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arXiv:quant-ph/0408023

On the Claim of the Observation of 'Macro-quantum effects' of Magnetic Vector Potential in the Classical Domain

C. S. Unnikrishnan

Published Aug 3, 2004• 0 citations
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Abstract

I present conclusive arguments to show that a recent claim of observation of quantum-like effects of the magnetic vector potential in the classical macrodomain is spurious. The `one dimensional interference patterns' referred to in the paper by R. K. Varma et al (Phys. Lett. A 303 (2002) 114-120) are not due to any quantum-like wave phenomena. The data reported in the paper are not consistent with the interpretation of interference, or with the topology of the Aharonov-Bohm effect. The assertion that they are evidence of A-B like effect in the classical macrodomain is based on inadequate appreciation of basic physical facts regarding classical motion of electrons in magnetic fields, interference phenomena, and the A-B effect.

DOI
10.48550/arxiv.quant-ph/0408023

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I present conclusive arguments to show that a recent claim of observation of quantum-like effects of the magnetic vector potential in the classical macrodomain is spurious. The `one dimensional interference patterns' referred to in the paper by R. K. Varma et al (Phys. Lett. A 303 (2002) 114-120) are not due to any quantum-like wave phenomena. The data reported in the paper are not consistent with the interpretation of interference, or with the topology of the Aharonov-Bohm effect. The assertion that they are evidence of A-B like effect in the classical macrodomain is based on inadequate appreciation of basic physical facts regarding classical motion of electrons in magnetic fields, interference phenomena, and the A-B effect.
I show that the claim of the observation of matter wave beat phenomena in the classical macrodomain by Varma et al. [Phys. Rev. E 65, 026503 (2002)] is based on a mistaken interpretation of effects arising from multiple focusing of an electron beam in an axial magnetic field. I present the basic physical facts that mimic wavelike phenomena and suggest a classical explanation of modulations reported by Varma et al. Realization that the macroscopic "de Broglie wavelength" used by Varma et al. is the same as the focusing distance of a monoenergetic electron beam in the uniform magnetic field leads to a full classical explanation of all the effects reported by Varma et al. The reported observations are not evidence for any quantumlike phenomenon in the macrodomain, and their results do not indicate any violation of the Lorentz equation of motion.
The recently reported curl-free vector potential observation (Varma et al 2012 Eur. Phys. J. D 66 38) in relation to a system of charged particles in a magnetic field points to the existence of a new state of the electron—a quantum modulated state—which arises through a scattering-induced transition across Landau levels. This quantum modulated state has been shown to account for some very unusual effects on the macro-scale, which are distinct from the ones which can be understood in terms of a 'classical electron' and also from the ones which can be understood in terms of a 'quantum electron' on the micro-scale characterized by the Planck quantum. This quantum modulated state has been shown to account for the observation of a static curl-free vector potential on the macro-scale alluded to above, as well as other matter wave manifestations on the macro-scale. The macro-scale curl-free vector potential observation differs fundamentally from the corresponding micro-scale effect—the well-known Aharonov–Bohm effect. These two effects—on the macro-scale and the macro-scale—are compared and contrasted to each other here in their manner of detection of the static curl-free vector potential. Such a comparative study helps gain a deeper understanding of the nature of the quantum modulated state and the macro-scale matter wave it represents.
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.
It is frequently stated that the electromagnetic vector potential acquires a fundamental role in quantum physics, whereas classically it only represents a convenient, but by no means necessary, way of representing the electromagnetic field. Here we argue that this is a historical accident due to the fact that the electromagnetic field was discovered before photons, while the electron itself was discovered first as a particle, before it became clear that it must also be treated as a wave and therefore as an excitation of the underlying electron field. We illustrate the fact that the vector potential ought to play a fundamental role classically using the Aharonov-Bohm effect. This effect is considered as the strongest argument for the role the vector potential plays in quantum physics, however, here we offer a fully classical account of it. This is a consequence of the fact that any account, be it classical or quantum, must involve the vector potential in order to preserve the local nature of the Aharonov-Bohm (as well as all the other) phases.
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