2014/08/16 by Timothy H. Boyer, Boyer, Timothy H. · 1 citation
Physics and Astronomy · #Classical Physics (physics.class-ph) #FOS: Physical sciences #Gyrotron and Vacuum Electronics Research #Mechanical and Optical Resonators #Quantum Physics (quant-ph) #Quantum, superfluid, helium dynamics #physics.class-ph #quant-ph
paper · pdf · doi:10.48550/arxiv.1408.3745
39 pages This paper has been withdrawn by the author due to a sign error in Eq. (75)
openalex publication_date 2014/08/16 · arxiv created 2014/08/26 · arxiv updated 2014/08/27 · openalex created_date 2022/10/07 · openalex updated_date 2026/07/28
A new classical electromagnetic analysis is presented suggesting that the Aharonov-Bohm phase shift is overwhelmingly likely to arise from a classical lag effect based upon classical electromagnetic forces. The analysis makes use of several aspects of classical electromagnetic theory which are unfamiliar to most physicists, including the Darwin Lagrangian, acceleration-based electric fields, internal electromagnetic momentum in a magnet, and a magnet model involving at least three mutually-interacting particles. Only when the acceleration-based electric forces acting on the passing charge are included do we find consistency with all the relativistic conservation laws: energy, linear momentum, angular momentum, and constant center-of-mass velocity. The electric forces on the passing charge lead to a lag effect which accounts quantitatively for the Aharonov-Bohm phase shift. Thus the classical analysis strongly suggests that the Aharonov-Bohm phase shift (observed when electrons pass a long solenoid which corresponds to a line of magnetic dipoles) is the analogue of the Matteucci-Pozzi phase shift (observed when electrons pass a line of electric dipoles). The classical electromagnetic analysis suggests experiments to distinguish the proposed classical-based lag effect from the presently accepted view that the Aharonov-Bohm phase shift is a quantum topological effect arising from magnetic fluxes in the absence of classical electromagnetic forces.