Theories without AB effect Misrepresent the Dynamics of the Electromagnetic Field

Abstract

The suggestion by Professor Bocchieri, Professor Loinger, and others¹ that the Aharonov-Bohm effect (AB) is not part of quantum mechanics or that it can be removed from quantum mechanics without ruining the theory, is an important one for many reasons. One reason which has perhaps been too little emphasized is that removing AB scattering from the theory would remove the justification for Dirac’s charge quantization law

$$ \frac{{eg}}{c} = \frac{n}{2}\hbar, $$

((1))

where e and g are the elementary units of electric and magnetic charge and n is an integer. In this discussion I shall summarize arguments that have been given in detail elsehwere^2,3 to show why AB cannot in fact be removed from the theory except by spoiling the conservation and quantization of angular momentum. It is of course no coincidence that the most general proofs of Dirac’s charge quantization law also rely mainly on the quantization of angular momentum.⁴ I will not deal with that in this talk, but I will return briefly in an appendix to the relation between AB and Dirac’s original derivation of the charge quantization law from the now-familiar singular strings.