Demystifying the nonlocality problem in Aharonov-Bohm effect

TL;DR

This paper proposes a semi-classical theory explaining the nonlocality in the Aharonov-Bohm effect by revealing the quantum nature of electrostatic and magnetostatic fields, which act locally on electron wave functions and relate to charge and flux quantization.

Contribution

It introduces a semi-classical framework that explains nonlocality in the Aharonov-Bohm effect through quantum properties of classical fields.

Findings

Fields have quantum nature manifesting in wave amplitudes in regions with zero classical fields.

Fields operate locally on electron wave functions as unitary phases.

Provides insights into the quantization of electric charges and magnetic flux.

Abstract

In this paper, we present a novel semi-classical theory of the electrostatic and magnetostatic fields and explain the nonlocality problem in the context of the Aharonov-Bohm effect [1]. Specifically, we show that the electrostatic and the magnetostatic fields possess a quantum nature that manifests if certain conditions are met. In particular, the wave amplitudes of the fields are seen to exist even in the regions where the classical fields vanish and they operate on the electron wave functions locally as unitary phases. This formulation also sheds light on the quantisation of electric charges and magnetic flux.