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Philosophy of Science

Is de Broglie-Bohm Theory Specially Equipped to Recover Classical Behavior?

Joshua Rosaler

Published Dec 1, 2015• 11 citations
Publisher

Abstract

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.

DOI
10.1086/683468

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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.
We define the de Broglie-Bohm (dBB) weak interpretation as the dBB interpretation restricted to particles in unbound states whose wave function is defined in the three-dimensional physical space, and the dBB strong interpretation as the usual dBB interpretation applied to all wave functions, in particular to particles in bound states whose wave function is defined in a 3N-dimensional configuration space in which N is the number of particules. We show that the current criticisms of the dBB interpretation do not apply to this weak interpretation and that, furthermore, there are theoritical and experimental reasons to justify the weak dBB interpretation. Theoretically, the main reason concern the continuity existing for such particles between quantum mechanics and classical mechanics: we demonstrate in fact that the density and the phase of the wave function of a single-particle (or a set of identical particles without interaction), when the Planck constant tends to 0, converges to the density and the action of a set of unrecognizable prepared classical particles that satisfy the statistical Hamilton-Jacobi equations. As the Hamilton-Jacobi action pilots the particle in classical mechanics, this continuity naturally concurs with the weak dBB interpretation. Experimentally, we show that the measurement results of the main quantum experiments (Young's slits experiment, Stern and Gerlach, EPR-B) are compatible with the de Broglie-Bohm weak interpretation and everything takes place as if these unbounded particles had trajectories. In addition, we propose two potential solutions to complete the dBB weak interpretation.
In this work celebrating the centenary of quantum mechanics, we review the principles of the de Broglie-Bohm theory (dBB), also known as pilot-wave theory. We assess the most common reading of it (the Nomological interpretation based on the notion of primitive ontology in tridimensional space) and defend instead a more causal and pluralistic approach, drawing on classical analogies with optics and hydrodynamics. Within this framework, we review some of the approaches exploiting mechanical analogies to overcome the limitations of the current dBB theory and perhaps quantum mechanics itself.
In the de Broglie Bohm pilot-wave theory and the many-worlds interpretation, unitary development of the quantum state is universally valid. They differ in that de Broglie and Bohm assumed that there are point particles with positions that evolve in time and that our observations are observations of the particles. The many-worlds interpretation is based on the fact that the quantum state can explain our observations. Both interpretations rely on the decoherence mechanism to explain the disappearance of interference effects at a measurement. From this fact, it is argued that for the pilot-wave theory to work, circumstances must be such that the many-worlds interpretation is a viable alternative. However, if this is the case, the de Broglie–Bohm particles become irrelevant to any observer. They are truly hidden. The violation of locality and the corresponding violation of Lorenz invariance are good reasons to believe that dBB particles do not exist.
Bohmian mechanics is endowed with an ontological package that supposedly allows to solve the main interpretational problems of quantum mechanics. We are concerned in this work by the emergence of classicality from the quantum mechanical substrate. We will argue that although being superficially attractive, the de Broglie-Bohm interpretation does not shed new light on the quantum-to-classical transition. This is due to nature of the dynamical law of Bohmian mechanics by which the particles follow the streamlines of the probability flow. As a consequence, Bohmian trajectories can be highly non-classical even when the wavefunction propagates along classical trajectories, as happens in semiclassical systems. In order to account for classical dynamics, Bohmian mechanics needs non-spreading and non-interfering wave packets: this is achieved for practical purposes by having recourse to decoherence and dense measurements. However one then faces the usual fundamental problems associated with the meaning of reduced density matrices. Moreover the specific assets of the de Broglie-Bohm interpretation – in particular the existence of point-like particles pursuing well-defined trajectories – would play no role in accounting for the emergence of classical dynamics.
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.