We compare the proposals that have appeared in the literature to describe a measurement of the time of arrival of a quantum particle at a detector. We show that there are multiple regimes where different proposals give inequivalent, experimentally discriminable, predictions. This analysis paves the way for future experimental tests.
We identify realizable regimes for experimentally discriminating these approaches. Our results show that discrepancies appear in strongly quantum regimes, namely when the particle displays quantum interference in the time of arrival: destructive interference at times when it is less likely to detect the particle, constructive interference when detection is more likely to happen.
 N. Vona and D. Dürr, The role of the probability current for time measurements, in The Message of Quantum Science: Attempts Towards a Synthesis, edited by P. Blanchard and J. Fröhlich (Springer, 2015) Chap. 5.
 R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integrals (McGraw-Hill, 1965).
 E. A. Galapon, F. Delgado, J. G. Muga, and I. L. Egusquiza, Transition from discrete to continuous time-of-arrival distribution for a quantum particle, Phys. Rev. A 72, 042107 (2005).
 J. Kijowski, On the time operator in quantum mechanics and the Heisenberg uncertainty relation for energy and time, Rep. Math. Phys. 6, 361 (1974).
 A. Ruschhaupt and R. F. Werner, Quantum mechanics of time, in The Message of Quantum Science: Attempts Towards a Synthesis, edited by P. Blanchard and J. Fröhlich (Springer, 2015) Chap. 14.
 T. Jurić and H. Nikolić, Arrival time from the general theory of quantum time distributions, Eur. Phys. J. Plus 137, 631 (2022).
 Y. Aharonov, S. Popescu, and J. Tollaksen, Each instant of time a new universe, in Quantum Theory: A Two-Time Success Story (Springer, 2014) pp. 21–36.
 L. Maccone and K. Sacha, Quantum measurements of time, Phys. Rev. Lett. 124, 110402 (2020).
 R. Brunetti, K. Fredenhagen, and M. Hoge, Time in quantum physics: From an external parameter to an intrinsic observable, Found. Phys. 40, 1368–1378 (2009).
 A. Ananthaswamy, Can we gauge quantum time of flight?, Sci. Am. 326, 1 (2022).
 M. Kozuma, L. Deng, E. W. Hagley, J. Wen, R. Lutwak, K. Helmerson, S. L. Rolston, and W. D. Phillips, Coherent splitting of Bose-Einstein condensed atoms with optically induced bragg diffraction, Phys. Rev. Lett. 82, 871 (1999).
 S. Pandey, H. Mas, G. Drougakis, P. Thekkeppatt, V. Bolpasi, G. Vasilakis, K. Poulios, and W. von Klitzing, Hypersonic Bose–Einstein condensates in accelerator rings, Nature 570, 205 (2019).
 C. R. Leavens, Spatial nonlocality of the “standard” arrival-time distribution, Phys. Lett. A 338, 19 (2005a).
 I. L. Egusquiza, J. G. Muga, B. Navarro, and A. Ruschhaupt, Comment on: “On the standard quantum-mechanical approach to times of arrival”, Phys. Lett. A 313, 498 (2003).
 C. R. Leavens, Reply to Comment on: “On the ‘standard’ quantum-mechanical approach to times of arrival” [Phys. Lett. A 313 (2003) 498], Phys. Lett. A 345, 251 (2005b).
 R. Gambini and J. Pullin, The solution to the problem of time in quantum gravity also solves the time of arrival problem in quantum mechanics, New J. Phys. 24, 053011 (2022).
 Ali Ayatollah Rafsanjani, MohammadJavad Kazemi, Alireza Bahrampour, and Mehdi Golshani, "Can the double-slit experiment distinguish between quantum interpretations?", Communications Physics 6 1, 195 (2023).
 Tajron Jurić and Hrvoje Nikolić, "Passive Quantum Measurement: Arrival Time, Quantum Zeno Effect and Gambler's Fallacy", Fortschritte der Physik 71 10-11, 2300014 (2023).
The above citations are from Crossref's cited-by service (last updated successfully 2023-12-07 05:56:50) and SAO/NASA ADS (last updated successfully 2023-12-07 05:56:51). The list may be incomplete as not all publishers provide suitable and complete citation data.
This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.