Semiclassical Explanation of the Matteucci–Pozzi and Aharonov–Bohm Phase Shifts

When a line of dipoles is placed between the beams of electrons forming an interference pattern, there is a shift in the interference pattern. In the case of a line of electric dipoles, the interference pattern shift was observed experimentally by Matteucci and Pozzi. (1) In the case of a line of magnetic dipoles (a solenoid), the phase shift was suggested by Aharonov and Bohm (2) and was first observed experimentally by Chambers. (3) Both these phase shifts take the same experimental form and both allow semiclassical interpretations as arising from lag effects due to classical electromagnetic forces. Only the second phase shift is mentioned in the textbooks (4) because it is purported to occur in the absence of classical forces. Here we will sketch the parallels between the electric and magnetic phase shifts and then discuss the forces in the magnetic case.