Aharonov-Bohm effect as a diffusion phenomenon

TL;DR

This paper offers a hydrodynamical interpretation of the Aharonov-Bohm effect using Nelson's quantum mechanics, explaining it through the direct action of surrounding currents rather than non-local magnetic influences.

Contribution

It demonstrates that the Aharonov-Bohm effect can be explained by local current interactions within Nelson's framework, challenging non-locality explanations.

Findings

The effect can be described by local current actions.

Magnetic fields and vector potentials are tools for fundamental quantities.

Hidden variables and quantum fluctuations are relevant to the phenomenon.

Abstract

This paper presents a hydrodynamical view of the Aharonov-Bohm effect, using Nelson's formulation of quantum mechanics. Our aim is to compare our results with other systems and gain a better understanding of the mysteries behind this effect, such as why the motion of a particle is affected in a region where there is no magnetic field. Some theories suggest that this effect is due to the non-local action of the magnetic field on the particle, or even the physical significance of vector potentials over magnetic fields. Our main purpose is to use Nelson's formulation to describe the effect and demonstrate that it can be explained by the direct action of the current surrounding the magnetic field region (i.e. a cylinder) on the particle outside of it. In this context, magnetic fields and vector potentials serve as tools for finding other fundamental quantities that arise from the interaction between two fields: the quantum background fields described by Nelson's quantum theory. Finally, we investigate the relationship between hidden variables and quantum fluctuations and their role in this phenomenon.