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arXiv:2312.01802

Comment on "the Spin Dependence of Detection Times and the Nonmeasurability of Arrival Times"

Siddhant Das, Serj Aristarhov

Published Dec 4, 2023• 2 citations
arXivHTMLPDF

Abstract

We respond to the recent article by S. Goldstein, R. Tumulka, and N. Zanghì [arXiv:2309.11835] concerning the spin-dependent arrival-time distributions reported in [S. Das and D. Dürr, Sci. Rep. 9: 2242 (2019)].
DOI
10.48550/arxiv.2312.01802

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According to a well-known principle of quantum physics, the statistics of the outcomes of any quantum experiment are governed by a Positive-Operator-Valued Measure (POVM). In particular, for experiments designed to measure a specific physical quantity, like the time of a particle's first arrival at a surface, this principle establishes that if the probability distribution of that quantity does not arise from a POVM, no such experiment exists. Such is the case with the arrival time distributions proposed by Das and Dürr, due to the nature of their spin dependence.
It is well known that orthodox quantum mechanics does not make unambiguous predictions for the statistics in arrival time (or time-of-flight) experiments. Bohmian mechanics (or de Broglie--Bohm theory) offers a distinct conceptual advantage in this regard, owing to the well-defined concepts of point particles and trajectories embedded in this theory. We revisit a recently proposed experiment [S. Das and D. D\"urr, Sci. Rep. 9, 2242 (2019)], the numerical analysis of which revealed a striking spin dependence in the (Bohmian) time-of-arrival distributions of a spin-1/2 particle. We present here a mathematically tractable variant of the same experiment, where the predicted effects can be established rigorously. We also obtain some results that can be compared with experiment.