Abstract

The Aharonov-Bohm effect is a celebrated quantum mechanical effect which some have claimed is an example of non-locality, i.e., of action at a distance. This thesis examines the theory and experimental tests of the effect, and compares it to another supposed example of non-locality, the EPR correlations. ;The role of the electromagnetic potentials in the quantum formalism, and especially gauge invariance and the physical significance of the vector potential, is detailed. I argue that K. H. Yang's proofs of the gauge arbitrariness of the conventional formalism are mistaken. Four central and conflicting theories of the AB effect are reviewed and critiqued: physically significant potentials, local effects of electromagnetic fluxes, multi-valued wave functions, and non-locality. An entire chapter is devoted to the topological interpretations of the effect which model the potentials as connections in higher-dimensional fiber bundle geometries. The relation between the AB effect and geometric phase phenomena, like Berry's phase, is studied. The new geometric models inherit the merits and demerits of the potentials interpretation. The quantum no-signalling proofs for the case of the EPR-Bohm-Bell experiments are analyzed and unified in a single theorem: they are simple consequences of the tenstor product representation of combined quantum systems. ;All proposed local theories of the AB effect are finally unsatisfactory--for a variety of reasons. However, given the lack of a clear criterion for non-locality, there are no decisive grounds for the claim that the AB effect is non-local