Re: SR fundamental contradiction
- From: "harry" <harald.vanlintelButNotThis@xxxxxxx>
- Date: Thu, 28 Sep 2006 11:38:46 +0200
Just in addition to other comments:
<mluttgens@xxxxxxxxxx> wrote in message
news:1159389848.201827.170900@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
SR fundamental contradictionSNIP
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Luttgens:
Let x = ct.
Then x' = g(x - vt), where gamma = 1/sqrt(1-v^2/c^2), becomes
x' = g(c-v)t
What represents the length (c-v)t?
Is that length "dilated" by g?
Luttgens:
Any object (stick) measures shorter in terms of a frame relative to
which it is moving with velocity v that it does as measured in a frame
relative to which it is at rest, the ratio of shortening being
sqrt(1-v^2/c^2).
This is a relation between measurements referred to different frames.
If a stick of length x' = g(c-v)t is at rest in the S' frame,
Aargh!
Usually sticks are supposed to have a constant length. But in your equation,
presumably c=lightspeed, v may be constant thus g=constant while t changes.
Thus at constant speed, at t=2 your stick is twice as long as at t=1 while
it even has zero length at t=0. Your "stick" is perhaps made of rubber, with
someone pulling on it?!
x' is normally used for position coordinates, *not* for lengths. x' is used
in transformation equations (=between position coordinates) as well as in
trajectory equations (= position coordinate of something as function of
local time).
Tom Roberts explained that rather well except for one important point: you
can of course combine the two sets of equations in order to obtain the
position coordinate of the wave front ^^^ in the moving frame.
You might help yourself as well as this kind of discussions a lot by first
trying "Galilean" relativity: Starting with the equation of motion x' = w t
of a bowling ball that is thrown along the full length of a train wagon
relative to the train in motion, and the transformation equation between
train coordinates and embankment coordinates x' = x - v t, describe the
trajectory x(t) of the ball relative to the embankment. Now do the same for
the trajectory x(t) of the train wagon's rear end. Is there a contradiction?
Why not?
Harald
.
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