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But how would we know that "c" represents a limiting speed?By hypothesis. The existence of a speed limit is intimately tied to the
ToThe answer is "yes" for #1, and "it is not absolutely necessary, but it sure
say that a photon mass "is not sufficient to invalidate special relativity"
does not respond to the deeper question, "Is special relativity a
consequence of the facts that (1)there is a limiting speed at which signals
can be transmitted [I carefully stipulated that the photon mass is the
smallest of all - no massless neutrinos] and (2) signals actually can be
transmitted at that speed?"
The Landau/Lifshitz derivation starts (Sec 1-2) with a definitionWith a lawyer's skill your quote deftly skips over the preceding discussion
of "intervals". They then go on to say (p.4 of the 1951 edition) "we
now express the invariance of the velocity of light in mathematical form",
having introduced (in modern language) ct as a "4th dimension". They
then proceed to obtain the Lorentz transformation in a very conventional
way by requiring the the "interval" between 2 events is an invariant.
So it seems to me that your answer is on a different logicalI'm sure that in a universe where all the particles had a mass whose rest
plane than the question that I posed. I thought that my question invited
some speculation on the interconnectedness of everything, and that a
universe with no massless particles would be much different from one
with just a few patches placed on E&M, as you have described.
Your appeal to gravity waves as the carrier of signals at theYou may have me here. (The suggestion of using gravity waves was with the
ultimate velocity is intriguing. Maybe someone can dream up a question
that probes the necessity for special relativity in this context.