@article{e6cbea0b3dbf45aa9b555e68739461b7,
title = "Non-inertial quantum clock frames lead to non-Hermitian dynamics",
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{\textquoteright}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.",
author = "Paiva, {Ismael Lucas} and Amit Te'eni and Peled, {Bar Y.} and Eliahu Cohen and Yakir Aharonov",
note = "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.",
year = "2022",
month = nov,
day = "22",
doi = "10.1038/s42005-022-01081-0",
language = "English",
volume = "5",
pages = "1--7",
journal = "Communications Physics",
issn = "2399-3650",
publisher = "Springer Nature",
}