The history of the assumption of the equality of light speeds in free space for observers in different rest frames is reviewed. The classical (Galilean) velocity transformation (GVT) is unable to explain the results of various experiments such as Fresnel-Fizeau light-damping in moving fluids, but this failure is shown to leave open an important class of experiments for which its application is essential. Einstein’s light-speed postulate (LSP) is shown to be unviable by considering a case in which a light source passes by a stationary observer at the same time that it emits a light pulse in the same direction. The fact that the relativistic velocity transformation (RVT) has many successful applications, despite its apparent reliance on the LSP,
is attributed to the fact that in all such cases it only considers the results of a single observer made under two different conditions. By contrast, the GVT is applicable when the objective is to deduce the relationship between the velocity measurements of two observers in relative motion.
A revised light-speed postulate is introduced which states that the speed of light relative to its source, as well as relative speeds of objects in general, is the same for all observers. This is because the unit of speed is the same in all rest frames. The application of the revised postulate to the Michelson-Morley experiment is considered in detail.