This has not made it back to me for over 4 hours so here goes again:
On Jan 19, 2006, at 8:11 AM, Stephen A. Lawrence wrote:
The speed of the flights is not a factor, either -- the same time
lag will be observed no matter how fast they go. However, in order
to keep the precision with which one needs to keep time down to
something manageable, it's important to go quickly. If you used a
ship and retraced Magellan's route instead of using an airplane,
for instance, the tiny difference in the readings would be totally
lost in the accumulated inaccuracy of the clocks over a period of
several months.
Interesting about the speed independence.
Reminds me of the old Jefimenko's clocks issues discussed here some
years back. There is something I have not understood about the twin
paradox, and relativity in general. SR appears to be based solely on
observational differences, i.e. retardation. This is true of
Jefimenko's view also, except possibly for relativistic mass
changes. However, in the case of the returned twin, the two twins
stand next to each other at the end. They are in the same reference
frame. If there is a difference in age between them then that
difference can not be simply a result of retardation. If the
"permanent" clock difference effect is due to acceleration (GR
effects), and the journey consisted of only brief acceleration
phases, followed by long segments of uniform motion, then it seems
that the final clock difference from a long journey would be the same
as that of a short journey with the same accelerations and no coasting.
You might find it interesting that in his book *Retardation and
Relativity*, Jefimenko takes a different but interesting view of the
relativistic clock paradox. He says the clock speed is a function of
what kind of clock is being obeserved in motion. He calculates the
speed of various natural clocks.
His calculations for the twelve clocks were based on "the fundamental
laws of electromagnetism and mechanics with no input from relativity
theory (although we shall use the longitudinal and transverse masses,
which may be regarded as either experimentally obtained masses, or as
relativistic concepts)" (p. 237)
However, his EM equations, based on retardation, are similar to SR
based equations. His view is interesting. In the twin paradox, as
viewed by Jefimenko, perhaps the "young" twin may have varied aging
effects, depending on the mechanics of some specific chemical
interactions.
Jefimenko's clocks consisted of:
1. A charged particle oscillating in the x axis, the central axis,
of an oppositely charged ring. Relative direction of motion of the
clock is in the x axis.
2. Two (outer) particles A and B of the same charge located on the y
axis at points +-a, an inner particle C, oppositely charged,
oscillates in the x axis between the two particles and near the
midpoint. Relative direction of motion of the clock is in the x axis.
3. Same as 2, but the motion of C is in the y axis, the two like
particles A and B are located in the z axis. Relative direction of
motion of the clock is in the x axis.
4. The time delta t it takes for two charges to separate (in the y
axis) a small fixed distance d when initially separated by distance
R. The ratio d/r ~ 0. Relative direction of motion of the clock is in
the x axis. If t_y is the time it takes for the same separation to
occur in the y axis, then t/t_y = gamma.
5. This clock is similar to clock 4, except one charge is replaced
by a long line of charge of uniform line density lambda, lying in the
z axis and having its midpoint at the origin. The point charge of
opposite sign is placed on the y axis at initial distance R from the
origin. Relative direction of motion of the clock is in the x axis.
6. This clock is similar to to Clock 2, except charges A and B are
replaced with line charges in the yz plane parallel to the z axis.
All of the above clocks appear to run gamma times slower than the
identical stationary clock, so t_moving = gamma * t_observer. All
the following clocks run at a different rate.
7. This clock is the same as Clock 3, but A and B are placed at
points +-a on the x axis. Charge C oscillates in the y axis.
Relative direction of motion of the clock is in the x axis. Here
t_moving = 1/(1-v^2/c^2)^(5/4) * t_observer, or gamma^(5/2) times
the rate for the same stationary clock.
8. This clock is similar to Clock 5, except the line charge is now
placed on the x axis with the midpoint at the origin. Again, the
point charge of opposite sign is placed on the y axis at initial
distance R from the origin. Relative direction of motion of the
clock is in the x axis. Here t_moving = 1/(1-v^2/c^2)^(3/4) *
t_observer, or gamma^(3/2) times the rate for the same stationary clock.
9. This clock is similar to Clock 3, except the two point charges A
and B are replaced with line charges that are parallel to the x axis
and are at distance +-a from the origin in the xz plane. The point
charge C of opposite sign oscillates about the origin in the y axis.
Relative direction of motion of the clock is in the x axis. Here
t_moving = 1/(1-v^2/c^2)^(3/4) * t_observer, or gamma^(3/2) times
the rate for the same stationary clock.
10. The time delta t it takes for a charge to separate from a plate
of surface charge density lambda, of the same polarity, lying in the
xy plane to separate (in the y axis) a small fixed distance d when
initially separated by distance R. The ratio d/r ~ 0. Relative
irection of motion is in the x axis. If t_y is the time it takes for
the same separation to occur in the y axis, then t/t_y = gamma. The
point charge C of opposite sign oscillates about the origin in the y
axis. Relative direction of motion of the clock is in the x axis.
Here t_moving = 1/(1-v^2/c^2)^(3/4) * t_observer, or gamma^(3/2)
times the rate for the same stationary clock.
11. The time delta t it takes for a charge to separate from a plate
of surface charge density lambda, of the same polarity, lying in the
yz plane to separate (in the x axis) a small fixed distance d when
initially separated by distance R. The ratio d/r ~ 0. (This is
similar to Clock 10, but rotated so the particle moves in the x
axis.) Relative direction of motion of the clock is in the x axis.
If t_y is the time it takes for the same separation to occur in the y
axis, then t/t_y = gamma. The point charge C of opposite sign
oscillates about the origin in the y axis. Relative direction of
motion is in the x axis. Here t_moving = 1/(1-v^2/c^2)^(3/4) *
t_observer, or gamma^(3/2) times the rate for the same stationary clock.
12. This clock is similar to Clock 4, except rotated into the x
axis. The time delta t it takes for two charges to separate (in the
x axis) a small fixed distance d when initially separated by distance
R. The ratio d/r ~ 0. Motion of the charges is in the x axis.
Relative direction of motion of the clock is in the x axis. This
clock is similar to Clock 4, except rotated into the x axis. Here
t_moving = 1/(1-v^2/c^2)^(5/4) * t_observer, or gamma^(5/2) times
the rate for the same stationary clock.
Horace Heffner
