Non-inertial quantum clock frames lead to non-Hermitian dynamics
arXiv:2204.04177 · doi:10.1038/s42005-022-01081-0
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.
arXiv comment7+2 pages, 2 figures. Author's published version
References in corpus (33)
- Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
- Complex Extension of Quantum Mechanics
- Reference frames, superselection rules, and quantum information
- Faster than Hermitian Quantum Mechanics
- Quantum mechanics and the covariance of physical laws in quantum reference frames
- Universal decoherence due to gravitational time dilation
- The Trinity of Relational Quantum Dynamics
- Quantum Time
- Observation of Fast Evolution in Parity-Time-Symmetric System
- Non-Hermitian Hamiltonians and no-go theorems in quantum information
- Quantum clocks and the temporal localisability of events in the presence of gravitating quantum systems
- Quantizing time: Interacting clocks and systems
- Quantum clocks observe classical and quantum time dilation
- Physics within a quantum reference frame
- Evolution without evolution, and without ambiguities
- Entanglement of quantum clocks through gravity
- Spacetime Quantum Reference Frames and superpositions of proper times
- How to switch between relational quantum clocks
- Mass-energy and anomalous friction in quantum optics
- History state formalism for scalar particles
- Gravitational mass of composite systems
- The group structure of dynamical transformations between quantum reference frames
- History state formalism for Dirac's theory
- Ideal clocks - a convenient fiction
- Universal quantum modifications to general relativistic time dilation in delocalised clocks
- Noncausal Page-Wootters circuits
- Relative Quantum Time
- Quantifying quantum reference frames in composed systems: local, global and mutual asymmetries
- Flow of time during energy measurements and the resulting time-energy uncertainty relations
- Quantifying resources for Page-Wootters mechanism: Shared asymmetry as relative entropy of entanglement
- Dynamical nonlocality in quantum time via modular operators
- Watching the Clocks: Interpreting the Page-Wootters Formalism and the Internal Quantum Reference Frame Programme
- Unitarity and quantum resolution of gravitational singularities
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- Robustness of the Page-Wootters construction across different pictures, states of the universe and system-clock interactions
- Spacetime quantum and classical mechanics with dynamical foliation
- Measurement events relative to temporal quantum reference frames
- Nonrelativistic spatiotemporal quantum reference frames
- 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