Contradiction Between Classical and Quantum Physics for the Aharonov–Bohm Deflection Direction

Although the magnitude of the shift in the double-slit interference pattern when two electron beams pass outside a long solenoid has been confirmed in beautiful experiments, the direction of the deflection does not seem to appear in the published literature. It is claimed that careful quantum analysis gives a deflection direction opposite from that given by a classical electrodynamic analysis. Here we give a classical analysis of the interaction, and emphasize that the angle of deflection does not involve Planck’s constant. It is again suggested that a classical lag effect of order \(1/c^{2}\) forms the basis for the observed shift in the particle interference pattern. The effect is claimed to be the analogue of a nonrelativistic electric effect, and the analogous magnetic and electric forces are given for the two different situations. The magnetic interaction is considered in two different inertial frames where different electromagnetic fields are involved. An optical analogy is also mentioned. Finally, we note that electromagnetic fluctuations might wash out the lag effect for macroscopic solenoids.