Quantum clocks observe classical and quantum time dilation

Alexander R. H. Smith () and Mehdi Ahmadi ()
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Alexander R. H. Smith: Saint Anselm College
Mehdi Ahmadi: Santa Clara University

Nature Communications, 2020, vol. 11, issue 1, 1-9

Abstract: Abstract At the intersection of quantum theory and relativity lies the possibility of a clock experiencing a superposition of proper times. We consider quantum clocks constructed from the internal degrees of relativistic particles that move through curved spacetime. The probability that one clock reads a given proper time conditioned on another clock reading a different proper time is derived. From this conditional probability distribution, it is shown that when the center-of-mass of these clocks move in localized momentum wave packets they observe classical time dilation. We then illustrate a quantum correction to the time dilation observed by a clock moving in a superposition of localized momentum wave packets that has the potential to be observed in experiment. The Helstrom-Holevo lower bound is used to derive a proper time-energy/mass uncertainty relation.

Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:nat:natcom:v:11:y:2020:i:1:d:10.1038_s41467-020-18264-4

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DOI: 10.1038/s41467-020-18264-4

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