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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Land, M.C. The Classical Coulomb Problem in Pre-Maxwell Electrodynamics. Foundations of Physics 28, 1489–1497 (1998). https://doi.org/10.1023/A:1018865413499
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DOI: https://doi.org/10.1023/A:1018865413499