Re: About the LT and the Euclidean geometry
- From: "Paul B. Andersen" <paul.b.andersen@xxxxxxxxxxxxxxxx>
- Date: Tue, 09 Sep 2008 16:02:45 +0200
Stamenin wrote:
THE EUCLIDEAN GEOMETRY AND THE LORENTZ TRANSFORMATION
The affirmation that the Euclidean geometry is errant theory is an
astonishing assumption done by Einstein and it is a wonder how was
that possible not to be criticized by other scientists. How is
possible to negate that the sum of two segments AB and BC is not equal
with AC.
__ __ __
AB + BC=AC
The only argument given for the support of this supposition, are the
magic words: “the evident is not evident”. For the word evident
Einstein uses in his book a “stronger” word far better and suggestive:
holds.
He didn’t take in consideration that evident means something
obviously plain and clean and something that can be seen. It is a
notorious truth that we can know everything about the nature, about
our environment, only if we can see it. How can we know what is the
infinity of the universe if we can’t go there and see what alike is
that? The theories done on the base of experiments are done
practically by the use of the term evident because there is used the
seeing and the experiments in order to know what is going on.
01 02 M
o----------------o--------------o-----x1, x2 where x1=01M,
and x2=02M
K1 K2
Fig.1.
(This is a short presentation of the two coordinate systems K1 and
K2. 01 and 02 are the origins of the two systems and M is the
projections of a material body that is moved with the speed v2 in the
positive direction.)
Einstein doesn’t support the former assumption, that the Euclidean
geometry is erroneous with the aid of the theory of the relativity,
for example by using the Lorentz transformation. He left it apart as
if it is understandable by itself. Let us see what the Lorenz
transformation says about this question.
In fig.1 are represented two coordinate systems K1 and K2
considered as being inertial systems. The Lorenz transformation
considering that the motion is done only in the direction of the
coordinates x1 and x2 are:
x1=(1/R) (x2+v.t2)……..(1) x2=(1/R)(x1-v.t1)………(3)
t1=(1/R)(t2+v.x2/c^2)….(2) t2=(1/R)(t1-v.x1/c^2)…..
(4)
Where R=(1-v^2/c^2)^0,5.
Making an analogy between the segments AB and BC, with the segments
0102 and 02M shown in fig.1 we can obtain the following results.
From the relation (1) of the Lorenz’s transformation we can obtain:
0102=(1/R)(v.t2)
02M=x2/R
From the relation (3) of the Lorenz’s transformation we can obtain:
0102=v.t1/R
02M=x2=(x1-v.t1)/R
So we can put now all these results together, considering that the two
segments must have a unique length.
0102=v.t2/R=v.t1/R.…..
5
02M=x2/R=x2=(x1-v.t1)/R…………6
From the relation 5 results that t1=t2 that shows that the correct
transformation is the Galileo transformation.
From the relation 6 we have got an absurd result
x2=x2/R
x2/R=(x1-vt1)/R, or x1/R=x2/R+v.t1/R
x1=x2+v.t1, that means again that the Galileo Transformation is
correct. So the LT could be correct if we suppose that the two
segments 0102 and 02M do not have a unique length. What could mean
this? Maybe we have to accept not only AB+BC=AC is not correct
relation but also and the segments AB and BC are not equal with it
selves.
It has always puzzled me how it is possible to write a lot
of utter nonsense without realizing that it is just that. :-)
--
Paul
http://home.c2i.net/pb_andersen/
.
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