Overcoming a challenge for Bohmian mechanics

TL;DR

This paper addresses a recent challenge to Bohmian mechanics by demonstrating that the velocity can be explicitly constructed to depend on the continuity equation, thus reaffirming its validity.

Contribution

The authors explicitly construct the velocity in Bohmian mechanics to show it can depend on the continuity equation, overcoming recent criticisms.

Findings

Bohmian velocity is generally defined by the continuity equation.

Explicit construction of velocity can resolve recent challenges.

Bohmian mechanics remains consistent when velocity is properly defined.

Abstract

Recently, Bohmian mechanics has been challenged [Nature 643, 67 (2025)] by studying a system in which the motion of particles cannot be associated only with the gradient of phase of the wave function. We point out that, in general, Bohmian velocity is defined by the continuity equation, which does not always lead to velocity depending only on the phase gradient. By constructing the appropriate velocity explicitly, we overcome the challenge.