Prof. Timothy Boyer, CCNY

"Unresolved Classical Electromagnetic Aspects of the Aharonov-Bohm Phase Shift"

**Abstract:** The classical electromagnetic interaction of a point charge with a magnetic solenoid has been a subject of controversy for decades. The contro- versy extends to the interaction of a point charge with a magnetic dipole moment, since a solenoid can be regarded as a stack of magnetic dipoles. Experimental work has shown that a long solenoid placed between the beams of an electron interferometer produces a double-slit double-slit interference- pattern shift proportional to the current in the solenoid. However, experiment has not yet clarified whether or not the phase shift is due to classical electromagnetic forces and velocity changes for the passing particles or is due to quantum behavior with no classical analogue. We will discuss classical electromagnetic aspects of the interaction of a point charge with a magnetic dipole moment and with a solenoid, pointing out that induced changes in a magnetic dipole produce electromagnetic fields back at a passing charge. We will note the unfamiliar penetration of magnetic velocity fields into ohmic conductors, and we will point out a possible electrostatic analogue of the magnetic Aharonov-Bohm phase shift. Finally, we will mention planned experiments to clarify the fundamental basis for the Aharonov-Bohm phase shift. The outcome of the experiments will influence understanding of the connections between classical and quantum theories.