Re: GPS CLOCK PARADOX

"Paul B. Andersen" <paul.b.andersen@xxxxxxxxxxxxxxx> wrote in message
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Jeckyl skrev:
"Dirk Van de moortel" <dirkvandemoortel@xxxxxxxxxxxxxxxxxxxxxxxxxxx>
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"Jeckyl" <noone@xxxxxxxxxxx> wrote in message
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"snapdragon31" <snapdragon31@xxxxxxxxx> wrote in message
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[snip]

4. x' = x * sqrt(1 - v^2/c^2)
5. t' = t * sqrt(1 - v^2/c^2)

So what do these equations mean?

It means that when M has travelled distance x in time t relative to S, it
will have seen S travel distance xz' in time t' relative to M

With that meaning (which is what I assumed the poster meant), the equations
are valid

They are not meant to be general transforms, but they are easily derived
from the Lorentz transforms

Conclusion:
the (x',t'), and the (x,t) in the equations:
x' = x * sqrt(1 - v^2/c^2)
t' = t * sqrt(1 - v^2/c^2)
cannot be the coordinates of an event in the respective frames

That's right .. they are not meant to be

No .. all fine for all values where x = vt (ie for all spacetime events
along the path of M). Lorentz transforms do work for values other than 0
you know !! :)

But the equations you double checked do not work for values other than 0.

Yes .. they do .. when you interpreat what the poster meant for x and x'.

Did you possibly miss what Dirk said was not fine?

No.

Did you not see my derivation of those formulas from the Lorentz transform
(ignoring that I wrote an assumed condition as "x=x'=0 and t=t'=0" instead
of "when x=0 and t=0 we have x'=0 and t'=0" (ie just making sure the origins
of the two frames of reference for M and S coincide at time 0.

I think you guys are being overly critical and not taking the time to work
out what the original poster was meaning.

When one does that, one sees that the OP error was not in the two large sets
of equations and calcs, but in equating the x and t values in the two sets
even though they are measuring different quantities, and then concluding
that there was a contradiction.


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