What is the arrival-time distribution of a free quantum particle?
In plain words
Quantum mechanics predicts where a particle will be found but has no single rule for when it reaches a detector. Competing rules give different predictions, notably for particles with spin, which an experiment could compare.
Precise statement
For a free particle of spin 0 or 1/2 with initial wave packet $\psi_0$ and an ideal detector surface at distance $L$, determine the distribution of detection times, comparing the quantum flux $J(L,t)$, the Kijowski distribution, Bohmian predictions including the spin term of the Pauli current (Das and Durr, Scientific Reports 2019), and absorbing-boundary models. An answer is a derivation from detector models that singles one out, or an experiment resolving their differences.
What would settle it
A time-of-flight experiment with spin-polarized cold atoms or electrons in a waveguide resolving the predicted differences, supported by a detector model.
Status in the literature
Goldstein, Tumulka and Zanghi (arXiv:2309.11835, 2023) argued the Das-Durr spin effect is not measurable as an arrival time, which a 2023 comment (arXiv:2312.01802) disputes.