The Aharonov-Bohm effect can be explained using local force fields
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CONTESTED
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refutedsupported
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Scientific literature presents conflicting arguments regarding whether the Aharonov-Bohm effect can be explained via local fields or forces; some studies and references support local descriptions or gauge-invariant local phases, whereas other experimental evaluations conclude the results cannot be explained by the action of a force.
In the Aharonov-Bohm (AB) effect, interference fringes are observed for a charged particle in the absence of the local overlap with the external electromagnetic field. This notion of the apparent “nonlocality” of the interaction or the significant role of the potential have recently been challenged and are under debate. The quantum electrodynamic approach provides a microscopic picture of the characteristics of the interaction between a charge and an external field. We explicitly show the gauge invariance of the local phase shift in the magnetic AB effect, which is in contrast to the results obtained using the usual semiclassical vector potential. Our study can resolve the issue of the locality in the magnetic AB effect. However, the problem is not solved in the same way in the electric counterpart wherein virtual scalar photons play an essential role.
The Aharonov-Bohm effect is a fundamental issue in physics that has been extensively studied in the literature and is discussed in most of the textbooks in quantum mechanics. The issues at stake are what are the fundamental electromagnetic quantities in quantum physics, if magnetic fields can act at a distance on charged particles and if the magnetic potentials have a real physical significance. The Aharonov-Bohm effect is a very controversial issue. From the experimental side the issues were settled by the remarkable experiments of Tonomura et al. (Phys Rev Lett 48:1443–1446, 1982; Phys Rev Lett 56:792–795, 1986) with toroidal magnets that gave a strong experimental evidence of the physical existence of the Aharonov-Bohm effect, and by the recent experiment of Caprez et al. (Phys Rev Lett 99:210401, 2007) that shows that the results of the Tonomura et al. experiments can not be explained by the action of a force. Aharonov and Bohm (Phys Rev 115:485-491, 1959) proposed an Ansatz for the solution to the Schrödinger equation in simply connected regions of space where there are no electromagnetic fields. It consists of multiplying the free evolution by the Dirac magnetic factor. The Aharonov-Bohm Ansatz predicts the results of the experiments of Tonomura et al. and of Caprez et al. Recently in Ballesteros and Weder (Math Phys 50:122108, 2009) we gave the first rigorous proof that the Aharonov-Bohm Ansatz is a good approximation to the exact solution for toroidal magnets under the conditions of the experiments of Tonomura et al. We provided a rigorous, simple, quantitative, error bound for the difference in norm between the exact solution and the Aharonov-Bohm Ansatz. In this paper we prove that these results do not depend on the particular geometry of the magnets and on the velocities of the incoming electrons used on the experiments, and on the gaussian shape of the wave packets used to obtain our quantitative error bound. We consider a general class of magnets that are a finite union of handlebodies. Each handlebody is diffeomorphic to a torus or a ball, and some of them can be patched though the boundary. We formulate the Aharonov-Bohm Ansatz that is appropriate to this general case and we prove that the exact solution to the Schrödinger equation is given by the Aharonov-Bohm Ansatz up to an error bound in norm that is uniform in time and that decays as a constant divided by vρ, 0 < ρ < 1, with v the velocity. The results of Tonomura et al., of Caprez et al., our previous results and the results of this paper give a firm experimental and theoretical basis to the existence of the Aharonov-Bohm effect and to its quantum nature. Namely, that magnetic fields act at a distance on charged particles, and that this action at a distance is carried by the circulation of the magnetic potential which gives a real physical significance to magnetic potentials.
The Aharonov-Bohm effect is one of the most comprehensible examples of quantum non-locality. The so called molecular Aharonov-Bohm effect displays great similarities with the latter, but still, we show how this effect can be explained using arguments relying solely on locality, whereby we mean that the effect can be traced down to a force acting locally on the phase space distribution. Our method hinges on studying the system in its momentum representation, and introducing a "conjugate gauge potential" which render an everywhere non-zero synthetic magnetic field. The resulting Lorenz force induces a transverse current which can be attributed the equivalence of an intrinsic spin Hall effect. The idea is demonstrated for the linear Exe Jahn-Teller model and applied to the Li3 molecule, for which its corresponding Hamiltonian is obtained by diabatization of ab intio determined adiabatic potential energy surfaces.
This paper presents a hydrodynamical view of the Aharonov-Bohm effect, using Nelson's formulation of quantum mechanics. Our aim is to compare our results with other systems and gain a better understanding of the mysteries behind this effect, such as why the motion of a particle is affected in a region where there is no magnetic field. Some theories suggest that this effect is due to the non-local action of the magnetic field on the particle, or even the physical significance of vector potentials over magnetic fields. Our main purpose is to use Nelson's formulation to describe the effect and demonstrate that it can be explained by the direct action of the current surrounding the magnetic field region (i.e. a cylinder) on the particle outside of it. In this context, magnetic fields and vector potentials serve as tools for finding other fundamental quantities that arise from the interaction between two fields: the quantum background fields described by Nelson's quantum theory. Finally, we investigate the relationship between hidden variables and quantum fluctuations and their role in this phenomenon.
in the well-known interference patterns. Also the shift of the interference pattern which occurs in presence of a magnetic field in the Aharonov–Bohm effect
The quantum potential or quantum potentiality is a central concept of the de Broglie–Bohm formulation of quantum mechanics, introduced by David Bohm in 1952.
Initially presented under the name quantum-mechanical potential, subsequently quantum potential, it was later elaborated upon by Bohm and Basil Hiley in its interpretation as an information potential which acts on a quantum particle. It is al
Also the shift of the interference pattern which occurs in presence of a magnetic field in the Aharonov–Bohm effect could be explained as arising from the quantum potential.
Recent work by Vaidman [Phys. Rev. A 86,040101 (2012)] showed that Aharonov-Bohm effect can be explained in terms of local fields, thus effectively restating an old problem of physicality of potentials. In this work, we propose an argument demonstrating the physicality of electromagnetic potential (upon the assumption of locality) based on the causal structure in flux quantization setup. Crucially, we discuss the fundamental difference between the considered setup and the Aharonov-Bohm experiment that allows for avoiding Vaidman's loophole in our scenario.
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