Physical Hilbert Spaces in Quantum Gravity

TL;DR

This paper explores how the choice of internal clock affects quantum gravitational dynamics, extending classical Hamilton-Jacobi theory and analyzing quantum effects through examples.

Contribution

It introduces an extended Hamilton-Jacobi framework for contact transformations of time and distinguishes quantum effects due to clock choice from quantization ambiguities.

Findings

Clock choice influences quantum gravitational dynamics.

Extended theory separates effects of clock choice from quantization.

Two examples illustrate different origins of clock effects.

Abstract

We summarize our investigation of the extent to which the choice of internal clock influences the dynamics in quantum models of gravity. Firstly, at the classical level, we define an extension to the Hamilton-Jacobi theory of contact transformations, which allows for transformations of time coordinates. Secondly, at the quantum level, we employ the extended theory to separate the quantum effects brought by the free choice of internal clock from those originating from inequivalent quantization maps. Next, we show with two examples two kinds of origin of the clock effect in quantum gravitational systems.