Dirac observables and the phase space of general relativity

TL;DR

This paper explores a new phase space formulation of general relativity tailored for localized observers, offering potential insights into the problem of time and quantum gravity.

Contribution

It introduces an alternative phase space description that yields different Dirac observables and proposes a novel approach to the problem of time in quantum gravity.

Findings

Different set of Dirac observables for localized observers

Potential solution to the problem of time

New phase space framework for quantum gravity

Abstract

In the canonical approach to general relativity it is customary to parametrize the phase space by initial data on spacelike hypersurfaces. However, if one seeks a theory dealing with observations that can be made by a single localized observer, it is natural to use a different description of the phase space. This results in a different set of Dirac observables from that appearing in the conventional formulation. It also suggests a possible solution to the problem of time, which has been one of the obstacles to the development of a satisfactory quantum theory of gravity.