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I agree with David (for the most part, see below) and I regret
opining earlier today that one needed at least to assume that
Maxwell's equations are laws of physics to obtain special
relativity. Along the lines that David pursues, several authors
(e.g., Jean�\Marc Lévy�\Leblond, "One more derivation of the
Lorentz transformation," AJP, 44, 271, 1976 and N. David Mermin,
"Relativity without light," AJP, 52, 119, 1984) have shown that
under only a few very general assumptions about the homogeneity and
isotropy of space and time one arrives at the Lorentz
transformations and finds that they depend on a single,
theoretically undetermined constant (call it, say, c) having the
dimensions of velocity and which can be interpreted as a maximum
observable speed.
The only reason I say that David is right for the most part is that
it seems to me that his second postulate (that there is no such
thing as instantaneous interaction at a distance) is neither
necessary nor even proper. There is nothing that prohibits an
infinite value for c.
The result is the Galilean transformation laws and the
corresponding possibility of instantaneous interaction at a
distance.
AFAIK, the fact that c is *not* infinite must still be taken as an
experimental fact and not a prediction of theory. Am I wrong?
John Mallinckrodt
Cal Poly Pomona