From: scerir (scerir@libero.it)
Date: Sun Aug 25 2002 - 04:46:26 MDT
Louis:
> The key here is INERTIAL. If the clocks are moving, but neither one
> changes speed, then yes, you could not tell which is which. As soon as
> one accellerates, it is NON-INTERTIAL, and all observers will agree
> which clock is accellerating.
The problem here is the same. Imagine a symmetrical situation with
two non-inertial frames. Two clocks go in opposite directions, they
accelerate, decelerate, come back. Which one is slow? Why?
Einstein avoided this situation. He imagined (1905) just one clock
moving, or (later) accelerating. What about the other?
Here is what Einstein wrote (Annalen Der Physik 1905, Vol 17, pages
904-5) : "From this there ensues the following peculiar consequence.
If at points A and B of K there are stationary clocks which, viewed
in the stationary system are synchronous; and if the clock at A is
moved with the velocity v along the line AB to B, then on its arrival
at B the two clocks no longer synchronise, but the clock moved from A
to B lags behind the other which has remained at B by 1/2 tv*2/c*2
(up to magnitudes of fourth and higher order), t being the time occupied
in the journey from A to B. It is at once apparent that this result holds
good if the clock moves from A to B in any polygonal line, and also when
the points A and B coincide. If we assume that the result proved for a
polygonal line is also valid for a continuously curved line, we arrive
at this result: If one of two synchronous clocks at A is moved in a closed
curve with constant velocity until it returns to A, the journey lasting
t seconds, then by the clock which has remained at rest the travelled
clock on its arrival at A will be 1/2 tv*2/c*2 second slow. Thence we
conclude that a balance-clock at the equator must go more slowly, by a
very small amount, than a precisely similar clock situated at one of the
poles under otherwise identical conditions."
Btw SR can manage non-inertial frames.
Can Special Relativity handle accelerations?
http://www.weburbia.com/physics/acceleration.html
Does a clock's acceleration affect its timing rate?
http://www.weburbia.com/physics/clock.html
My point was just to show that the situation is still messy,
after all these years. In general you can not easily introduce a
preferred frame, a preferred geodesic, trying to explain the
asymmetrical (experimental) effect.
>From the experimental pov Hafele and Keating, who performed that
famous experiment, say something interesting.
"The Lorentz transformations leading to this result are
derived from clocks that are synchronized by a convention
that does not have the same meaning in different inertial
frames of reference ..... indeed, clocks synchronized
within an inertial frame according to the Einstein simultaneity
convention are not found to be synchronized when they are
examined again in other inertial frames according to the 'same'
convention for distant simultaneity. Given a set of events
P_1, P_2, ... P_n with time and space coordinates (t_1,x_1),
(t_2,x_2), ... (t_n,x_n) that are simultaneous in one frame,
t_i = t_j, but spatially separated, x_i not equal to x_j, then
the same set of physical events will, in all other inertial frames,
according to the 'same' simultaneity convention, have coordinates
(t'_i, x'_i) that are not simultaneous, t'_i not equal to t'_j.
This can easily be proved by mere inspection of the Lorentz
transformations or by Lorentz-transforming the coordinates of
two point events P_1 and P_2 for which, initially, t_1 = t_2 and
x_1 not equal to x_2.
Thus, unless additional information is supplied, the statement
that 'moving clocks run slow' is an artifact completely without
physical significance. Time dilation is not a philosophical
statement as to what is or is not real, and it tells nothing about
the physical time differences that might exist between spatially
separated clocks, were they (as is impossible) magically and
instantaneously reunited. It is purely a symmetric, definitional
artifact of measurement created by the adoption of the Einstein
simultaneity convention, a 'bookkeeping procedure' adopted to give
empirical meaning to the statement that two or more spatially
separated events occur simultaneously. This convention depends on
the reference frame in the same way that the magnitudes of the
components of an ordinary vector depend on the location and
orientation of the axes of the reference frame in which the vector is
to be resolved into components."
Over
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