The Physics of Tachyons III. Tachyon Electromagnetism

Abstract

A new formulation of the theory of tachyons using the same two postulates as in special relativity is applied to electromagnetism. Tachyonic transformations of the electromagnetic fields E and B are rigorously derived from Maxwell's equations and are shown to be the same as for bradyonic transformations. Tachyonic transformations of current density, charge density, scalar and vector potentials are also derived and discussed. Tachyonic optics and the four-potential of a moving tachyonic charge are also discussed, along with generalised four-vector transformations and electromagnetic four-tensors in extended relativity. Use is made of a switching principle to show how tachyons automatically obey the law of conservation of electric charge in any inertial reference frame, even though the observed tachyon electric charge is not an invariant between observers. The electromagnetic field produced by a charged tachyon takes the form of a Mach cone, inside which the electromagnetic field is real and detectable, while outside the cone the field generated by the tachyon is imaginary and undetectable.