The relativity of timelike and spacelike particles from first principles

The Lorentz transformations (LT) of timelike motion are derived from first principles of geometry and the aberration phenomenon is shown to be inherent in the geometry. An extension of this procedure leads to the main features of spacelike motion. The LT for tachyons are derived and the moving observer in this LT is determined. The LTs for both timelike and spacelike motions are derived by a single method-perhaps the simplest approach to the LT. The temporal order of events and causality in tachyon motion are discussed, and the inhomogeneous wave equation for the electromagnetic potentials of a charged tachyon is solved by the use of integral transforms. © 1984, Taylor & Francis Group, LLC.