Grimer wrote:
At 03:50 pm 19/01/2006 -0900, Horace wrote:
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.
I think one has to be careful what one means by
speed independence here.
Here's what we mean by that:
Consider a rotating disk. Select a point on the perimeter.
Send two signals around the disk, starting from that point,
circumnavigating the disk, and returning to that point (which has, of
course, moved by the time the signals get back to it). Make sure the
two signals travel at the same speed relative to the rim of the disk.
The signal which went around in the same direction as the disk's
rotation will arrive back at the start _after_ the signal which went the
other way around. The difference in the arrival times is a function of
the rotation rate of the disk, but it is _not_ a function of the speed
of the signal. Fast signal, slow signal, the absolute delay between the
return of the signal on the "fast" path and the return of the signal on
the "slow" path is the same.
As I mentioned previously, this can be demonstrated without the use of
any clocks, and in fact it is demonstrated all the time. Current
generation inertial navigation systems use ring-laser gyroscopes which
only work as a result of this effect. In a ring-laser gyro the signal
is a a light pulse carried in a fiber optic cable, and it travels at
roughly 3/4 C relative to the rim of the disk. The signal speed is the
same in both directions, relative to the disk (signal speed on a moving
body is trivial to measure, and if it weren't invariant with respect to
the motion, moving computers would not work). The arrival time
difference is measured by looking at interference fringe shifts between
the counter-traversing pulses, and it's used to determine the rate at
which the disk is turning, which datum is used by the navigation system.
It's sometimes claimed that the Sagnac effect is difficult to explain in
special relativity, or that the math is a horrible mess. That's not
true. The effect is actually pretty simple; in fact it can be explained
in a few pictures without a (whole) lot of messy math. See here:
http://physicsinsights.org/sagnac_1.html
In a nutshell, the rotation doesn't make a difference; straighten out
the path so it's just a long straight rod that's being traversed, and it
becomes a lot more obvious what's going on.
In it's rotation the earth (and clocks on its
surface) is moving in relation to the Beta-atmosphere
which reduces the speed of the caesium clock.
If you go towards the setting sun then it is not
that the clock will speed up. It is that the slow
running will be reduced to a minumum when the speed
is stationary in relation to the local B-atm.
Going round towards the rising sun slow running will
be increased.
But the difference in speed between planes and ships
is small compared to light speed. If one projected
a caesium clock at close to the speed of light
relative to the absolute frame of reference for
motion then its speed would slow right down since
mass is the reciprocal of internal closed path
velocity (see IHM note on Beta-atm.Yahoo site).
The fact that the caesium clocks rate can be altered
merely by flying it around the globe shows the utter
insanity of using it to define length. If you do, then
you end up with the ludicrous result that the distance
around the globe clockwise is different from that around
the globe widdershins.
Ring-laser gyros make hardly any sense, it's true. You're right.
However, they exist and they work. All of special relativity has this
problem: Intuitively it's absurd. But it's born out by an enormous
mass of experimental data.
But there's a point you may have missed in the "airplane" experiment.
The two aircraft don't arrive back at the starting point at the same
moment. According to each airplane's onboard clock, the time to go
around the world was the same -- that doesn't depend on the direction!
And so neither does the distance the airplane traveled. What changes is
how long it takes in Earth-minutes for the planes to go around the world.
At the point at which the planes meet -- which is _NOT_ the starting
point, because they got back to the start at different times -- they
really have traveled different distances, and their clocks really do
show different readings. There's no contradiction and little surprise
in that. The odd thing is that the don't get back to the starting point
at the same time.
Frank Grimer
