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

TL;DR

This paper demonstrates that when considering non-inertial quantum frames, the effective dynamics become non-Hermitian, revealing new insights into the nature of quantum evolution in relativistic and gravitational contexts.

Contribution

It introduces a framework combining relativistic mass-energy equivalence with quantum clocks, showing non-Hermitian dynamics arise in accelerating quantum systems.

Findings

Non-inertial quantum clock frames lead to non-Hermitian evolution.

The effective Hamiltonian for gravitationally interacting particles is non-Hermitian from each particle's perspective.

Results do not depend on specific clock implementations.

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.