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Nuovo cimento della Società italiana di fisica. A, Nuclei, particles and fields

The role of the electromagnetic potentials in quantum mechanics. The marton experiment

P. Bocchieri, A. Loinger, Giovanni Siragusa

Published May 1, 1980• 29 citations
Publisher
DOI
10.1007/bf02729980

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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.
A new theorem about the interference between particle beams is established. The Collela-Overhauser-Werner and Marton experiments are theoretically explained with a theorem established by Chiu and Stodolsky. The Feynman theory is applied to obtaining the propagator for a particle beam in a gravitational field, and the Collela-Overhauser-Werner experiment is further analyzed. Another theorem, established by Chiu and Stodolsky, and our new theorem are proved with the method of Feynman's path integrals.
In this paper, we demonstrate novel relationships between quantum mechanics and the electromagnetic wave equation. In our approach, an invariant interference-dependent electromagnetic quantity, which we call "quantum rest mass", replaces the conventional role of the inertial rest mass. In the ensuing results, photons, during interference, move slower than the speed of light in vacuum, and possess de Broglie wavelength. Further, we use our electromagnetic approach to examine double-slit photon trajectories, and to arrive at the Schrodinger equation's results for a particle in an infinite square well potential.