The Aharonov-Bohm Effect

"AB showed that one of the results of elementary quantum theory is that there are physical effects on charged particles in regions in which the electromagnetic field is nonexistant. The controversial features of the AB effect concern its interpretation; there is no disagreement as to the effect itself. The interpretation problem arises because the charge particles are influenced although they always move in field free regions. Hence the key question of the AB effect concerns localization and action-at-a-distance. AB claimed a special significance for the electromagnetic potentials because they are non-zero 'where the action is,' whereas the fields are zero in the regions to which the charged particles are confined."

Herman Erlichson, Erlichson, 1970