"...which is
-- what I wrote yesterday, and
-- which I and many many others have written on previous occasions, and
-- which is properly called the /spacetime/ approach to the task,
since it has a direct interpretation in terms of 4-vectors and the
geometry of spacetime."
My derivation starts explicitly from definition of the 4-momentum vector.
This is as much spacetime approach as you can get.
If this is the same as you wrote yesterday, then why at all are we having
any dispute?
"This appeal to authority just cracks me up. Even if it
were true, it would have negligible weight ... and there is no
reason to think it is true"
It is really strange to read this from one who boasted in his
previous email to be in one camp with Einstein. I never thought
the appeal to an authority a good argument, and used it myself
only as a response preconditioned by this kind of argument.
"The idea of a speed-dependent mass is part and parcel of the
approach that uses rulers that can't be trusted and clocks that
can't be trusted ... an approach that predates any notion of
spacetime"
Oh, really? So the observation of muons born in upper atmosphere
and decaying at the sea-level where they could not be observed
classically, cannot be trusted because the inner clock determining
the mean lifetime of a muon cannot be trusted? And the experiments
(long after 1908!) with slowed decay of muons cirling in magnetic
field cannot be trusted for the same reason? And behavior of rulers
as dynamic systems cannot be trusted? What then constitutes
space-time measurements if not readings of clocks and rulers?
Just because I believe the concept of space-time is still alive,
I think it is appropriate to tell the physics students that the
cyclotron frequency w = (q/m)B in a fixed magnetic field B decreases
with electron speed v because the corresponding increase of
relativistic mass m = m0 gamma (v).
"Next year is the 100th anniversary of spacetime. All the
students have heard of spacetime; it's well established as
part of pop culture. It gets mentioned in /Star Trek/ and
/Buffy/ and who-knows-where else. Isn't it about time we
taught folks what spacetime really is, and how to use it?"
I would not say that spacetime is a part of pop-culture.
I would rather say that it became part of modern classics.