Against a proposed alternative explanation of the Aharonov-Bohm effect

Abstract

The Aharonov-Bohm effect is understood to demonstrate that the Maxwell fields can act nonlocally in some situations. However it has been suggested from time to time that the AB effect is somehow a consequence of a local classical electromagnetic field phenomenon involving energy that is temporarily stored in the overlap between the external field and the field of which the beam particle is the source. That idea was shown in the past not to work for some models of the source of the external field. Here a more general proof is presented for the magnetic AB effect to show that the overlap energy is always compensated by another contribution to the energy of the magnetic field in such a way that the sum of the two is independent of the external flux. Therefore no such mechanism can underlie the Aharonov-Bohm effect.