Aharonov-Bohm Effect and Coordinate Transformations

Abstract

Resorting to a Gedankenexperiment which is very similar to the famous Aharonov-Bohm proposal it will be shown that, in the case of a Minkowskian spacetime, we may use a nonrelativistic quantum particle and a noninertial coordinate system and obtain geometric information of regions that are, to this particle, forbidden. This shows that the outcome of a nonrelativistic quantum process is determined not only by the features of geometry at those points at which the process takes place, but also by geometric parameters of regions in which the quantum system can not enter. From this fact we could claim that geometry at the quantum level plays a non-local role. Indeed, the measurement outputs of some nonrelativistic quantum experiments are determined not only by the geometry of the region in which the experiment takes place, but also by the geometric properties of spacetime volumes which are, in some way, forbidden in the experiment.