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 two-parameter 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.

This variant has been accepted for publication in Found. Phys. Letters

References in corpus (6)

• From Lorenz to Coulomb and other explicit gauge transformations
• About Superluminal motions and Special Relativity: A Discussion of some recent Experiments, and the solution of the Causal Paradoxes
• On the theoretical possibility of the electromagnetic scalar potential wave spreading with an arbitrary velocity in vacuum
• On vector potential of the Coulomb gauge
• On the Electrodynamics with Faster-Than-Light Motion
• On Two Complementary Types of Total Time Derivative in Classical Field Theories and Maxwell's Equations

Cited by in corpus (3)

• 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)]
• Reply to `Comment on ``Helmholtz Theorem and the V-Gauge in the Problem of Superluminal and Instantaneous Signals in Classical Electrodynamics" by A. Chubykalo Et Al' by J. A. Heras [FOUND. Phys. Lett. vol. 19(6) p. 579 (2006)]
• On the Possibility of Faster-Than-Light Motion of the Compton Electron