Postulates of special relativity

1. First postulate (principle of relativity)

2. Second postulate (invariance of c)

The two-postulate basis for special relativity is the one historically used by Einstein, and it remains the starting point today. As Einstein himself later acknowledged, the derivation of the Lorentz transformation tacitly makes use of some additional assumptions, including spatial homogeneity, isotropy, and memorylessness. Also Hermann Minkowski implicitly used both postulates when he introduced the Minkowski space formulation, even though he showed that c can be seen as a space-time constant, and the identification with the speed of light is derived from optics.

Historically, Hendrik Lorentz and Henri Poincaré (1892–1905) derived the Lorentz transformation from Maxwell's equations, which served to explain the negative result of all aether drift measurements. By that the luminiferous aether becomes undetectable in agreement with what Poincaré called the principle of relativity (see History of Lorentz transformations and Lorentz ether theory). A more modern example of deriving the Lorentz transformation from electrodynamics (without using the historical aether concept at all), was given by Richard Feynman.

Following Einstein's original derivation and the group theoretical presentation by Minkowski, many alternative derivations have been proposed, based on various sets of assumptions. It has often been argued (such as by Vladimir Ignatowski in 1910, or Philipp Frank and Hermann Rothe in 1911, and many others in subsequent years) that a formula equivalent to the Lorentz transformation, up to a nonnegative free parameter, follows from just the relativity postulate itself, without first postulating the universal light speed. (Also these formulations rely on the aforementioned various assumptions such as isotropy). 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 Vacuum permittivity 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.

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