The Theory of Relativity
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If you have read the other papers on this site, especially Cosmos, and you are still not convinced of Hyperspace, this article will convince you. From now on, it will be out of the question to study modern physics without calling upon hypergeometry. In the beginning of the 20th century hypergeometry was still unknown, and that is the sole and only reason why Einstein did not realize that relativity is a hyperspace phenomenon. ...........................................................
Let me explain. .........................................................................................
Although the book ‘Hypergeometry’ has not been published as yet, I am going to use this notion here. Proceeding stepwise, there will be no problem whatsoever. .........................................................................................
Although, generally speaking, I use to be somewhat greedy with mathematics, I cannot help to outline a few mathematical results to show their beauty and relevance. But it will be no more than a tiny bit of maths. .........................................................................................
When talking about the restricted relativity theory we discuss contraction of space and expansion of time. Let us speak about contraction of space to begin. Formula .........................................................................................



also known as the Lorenz Contraction, is a mathematical translation of what we are talking about. .........................................................................................
What does Space Contraction mean? Let us make an initial correction: it is not a contraction of space, it is a dimensional contraction. .........................................................................................
Why dimensional contraction? Because space never contracts; the dimensions of the object submitted to relativistic speed do. .........................................................................................
Now let us try to solve the paradox. The observer at rest sees a vessel, size L, moving at relativistic speed v and having the apparent dimension l, smaller than L. .........................................................................................
This is a hyperphysics phenomenon that has been drawing my attention since the very beginning. As a matter of fact, as the vessel is not only in three-dimensional space where it is submitted to relativistic speed, it projects a dimension that is smaller than its real dimension onto our Guimel space. .........................................................................................
What are Guimel spaces, after all? In hypergeometry language, three-dimensional spaces are called ‘Guimel spaces’. They are spaces that have three dimensions. Nothing more. The space in which we live is a Guimel space. A space that has four dimensions will be called ‘Daled space’. All this is not quite complicated; it is merely a matter of hypergeometry nomenclature. .........................................................................................
Let me explain. .........................................................................................
Let us imagine a Guimel space inside a Daled space. .........................................................................................
That is all I need. .........................................................................................
It is true that we cannot see the fourth dimension. However, this is exactly what happens. The vessel points to the fourth dimension and its projection in our Guimel space shows a shrunken vessel. .........................................................................................
Here comes an example. .........................................................................................
At noon sharp of a sunny day, lay a ruler on the ground. .........................................................................................
Hypergeometry does not tend to complicate things. Much to the contrary, it helps us understand complex problems, including those problems which, quite logically, appear to be incoherent. Hence, we are going to use it once again.
Hypergeometry allows us to study any multidimensional phenomenon by making use of the necessary dimensions only, and the appropriate axes. We shall therefore consider axes X and X’ only. As we are taking no more than two axes into consideration, we are in a position to imagine it and draw up a direct representation of this two-dimensional space (a plane).
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Axis X is the axis parallel to the motion speed of the vessel at dimension L. Axis X’ is the fourth axis of the Daled space. .........................................................................................
See Figure 1. It is self-explanatory. .........................................................................................

Figure 1

Ruler L, when in horizontal position, projects X on L. When in an inclined position at angle eta, the same ruler will make projection l , where l = L cos(eta). .........................................................................................
If we call it
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in which v is the speed of the vessel and c is the speed of light, we agree to the very simplified formulae set forth by Paul A. Tripler in his book ‘Modern Physics’. I shrewdly used ‘cosine’ . Why? Because cosine suggests projection. And that is exactly what I want to suggest. .........................................................................................
Let us once again call upon our little ant. The ant is, essentially and by definition, a small, two-dimensional creature. The ant moves on planes. If you give a playing card to the ant to climb it, it does what, geometrically speaking? In three-dimensional space, there are infinite two-dimensional spaces. One of them is the plane. When the ant begins climbing the playing card, it leaves a plane (the floor) and begins moving on a different plane. In four-dimensional space, Daled, are an infinity of three-dimensional spaces, Guimel.
Let us see whether you understand:
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Upon reaching relativistic speed, the vessel and its Guimel space distance from our Guimel space. All this occurs within a four-dimensional space, Daled. .........................................................................................
In a quite simple manner, the length of the vessel moves in the sense of axis X’. The real length L of the vessel remains unchanged. What we are able to see is merely the projection l of the vessel´s length L in our three-dimensional space.
Look at the figure and think.
Hypergeometry allows to draw conclusions without using the other axes.
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Now l = L cos(eta). .........................................................................................
There remains a lot to be said about this figure, but I would like to avoid this paper to become too extensive. .........................................................................................
Let us enter the vessel. .........................................................................................
Now look at the figure. Let us suppose that l is the length of a runway. To whom is in position L in plane XX’, the landing distance appears shorter as well. The dimension will not be seen as l (AB), but as (AD) ; using exactly the same projection: (AD) = (AB) cos(eta). .........................................................................................
Look how hypergeometry simplifies everything. But is this really so? Let´s check. .........................................................................................
In his book ‘Concepts of modern physics’ Arthur Beiser gives us a good example of the contrary. According to Beiser, a meson µ disintegrates into an electron in 2.10-6 seconds after it has been created. Mesons are created by cosmic rays in the upper atmosphere. Their speed is 2,994.108 meters/second, that is 99.8% of the speed of light. Figuring it out, one will see that they can move no more than 600 meters. But these 600 meters are to be seen as seen from the mesons. Figuring it out again after having made the cos(eta) correction, one will notice that, for us, nearly 10 km have been covered.
This explains why mesons can reach Earth, coming from very high.
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In the light of these new concepts, this is all becoming very obvious. .........................................................................................
But... time?
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To those who do not know what chronic dimensions are, it is recommended to read Cosmos. .........................................................................................
Incredible but true; exactly the same thing happens. .........................................................................................
The only difference is that axes will be chronic: T and T’. Of course, we will check a chronic plane. I am not going to make a new figure, for it will be equal to the foregoing. Relativity teaches us:
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“Time measured in any relativistic reference system will always be slower than stationary reference time.” .........................................................................................
If, in the present case, we use cos(eta) to compute the length of the vessel, we should use 1/cos(eta).
How can they be equal? Did you pay very careful attention with respect to the metric case? Hence, you are aware of how important it is to know on whose point of view you are.
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In the paradox case of the twins, the one who goes on a journey remains younger. And you have changed your mind. Your may want to know how much time was counted by the clock of the one who stayed home as compared to the time measured by the clock of the one who traveled. What will have happened is exactly the same as what has happened in the example of the meson. The distance covered in the atmosphere was in fact much longer than the distance covered by the meson in its relativistic reference. .........................................................................................
Exactly the same. .........................................................................................
Look how well the hypergeometric model is doing. .........................................................................................
I am only opening the path There is still a lot of work to be done. I myself would still have a lot of comments to make. The physical meaning of angle eta, the meaning of the fourth coordinate, what is the meaning, in physics, of sine(eta), etc. Only through exchange of information science will really progress. I hope I am contributing.
Have a fun!
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