Bohmian Mechanics fails to compute multi-time correlations

TL;DR

This paper demonstrates that Bohmian mechanics cannot accurately reproduce multi-time correlations in quantum systems, highlighting fundamental limitations in its ability to fully replicate quantum predictions without additional collapse mechanisms.

Contribution

The authors show that Bohmian mechanics fails to match quantum predictions for multi-time correlations in a spatial GHZ system unless extended with a wave function collapse theory.

Findings

Bohmian mechanics does not reproduce quantum multi-time correlations.

Positions at different times do not commute, causing discrepancies.

Bohmian theory requires an added collapse mechanism to align with quantum results.

Abstract

The violation of Bell type inequalities in quantum systems manifests that quantum states cannot be described by classical probability distributions. Yet, Bohmian mechanics is a realistic, non-local theory of classical particle trajectories that is claimed to be indistinguishable by observations from more traditional approaches to quantum mechanics. We set up a spatial version of the GHZ system with qubits realised as positional observables that demonstrates that the Bohmian theory fails to match predictions of textbook quantum mechanics (and most likely experients) unless enlarged by a microscopic theory of collapse of the wave function after observation. For this discrepancy to occur it is essential that positions at different times do not commute.