Relativity Theory Based Directly on the Velocity Transformation
The history of the derivations of relativistic space-time transformations is reviewed. Starting with Voigt in 1887, the key assumption was that the speed of light is the same for all observers independent of their state of motion and that of the light source. The fact that fundamentally different transformations have been deduced on this basis can be traced to distinctions that were imposed by their respective authors regarding the relationship between space and time variables.
It is pointed out that the same velocity transformation can be derived from each of them by simply dividing each set of spatial variables by the corresponding time coordinate. Many key results of relativity theory, each of which is consistent with all experimental observations made to date, can be obtained on the basis of the velocity transformation alone.