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

Ismael L. Paiva*, Amit Te’eni, Bar Y. Peled, Eliahu Cohen, Yakir Aharonov

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Article number298
JournalCommunications Physics
Issue number1
StatePublished - Dec 2022


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