TY - JOUR

T1 - Non-inertial quantum clock frames lead to non-Hermitian dynamics

AU - Paiva, Ismael L.

AU - Te’eni, Amit

AU - Peled, Bar Y.

AU - Cohen, Eliahu

AU - Aharonov, Yakir

N1 - Publisher Copyright:
© 2022, The Author(s).

PY - 2022/12

Y1 - 2022/12

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85142414023&partnerID=8YFLogxK

U2 - 10.1038/s42005-022-01081-0

DO - 10.1038/s42005-022-01081-0

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AN - SCOPUS:85142414023

SN - 2399-3650

VL - 5

JO - Communications Physics

JF - Communications Physics

IS - 1

M1 - 298

ER -