Relativistic analysis of application of Helmholtz theorem to classical electrodynamics - Chubykalo, Andrew; Alvarado-Flores, R.; Espinoza, A. (JOURNAL OF ADVANCES IN PHYSICS, 2014)
In this work we discuss the relationship between the instantaneous-action-at-a-distance solutions of Maxwells equations obtained using Helmholtz theorem and the Lorentzs invariant solutions of the same equations obtained using Special Relativity postulates. We show that Special Relativity postulates are not consistent with Helmholtzs theorem in the presence of charges and currents, but in the vacuum, without charges and currents, Helmholtzs theorem and Special Relativity agree because the instantaneous-action-at-a-distance solutions can be eliminated using a gauge transformation.