Re: special relativity

["John S. Denker" <jsd@MONMOUTH.COM>]

David Bowman wrote:
> > 1)  The laws of physics are the same in all reference frames
...
> logically compact and elegant ...
...
> 2) There are no instantaneous interactions at a distance in
> physics, (and consequently, there exists an upper bound, i.e. a
> speed limit, on the rate at which causally informative influences
> can propagate from an event at one spacetime point to another one
> physically separated from it in space).

Excellent point.

> The fact that this speed limit of causation has the same value in
> all inertial frames is a *theorem* from the first 2 postulates.

That's an even better statement, since it speaks of causation,
which is clearer than speaking of "interactions".  In the
Einstein-Podolsky-Rosen experiment, "something" happens at a
spacelike separation -- but whatever it is, it can't be used
to carry information, so the speed limit of causation isn't
violated.

> The forms of the laws of relativistic dynamics (i.e. energy,
> momentum, & velocity interrelationships) for particles are dictated
> by the first 2 postulates above *plus* a *third* postulate, which
> effectively states that the laws of classical mechanics satisfy
> Hamilton's Principle of least (er, stationary) action.  Once we
> have Hamilton's Principle and have the other 2 postulates the
> usual formulae for special relativity follow (for motions observed
> in inertial frames).  A couple of important consequences of these
> laws are that all particles with a positive (rest) mass *must*
> travel at speeds strictly *slower* than the speed limit c--no matter
> how high their momentum and kinetic energy, and also particles that
> have a strictly *zero* value for their (rest) mass *must* travel *at*
> the speed limit c no matter how low their momentum and energy.  The
> direction of the velocity vector and the (mechanical) momentum
> vectors are *always* parallel to each other regardless of whether or
> not the particle's mass is zero or not.  The fact that neither
> massless *nor* massive particles travel *faster* than c is a direct
> consequence of (the corrected) postulate 2.

All true.

> The fact that light happens to travel *at* this speed limit of
> causation is a theorem that depends on the observed masslessness
> of the photon and on relativistic dynamics.

True.  Good point.

> Since it is a theorem it
> is not a good idea to claim it is a postulate.

Indeed.

> If photons happened to have a positive (rest) mass then it would
> mean that (the group velocity of) EM waves in a vacuum would travel
> *slower* than c with a speed that was dependent on the frequency.
> The validity of special relativity is independent of the issue of
> whether or not light always travels at speed c in all inertial
> frames.

Right.  Relativity isn't about light.

Historically, light was a powerful guide to the invention of
relativity.  But the way we understand it now isn't the same
as the way it was understood back then.  Good history isn't
the same as good logic, good pedagogy, or elegance.