In 1905 Albert Einstein published his paper on the Special Theory of Relativity, which, as is well known, is concerned with the characteristics of space, time and matter when a mass possesses a constant velocity in Pseudo - Euclidean Space - Time. Subsequently, Hermann Minkowski showed that Pseudo - Euclidean Space - Time could be represented by a four dimensional `World', in which three dimensions were spatial in nature, and the fourth, temporal. A point within such a `World' was said to exist at the co-ordinate positions representing its location. Minkowski's development subsequently led to the mathematical formulation of the Special Theory using such tools as the Tensor Calculus.

By utilising Minkowski's representation of space-time in a new way e.g. as a linear complex spatial/temporal manifold, in which the temporal dimension is represented as the imaginary part and the spatial dimensions as the real part, and the introduction within it of a new concept, Existence Velocity, a Space - Time Domain designated D₀ is created. The simple process of induced spatial rectilinear motion within this Domain then permits the derivation, using classical analytical methods, of the main kinematic and kinetic relationships extant within the Special Theory, together with a number of new ones. As a demonstration of applicability, the concept is then extended to planar, and central orbital motions. Finally, via conformance to the appropriate criteria, the Domain D₀ is subsequently shown in Appendix A, to be equivalent to Pseudo - Euclidean Space - Time. This is augmented by the reduction of selected derivations to their classical equivalents in Appendix B.