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.
Hamilton-Jacobi equation which governs classical mechanics and electrodynamics explicitly depends on the electromagnetic potentials (A,ϕ), similar to Schroedinger equation. We derived the Aharonov-Bohm effect from Hamilton-Jacobi equation thereby having proved that this effect is of classical origin. These facts enable us to arrive at the following conclusions: a) the very idea of special role of potentials (A,ϕ) in quantum mechanics (different from their role in classical physics) lost the ground, and becomes dubious, as this idea is based on the Aharonov-Bohm effect, b) failure to find any signs of a special role of these potentials in the appropriate experiments (Feinberg, 1963) is thereby explained, and c) discovery of classical analogues of the Aharonov-Bohm effect (Berry et al., 1980) is also explained by a classical nature of this effect. Elucidation of the "unlocal" interaction problem was made.