Helmholtz theorem and the V-Gauge in the problem of superluminal and instantaneous signals in classical electrodynamics

Abstract

In this work we substantiate the applying of the Helmholtz vector decomposition theorem (H-theorem) to vector fields in classical electrodynamics. Using the H-theorem, within the framework of the twoparameter Lorentz-like gauge (so called v-gauge), we show that two kinds of magnetic vector potentials exist: one of them (solenoidal) can act exclusively with the velocity of light c and the other one (irrotational) with an arbitrary finite velocity v (including a velocity more than c) . We show also that the irrotational component of the electric field has a physical meaning and can propagate exclusively instantaneously.