Special relativity (alternative formulations)
Hendrik Lorentz and Henri Poincaré developed their version of special relativity in a series of papers from about 1900 to 1905. They used Maxwell's equations and the principle of relativity to deduce a theory that is mathematically equivalent to the theory later developed by Einstein.
Sagnac effect
The first description of the Sagnac effect in the framework of special relativity was done by Max von Laue in 1911, two years before Sagnac conducted his experiment. By continuing the theoretical work of Michelson (1904), von Laue confined himself to an inertial frame of reference (which he called a "valid" reference frame), and in a footnote he wrote "a system which rotates in respect to a valid system formula_7 is "not" valid". Assuming constant light speed formula_8, and setting the rotational velocity as formula_9, he computed the propagation time formula_10 of one ray and formula_11 of the counter-propagating ray, and consequently obtained the time difference formula_12. He concluded that this interferometer experiment would indeed produce (when restricted to terms of first order in formula_13) the same positive result for both special relativity and the stationary aether (the latter he called "absolute theory" in reference to the 1895-theory of Lorentz). He also concluded that only complete-aether-drag models (such as the ones of Stokes or Hertz) would give a negative result.