The solution to the problem of time in quantum gravity also solves the time of arrival problem in quantum mechanics

TL;DR

This paper demonstrates that a quantum gravity solution involving real clocks also addresses the quantum mechanics time of arrival problem, establishing a consistent time-energy uncertainty relation.

Contribution

It introduces a unified approach using real clocks that resolves the time of arrival issue in quantum mechanics and links it to quantum gravity.

Findings

Provides a natural solution to the time of arrival problem.

Establishes a well-defined time-energy uncertainty relation.

Connects quantum gravity concepts with quantum mechanics timing issues.

Abstract

We introduced with coauthors some years ago a solution to the problem of time in quantum gravity which consists in formulating the quantum theory in terms of real clocks. It combines Page and Wootters' relational proposal with Rovelli's evolving constants of the motion. Time is associated with an operator and not a classical parameter. We show here that this construction provides a natural solution to the time of arrival problem in quantum mechanics and leads to a well defined time-energy uncertainty relation for the clocks.