance of a dust fluid in the classical limit. The main issue of our analysis is to claim that a theory, in which the time displacement invariance, on a quantum level, is broken, is indistinguishable from a theory for which this symmetry holds, but a real reference fluid is included.