Dualism between Physical Frames and Time in Quantum Gravity

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.