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'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.

7+2 pages, 2 figures. Author's published version

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• Atomic clock interferometry using optical tweezers
• Measuring time in a timeless universe
• Parallel-in-time quantum simulation via Page and Wootters quantum time
• A spacetime-covariant approach to inertial and accelerated quantum clocks in first-quantization
• Proposal for a Bell Test with Entangled Atoms of Different Mass
• Gravitational null rays: Covariant Quantization and the Dressing Time
• Unveiling quantum complementarity tradeoffs in relativistic scenarios
• Computational Complexity and Simulability of Non-Hermitian Quantum Dynamics