Caveat: We are using Einsteins second postulate about the constancy of c, but
is it an empirical fact, ie., are photon worldlines the same for all
observers? Yes: This is a direct result
of the famous Michelson-Morley null experiment, though Einstein probably did
not rely on their work in constructing SR. See Gerald Holton, "Einstein,
Michelson, and the "Crucial" Experiment," in Thematic Origins
of Scientific Theough: Kepler to Einstein (Cambridge, Massachusetts: Harvard
University Press, 1973/1980). Yes, too, if we once again use the right math,
namely the Lorentz transformation!
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