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Non-inertial quantum clock frames lead to non-Hermitian dynamics
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Non-inertial quantum clock frames lead to non-Hermitian dynamics
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Journal Article
Non-inertial quantum clock frames lead to non-Hermitian dynamics
2022
Overview
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.
Relativistic theories brought the operational notion of time to the center stage of physics. Here, the authors show that effective unitary dynamics is not guaranteed if this notion is extended to quantum mechanics when relativistic corrections are considered in relational frameworks.
Publisher
Nature Publishing Group UK,Nature Publishing Group,Nature Portfolio
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