The Aharonov-Bohm Effect: Solved
James Mattingly, Philosophy
Department of Philosophy
Georgetown University

Abstract: Work in the foundations of gauge theory is of two general sorts.  On the one hand is work that addresses the methodological aspects of our use of gauge theories in contemporary physics---included within this class is the vast body of technical results produced over the past half century.  On the other hand is work on what might be called metaphysical foundations of gauge theory.  While highly interesting and technically rich, this work is predicated on an error, a claim made by Aharonov and Bohm and subsequently assumed as the foundational for all subsequent work in the metaphysics of gauge theory.  The error is the supposition that either gauge potentials or non-local action of field quantities are required to explain the empirical features of our premiere gauge theory, quantum electrodynamics, especially the Aharonov-Bohm effect.  In fact the effect can be explained by plain old local field strength quantities.  I explain how this works, why it matters, and why it has been so difficult to see the obvious solution to the difficulty. And part of the answer to the question of what isn't there: Gauge fields which are, after all mere calculational devices.