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Reaffirming a Challenge to Bohmian Mechanics

Jan Klaers, Violetta Sharoglazova, Marius Puplauskis

TL;DR

The paper investigates whether Bohmian trajectories can yield objective particle speeds and times, focusing on how the guiding equation choice shapes results for tunneling and dwell times. It introduces a dilation-invariant speed measure derived from the spatio-temporal transformation of density in a coupled-waveguide system, and shows how this speed governs the density redistribution and can be inferred experimentally from population data. A bidirectional Bohmian model is proposed to reconcile motion across propagating and evanescent regimes, yielding dwell times identical to standard quantum mechanics and aligning with Büttiker–Landauer times for opaque barriers. The authors argue that, because the density can be preserved by many guiding equations yet yield different motions, selecting physically meaningful guiding equations via a correspondence principle is essential, highlighting a challenge for Bohmian mechanics in providing a unique ontology.

Abstract

In our recent work (Sharoglazova et al., Nature 643, 67 (2025)), we reported the measurement of the speed of tunnelling particles using a coupled waveguide system. The measured speed was found to disagree with the standard guiding equation of Bohmian mechanics, which we regard as a challenge to that framework. In the present work, we provide a more detailed account of this issue. In particular, we argue that agreement or disagreement between standard quantum mechanics and Bohmian mechanics on quantities such as particle velocity, speed, tunnelling, and dwell times depends solely on the choice of guiding equation. If this choice is made based on observable spatio-temporal transformation behaviour of the particle density, the two theories agree on these phenomena.

Reaffirming a Challenge to Bohmian Mechanics

TL;DR

The paper investigates whether Bohmian trajectories can yield objective particle speeds and times, focusing on how the guiding equation choice shapes results for tunneling and dwell times. It introduces a dilation-invariant speed measure derived from the spatio-temporal transformation of density in a coupled-waveguide system, and shows how this speed governs the density redistribution and can be inferred experimentally from population data. A bidirectional Bohmian model is proposed to reconcile motion across propagating and evanescent regimes, yielding dwell times identical to standard quantum mechanics and aligning with Büttiker–Landauer times for opaque barriers. The authors argue that, because the density can be preserved by many guiding equations yet yield different motions, selecting physically meaningful guiding equations via a correspondence principle is essential, highlighting a challenge for Bohmian mechanics in providing a unique ontology.

Abstract

In our recent work (Sharoglazova et al., Nature 643, 67 (2025)), we reported the measurement of the speed of tunnelling particles using a coupled waveguide system. The measured speed was found to disagree with the standard guiding equation of Bohmian mechanics, which we regard as a challenge to that framework. In the present work, we provide a more detailed account of this issue. In particular, we argue that agreement or disagreement between standard quantum mechanics and Bohmian mechanics on quantities such as particle velocity, speed, tunnelling, and dwell times depends solely on the choice of guiding equation. If this choice is made based on observable spatio-temporal transformation behaviour of the particle density, the two theories agree on these phenomena.

Paper Structure

This paper contains 4 sections, 18 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Particle speed in coupled waveguides
  3. A bidirectional Bohmian model
  4. Discussion

Figures (1)

  • Figure 1: Coupled waveguides. A stream of particles (red arrow) is confined in a waveguide potential and propagates towards a potential step (vertical black arrow). At the step, a second waveguide opens up. The particle transfer between the upper and the lower waveguides, described by the coupling constant $J>0$, effectively acts as a clock allowing particle speeds to be determined by considering the population build-up in $\psi_{a}$.