Relational Observables in Gravity: a Review

TL;DR

This review discusses the development of relational observables in gravity, focusing on their conceptual foundations, progress in constructing gauge-invariant quantities, and implications for quantum gravity, especially within loop quantum gravity.

Contribution

It summarizes 20 years of progress in constructing gauge-invariant relational observables in gravity, highlighting analytic, perturbative, and toy model approaches.

Findings

Progress in complete observables for gravity

Construction of gauge-invariant observables in toy models

Implications for quantum gravity research

Abstract

We present an overview on relational observables in gravity mainly from a loop quantum gravity perspective. The gauge group of general relativity is the diffeomorphism group of the underlying manifold. Consequently, general relativity is a totally constrained theory with vanishing canonical Hamiltonian. This fact, often referred to as the problem of time, provides the main conceptual difficulty towards the construction of gauge-invariant local observables. Nevertheless, within the framework of complete observables, that encode relations between dynamical fields, progress has been made during the last 20 years. Although analytic control over observables for full gravity is still lacking, perturbative calculations have been performed and within de-parameterizable toy models it was possible for the first time to construct a full set of gauge invariant observables for a background independent field theory. We review these developments and comment on their implications for quantum gravity.