Bohmian mechanics contradicts quantum mechanics

TL;DR

This paper demonstrates that Bohmian mechanics and quantum mechanics make fundamentally different predictions for certain time correlations in a harmonic oscillator, challenging the claim that Bohmian mechanics fully reproduces quantum results.

Contribution

It reveals a fundamental contradiction between Bohmian mechanics and quantum mechanics regarding time correlations, highlighting limitations of Bohmian mechanics in reproducing quantum predictions.

Findings

Bohmian mechanics predicts opposite signs for certain correlations.

Discrepancies arise from the treatment of the Heisenberg picture.

Bohmian mechanics cannot fully reproduce quantum measurement results.

Abstract

It is shown that, for a harmonic oscillator in the ground state, Bohmian mechanics and quantum mechanics predict values of opposite sign for certain time correlations. The discrepancy can be explained by the fact that Bohmian mechanics has no natural way to accomodate the Heisenberg picture, since the local expectation values that define the beables of the theory depend on the Heisenberg time being used to define the operators. Relations to measurement are discussed, too, and shown to leave no loophole for claiming that Bohmian mechanics reproduces all predictions of quantum mechanics exactly.