bcrowell said:
My answer would be that I don't know, because the question refers to a particular formulation of an obsolete axiomatization, and I don't think anyone in the year 2015 should be memorizing that kind of historical trivia (what's postulate #1, what's postulate #2, etc.). I think it's unfortunate if people are still teaching their students SR using Einstein's postulates, because they reinforce various misconceptions, such as the belief that c has something to do with the speed of light, or that light plays some fundamental role in relativity. Since Einstein himself had a view of SR that, looking back from 2015, seems to have been in many ways hazy and incorrect, why would it be of interest to anyone other than historians of science to try to figure out exactly what he had in mind?
In general I agree with you that teaching physics in the "historical" way is not always the best choice, also some knowledge about the history of physics is also good to gain understanding of the meaning of concepts, despite the fact that history is also an interesting subject in itself.
On the other hand, in this case, I'm not so sure. Physics is, after all, an empirical science and based on observations and the attempt to find some fundamental observations that can be used to build mathematical models in a bit like an axiomatic approach (although I don't think that we have a sharp axiomatic system of all of contemporary physics).
It is no surprise that relativity was discovered by thinking about electromagnetic phenomena as they were summarized brillantly in form of Maxwell's equations and a bit later in form of Lorntz's "elctron theory". The speed of light has been part of Maxwell's equations and was found to be the phase velocity of electromagnetic waves, which finally were experimentally discovered and investigated in detail by H. Hertz. This is still the most convincing empirical manifestation of the relativistic space-time model.
Of course, it is important to stress that relativity is comprehensive and not limited to electromagnetic/optical phenomena. You can derive the special-relativistic space-time structure just from the special principle of relativity and symmetry assumptions (which boils down to postulate euclidicity of space for any inertial observer). Then you get two space-time models in terms of the corresponding symmetry groups, i.e., the Galilei-Newton spacetime and Einstein-Minkowski spacetime. It is, of course, still an empirical question to decide which one describes nature better, and then again the most convincing arguments come from electromagnetism and optics. Last but not least the question, whether the limiting universal speed of Einstein-Minkowski spacetime is the phase velocity of light or not, is still just really empirical. There is no fundamental law in contemporary physics, which can be used as an argument that electromagnetic waves are strictly massless vector fields (or in QFT language that the photons are really exactly massless). There is of course overwhelming empirical evidence that this is true.
Of course, nowadays another strong argument for the correctness of the relativistic spacetime models is high-energy particle physics. To construct the accelerators to do experiments with particles and nuclei at high energies, the use of relativistic dynamics is mandatory. You couldn't use Newtonian physics to plan an accelerator like the LHC. Note that this part is also very much (classical) electrodynamics and relativistic mechanics of (bunches of) charged particles. Then the tremendous success of the Standard Model is of course further strong evidence for the relativistic spacetime model which is the most important building block of the underlying local microcausal QFT paradigm (which to a large part is representation theory of the Poincare group, which strongly hints towards the usefulness of gauge theories).
But a modern physics didactics does not wait to introduce relativity at the end of the undergrad level, and in my opinion, right so. You can not start early enough to introduce special relativity at least in the theory curriculum (in Frankfurt that's usualy already done at the end of the very 1st freshmen semester). Then you cannot use high-brow group theory or field theory to establish relativity, but the traditional approach a la Einstein is very valuable. It comes with a minimum of assumptions, and you can do relativistic mechanics of point particles in this way, which is nice as a conclusion for the 1st theory semester and a good starting point for E+M in the 3rd (in the 2nd semester usually you have analytical mechanics (Hamilton's action principle etc), where usually also the relativistic case is treated again).
