Comment on 'Helmholtz theorem and the v-gauge in the problem of superluminal and instantaneous signals in classical electrodynamics,' by Chubykalo et al [Found. of Phys. Lett, 19, 37-46 (2006)]

Abstract

Fundamental errors in the Chubykalo et al paper [Found. of Phys. Lett, 19, 37-46 (2006)] are highlighted. Contrary to their claim that "... the irrotational component of the electric field has a physical meaning and can propagate exclusively instantaneously," it is shown that this instantaneous component is physically irrelevant because it is always canceled by a term contained into the solenoidal component. This result follows directly from the solution of the wave equation that satisfies the solenoidal component. Therefore the subsequent inference of these authors that there are two mechanisms of transmission of energy and momentum in classical electrodynamics, one retarded and the other one instantaneous, has no basis. The example given by these authors in which the full electric field of an oscillating charge equals its instantaneous irrotational component on the axis of oscillations is proved to be false.