Arrival Times Versus Detection Times

TL;DR

This paper examines the differences between arrival times and detection times in quantum mechanics, highlighting how detectors influence wave function evolution and challenging previous assumptions about their equivalence.

Contribution

It clarifies the relationship between arrival and detection times in Bohmian mechanics, emphasizing the impact of detectors on particle trajectories and correcting prior misconceptions.

Findings

Detectors alter wave function evolution and particle trajectories.

Bohmian arrival times without detectors may not match detection times with detectors.

Previous assumptions about the equivalence of different time distributions are incorrect.

Abstract

How to compute the probability distribution of a detection time, i.e., of the time which a detector registers as the arrival time of a quantum particle, is a long-debated problem. In this regard, Bohmian mechanics provides in a straightforward way the distribution of the time at which the particle actually does arrive at a given surface in 3-space in the absence of detectors. However, as we discuss here, since the presence of detectors can change the evolution of the wave function and thus the particle trajectories, it cannot be taken for granted that the arrival time of the Bohmian trajectories in the absence of detectors agrees with the one in the presence of detectors, and even less with the detection time. In particular, we explain why certain distributions that Das and D\"urr [arXiv:1802.07141] presented as the distribution of the detection time in a case with spin, based on assuming that all three times mentioned coincide, is actually not what Bohmian mechanics predicts.