Ned Heath:
On Wed, 09 Jul 2003 (Bilge) wrote:
That makes the galilean transformations a special case of
the general result.

Galilean transformations do not have finite c, so if your
derivation doesn't rule them out (which it doesn't), you can't
legitimately claim to have derived the finiteness of c.

I already cited a reference written by mathematicians who state
explicitly the equivalence of the affine space for M_c and M_\infty.

[...]

He did NOT select Newtonian mechanics, because he knew it was
not strictly valid.

Einstein could not have made a statement about "inertial frames"
at all without appealing to newtonian mechanics. In fact, special
relativity suffers from the defect of being unable to adequately
define an inertial frame, newton or no newton. If einstein can rely
on classical mechanics to help define the meaning of "inertial",
then it's certain;y reasonable to use the first postulate and
the fact that one cannot turn around in the time direction to rule
out a euclidean metric.

[...]
I did. Infinite `c' doesn't agree with observation.

Of course it doesn't, but particular "observations" are not part
of the principle of relativity. You are not entitled to invoke
observations ("you can't use a marked ruler") when you claim to
be deriving something from the principle of relativity alone.

In a semantics game, I'm entitled to do anything I wish.
And, I can use a marked ruler, since any ruler is marked by
virtue of having endpoints. It sounds like you are trying
to turn special relativity into LET.

[...]
In particular, it states "electrodynamics and optics" in frames
in which "the equations of mechanics hold good". If I wanted to
haggle over semantics, I would have simply said that was enough
to choose a value for `c' as well, since the electrodymanics
at the time, were maxwell's equations.

Bilge, for goodness sakes! That's totally wrong! Einstein
specifically (and famously) AVOIDED basing special relativity
on Maxwell's equations.

I know that quite well. However, since you insist on playing a
game of semantics under the guise of pedantry, I'm going to
simply be pedantic about the wording of the first postulate
stated in the introduction so I can play along.

Your mis-reading of his postulates has already been explained.

I didn't misread anything. I intentionally read what was literally
written for the purpose of responding to your last post, just to
demonstrate that I can play the same game of picking and choosing
the text as I see fit.

[...]
Obviously Newton's equations do NOT hold good in ANY frame,
because if they did, spacetime would have to be Galilean.

Newtonian mechanics can be formulated via a lagrangian and more
generally,

L'[x] = L[x + a] = L[x] + \delta L[x]


\delta L = L[x'] - L[x] = a^{u} dL/dx^{u}

From here it takes just a few more lines to obtain the classical
conservation laws via noether's theorem: energy, momentum and angular
momentum.

So are you going to tell me "mechanics at the time was Newtonian
mechanics, so Einstein could have inferred that spacetime was
Galilean"?

He could have, but his immediate goal was to explain electrodynamics
with a geometric theory. His second postulate is unfortunate in that
he defined the speed of light to be `c' for that reason. The value
of `c' is an experimental issue, not a theoretical issue.

This just further emphasizes how completely you
have failed to understand the foundations of special relativity.

I haven't failed to understand anything in this thread. If I'm
going to play along, I'm going to twist the semantics and make a
game of it, which is different from the one you're playing. I'm
not going to make a serious effort to defend statements you've
misconstrued by shifting the meaning of the question.