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

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

doi:10.1038/s42005-022-01081-0

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

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

Bar-Ilan University - The Alexander Kofkin Faculty of Engineering

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

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 language	English
Article number	298
Journal	Communications Physics
Volume	5
Issue number	1
DOIs	https://doi.org/10.1038/s42005-022-01081-0
State	Published - Dec 2022

Bibliographical note

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

Funding

We thank the anonymous referees for their constructive comments that helped to highly improve this work. We also thank Magdalena Zych for insightful comments on a previous version of this work. This research was supported by the Fetzer-Franklin Fund of the John E. Fetzer Memorial Trust and by Grant No. FQXi-RFP-CPW-2006 from the Foundational Questions Institute and Fetzer Franklin Fund, a donor-advised fund of Silicon Valley Community Foundation. E.C. was supported by the Israeli Innovation Authority under Projects No. 70002 and No. 73795, by the Pazy Foundation, by the Israeli Ministry of Science and Technology, and by the Quantum Science and Technology Program of the Israeli Council of Higher Education. Y.A. thanks the Federico and Elvia Faggin Foundation for support.

Funders	Funder number
Fetzer Franklin Fund
Fetzer-Franklin Fund of the John E. Fetzer Memorial Trust	FQXi-RFP-CPW-2006
Israeli Innovation Authority	70002, 73795
Quantum Science and Technology Program of the Israeli Council of Higher Education
Silicon Valley Community Foundation
Foundational Questions Institute
Federico and Elvia Faggin Foundation
Ministry of science and technology, Israel
PAZY Foundation

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Cite this

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

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