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Entropy

On a Common Misconception Regarding the de Broglie–Bohm Theory

O. Passon

Published Jun 5, 2018• 9 citations
Publisher

Abstract

We discuss a common misconception regarding the de Broglie-Bohm (dBB) theory; namely, that it not only assigns a position to each quantum object but also contains the momenta as "hidden variables". Sometimes this alleged property of the theory is even used to argue that the dBB theory is inconsistent with quantum theory. We explain why this claim is unfounded and show in particular how this misconception veils the true novelty of the dBB theory.

DOI
10.3390/e20060440

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In a recent paper, Brida et al (2002 J. Phys. B: At. Mol. Opt. Phys. 35 4751) reported the first experimental realization for testing of de Broglie–Bohm (dBB) theory against standard quantum mechanics (SQM), based on a suggested scheme presented in Golshani and Akhavan (2001 J. Phys. A: Math. Gen. 34 5259). However, some details of their experiment are not compatible with our suggestion. Therefore, their conclusion, in which the experimental data are in complete agreement with SQM but show some deviations from dBB predictions, cannot be considered as a final verdict.

Journal of Physics B Atomic Molecular and Optical Physics•Sep 15, 2004•3 citations
We discuss a common misconception regarding the de Broglie-Bohm (dBB) theory; namely, that it not only assigns a position to each quantum object but also contains the momenta as "hidden variables". Sometimes this alleged property of the theory is even used to argue that the dBB theory is inconsistent with quantum theory. We explain why this claim is unfounded and show in particular how this misconception veils the true novelty of the dBB theory.
Supporters of the de Broglie-Bohm (dBB) interpretation of quantum theory argue that because the theory, like classical mechanics, concerns the motions of point particles in 3D space, it is specially suited to recover classical behavior. I offer a novel account of classicality in dBB theory, if only to show that such an account falls out almost trivially from results developed in the largely interpretation-neutral context of decoherence theory. I then argue that this undermines any special claim that dBB theory is purported to have on the unification of the quantum and classical realms.
Abstract We will first define what is meant by “hidden variables”. Then, we will review theorems proving the impossibility of theories introducing such variables in a naive way. Next, we will outline the de Broglie-Bohm theory and show that it is not refuted by those theorems. To do that, we will explain how “measurements” work in that theory, using the examples of spin measurements and of momentum measurements. Those measurements do not reveal pre-existing properties of the quantum particle but are the result of interactions between that particle and the measuring apparatus. And this is why the de Broglie-Bohm theory is not refuted by the theorems on the impossibility of hidden variables. We will also explain the relationship between the no “hidden variables” theorems and nonlocality, with and without introducing Bell’s inequalities.
Within the de Broglie–Bohm (dBB) theory, the measurement process and the determination of its outcome are usually discussed in terms of the effect of the Bohmian positions of the measured system S. This article shows that the Bohmian positions associated with the measurement apparatus M can actually play a crucial role in the determination of the result of measurement. Indeed, in many cases, the result is practically independent of the initial value of a Bohmian position associated with S, and determined only by those of M. The measurement then does not reveal the value of any pre-existing variable attached to S, but just the initial state of the measurement apparatus. Quantum contextuality then appears with particular clarity as a consequence of the dBB dynamics for entangled systems.
A salient feature of de Broglie-Bohm (dBB) quantum theory is that particles have determinate positions at all times and in all physical contexts. Hence, the trajectory of a particle is a well-defined concept. One then may expect that the closely related notion of inertial trajectory is also unproblematically defined. I show that this expectation is not met. I provide a framework that deploys six different ways in which dBB theory can be interpreted, and I state that only in the canonical interpretation the concept of inertial trajectory is the customary one. However, in this interpretation the description of the dynamical interaction between the pilot-wave and the particles, which is crucial to distinguish inertial from non-inertial trajectories, is affected by serious difficulties, so other readings of the theory intend to avoid them. I show that in the alternative interpretations the concept at issue gets either drastically altered, or plainly undefined. I also spell out further conceptual difficulties that are associated to the redefinitions of inertial trajectories, or to the absence of the concept.
In a recent paper, Brida et al (2002 J. Phys. B: At. Mol. Opt. Phys. 35 4751) reported the first experimental realization for testing of de Broglie–Bohm (dBB) theory against standard quantum mechanics (SQM), based on a suggested scheme presented in Golshani and Akhavan (2001 J. Phys. A: Math. Gen. 34 5259). However, some details of their experiment are not compatible with our suggestion. Therefore, their conclusion, in which the experimental data are in complete agreement with SQM but show some deviations from dBB predictions, cannot be considered as a final verdict.