Light-speed constancy versus light-speed invariance in the derivation of relativistic kinematics

It is still perhaps not widely appreciated that in 1905 Einstein used his postulate concerning the ‘constancy’ of the light-speed in the ‘resting’ frame, in conjunction with the principle of relativity, to derive numerical light-speed invariance. Now a ‘weak’ version of the relativity principle (or, alternatively, appeal to the Michelson—Morley experiment) leads from Einstein's light postulate to a condition that we call universal light-speed constancy. which is weaker than light-speed invariance. It follows from earlier independent investigations (Robertson [1949]; Steigler [1952]; Tzanakis and Kyritsis [1984]) that this condition is none the less sufficient to derive the Lorentz transformations up to a scale factor, given the well-known kinematic principle of ‘reciprocity’. In this paper, we follow Robertson and explore the kinematics consistent with universal light-speed constancy without imposing reciprocity, and we recover the Lorentz transformations by further appeal only to the weak relativity principle and spatial isotropy.
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DOI 10.1093/bjps/44.3.381
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Harvey R. Brown & Roland Sypel (1995). On the Meaning of the Relativity Principle and Other Symmetries. International Studies in the Philosophy of Science 9 (3):235 – 253.
Harvey R. Brown (1997). On the Role of Special Relativity in General Relativity. International Studies in the Philosophy of Science 11 (1):67 – 81.
T. Budden (1997). A Star in the Minkowskian Sky: Anisotropic Special Relativity. Studies in History and Philosophy of Science Part B 28 (3):325-361.

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