Beyond the Dirac phase factor: Dynamical Quantum Phase-Nonlocalities in the Schr\"odinger Picture

TL;DR

This paper introduces generalized gauge solutions that reveal nonlocal quantum phase behaviors, explaining Aharonov-Bohm phenomena and preserving causality, thus addressing longstanding paradoxes and misconceptions in quantum theory.

Contribution

It presents a new class of solutions beyond Dirac phases, elucidating nonlocal quantum effects and resolving causality issues in Aharonov-Bohm phenomena.

Findings

Nonlocal phase behaviors explain Aharonov-Bohm effects.

Cancellation of phases preserves relativistic causality.

Corrects sign-errors and clarifies semiclassical vs quantum results.

Abstract

Generalized solutions of the standard gauge transformation equations are presented and discussed in physical terms. They go beyond the usual Dirac phase factors and they exhibit nonlocal quantal behavior, with the well-known Relativistic Causality of classical fields affecting directly the phases of wavefunctions in the Schr\"odinger Picture. These nonlocal phase behaviors, apparently overlooked in path-integral approaches, give a natural account of the dynamical nonlocality character of the various (even static) Aharonov-Bohm phenomena, while at the same time they seem to respect Causality. For particles passing through nonvanishing magnetic or electric fields they lead to cancellations of Aharonov-Bohm phases at the observation point, generalizing earlier semiclassical experimental observations (of Werner & Brill) to delocalized (spread-out) quantum states. This leads to a correction of previously unnoticed sign-errors in the literature, and to a natural explanation of the deeper reason why certain time-dependent semiclassical arguments are consistent with static results in purely quantal Aharonov-Bohm configurations. These nonlocalities also provide a remedy for misleading results propagating in the literature (concerning an uncritical use of Dirac phase factors, that persists since the time of Feynman's work on path integrals). They are shown to conspire in such a way as to exactly cancel the instantaneous Aharonov-Bohm phase and recover Relativistic Causality in earlier " paradoxes" (such as the van Kampen thought-experiment), and to also complete Peshkin's discussion of the electric Aharonov-Bohm effect in a causal manner. The present formulation offers a direct way to address time-dependent single- vs double-slit experiments and the associated causal issues -- issues that have recently attracted attention, with respect to the inability of current theories to address them.