Re: I Owe Einstein an Apology. Sorry Albert!

From: Androcles (dummy_at_dummy.net)
Date: 12/12/04 

Date: Sun, 12 Dec 2004 20:07:09 GMT

"The Ghost In The Machine" <ewill@sirius.athghost7038suus.net> wrote in
message news:e57u82-fav.ln1@sirius.athghost7038suus.net...

>
> The SR correction is t' = (t-vx/c^2) * gamma .
>
> The vx/c^2 is merely a reflection that the two clocks are
> communicating through speed-of-light (e.g., radio), but
> the gamma is the killer; gamma = 1/sqrt(1-v^2/c^2).
>
> It's a very slow killer, of course; the typical speed
> of a spacecraft is on the order of 9 km/s = 3 * 10^-5 c, which
> results in a gamma of about 4.5 * 10^-10. The GPS delta is
> almost exactly this: 4.46 * 10^-10. However, this is at
> best a very very rough estimate, just to give one the feel.
> It's also the wrong sign. :-)

LOL.
"That is, we can reverse the directions of the frames
 which is the same as interchanging the frames,
 which - as I have told you a LOT of times,
 OBVIOUSLY will lead to the transform:
  t = (tau-xi*v/c^2)/sqrt(1-v^2/c^2)
  x = (xi - v*tau)/sqrt(1-v^2/c^2)
 or:
  tau = (t+xv/c^2)/sqrt(1-v^2/c^2)
  xi = (x + vt)/sqrt(1-v^2/c^2)" -Paul B. Andersen

>From this there ensues the following peculiar consequence. If at the
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 synchronize, but the clock moved from A to B leads in
front of 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 still 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 fast. Thence we conclude that a
balance-clock at the equator must go more quickly, by a very small
amount, than a precisely similar clock situated at one of the poles
under otherwise identical conditions.

Androcles, with tongue in cheek.

> An accurate clock left running for a year in a GPS orbit
> will gain about a hundredth of a second. (SR predicts loss
> of time, but then SR requires straight-line freespace
> travel. :-) ). Therefore, GPS clocks are "broken" by
> design, coding in this adjustment factor -- and even
> then, they have to be steered from the ground using
> synchronization signals from the TAI.
>
> Presumably the spacecraft time can be kept accurate by
> common-view GPS time transfer techniques as detailed
> in the above article. I for one can't say.
>
> [rest snipped]
>
> --
> #191, ewill3@earthlink.net
> It's still legal to go .sigless.

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