Observer Time from Causality in Perturbative Quantum Gravity

TL;DR

This paper introduces a new observable notion of time in perturbative quantum gravity based on causality and light cones, and demonstrates it as a quantum operator with quantum corrections affecting two-point functions.

Contribution

It defines an observable proper time in quantum gravity using causality and computes quantum corrections, establishing time as a quantum operator.

Findings

Quantum gravity corrections modify two-point correlation functions of elapsed time.

The proposed time notion is a quantum operator with nonzero commutators.

Quantum corrections arise at all orders in the gravitational coupling.

Abstract

It is unclear whether an observable notion of time exists in quantum gravity even in principle because spacetime itself fluctuates. We propose a form of observable time in perturbative quantum gravity. First, we define an elapsed proper time in curved space using intersections of worldlines and future light cones. Here, time arises from causality via the dependence on light cones. We then propose that performing the gravitational path integral describes quantum gravity corrections to this notion of proper time at all orders in $G_N$. Using this prescription, we compute the leading quantum gravity corrections to two-point correlation functions of elapsed time. We find that the commutators can be nonzero, showing this notion of time is a quantum operator in quantum gravity.