Darwin–Lagrangian analysis for the interaction of a point charge and a magnet: considerations related to the controversy regarding the Aharonov–Bohm and Aharonov–Casher phase shifts

Macroscopic test of the Aharonov-Bohm effect

The Aharonov-Bohm (AB) effect is a purely quantum mechanical effect. The original (classified as type-I) AB-phase shift exists in experimental conditions where the electromagnetic fields and forces are zero. It is the absence of forces that makes the AB effect entirely quantum mechanical. Although the AB-phase shift has been demonstrated unambiguously, the absence of forces in type-I AB effects has never been shown. Here, we report the observation of the absence of time delays associated with forces of the magnitude needed to explain the AB-phase shift for a macroscopic system.