Re: SR fundamental contradiction
- From: "Dirk Van de moortel" <dirkvandemoortel@xxxxxxxxxxxxxxxxxxxxxxxxxxx>
- Date: Wed, 27 Sep 2006 21:30:00 GMT
<mluttgens@xxxxxxxxxx> wrote in message news:1159389848.201827.170900@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
SR fundamental contradiction
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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?
Van de Moortel:
Consider the event E on the light signal with x = c t for some
chosen value of t.
Then c t - v t is the distance between the origin of S' (the 'moving
observer') and the light signal, as seen at time t in the S-frame
(the 'stationary frame'), and, by the way, so c - v is by definition
the closing velocity between the two.
For this event E, as seen in S', the light signal has covered the
distance
x' = c t' = g (c - v) t
This is a distance of the event E in the S' frame.
Now imagine a stick with this particular length
x' = g (c-v) t
at rest in the S' frame.
What is the length of such a stick in the S-frame?
If you apply length contraction, you find that this length
would be
x' / g = (c - v) t
in the S frame.
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).
which equals 1/g just like I explained.
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,
it is moving at v relative to the frame S. So, measured in S, its
length is contracted by 1/g and becomes x = g(c-v)t * 1/g = (c-v)t.
yes
This corresponds to Van de Moortel's reasoning, which is circular.
Marcel calls the bleeding obvious "circular".
Indeed, x' = g(c-v)t has been obtained *by applying the LT* to
x = (c-v)t, when S' was considered as moving relative to S, and thus
relative to the stick. No wonder that one gets back x = (c-v)t
when S is afterwards considered as moving wrt S'.
Indeed no wonder.
The transformation is consistent with length contraction.
Do we have a breaktrough here?
Has Marcel's Precious Penny dropped?
One has instead to consider a stick of length x = (c-v)t at rest
in the frame S. Relative to the frame S', such stick is moving
at v, hence its length, measured in S', is shortened by 1/g wrt its
length measured in S. Thus, x' = (c-v)t / g.
But *according to the LT*, x' = (c-v)t * g !
Such contradiction demonstrates the falseness of the Lorentz
transformation, falseness whose origin lies in the postulate
that when x = ct, x' = ct'.
You had a light signal going at c and an object going at v
in some frame S and you wondered
"What represents the length (c-v)t?"
I gave you a possible physical object, namely one with length
g (c-v) t at rest in S', that can have this value (c-v) t as its length
in the S-frame. So your question was answered.
Now you imagine another possible physical object, namely one
with lenght (c-v) t at rest in S, which has of course lenght
1/g (c-v) t in frame S', according to the same rules.
Since we are talking about two different objects, there is no
contradiction. Quite on the contrary ;-)
You are suffering from your original syndrome again:
http://users.telenet.be/vdmoortel/dirk/Stuff/MarcelAtSchool.gif
See a doctor about it. Trust me.
Dirk Vdm
.
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