Does the Aharonov–Bohm Effect Exist?
 Timothy H. Boyer
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Abstract
We draw a distinction between the Aharonov–Bohm phase shift and the Aharonov–Bohm effect. Although the Aharonov–Bohm phase shift occurring when an electron beam passes around a magnetic solenoid is wellverified experimentally, it is not clear whether this phase shift occurs because of classical forces or because of a topological effect occurring in the absence of classical forces as claimed by Aharonov and Bohm. The mathematics of the Schroedinger equation itself does not reveal the physical basis for the effect. However, the experimentally observed Aharonov–Bohm phase shift is of the same form as the shift observed due to electrostatic forces for which the consensus view accepts the role of the classical forces. The Aharonov–Bohm phase shift may well arise from classical electromagnetic forces which are simply more subtle in the magnetic case since they involve relativistic effects of the order v^{ 2 }/c^{ 2 }. Here we first review the experimentally observable differences between phenomena arising from classical forces and phenomena arising from the quantum topological effect suggested by Aharonov and Bohm. Second we point out that most discussions of the classical electromagnetic forces involved when a charged particle passes a solenoid are inaccurate because they omit the Faraday induction terms. The subtleties of the relativisitic v^{ 2 }/c^{ 2 } classical electromagnetic forces between a point charge and a solenoid have been explored by Coleman and Van Vleck in their analysis of the Shockley–James paradox; indeed, we point out that an analysis exactly parallel to that of Coleman and Van Vleck suggests that the Aharonov–Bohm phase shift is actually due to classical electromagnetic forces. Finally we note that electromagnetic velocity fields penetrate even excellent conductors in a form which is unfamiliar to many physicists. An ohmic conductor surrounding a solenoid does not screen out the magnetic field of the passing charge, but rather the timeintegral of the magnetic field is an invariant; this time integral is precisely what is involved in the classical explanation of the Aharonov–Bohm phase shift. Thus the persistence of the Aharonov–Bohm phase shift when the solenoid is surrounded by a conductor does not exclude a classical forcebased explanation for the phase shift. At present there is no experimental evidence for the Aharonov–Bohm effect.
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 Title
 Does the Aharonov–Bohm Effect Exist?
 Journal

Foundations of Physics
Volume 30, Issue 6 , pp 893905
 Cover Date
 20000601
 DOI
 10.1023/A:1003602524894
 Print ISSN
 00159018
 Online ISSN
 15729516
 Publisher
 Kluwer Academic PublishersPlenum Publishers
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 Authors

 Timothy H. Boyer ^{(1)}
 Author Affiliations

 1. Department of Physics, City College of the City University of New York, New York, New York, 10031