Implicit Assumptions in the Standard Light-Signal Derivation of Special Relativity

This paper analyzes the standard light-signal argument used in the introductory derivation of special relativity, focusing on its logical structure rather than its empirical content. It is shown that the derivation implicitly presupposes the existence of a reference system relative to which the speed of light is assumed to be constant, even when this assumption is not stated explicitly. In particular, common formulations that refer to a “rest system” are shown to be logically insufficient unless such a system is defined independently of the quantities introduced within it. An alternative, non-circular formulation is presented in which an inertial reference system is introduced explicitly prior to the derivation. This allows the standard light travel-time relations to be obtained without logical gaps, while leaving the empirical predictions of special relativity unchanged. The analysis is intended to clarify the conceptual and definitional assumptions underlying a widely used derivation and to contribute to a more logically transparent presentation of the foundations of special relativity.