Re: GPS CLOCK PARADOX

"Dirk Van de moortel" <dirkvandemoortel@xxxxxxxxxxxxxxxxxxxxxxxxxxx> wrote
in message news:fnqdd0$sv5$1@xxxxxxxxxxxxxxxxxxxxxx
"snapdragon31" <snapdragon31@xxxxxxxxx> wrote in message
news:334d88d4-ff89-4573-bf6d-f377ec0a220d@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Please note that x' is defined as a distance measured by twin M not
displacement.
Both x and x' are not vectors.
A more correct equation should be
x' = |v| * t'
distance = speed * time

then the other equation should be
x = - |v| * t
so you induce a new error.

Not if x and x' are distances .. distances are non-negative numbers



4. x' = x * sqrt(1 - v^2/c^2)

Only valid for events satifying
t' = 0
Exercise: Why?

x' = x * sqrt(1 - v^2/c^2) Length contraction

Only valid for measurements of two sides of an object
when measured simultaneously in the primed frame,
expressed by
t' = 0
Check the definition of length contraction.

The formula given is correct, and what LT predict .. given that x' refers to
the distance M sees S having moved (in M's corrdinates) at the time M gets
to position x wrt S.
Congratulation, you figure out that both the Length Contraction and
Time Dilation equations can be true only when x' = 0, x = 0, t' = 0
and t = 0. If they are not valid equations then twin paradox is not a
paradox any more.

The two are *together* valid if and only if everything
is zero, so when you write
x' = x * sqrt(1 - v^2/c^2) Length contraction
t' = t * sqrt(1 - v^2/c^2) Time dilation,
you actually write
0 = 0
0 = 0 ,
and that is something we all know, thank you.

Not correct. The figures he shows are just fine .. the show the results of
length contraction and time dilation correctly. However, the x and t in the
first set of equations is measuring something different to the x and t in
the second set, and so it is not valid to directly compare the results as
the OP did.

What he is doing is the equivalent of

x = vt

so at t = 1 and v = 1 we get x = 1
but at t = 2 and v = 1 we get x = 2
therefore 1 = 2


.

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