A Derivation of the Speed of Light Postulate

Abstract

The speed of light postulate, one of the two fundamental assumptions upon which the special theory of relativity (SR) is based, still seems as mysterious today as when it was first introduced. This paper presents a derivation of the postulate from three axioms:1) A definition of motion in proper time that captures most of the mathematical aspects of SR except for the speed of light postulate itself, 2) An axiom concerning the nature of the existence of entities which do not age, and finally 3) an axiom which defines existence in a spacetime to be transitive. The second axiom is motivated by an apparent paradox inherent in the structure of SR, called the existence paradox, pertaining to entities which do not age. The duration of existence of such entities in their proper frame is precisely equal to zero, which would normally be interpreted to be consistent with non- existence and inconsistent with the empirical evidence for the existence of such entities. The resolution of this apparent paradox is guided by a quasi-philosophical principle, called the Principle of least Speciality. The second axiom presents a resolution to the existence paradox that follows this principle while at the same time providing the essence of the explanation for the speed of light postulate. Given the three axioms, it is straightforward to show that the speed of light postulate is a logical consequence. Furthermore, this framework implies a direct experimentally testable prediction that is, according to currently prevailing views, unexpected.