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

TL;DR

This paper extends a de Broglie-Bohm style interpretation of quantum mechanics to the Schrödinger case, incorporating action-reaction dynamics between particles and fields, and reveals gauge transformations as a natural part of the formalism.

Contribution

It demonstrates that action and reaction can be incorporated into a Schrödinger-based quantum model using Lagrangian techniques, enhancing physical plausibility and linking gauge transformations to particle dynamics.

Findings

Action-reaction dynamics are successfully integrated into the Schrödinger framework.

Gauge transformations naturally emerge as part of the formalism.

The model maintains consistency with standard experimental predictions.

Abstract

This paper follows on from a previous one in which it was shown that it is possible, within a de Broglie-Bohm style ontology for quantum mechanics, to incorporate action and reaction between the particle and its guiding field while remaining consistent with the usual experimental predictions. Whereas the previous paper focussed on the Dirac equation, the present work addresses the Schrodinger case and demonstrates that the same two-way interaction can be achieved. The aim in each case is to increase the physical plausibility of such models. The transition to include the reaction of the particle back on the field, and hence energy and momentum conservation, is attained by employing standard Lagrangian techniques. In formulating this description an interesting bonus emerges in 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.