[Phys-L] Re: "moving clock runs slower" (yes)

[John Denker <jsd@AV8N.COM>]

Fayngold, Moses wrote:
> I think my example with 3-velocity serves its purpose, but Bob Sciamanda's example with energy E
> and momentum P does it much better, because the pseudo-Pythagorean theorem
>
> E^2 - p^2c^2 = Eo^2    (1)
>
> with the rest energy Eo in the energy-momentum space directly echoes the theorem
>
> c^2t^2 - r^2 = c^2to^2   (2)
>
> with the proper time "to" of a clock in Minkowski's space. If, according to John, only "to" has
> the status of real physical time, then, by the same logics, only "Eo" must have the satus of the
> object's actual energy. Then no references to quaternions or Clifford algebra can save us from
> the conclusion that there is no such thing as relativistic energy E and momentum p, and therefore
> motion is merely an illusion.

This is an abuse of the terminology.

The RHS of equation (1) is called the "mass" squared.  And yes, mass
is invariant under rotations, and invariant under boosts.

The RHS of equation (2) is called the "interval" squared.  And (big
surprise) it is invariant with respect to rotations, and invariant
with respect to boosts.

Some things are invariant.  Some things are not.  Arguing that mass
is invariant does not prove that momentum is invariant, and certainly
doesn't prove that momentum does not exist.

I drew some analogies that are well known to be accurate and useful.
The fact that you can draw other analogies that are completely bogus
does not detract in any way from what I said.
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