Gao, Shan (2026) Impossibility of Gauge-Invariant Explanations of the Aharonov–Bohm Effect. [Preprint]

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Abstract

We present a rigorous no-go theorem that excludes \emph{all} gauge-invariant dynamical explanations of the generalized, time-dependent Aharonov--Bohm (AB) effect. In this generalization, the AB phase is determined by the time-averaged magnetic flux enclosed by the particle's path, $\Delta \phi_{\mathrm{AB}} = \frac{e}{\hbar} \cdot \frac{1}{T} \int_0^T \Phi(t) \, dt$. Using a carefully designed protocol in which a constant flux $\Phi$ persists only for a finite interval $\Delta t$ after wavepacket splitting and is switched to zero before detection, we demonstrate that during the phase-generating period all gauge-invariant observables of the electron remain identical to those in a zero-flux experiment. Relativistic causality further prohibits backreaction from the source. Consequently, no gauge-invariant quantity---whether local or nonlocal, field-based or source-mediated---can account for the observed phase, which depends solely on flux history. We also critically examine Healey's holonomy interpretation and show that it, too, fails to explain the time-dependent AB effect, as its static formalism lacks the dynamical structure needed to capture temporal averaging. This result establishes the inescapable physical reality of gauge potentials in quantum theory and clarifies the foundational status of the AB effect as a genuine manifestation of potentials rather than fields.

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Item Type:	Preprint
Creators:	Creators Email ORCID Gao, Shan sgao7319@uni.sydney.edu.au
Keywords:	Aharonov–Bohm Effect, generalized AB effect, gauge-invariant explanations, time-averaged magnetic flux, holonomy interpretation, reality of gauge potentials
Subjects:	Specific Sciences > Physics > Classical Physics Specific Sciences > Physics > Quantum Mechanics Specific Sciences > Physics > Relativity Theory Specific Sciences > Physics > Symmetries/Invariances
Depositing User:	Prof. Shan Gao
Date Deposited:	12 Feb 2026 12:13
Last Modified:	12 Feb 2026 12:13
Item ID:	28224
Subjects:	Specific Sciences > Physics > Classical Physics Specific Sciences > Physics > Quantum Mechanics Specific Sciences > Physics > Relativity Theory Specific Sciences > Physics > Symmetries/Invariances
Date:	12 February 2026
URI:	https://philsci-archive.pitt.edu/id/eprint/28224

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