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arXiv:2105.07803

On the Interpretation of the Aharonov-Bohm Effect

Jay Solanki

Published May 14, 2021• 0 citations
arXivHTMLPDF

Abstract

The Aharonov-Bohm (A-B) effect showed that the phase of electron wave pattern could be changed by the excluded electromagnetic field, the region where electromagnetic field is zero. This apparent non-local effect has been explained by mainly two salient interpretations called "the interpretation of electromagnetic potentials" and "the interpretation of interaction energy". In this paper the author reviews and investigates both the interpretations and analysis their differences. Then the author clarifies in details and extend the approach of interaction energy interpretation and argue that as quantum mechanics involved energy of quantum systems and electromagnetic energy contained in electromagnetic field, the natural and more physically acceptable interpretation of the effect should be "the interpretation of interaction energy".

DOI
10.48550/arxiv.2105.07803

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The Aharonov-Bohm (A-B) effect showed that the phase of electron wave pattern could be changed by the excluded electromagnetic field, the region where electromagnetic field is zero. This apparent non-local effect has been explained by mainly two salient interpretations called "the interpretation of electromagnetic potentials" and "the interpretation of interaction energy". In this paper the author reviews and investigates both the interpretations and analysis their differences. Then the author clarifies in details and extend the approach of interaction energy interpretation and argue that as quantum mechanics involved energy of quantum systems and electromagnetic energy contained in electromagnetic field, the natural and more physically acceptable interpretation of the effect should be "the interpretation of interaction energy".
There are two interpretations of the Aharonov-Bohm (A-B) effect. One interpretation asserts that the A-B effect demonstrates that the vector potential is a physical reality that can result in the phase shift of a moving charge in quantum mechanics. The other interpretation asserts that the phase shift of the moving charge results from the interaction energy between the electromagnetic field of the moving charge and external electromagnetic fields. This paper briefly reviews these two interpretations and analyzes their differences. In addition, a new experimental scheme is proposed to determine which interpretation is correct.
There is a consensus today that the the main lesson of the Aharonov-Bohm effect is that a picture of electromagnetism based on the local action of the field strengths is not possible in quantum mechanics. Contrary to this statement, it is argued here that when the source of the electromagnetic potential is treated in the framework of quantum theory, the Aharonov-Bohm effect can be explained without the notion of potentials. It is explained by local action of the field of the electron on the source of the potential. The core of the Aharonov-Bohm effect is the same as the core of quantum entanglement: the quantum wave function describes all systems together.
The Aharonov-Bohm effect is a quantum mechanical effect, that is, has no classical counterpart. The effect was predicted in 1959 in a seminal paper of Y. Aharonov and D. Bohm [AB59] in which they demonstrated that a beam of electrons is affected by the existence of the electric/magnetic field even though electrons travel through field-free regions. Aharonov and Bohm carried out two hypothetical experiments to support their claim that potentials are more fundamental than fields and they are respon-sible of the effect. Since then, the debate has arisen around whether potentials are mathematical tools or fundamental entities in physics. Different arguments have been set to explain the results predicted by Aharonov and Bohm and experimentally confirmed. Amongst these arguments, the first argument adopted by Aharonov and Bohm was that potentials are physically significant. Many have claimed that fields do have non-local features, i.e. action at a distance. Others have claimed that topological effects may interpret the effect in which potentials are modeled as connections in higher-dimensional fiber bun-dle geometries. The most recent argument has been proposed by Vaidman [Vai12] who claimed that the the composite system is represented by one state, an entangled state, and due to the electromagnetic interactions part of this state is changed, hence, the total state. In the present essay, I will discuss the latter argument as well as reviewing some other arguments. i
This work presents an analysis of the Aharonov-Bohm effect taking into account both regions where the electron is present and where it is excluded, and also the time variations of the magnetic vector potential and the magnetic induction field as they change between two of their stationary values. This analysis allows the identification of the electrical force field induced in the region where the electron is present by the time variation of the magnetic flux in the region where the electron is excluded, thus providing a classical explanation of the changes in the stationary properties of the electron when the magnetic potential and field change from one set of stationary values to another. Some apparent contradictions in attempts to interpret the A-B effect are also discussed and clarified.
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.
The magnetic Aharonov-Bohm effect shows that charged particles may be affected by the vector potential in regions without any electric or magnetic fields [1]. The Aharonov-Bohm effect was experimentally confirmed [2-3] and has been found in many situations [4-6]. A common explanation is based on quantum mechanics, which states that the wavefunctions associated with the charges will accumulate a phase shift due to the vector potential. However, consensus about its nature and interpretation has not been achieved [7-14]. We here propose a simple but reasonable interpretation based on the theory for electromagnetic radiation and couplings [15]. The energy associated with a pulse radiator is divided into a Coulomb-velocity energy and a radiative energy, together with a macroscopic Schott energy accounting for the energy exchange between them. All these energies are expressed with terms including the potentials, so are the mutual coupling energies. There exists a force acting on the moving charges even though the fields completely vanish. This force makes the charges pass through the magnetic solenoid in different velocity with different path length, causing a phase shift the same as that obtained with quantum mechanics. The theory is originally aimed for providing an interpretation for electromagnetic radiation and mutual coupling. It is derived directly from the Maxwell theory with no modification but only substitution and reorganization.