Hidden variable interpretation of spontaneous localization theory

TL;DR

This paper interprets the GRW spontaneous localization theory through a Bohmian mechanics framework, showing how wavefunctions and particle distributions can be coherently linked with noisy information and nonlinear filtering.

Contribution

It provides a novel hybrid interpretation of GRW and Bohmian mechanics, clarifying their relationship and introducing a continuous noisy information framework.

Findings

GRW wavefunction acts as a pilot wave for particles

Nonlinear filtering determines particle distribution dynamics

Hybrid BM-GRW theory offers new interpretative insights

Abstract

The spontaneous localization theory of Ghirardi, Rimini, and Weber (GRW) is a theory in which wavepacket reduction is treated as a genuine physical process. Here it is shown that the mathematical formalism of GRW can be given an interpretation in terms of an evolving distribution of particles on configuration space similar to Bohmian mechanics (BM). The GRW wavefunction acts as a pilot wave for the set of particles. In addition, a continuous stream of noisy information concerning the precise whereabouts of the particles must be specified. Nonlinear filtering techniques are used to determine the dynamics of the distribution of particles conditional on this noisy information and consistency with the GRW wavefunction dynamics is demonstrated. Viewing this development as a hybrid BM-GRW theory, it is argued that, besides helping to clarify the relationship between the GRW theory and BM, its merits make it worth considering in its own right.