Time of arrival on a ring and relativistic quantum clocks
Phys. Rev. D 114, 045025 – Published 25 August, 2026
DOI: https://doi.org/10.1103/2dtk-q4wp
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 properties. 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 multitime measurements and demonstrate the emergence of nonclassical temporal correlations due to entanglement.
