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The Metric Tensor Of Riemann.


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Recall that the basis of Riemann's and Einstein's work
is the metric tensor — that is, a collection often numbers defined at each
point in space. This was a natural generalization of Faraday's field con-
cept. In Figure we saw how these ten numbers can be arranged as
in the pieces of a checker board with dimensions 4X4 . We can denote
these ten numbers as g„, g„ ...

Furthermore, the field of Maxwell is
a collection of four numbers defined at each point in space. These four
numbers can be represented by the symbols A1, A2, A3, A4.

To understand Kaluza's trick, let us now begin with Riemann's theory
in five dimensions. Then the metric tensor can be arranged in a 5 X 5
checkerboard. Now, by definition, we will rename the components of Figure. Kaluza's brilliant idea was to unite down the Riemann metric in five
dimensions. The fifth column and row are identified as the electromagnetic field
of Maxwell, while the remaining 4X4 block is the old four-dimensional metric
of Einstein.

In one stroke, Kaluza unified the theory of gravity with light simply
by adding another dimension. Kaluza's field, so that some of them become Einstein's original field and some of them become Maxwell's field. This is the essence
of Kaluza's trick, which caught Einstein totally by surprise. By simply
adding Maxwell's field to Einstein's, Kaluza was able to reassemble both
of them into a five-dimensional field.

"Michio Kaku. Hyperspace. A Scientific Odyssey Through Parallel Universes, Time Warps, And The 10th Dimens Ion"

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When carefully analyzing the full five-dimensional the-
ory, we find that Maxwell's field is nicely included within the Riemann
metric tensor, just as Kaluza claimed. This innocent-looking equation
thus summarized one of the seminal ideas of the century.
In summary, the five-dimensional metric tensor included both Max-
well's field and Einstein's metric tensor. It seemed incredible to Einstein
that such a simple idea could explain the two most fundamental forces
of nature: gravity and light.

Was itjust a parlor trick? Or numerology? Or black magic? Einstein
was deeply shaken by Kaluza's letter and, in fact, refused to respond to
the article. He mulled over the letter for 2 years, an unusually long time
for someone to hold up publication of an important article. Finally,
convinced that this article was potentially important, he submitted it for
publication in the Sitzungsberichte Preussische Akademie der Wissenschaften.
It bore the imposing title "On the Unity Problem of Physics."

In the history of physics, no one had found any use for the fourth
spatial dimension. Ever since Riemann, it was known that the mathe-
matics of higher dimensions was one of breathtaking beauty, but without
physical application. For the first time, someone had found a use for the
fourth spatial dimension: to unite the laws of physics! In some sense,
Kaluza was proposing that the four dimensions of Einstein were "too
small" to accommodate both the electromagnetic and gravitational

We can also see historically that Kaluza's work was not totally unex-
pected. Most historians of science, when they mention Kaluza's work at
all, say that the idea of a fifth dimension was a bolt out of the blue, totally
unexpected and original. Given the continuity of physics research, these
historians are startled to find a new avenue of science opening up without any historical precedent. But their amazement is probably due to
their unfamiliarity with the nonscientific work of the mystics, literati,
and avante garde.

"Michio Kaku. Hyperspace. A Scientific Odyssey Through Parallel Universes, Time Warps, And The 10th Dimens Ion"

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And you have successfully proven why people that don't understand higher level math should post nothing about it, you act as if it is something magical it is just a peice of mathematics with no symbolic meaning and the parts about 55 being something special is nonsense, Obviously you don't understand how Tensors nor matrices work by the body of this thread, if you don't understand it don't post about it. Multi-dimension matrices and tensors are used all the time a 5x5 matrix is nothing special mathematically.

Edited by VictorMedvil
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MILLIONS of mathematicians over the course of 160 years of looking at the metric tensor of the Riemann -- did NOT SEE !
And just AS I NOTICED the strange above  "coincidence" : 






g22 + g33 = g55
g32 + g23 = g55
g11 + g44 = g55
g41 + g14 = g55
g21 + g34 = g55
g31 + g24 = g55

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55 is the sum of ten digits of the decimal system
55 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10
55 is the tenth number of the Fibonacci series 1, 1, 2, 3, 5, 8, 13, 21, 34, 55
55 is the tenth triangular number 1, 3, 6, 10, 15, 21, 28, 36, 45, 55
55 is the sum of the first five square numbers 1, 4, 9, 16, 25
55 is the fifth square pyramidal number 1, 5, 14, 30, 55
Only four numbers 1, 55, 91, 208335 are both triangular and square pyramidal



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The Metric Tensor Of Riemann.


  gij =    g31--g32--g33--g34



                 1      2       3      4
      1     g11--g12--g13--g14    4
      2     g21--g22--g23--g24    4
      3     g31--g32--g33--g34    4
      4     g41--g42--g43--g44    4
                 1      2       3      4


                 1 + 2 + 3 + 4 = 10


        The tetractys of the decad .




           1 + 2 + 3 + 4 = 10

Pythagorean symbol, the tetractys, or tetrad, or the tetractys of the decad is a triangular figure consisting of ten points arranged in four rows: one, two, three, and four points in each row, which is the geometrical representation of the fourth triangular number. As a mystical symbol, it was very important to the secret worship of Pythagoreanism. There were four seasons, and the number was also associated with planetary motions and music.


1.The first four numbers symbolize the musica universalis and the Cosmos as:
(1) Monad  (Unity)
(2) Dyad   (Power – Limit/Unlimited (peras/apeiron)
(3) Triad  (Harmony)
(4) Tetrad (Kosmos)


2.The four rows add up to ten, which was unity of a higher order (The Dekad).


3.The Tetractys symbolizes the four classical elements—fire, air, water, and earth.


4.The Tetractys represented the organization of space:
(1) the first row represented zero dimensions (a point)
(2) the second row represented one dimension (a line of two points)
(3) the third row represented two dimensions (a plane defined by a triangle of three points)
(4) the fourth row represented three dimensions (a tetrahedron defined by four points)

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