  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.
