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Physical Review Letters

Aharonov-Bohm Effect from the "Hydrodynamical" Viewpoint

Giulio Casati, Italo Guarneri

Published Jun 11, 1979• 34 citations
Publisher

Abstract

It is shown that the adoption of the hydrodynamical viewpoint in quantum mechanics provides a way to explain experimental results while giving electromagnetic potentials no more physical significance than they have in classical physics.
DOI
10.1103/physrevlett.42.1579

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Hamilton-Jacobi equation which governs classical mechanics and electrodynamics explicitly depends on the electromagnetic potentials (A,ϕ), similar to Schroedinger equation. We derived the Aharonov-Bohm effect from Hamilton-Jacobi equation thereby having proved that this effect is of classical origin. These facts enable us to arrive at the following conclusions: a) the very idea of special role of potentials (A,ϕ) in quantum mechanics (different from their role in classical physics) lost the ground, and becomes dubious, as this idea is based on the Aharonov-Bohm effect, b) failure to find any signs of a special role of these potentials in the appropriate experiments (Feinberg, 1963) is thereby explained, and c) discovery of classical analogues of the Aharonov-Bohm effect (Berry et al., 1980) is also explained by a classical nature of this effect. Elucidation of the "unlocal" interaction problem was made.