Arrival Times Versus Detection Times

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 Dürr [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.

24 pages LaTeX, 2 figures; v2 appendices added, two paragraphs on page 2 added

References in corpus (11)

• On the Common Structure of Bohmian Mechanics and the Ghirardi-Rimini-Weber Theory
• Bell-Type Quantum Field Theories
• Bohmian Mechanics Revisited
• Quantum Equilibrium and the Role of Operators as Observables in Quantum Theory
• Quantum Dynamics under continuous projective measurements: non-Hermitian description and the continuous space limit
• What does one measure, when one measures the arrival times of a quantum particle?
• The zig-zag road to reality
• On the Spin Dependence of Detection Times and the Nonmeasurability of Arrival Times
• Diffraction and interference with run-and-tumble particles
• On the zig-zag pilot-wave approach for fermions
• On a Derivation of the Absorbing Boundary Rule

Cited by in corpus (5)

• Existence of Schrodinger Evolution with Absorbing Boundary Condition
• On a Derivation of the Absorbing Boundary Rule
• Double-slit experiment revisited
• Detection Time Distribution Predicted Using Absorbing Boundary Conditions and Imaginary Potentials
• A solution of the quantum time of arrival problem via mathematical probability theory