I think my example with 3-velocity serves its purpose, but Bob Scia=
manda's example with energy E and momentum P does it much better, bec=
ause the pseudo-Pythagorean theorem=20
E^2 - p^2c^2 =3D Eo^2 (1)
with the rest energy Eo in the energy-momentum space directly echoes =
the theorem
c^2t^2 - r^2 =3D c^2to^2 (2)=20
with the proper time "to" of a clock in Minkowski's space. If, accord=
ing 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 actua=
l energy. Then no references to quaternions or Clifford algebra can s=
ave us from the conclusion that there is no such thing as relativisti=
c energy E and momentum p, and therefore motion is merely an illusion=
.
Moses Fayngold,
NJIT=20
-----Original Message-----
=46rom:=09Forum for Physics Educators on behalf of Bob Sciamanda
Sent:=09Sun 9/11/2005 5:37 PM
To:=09PHYS-L@LISTS.NAU.EDU
Cc:=09
Subject:=09Re: "moving clock runs slower" (yes)
Apply JD's analogy to the momentum-energy four vector of a particle. =
In its
proper frame its 3-momentum and 3-velocity are zero. In another iner=
tial
frame, it has non-zero 3-momentum/velocity. This spatial component o=
f the
momentum-energy four vector is merely a projection (a shadow) of the
magnitude invariant 4-vector upon the space axes of the new frame. I=
t must
follow, by the JD analogy, that the particle is not really moving.