Observables in effective gravity

TL;DR

This paper explores the construction of diffeomorphism-invariant, non-local observables in effective quantum gravity, analyzing their measurement limitations and implications for the degrees of freedom in finite-region theories.

Contribution

It introduces a class of pseudo-local observables in effective gravity and examines their measurement constraints, linking non-locality to reduced degrees of freedom.

Findings

Pseudo-local observables can recover local QFT physics in suitable limits.

Quantum and gravitational effects limit the measurement of these observables.

Finite-region quantum gravity theories have fewer degrees of freedom than local field theories.

Abstract

We address the construction and interpretation of diffeomorphism-invariant observables in a low-energy effective theory of quantum gravity. The observables we consider are constructed as integrals over the space of coordinates, in analogy to the construction of gauge-invariant observables in Yang-Mills theory via traces. As such, they are explicitly non-local. Nevertheless we describe how, in suitable quantum states and in a suitable limit, the familiar physics of local quantum field theory can be recovered from appropriate such observables, which we term `pseudo-local.' We consider measurement of pseudo-local observables, and describe how such measurements are limited by both quantum effects and gravitational interactions. These limitations support suggestions that theories of quantum gravity associated with finite regions of spacetime contain far fewer degrees of freedom than do local field theories.