Evidence for Bohmian velocities from conditional Schrodinger equation

TL;DR

This paper argues that Bohmian velocities can be distinguished from arbitrary modified velocities through their influence on the conditional wave function of a subsystem, especially when approximated by classical trajectories, supporting the observational preference for Bohmian velocities.

Contribution

It demonstrates that measurable differences in predictions arise from Bohmian velocities compared to other velocity modifications, especially via the conditional wave function in energy eigenstates.

Findings

Conditional wave function depends on Bohmian trajectories.

Approximation by classical trajectories aligns with observations.

Deviations from Bohmian velocities are not justifiable observationally.

Abstract

It is often argued that measurable predictions of Bohmian mechanics cannot be distinguished from those of a theory with arbitrarily modified particle velocities satisfying the same equivariance equation. By considering the wave function of a closed system in a state with definite total energy, we argue that a distinction in measurable predictions is possible. Even though such a wave function is time-independent, the conditional wave function for a subsystem depends on time through the time-dependent particle trajectories not belonging to the subsystem. If these trajectories can be approximated by classical trajectories, then the conditional wave function can be approximated by a wave function which satisfies Schrodinger equation in a classical time-dependent potential, which is in good agreement with observations. However, such an approximation cannot be justified for particle velocities significantly deviating from the Bohmian ones, implying that Bohmian velocities are observationally preferred.