Re: Annotated Einstein Clock
- From: "Paul B. Andersen" <paul.b.andersen@xxxxxxxxxxxxxxxx>
- Date: Tue, 02 Aug 2005 14:54:32 +0200
sue jahn wrote:
Annotated Exerpt from: XII. The Behaviour of Measuring-Rods and Clocks in Motion Albert Einstein (1879-1955). Relativity: The Special and General Theory. 1920 http://www.bartleby.com/173/12.html ============================================ [Begin non-clock fluff] A priori it is quite clear that we must be able to learn something about the physical behaviour of measuring-rods and clocks from the equations of transformation, for the magnitudes x, y, z, t, are nothing more nor less than the results of measurements obtainable by means of measuring-rods and clocks. If we had based our considerations on the Galilei transformation we should not have obtained a contraction of the rod as a consequence of its motion. 4 Let us now consider a seconds-clock which is permanently situated at the origin (x' = 0) of K'. t' = 0 and t' = 1 are two successive ticks of this clock. The first and fourth equations of the Lorentz transformation give for these two ticks: t = 0 and
(eqution for interval t)
[End non-clock fluff]
As judged from K, the clock is moving with the velocity v; as judged [ note that judgement over a non zero length path is the only mechanism stated to cause a variation in local and remote clocks] from this reference-body, the time which elapses between two strokes of the clock is not one second, but
http://www.bartleby.com/173/M5.GIF (equation for interval)
seconds, i.e. a somewhat larger time. [here we must make the assumtion that the clock is moving away from the observer. if it was moving toward the observer, he would say "a somewhat smaller time" ] As a consequence of its motion [away from the observer] [Doppler effect] the clock goes more slowly than when at rest.
You are indeed confused. Time dilation has nothing whatsoever with Doppler effect to do, and it is irrelevant in which direction the clock is moving. When measured in K, the moving clock is running slow. It doesn't matter where an optional observer might be. And a clock that is running slow has _longer_ seconds. That is why it is called time _dilation_.
Here also the velocity c plays the part of an unattainable limiting velocity. [the result of Coulomb coupling to matter in the local FoR]
======================== Comments The clock described, in order to slow with motion, depends on the *inclusion* of an optical path delay, which increases with the motion. The clock is not characterized for motion which would decrease the path length.
Utter nonsense. :-)
Absent is any inversse form of equation http://www.bartleby.com/173/M5.GIF
And why would you have an inverse form of said equation? The LT is: x' = (x - vt)/sqrt(1-v^2/c^2) t' = (t - vx/c^2)/sqrt(1-v^2/c^2) the inverse transform is: x = (x' + vt')/sqrt(1-v^2/c^2) t = (t' + vx'/c^2)/sqrt(1-v^2/c^2)
> further absent is a rigorous demonstration that such > inverse application will conserve all clock strokes > emitted as images.
What is this? New-speek? :-)
Paul .
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