How to test the gauge-invariant non-local quantum dynamics of the Aharonov-Bohm effect

TL;DR

This paper proposes experimental methods to test the gauge-invariant non-local quantum dynamics of the Aharonov-Bohm effect by measuring instantaneous velocity shifts, demonstrating feasibility in both relativistic and non-relativistic regimes.

Contribution

It introduces a way to experimentally verify the gauge-invariant non-local quantum effects of the Aharonov-Bohm phenomenon through velocity measurements.

Findings

Instantaneous velocity shifts can be measured when particles pass the flux line.

Relativistic quantum theory allows for velocity measurements with sufficient accuracy.

Non-relativistic quantum theory permits arbitrary accuracy in velocity measurement.

Abstract

The gauge invariant non local quantum dynamics of the Aharonov-Bohm effect can be tested experimentally by measuring the instantaneous shift of the velocity distribution occurring when the particle passes by the flux line. It is shown that in relativistic quantum theory it is possible to measure the instantaneous velocity with accuracy sufficient to detect the change of the velocity distribution. In non relativistic quantum theory the instantaneous velocity can be measured to any desired accuracy.