By restricting the Relativity Principle to Maxwell's equations in vacuum and making some hypothesis of simplicity, the transformation equations for the electric and magnetic fields among equivalent observers are derived. Later, the transformation for the charge and current density and, finally, the Lorentz transformations are also computed. What is left is to extend the Relativity Principle to all physical phenomena.

In his first 1905 article on special relativity, clock synchronization by means of light rays was used by Einstein to derive the Lorentz transformations (Ann. Phys., Lpz. 322 891–921). However, the same goal can be achieved by using bodies in free motion to synchronize clocks. To this end, one has to accept the principle of relativity, the law of inertia and the existence of a limit value for the speed of massive bodies with no appeal to electromagnetic phenomena until the very last step of the derivation, when the limit speed must be identified with that of light in vacuum. (In the absence of this speed limit one recovers the Galilean transformations.)

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