The Most Fundamental Formulation of the Special Theory of Relativity

The special theory of relativity is conventionally formulated using five postulates: the homogeneity of time, the homogeneity of space, the isotropy of space, the Einstein principle of relativity, and the invariance of the speed of light.

Though valid, the conventional formulation is not the most fundamental. Two superfluous assumptions are made. The first is the invariance of the speed of light postulate, which can be deduced from the remaining four, as proven by Vladimir Ignatowski. The second, which is lesser known, is the conventional definition of simultaneity---a consequence of the assumption that first signals travel with the same speed in their departing and returning directions with respect to an observer, an epistemological indeterminacy addressed by Hans Reichenbach.

In this paper, the special theory of relativity is formulated in the most fundamental manner currently known. The K-Calculus method is used, which permits a complete formulation of the theory without having to define explicit coordinate systems, the invariance of the speed of light is proven rather than assumed, and the definition of simultaneity is generalized.