Time of arrival on a ring and relativistic quantum clocks

Abstract:We study the time-of-arrival problem for relativistic particles constrained to move on a ring, formulating the problem entirely within Quantum Field Theory (QFT). In contrast to its counterpart for motion in a line, the circle topology implies that particles may encounter the detector multiple times before detection, making a field-theoretic treatment of the measurement interaction essential. We employ the Quantum Temporal Probabilities (QTP) method to derive a class of Positive-Operator-Valued Measures (POVMs) for time-of-arrival observables directly from QFT. We analyze the resulting detection probabilities in both semiclassical and fully quantum regimes, identifying the relevant timescales and their dependence on the field-theoretic parameters. For ensembles of particles, the detection signal is a periodic function, providing a realization of a quantum clock whose operation reflects the local spacetime structure. We also extend the formalism to rotating rings and show that rotation induces additional noise in detection probabilities, interpretable as a manifestation of the rotational Unruh effect. Finally, we investigate multi-time measurements and demonstrate the emergence of non-classical temporal correlations due to entanglement.

21 pages, 4 figures. Added explanations and corrections. To appear in PRD

arXiv:2603.27311 [quant-ph]

(or arXiv:2603.27311v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2603.27311 Focus to learn more arXiv-issued DOI via DataCite

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