The Aharonov-Bohm (AB) effect, wherein an electron acquires a phase shift in a field-free region due to electromagnetic potentials, poses a profound challenge to the ontology of quantum mechanics and gauge theories. This paper demonstrates that gauge-invariant explanations, which attribute the phase to measurable quantities, rely on nonlocal and discontinuous mechanism and fail to account for its continuous accumulation along the electron's path—a process evident in the generalized AB effect, where a time-varying magnetic flux induces a phase that builds gradually over time, as predicted by quantum mechanics. Through a new analysis spanning quantum mechanics and quantum electrodynamics, I argue that the electromagnetic potentials
Aμ, fixed in the Lorenz gauge, emerge as the fundamental physical reality, offering a local, relativistically consistent account of the phase’s generation. This exclusion of gauge-invariant paradigms reverberates across gauge theories: it redefines the Higgs mechanism, favoring dynamic potentials over static invariants, and extends to general relativity, where gravitational potentials
gμν may anchor spacetime’s substantival reality via a gravitational AB effect. By unraveling the AB phase’s continuous generation—locally mediated by potentials—this study not only addresses a long-standing conundrum but also bridges electromagnetic, gravitational, and Yang-Mills frameworks, offering a unified potential-centric perspective with novel implications for physics and philosophy.
The Aharonov-Bohm (AB) effect highlights the fundamental role of electromagnetic potentials in quantum mechanics, manifesting as a phase shift for a charged particle in field-free regions. While well-established for static magnetic fluxes, the effect's behavior under time-varying fluxes remains an open and debated question. Employing the WKB method, we derive the AB phase shift for a time-dependent magnetic vector potential, demonstrating that for circular paths in the quasistatic regime, it is proportional to the time-averaged enclosed magnetic flux,
ΔφAB=T1∫0TeΦ(t)dt, with the total phase shift, including kinetic contributions, equaling
eΦ(0). For non-circular paths, the phase shift depends on both the flux history and path geometry, revealing the effect's hybrid nature involving gauge potentials and induced electric fields. We verify the consistency of our gauge choice with Maxwell's equations and discuss the implications for local versus nonlocal interpretations of the AB effect. We also generalize the results to scenarios with nonzero external magnetic fields, where the enclosed flux is through the actual electron paths, and for circular paths of radius
R, the AB phase shift is also proportional to the time average of the enclosed flux
Φenc(R,t), with the total phase shift depending only on the initial enclosed flux
eΦenc(R,0); for general non-circular paths, the external magnetic field affects trajectories and phase accumulation through the Lorentz force, leading to additional path dependence. These findings clarify the role of gauge-dependent potentials and induced fields in the generalized AB effect, offering new theoretical insights and potential applications in quantum technologies.
We discuss two possible covariant generalizations of the Aharonov–Bohm effect – one expression in terms of the space–time line integral of the four-vector potential and the other expression in terms of the space–time “area” integral of the electric and magnetic fields written in terms of the Faraday 2-form. These expressions allow one to calculate the Aharonov–Bohm effect for time-dependent situations. In particular, we use these expressions to study the case of an infinite solenoid with a time varying flux and find that the phase shift is zero due to a cancellation of the Aharonov–Bohm phase shift with a phase shift coming from the Lorentz force associated with the electric field, E=−∂tA, outside the solenoid. This result may already have been confirmed experimentally.
We investigate the gravitational Aharonov-Bohm effect by placing a quantum system in free fall around a gravitating body, e.g., a satellite orbiting the Earth. Since the system is in free fall, by the equivalence principle, the quantum system is local in flat, gravity free space-time---it is screened from the gravitational field. For a slightly elliptical orbit, the gravitational potential will change with time. This leads to the energy levels of the quantum system developing sidebands which is the signature for this version of the Aharonov-Bohm effect. This contrasts with the normal signature of the Aharonov-Bohm effect of shifting of interference fringes.
The Aharonov-Bohm (AB) effect highlights the fundamental role of electromagnetic potentials in quantum mechanics. While extensively studied in the static case, the impact of a time-varying magnetic flux on the electron's phase shift remains an open and debated question. In this paper, we derive the AB phase shift for a time-dependent magnetic vector potential and show that it is proportional to the time average of enclosed magnetic flux. Our analysis reveals that the AB phase is continuously accumulated as the electron traverses its path, challenging the conventional view that it emerges instantaneously at the point of interference. This generalized AB effect may provide deeper insight into the role of gauge-dependent potentials in quantum mechanics and also suggest novel experimental tests using alternating or pulsed magnetic flux.