The Light Postulate and Relative Velocity – A Conceptual Analysis

The Light Postulate and Relative Velocity — A Conceptual Analysis This article presents a conceptual analysis of the formulation of the light postulate in the Special Theory of Relativity (SR). A distinction is made between:(i) the speed of light in vacuum as a physical constant c — the absolute velocity of light relative to vacuum, and(ii) the relative velocity of light with respect to an inertial reference frame (IRF), measured locally in that frame. Two formulations of the postulate are analyzed:A - Source independence: the speed of light in vacuum does not depend on the motion of the source. This formulation is accepted as uncontroversial.B - Observer independence: the speed of light is c for all inertial observers. This formulation is questioned. It is shown that the conventional result u' = c when u = c in Einstein's velocity addition law u' = (u-v)/(1-uv/c²) is a mathematical consequence of the definition itself, which is constructed to preserve c, and not an independent empirical proof that the relative velocity (ii) is c in all IRFs. Using the same x-coordinates in two reference frames F and F' with relative velocity v, it is shown for the instant when the light reaches F' that:cΔt = vt₀ + vΔt and cΔt' = vt₀ + vΔt'which gives (c-v)(Δt-Δt')=0. Classically Δt=Δt' with v ≠ c — no contradiction. Requiring c in both systems with Δt ≠ Δt' forces v=c. The Michelson-Morley experiment measured (i) in different directions in the F where the apparatus was at rest. Its null result shows no direction-dependent difference c ± v in F. The step to claiming (ii) = c in all IRFs is an interpretation beyond the experiment itself. The article argues that to avoid circular reasoning, (i) and (ii) must be kept distinct. In physics there is no velocity in itself, only velocity with respect to something.