26/05/2014
Calabi-Yau, Euler characteristics, and the current state of Theoretical Physics compared to Mathematical and Experimental Results
The Calabi-Yau, with all of its beauty and mathematical inspiration, has been adapted to the Standard model, in the concept that all the elementary particles are divided into only three families or generations.
Candelas and others worked a manifold, which yielded 4 families of particles; even if the difference was only one, the scales of particles are logarithmical, and so, it is logical that the difference between 3 and 4 is enormous. A heavy neutrino (the fourth one), found in other theories, has room in Candela’s approach.
In order to adapt the conditions of the Standard Model, the Calabi-Yau needed a manifold with an Euler characteristic of 6 or -6. Using a manifold with an Euler number of -6, Yau obtained 4 complex dimensions. He cut this into 3 complex dimensions (or six real dimensions). The manifold yielded 9 families of particles, rather than the desired 3. Creating a quotient manifold in which every point corresponds to three points in the original, taking the quotient and dividing the original into 3 equivalent pieces, the number of points was decreased by a factor of 3, and so the Standard Model’s number of families was obtained: 3. The geometry and mathematics uses have been spectacular; but there has been a deficiency in the concepts of theoretical physics. The Standard Model is excellent for talking over the known particles and forces that can be tested, but it is impossible to guess about unknown particles or at least, particles, whose corresponding scales of power (too heavy or too light), have been impossible to reach.
Since the mathematical concept is one half of Euler’s Number, +6 or -6, it is possible to obtain two manifold, one for Euler +6, and the other, for Euler -6 obtaining 1/2 (6)+1/2 (6)=6 families.
The importance is in the physical theory, solving first some fundamental doubts:
-How many dimensions does the dimensional modulus have?
-How many components does each particular dimension have?
-Does all the components of each dimension have the same footing?
-Does each dimension have a different footing among other dimensions?
-Does the number of dimensions in a dimensional modulus diminish when the dimensions stretch (4 in our Universe)?
-Why do the dimensions of strings are 10 and 26?
-How many families (or generations) of particles have existed in our Universe, from its beginning to its end?
-Will all the dimensions eventually stretch out?
-How did massless particles of matter existed before the appearance of the Higgs weak boson?
-Why does the Higgs weak boson give mass to the particles of matter?
-Why do massless particles of matter existed before the Higgs weak boson?
-Why is the Higgs field destroyed by heat?
-Etc., etc.
It is impossible to request a solution to mathematics and geometry if the physical theory is still incomplete.
Note: The Calabi Yau is a beautiful and marvelous mathematical artifact. But the Standard Model sets up the rules on how many families of particles are there. Although Yau suspected that there are an undefined number of families of particles, the Calabi Yau was then adapted to fit the Standard Model's supposition of only 3 families of vibrational patterns, and thus only 3 families of particles will be observed experimentally. We disagree with this particular point. For us, the number of holes in the Calabi Yau is 6, and it is necessary to find a new heavier scale of 3 families, besides the known lighter scale.
The lightest particle of this heavy scales, and thus, beyond the Standard Model, is the sterile neutrino, fundamental component of Dark Matter, whose mass is approximately 132 GeV/c^2, which we call neutronio.
