Postulates of Special Relativity - Alternate Derivations of Special Relativity

Alternate Derivations of Special Relativity

The two-postulate basis for special relativity outlined above is the one historically used by Einstein, and it remains the starting point today. However Hendrik Lorentz and Henri Poincaré derived their version of the theory from Maxwell's equations and the principle of relativity. The Minkowski space formulation is also used. As Einstein himself later acknowledged, the derivation tacitly makes use of some additional assumptions, including spatial homogeneity, isotropy, and memorylessness. Following Einstein's original derivation, many alternative derivations have been proposed, based on various sets of assumptions. It has often been claimed (such as by Ignatowsky in 1910 and many others in subsequent years) that special relativity follows from just the relativity postulate itself. This claim can be misleading because actually these formulations rely on the aforementioned various assumptions such as isotropy. Nevertheless the Lorentz transformations, up to a nonnegative free parameter, can be derived without first postulating the universal lightspeed. The numerical value of the parameter in these transformations can then be determined by experiment, just as the numerical values of the parameter pair c and the permittivity of free space are left to be determined by experiment even when using Einstein's original postulates. Experiment rules out the validity of the Galilean transformations. When the numerical values in both Einstein's and other approaches have been found then these different approaches result in the same theory.

See also Special relativity (alternative formulations).