Inequivalence of stochastic and Bohmian arrival times in time-of-flight experiments

TL;DR

This paper compares stochastic and Bohmian interpretations of quantum mechanics in time-of-flight experiments, showing they predict different arrival time distributions, which could allow experimental discrimination between these interpretations.

Contribution

It demonstrates that stochastic and Bohmian interpretations yield different arrival time distributions in quantum experiments, highlighting potential for experimental tests of quantum interpretations.

Findings

Stochastic interpretation predicts a different arrival time distribution than Bohmian interpretation.

Simulation confirms the theoretical difference in arrival times.

Results suggest trajectory-based interpretations can be experimentally distinguished.

Abstract

Motivated by a recent prediction [Com. Phys., 6, 195 (2023)] that time-of-flight experiments with ultracold atoms could test different interpretations of quantum mechanics, this work investigates the arrival times predicted by the stochastic interpretation, whereby quantum particles follow definite but non-deterministic and non-differentiable trajectories. The distribution of arrival times is obtained from a Fokker-Planck equation, and confirmed by direct simulation of trajectories. It is found to be in general different from the distribution predicted by the Bohmian interpretation, in which quantum particles follow definite deterministic and differentiable trajectories. This result suggests that trajectory-based interpretations of quantum mechanics could be experimentally discriminated.