Non-inertial quantum clock frames lead to non-Hermitian dynamics

The operational approach to time is a cornerstone of relativistic theories, as evidenced by the notion of proper time. In standard quantum mechanics, however, time is an external parameter. Recently, many attempts have been made to extend the notion of proper time to quantum mechanics within a relat...

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Bibliographic Details
Published in:arXiv.org 2022-11
Main Authors: Paiva, Ismael L, Te'eni, Amit, Peled, Bar Y, Cohen, Eliahu, Aharonov, Yakir
Format: Article
Language:English
Subjects:
Clock systems
Clocks
Quantum mechanics
Online Access:Get full text
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Summary:The operational approach to time is a cornerstone of relativistic theories, as evidenced by the notion of proper time. In standard quantum mechanics, however, time is an external parameter. Recently, many attempts have been made to extend the notion of proper time to quantum mechanics within a relational framework. Here, we use similar ideas combined with the relativistic mass-energy equivalence to study an accelerating massive quantum particle with an internal clock system. We show that the ensuing evolution from the perspective of the particle's internal clock is non-Hermitian. This result does not rely on specific implementations of the clock. As a particular consequence, we prove that the effective Hamiltonian of two gravitationally interacting particles is non-Hermitian from the perspective of the clock of either particle.
ISSN:2331-8422
DOI:10.48550/arxiv.2204.04177