Covariant Electrodynamics in Vacuum

Abstract

The generalized Galilei covariant Maxwell equations and their EM field transformations are applied to the vacuum electrodynamics of a charged particle moving with an arbitrary velocity v in an inertial frame with EM carrier (ether) of velocity w. In accordance with the Galilean relativity principle, all velocities have absolute meaning (relative to the ether frame with isotropic light propagation), and the relative velocity of two bodies is defined by the linear relation uG = v₁ - v₂. It is shown that the electric equipotential surfaces of a charged particle are compressed in the direction parallel to its relative velocity v - w (mechanism for physical length contraction of bodies). The magnetic field H(r, t) excited in the ether by a charge e moving uniformly with velocity v is related to its electric field E(r, t) by the equation H=ε₀(v - w)xE/[ 1 +w • (t>- w)/c²₀], which shows that (i) a magnetic field is excited only if the charge moves relative to the ether, and (ii) the magnetic field is weak if v - w is not comparable to the velocity of light c0 . It is remarkable that a charged particle can excite EM shock waves in the ether if |i> - w\ > c0. This condition is realizable for anti-parallel charge and ether velocities if |v-w| > c₀- | w|, i.e., even if |v| is subluminal. The possibility of this Cerenkov effect in the ether is discussed for terrestrial and galactic situations