Relational observables in 2d quantum gravity

TL;DR

This paper explores the concept of relational observables in 2D quantum gravity, addressing the challenge of defining local measurements in a gauge-invariant way within a controlled theoretical setting.

Contribution

It provides a detailed analysis of relational observables in 2D quantum gravity, illustrating their properties and limitations in a highly analyzable model.

Findings

Relational observables approximate local observables in certain states.

Quantum mechanics and gravity impose limits on localization precision.

The 2D gravity model offers insights into the nature of gauge-invariant observables.

Abstract

Local observation is an important problem both for the foundations of a quantum theory of gravity and for applications to quantum-cosmological problems such as eternal inflation. While gauge invariant local observables can't be defined, it has been argued that appropriate relational observables approximately reduce to local observables in certain states. However, quantum mechanics and gravity together imply limitations on the precision of their localization. Such a relational framework is studied in the context of two-dimensional gravity, where there is a high degree of analytic control. This example furnishes a concrete example of some of the essential features of relational observables.