  It is frequently stated that the electromagnetic vector potential acquires a
fundamental role in quantum physics, whereas classically it only represents a
convenient, but by no means necessary, way of representing the electromagnetic
field. Here we argue that this is a historical accident due to the fact that
the electromagnetic field was discovered before photons, while the electron
itself was discovered first as a particle, before it became clear that it must
also be treated as a wave and therefore as an excitation of the underlying
electron field. We illustrate the fact that the vector potential ought to play
a fundamental role classically using the Aharonov-Bohm effect. This effect is
considered as the strongest argument for the role the vector potential plays in
quantum physics, however, here we offer a fully classical account of it. This
is a consequence of the fact that any account, be it classical or quantum, must
involve the vector potential in order to preserve the local nature of the
Aharonov-Bohm (as well as all the other) phases.
