Relativistic analysis of application of Helmholtz theorem to classical electrodynamics
Journal: Journal of Advances in Physics (Vol.7, No. 1)Publication Date: 2014-12-26
Authors : Andrew Chubykalo; R. Alvarado-Flores; A. Espinoza;
Page : 1297-1308
Keywords : Helmholtz theorem; Lorentz gauge; space-time theories.;
Abstract
In this work we discuss the relationship between the instantaneous-action-at-a-distance solutions of Maxwell’s equations obtained using Helmholtz theorem and the Lorentz’s invariant solutions of the same equations obtained using Special Relativity postulates. We show that Special Relativity postulates are not consistent with Helmholtz’s theorem in the presence of charges and currents, but in the vacuum, without charges and currents, Helmholtz’s theorem and Special Relativity agree because the instantaneous-action-at-a-distance solutions can be eliminated using a gauge transformation.
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