The Classical Coulomb Problem in Pre-Maxwell Electrodynamics

Foundations of Physics 28 (9):1489-1497 (1998)
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Abstract

We explore certain difficulties in the covariant classical mechanics associated with off-shell electrodynamics, through an examination of the classical Coulomb problem. We present a straightforward solution of the classical equations of motion for a test event traversing the field induced by a “fixed” event (an event moving uniformly along the time axis at a fixed point in space). This solution reveals the essential difficulties in the formalism at the classical level. We then offer a new model of the particle, as a certain distribution of events on the worldline, which eliminates these difficulties and permits comparison of classical off-shell electrodynamics with the standard Maxwell theory In this model, the “fixed” event induces a Yukawa-type potential, permitting a semiclassical identification of the pre-Maxwell time scale λ with the inverse mass of the intervening photon. Numerical solutions to the equations of motion are compared with the standard Maxwell solutions—they are seen to coincide when λ > 10–6 sec, providing an initial estimate of this parameter

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Pre-Maxwell Electrodynamics.M. C. Land - 1998 - Foundations of Physics 28 (9):1479-1487.

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