Solving the Problem of Time in Mini-superspace: Measurement of Dirac Observables

TL;DR

This paper addresses the problem of time in quantum gravity by proposing a method to measure Dirac observables through specific interactions, clarifying their interpretability and measurement in the context of quantum cosmology.

Contribution

It introduces a class of interactions that can measure Dirac observables and develops a perturbation theory for the rigging map in group averaging.

Findings

Identifies interactions that implement measurements of Dirac observables.

Develops a perturbation theory for the rigging map eta.

Clarifies the interpretability of evolving constants of motion.

Abstract

One solution to the so-called problem of time is to construct certain Dirac observables, sometimes called evolving constants of motion. There has been some discussion in the literature about the interpretation of such observables, and in particular whether single Dirac observables can be measured. Here we clarify the situation by describing a class of interactions that can be said to implement measurements of such observables. Along the way, we describe a useful notion of perturbation theory for the rigging map eta of group averaging (sometimes loosely called the physical state "projector"), which maps states from the auxiliary Hilbert space to the physical Hilbert space.