A Critical Reexamination of the Electrostatic Aharonov-Bohm Effect

TL;DR

This paper critically reexamines the electrostatic Aharonov-Bohm effect, concluding it does not exist when considering the entire system, and refutes previous claims of its observation.

Contribution

It provides a rigorous theoretical critique showing the electrostatic AB effect is invalid when the full system is considered, challenging prior experimental claims.

Findings

Aharonov and Bohm's 1959 explanation is invalid.

Electrostatic AB effect does not exist as originally proposed.

Previous experimental claims are mistaken.

Abstract

This paper undertakes a critical reexamination of the electrostatic version of the Aharonov-Bohm ("AB") effect. The conclusions are as follows: 1. Aharonov and Bohm's 1959 exposition is invalid because it does not consider the wavefunction of the entire system, including the source of electrostatic potential. 2. As originally proposed, the electrostatic AB effect does not exist. Perhaps surprisingly, this conclusion holds despite the relativistic covariance of the electromagnetic four-potential combined with the well-established magnetic AB effect. 3. Although the authors attempted, in a 1961 paper, to demonstrate that consideration of the entire system would not change their result, they inadvertently assumed the desired outcome in their analysis. 4. Claimed observations of the electrostatic AB effect or an analogue thereof are shown to be mistaken.