Classical Electrodynamics without Fields and the Aharonov-Bohm effect

TL;DR

This paper demonstrates that the Aharonov-Bohm effect can be explained without electromagnetic potentials or fields by using the Darwin-Breit Hamiltonian, challenging the traditional field-based interpretation.

Contribution

It offers a novel explanation of the Aharonov-Bohm effect solely through interaction energies, without relying on electromagnetic potentials or topological space properties.

Findings

Force on electrons vanishes in the model

Interaction energies are non-zero

Phase factors of electron wave packets are non-zero

Abstract

The Darwin-Breit Hamiltonian is applied to the Aharonov-Bohm experiment. In agreement with the standard Maxwell-Lorentz theory, the force acting on electrons from infinite solenoids or ferromagnetic rods vanishes. However, the interaction energies and phase factors of the electron wave packets are non-zero. This allows us to explain the Aharonov-Bohm effect without involvement of electromagnetic potentials, fields, and topological properties of space.