mat (01/21/83)
Recently, there has been a discussion about relativistic affects
on net.misc . The situation is as follows:
A common elsectric desk clock, made with a VERY strong cord, is
swung in circles over the head at relativistic velocity, with
the cord still plugged in.
Does the clock register Con Ed ( Met Ed, JCP&L, ... ) time,
or does it register time in a relativistic frame different from
that of the observer ( and perpetrator ).
--Since the common electric desk clock is a COUNTER, when it has come to rest
it will register the number of 60 Hz ( observer time frame ) cycles it has
seen, and will therefore still be syncronized wth the local utility. If
a small cesium clock had been attatched to the cord, it would be running
BEHIND the utility, assuming that the utility is using a sufficiently
accurate reference standard.
--Someone commented that the clock is in an inertial frame. Wrong! The
clock, undergoing continual radial acceleration is NOT in an inertial
(Newtonian) frame.
--Someone else suggested that since the clock ends up where it started,
the effects of the motion and acceleration cancel (vector addition
argumnt). WRONG! General Relativity (Not Special Relativity, which
deals with constant velocity) predicts that the effects of acceleration
do not simply add in a linear 3-space. This has is the source of the famous
clock paradox, and has been tested as follows: Two portable cesium clocks
were each placed in airplanes. One was flown around the earth from West
to East, adding to the earths rotational velocity the velocity of the plane
about the earth, and the other from East to West, diminishing the velocity
at which the clock was revolving about the earth's axis. When the clocks
were brought together the West-to-East clock was found to be measureably
and significantly behind the East-to-West clock, by an amount consistant
with that predicted by General Relativity.
--Maxwell's equations, the pillar of classical electromagnetic theory,
do not work in a Newtonian system under acceleration. Since Relativity
deals with the propagaion of light (electromagnatism) under conditions
of differring object and reference frames, Maxwell's equations DO hold
under any conditions of acceleration, gravity, etc. Note that this
requires light, whose quanta have relativistic mass, to be affected by
gravity, which becomes indestiinguishable from acceleration. Not only
light is affected. All forms of electromagnetic propagation are affected,
including even the electromagnetic field waves that operate electric motors.
Of course, most of the things we deal with daily in a Newtonian way are
not significantly affected.
--Someone recently brought up the fact that the PHASE velocity can exceed
the speed of light. Since the speed of causality ( the speed at which
cause-and-effect can operate ) is limited to the GROUP velocity, this
is of little practical use. Without going too deeply into transmission
line theory, let me illustrate the meaning of phase velocity:
Consider a wave approaching a shore. The wavefront is straight, the shore
is straight, and the wave is approaching at nearly, but visibly not, at
a right angle to the shore. An observer watching the shoreline from one
end of the beach will see the point of contact of the wave and the shore
move rapidly along the shore at a speed considerably greater than that
of the wavefront. This is phase velocity. If someone drops a firecracker
into the wave, and it expodes where and as the wave hits the shore,
the resulting wavelet along the crest of the wave will not keep up with
the point of contsct of the wave and the shore.
--Finally, if I am wrong, will someone please set me right. If you have
CREDENTIALS, and can show me an error in the above, please mail to me
or post an article. If you DON'T have credentials, be prepared to justify
your argument rather rigorously from an authoritative statement of the
appropriate Theory of Relativity.
-hou5a!mat
M Terribile, BE