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Why Aharonov-Bohm Effect Does Not Violate Locality Principle

Alexander V. Gritsunov

Published Jan 1, 2013• 1 citation
OpenAlex

Abstract

Two hypotheses concerning the Lagrange function postulating for a system with electromagnetic interactions: (classic) and (new) are compared. It is shown that the gradient hypothesis, unlike the vortex one, does not result in conflict between the Aharonov-Bohm (AB) effect and the locality principle. A modification of AB effect in Zero Magnetic (ZM) oscillation of potential around excited closed waveguide is predicted.

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Journal of Energy and Power Engineering•Jun 28, 2024•1 citation
Two hypotheses concerning the Lagrange function postulating for a system with electromagnetic interactions: (classic) and (new) are compared. It is shown that the gradient hypothesis, unlike the vortex one, does not result in conflict between the Aharonov-Bohm (AB) effect and the locality principle. A modification of AB effect in Zero Magnetic (ZM) oscillation of potential around excited closed waveguide is predicted.
The locality principle fulfillment in the Aharonov-Bohm (AB) effect is analyzed from the point of view of a self-sufficient potential formalism based on so-called gradient hypothesis in electrodynamics. The "magnetic" kind of AB effect is examined (as the quantum charged particle moves to an infinitely long solenoid with a permanent current), and no locality principle violation recognized if the gradient hypothesis is used. A conclusion is made that AB effect is no longer a physical and electrodynamic "paradox".
We propose a quantitative test of the quantum locality in the electromagnetic interaction that generates the Aharonov-Bohm effect. For this purpose, we analyze the Lorentz-covariant field interaction approach based on the local action of gauge-invariant quantities only (“local” theory), and compare it with the standard potential-based (“nonlocal”) theory. Whereas the two approaches yield identical results for topological phase and any phenomenon involving classical equation of motion, an example violating this equivalence is presented; interference of the Andreev reflections from two independent superconducting inputs into a single normal metallic output. A well-defined phase shift of the interference is predicted in the “local” theory. In contrast, the potential-based Lagrangian fails the corresponding prediction. This result is significant as it can settle the issue of quantum locality in the electromagnetic interaction.
A field-interaction scheme is introduced for describing the Aharonov-Bohm effect, fully consistent with the principle of relativity. Our theory is based on the fact that local field interactions are present even when a particle moves only in a field-free region. The interaction Lagrangian between a charge and a flux is uniquely constructed from three principles: Lorentz covariance, linearity in the interaction strength, and a correct stationary limit of charge. Our result resolves fundamental questions raised on the standard interpretation of the Aharonov-Bohm effect, concerning its duality with the Aharonov-Casher effect and the equivalence between the potential and the field-interaction models for describing the electromagnetic interaction. Most of all, potential is eliminated in our theory, and all kind of the force-free Aharonov-Bohm effect is understood in a unified framework of the Lorentz-covariant local interaction of electromagnetic fields.
We propose a quantitative test of the quantum nonlocality in the electromagnetic interaction that generates the Aharonov-Bohm effect. For this purpose, we derive an interaction Lagrangian based on the local action of gauge-invariant quantities only, and compare it with the standard potential-based (nonlocal) Lagrangian. It is shown that the two models provide identical results for any phenomena involving classical equations of motion or topological quantum phases. Interestingly, we find an example violating this equivalence, that is, the interference of single charges coproduced from two independent sources. The two models yield different predictions of the interference fringe produced by the electromagnetic interaction and, therefore, one can decide which model is appropriate for describing the electromagnetic interaction in general. This result has profound implications as it can settle the issue of dynamical nonlocality in the quantum electromagnetic interaction.
We propose a quantitative test of the quantum nonlocality in the electromagnetic interaction that generates the Aharonov-Bohm effect. For this purpose, we derive an interaction Lagrangian based on the action of gauge-invariant quantities only, and compare it with the standard potential-based (nonlocal) Lagrangian. It is shown that the two models provide identical results for any phenomena involving classical equations of motion or topological quantum phases. Interestingly, we find an example violating this equivalence, that is, the interference of single charges coproduced from two independent sources. Whereas a well-defined phase shift of the interference is predicted in the local model, the standard nonlocal Lagrangian does not provide a gauge-invariant phase shift. This implies that an observation of the interference in the proposed setup can rule out the gauge-dependent potential-based model. This result has profound implications as it can settle the issue of dynamical nonlocality in the quantum electromagnetic interaction.
The AB (Aharonov-Bohm) effect is a pivotal quantum mechanical phenomenon that illustrates the fundamental role of the electromagnetic vector potential A in determining the phase of a charged particle's wave function, even in regions where the magnetic field B is zero.This effect demonstrates that quantum particles are influenced not only by the fields directly present but also by the potentials associated with those fields.In the AB effect, an electron beam is split into two paths, with one path encircling a solenoid and the other bypassing it.Despite the absence of a magnetic field in the regions traversed by the beams, the vector potential A associated with the magnetic flux  through the solenoid induces a phase shift in the electron's wave function.This phase shift, quantified by qc     , manifests as a change in the interference pattern observed in the detection screen.The phenomenon underscores the principle of gauge invariance in QED (quantum electrodynamics), where physical observables remain invariant under local gauge transformations of the vector and scalar potentials.This reinforces the notion that the vector potential A has a profound impact on quantum systems, beyond its classical role.This article outlines the AB effect, including its theoretical framework, experimental observations, and implications.The focus on the role of the vector potential in quantum mechanics provides a comprehensive understanding of this important phenomenon.