The complex interplay between the ontological status of the wave-function and the motion of the particles in the De Broglie-Bohm Theory

Abstract

This contribution aims to show the complex interplay between the ontological status of the wave-function and the kinematics and dynamics of the particles within the guidance view of the de Broglie-Bohm theory. In particular, it deals with two formulations of the theory. The former, which goes under the name of Bohmian mechanics, puts the particles in a Galilean space-time and considers the wave-function as a nomological entity; the latter, which is normally known as the pilot-wave theory, puts the particles in an Aristotelian space-time and regards the wave-function as a physical field. On one hand, I will show that the difference of the ontological status of the wave-function is due to a difference in how the theory is formulated. On the other hand, I will show that in both cases the dynamics and kinematics of the particles are determined by a prior ontological commitment concerning the wave-function. My talk will open with a brief summary of Bohmian Mechanics and its nomological view in connection with the dispositional view. After that, I will claim that, given the Galilean space-time and the law of motion for the particles, the natural choice is to attribute a nomological status to the wave-function. I will argue, however, that this is true only if we adopt a certain argument according to which we derive the dynamics from the kinematics. I will also point out that the nomological status of the wave-function was already presupposed before building the guiding law of motion. My last consideration will be that, given the nomological status of the wave-function, the kinematics of the theory becomes ambiguous. In particular, we need a clarification of the meaning of ‘natural state’, otherwise we have two possible natural motions for Bohmian Mechanics, which are either uniform velocity or the velocity given by the wave-function through the law of motion. This last inertial motion, however, would on one hand endorse a dispositional interpretation of the wave-function, on the other hand, it would imply the abandonment of perhaps Galilean space-time and certainly Newtonian mechanics. In the second part of my talk, I will investigate the ontological status of the wave-function in the Pilot-wave theory. I will show that on one hand the realist interpretation of the wave-function is a necessary commitment once we hold true the dynamics and the kinematics of the particles, and in particular once we hold true that we derive the kinematics from the dynamics. I will however point out that this derivation is straightforward if and only if we first assume that the wave-function represents a physical field. I will draw a two-fold conclusion, which is useful for any theory. On one hand it is methodologically wrong to decide on the ontological status of the wave-function regardless of the structure of the theory. On the other hand, it is sometimes naïve to say that we should not read off the ontology from the formalism, since the formalism may be determined by a certain ontological choice.