Incorporating action and reaction into a particle interpretation for quantum mechanics -- Dirac case

TL;DR

This paper proposes a new particle interpretation of quantum mechanics that incorporates action and reaction between particles and fields, resolving a longstanding artificial asymmetry and aligning with quantum predictions.

Contribution

It introduces a Lagrangian density that includes action-reaction dynamics and explains the emergence of gauge transformations within quantum formalism.

Findings

Eliminates the artificial lack of action-reaction in particle models

Demonstrates compatibility with standard quantum predictions

Provides a natural explanation for gauge transformations and localised particles

Abstract

A weakness which has previously seemed unavoidable in particle interpretations of quantum mechanics (such as in the de Broglie-Bohm model) is addressed here and a resolution proposed. The weakness in question is the lack of action and reaction occurring between the model's field (or "pilot wave") and the particle. Although the field acts on the particle, the particle does not act back on the field. It is shown here that this rather artificial feature is, in fact, not necessary and can be fully eliminated while remaining consistent with the usual quantum predictions. Mathematically this amounts to demonstrating that there exists a suitable Lagrangian density function which generates equations coinciding with quantum mechanics yet incorporates the desired action and reaction. As a by-product, an appealing explanation emerges to another long-standing question, namely why the mathematical formalism of quantum mechanics seems only to be describing fields when measurements generally detect localised particles. A further bonus is that the hitherto unrelated concept of a gauge transformation is found to arise naturally as an essential part of the formalism. In particular, the phase S of the gauge transformation is seen to be the action function describing the hidden motion of the particle.