The Electrodynamics of Moving Material Fields and the Two Speeds Implied by the Expanding Earth

This work identifies the branch point, which was never explicit in EM treatises, from which came the choice of abandoning the Galilean transformations in favor of the Lorentz covariance, a path that originated the various relativistic theories. The need arising from the expanding Earth for a hydrodynamic mechanism for Newtonian and Coulomb fields is discussed. This hydrodynamic material mechanism is shown to constitute a completion of the Newton and Maxwell concepts of the fields, which were only a phenomenological description of physical reality. It is shown that the analogy between Maxwell’s equations and hydrodynamics cannot become a perfect correspondence. The lack of coupling of the electromagnetic field to the underlying material “causing field”—which induces hydrodynamical forces and accelerations observed only phenomenologically—gives rise to inaccuracies in the formulation of its equations, which are incorrect for Galilean covariance. But the most serious flaw in the original formulation of electromagnetism is the erroneous identification of the flow velocity of the field (variable as $1/r^2$ ) with the speed of light $c$ , with which it was demonstrated that the fields of charges in motion contract in the direction of motion (the Heaviside ellipsoid, 1888, 1889). From this error, historically due to the incomplete development of many hydrodynamics sectors (a situation that persists today), came Fitz Gerald’s contractions and finally, the relativistic theories. Some future research lines are proposed for a return to realistic physics and a possible but still weak form of Galilean covariance.