Can the wave function in configuration space be replaced by single-particle wave functions in physical space?

TL;DR

This paper explores replacing the configuration space wave function in Bohmian mechanics with single-particle wave functions in physical space, aiming for a more ontologically modest reformulation that still reproduces quantum predictions.

Contribution

It introduces a reformulation of Bohmian mechanics using single-particle fields in physical space, replacing the configuration space wave function, and discusses its empirical and ontological implications.

Findings

Reformulation reproduces standard quantum statistical predictions.

Requires an infinite network of interacting potential fields in physical space.

Offers a more ontologically modest alternative to traditional Bohmian mechanics.

Abstract

The ontology of Bohmian mechanics includes both the universal wave function (living in 3N-dimensional configuration space) and particles (living in ordinary 3-dimensional physical space). Proposals for understanding the physical significance of the wave function in this theory have included the idea of regarding it as a physically-real field in its 3N-dimensional space, as well as the idea of regarding it as a law of nature. Here we introduce and explore a third possibility in which the configuration space wave function is simply eliminated -- replaced by a set of single-particle pilot-wave fields living in ordinary physical space. Such a re-formulation of the Bohmian pilot-wave theory can exactly reproduce the statistical predictions of ordinary quantum theory. But this comes at the rather high ontological price of introducing an infinite network of interacting potential fields (living in 3-dimensional space) which influence the particles' motion through the pilot-wave fields. We thus introduce an alternative approach which aims at achieving empirical adequacy (like that enjoyed by GRW type theories) with a more modest ontological complexity, and provide some preliminary evidence for optimism regarding the (once popular but prematurely-abandoned) program of trying to replace the (philosophically puzzling) configuration space wave function with a (totally unproblematic) set of fields in ordinary physical space.