Trajectories in coupled waveguides: an application to a recent experiment and Hiley's lessons on the falsification of the Bohmian model

TL;DR

This paper demonstrates that when correctly applied, the de Broglie-Bohm model produces results identical to standard quantum mechanics in coupled waveguide experiments, challenging claims against its validity.

Contribution

It provides a detailed computation of Bohmian trajectories in coupled waveguides, clarifying misconceptions and emphasizing the model's consistency with quantum mechanics.

Findings

Bohmian trajectories match standard quantum results when correctly applied.

The model's predictions are consistent in both 1D and 2D coupled waveguide scenarios.

Contextuality of trajectories explains differences between closed systems and measurement interactions.

Abstract

From "surreal" trajectories to which-way measurements, Basil Hiley had a lesson: claims of falsifying the Bohmian model do not withstand scrutiny provided the model is applied correctly. In this work we compute de Broglie-Bohm trajectories for particles tunneling in coupled waveguides relevant to a recent experiment having claimed to challenge the Bohmian model. We show that the Bohmian model - correctly applied - gives results identical to the standard quantum approach, first by working out a simple one-dimensional model, and then by computing Bohmian trajectories for the full two-dimensional problem representing a quantum particle propagating inside coupled waveguides. We further recall the contextual nature of the Bohmian trajectories whereby the trajectories of a closed system differ from the ones observed when an interaction with a measurement apparatus takes places.