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)]

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.Comment: An alternative discussion can be found in the paper: Jose A. Heras, "How potentials in different gauges yield the same retarded electric and magnetic fields," Am. J. Phys. 75, 176-183 (2007

A short proof that the Coulomb-gauge potentials yield the retarded fields

A short demonstration that the potentials in the Coulomb gauge yield the retarded electric and magnetic fields is presented. This demonstration is relatively simple and can be presented in an advanced undergraduate curse of electromagnetic theory