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

• URL: http://arxiv.org/abs/2204.08371v1
• Date: Mon, 18 Apr 2022 15:30:24 GMT
• Title: The solution to the problem of time in quantum gravity also solves the time of arrival problem in quantum mechanics
• Authors: Rodolfo Gambini, Jorge Pullin
• Abstract summary: We introduce a solution to the problem of time in quantum gravity which consists in formulating the quantum theory in terms of real clocks. 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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