On 10/01/2010 09:25 PM, John Mallinckrodt mentioned this paper:
N. David Mermin,
"Relativity without light," AJP, 52, 119, 1984
That is indeed an important paper.
Basically it says that given Galileo's principle of relativity
plus some clever symmetry arguments, the entire structure of
spacetime is determined.
If photons and other fast-moving particles ceased to exist, it
would have *no* effect on special relativity.
I reckon the number of people who are aware of this greatly exceeds
the number of people who have actually read the article. In any case,
the article is worth reading, if you have even the slightest interest
in special relativity.
The number we call "c" is primarily a conversion factor, allowing
you to convert from conventional units of velocity to radians of
rapidity in the xt plane.
Everything else, including the existence of a limiting speed, and
the frame-independence of the limiting speed, can be seen as an
almost-trivial consequence of the geometry and trigonometry of
spacetime.
... which explains that Mermin's calculation is only good in D=1+1
dimensions (time plus one spatial dimension). The physics in
higher dimensions is much richer. To obtain these richer results
requires additional work, additional attention to detail, and
additional cleverness.
Some people may find this paper to be more than they want to deal
with, but still I would recommend reading at least the introduction
and the conclusions.
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Pedagogical remarks:
Special relativity is the geometry and trigonometry of spacetime.
Some parts of Mermin's proofs are too intricate to be suitable in an
introductory class. However, the same can be said for other proofs,
including Einstein's derivation in terms of "postulates" involving
electromagnetism and whatnot. IMHO the sensible introductory strategy
is to just say "this is what spacetime looks like" in terms of 4-vectors
spacetime diagrams, et cetera ... and then work out the consequences,
showing that this structure is /consistent/ with everything else we know,
experimentally and theoretically. The proof that this is not just "a"
consistent structure but the /only/ consistent structure can wait.