The Model
Supplementary proof of the reality of the three-coloured electron, it has its mathematical model in the Group of permutations G3.
The mathematical Group G3 is the set of the 6 permutations of 3 objects, symbolized by letters a, b, c in the mathematical speech and, in physics, by 3 charges of color, red, green, blue of the quantum chromodynamique.
The geometrical interpreter of the group G3 is the equilateral triangle which 6 permutations are presented in the picture below.
The triangle of G3 is inevitably the model of the triangle which symbolizes the quantum electron, because they are both a set of 3 elements which switch around.
As any set of 3 elements, each of 6 permutations of G3 has 8 subsets, there is thus 6 x 8 = 48 subsets which are presented in the two pictures below.
However it seems to exist a difference between the origin of the two tables: the mathematical arises of a set of 3 letters, whereas that of the physics arises from a single letter, γ which symbolizes the photon, the set of the 3 mixed colors.
Actually, the origin of mathematical table is not between brackets: (a, b, c) but between braces, that is to say {a, b, c}, to mean that its elements are mixed, like those of the photon.
In this table, 6 arrows which connect the original Photon γ to the matter: (e-, µ-, t-) and to the antimatter: (e +, µ +, t +) are the 6 Bosons de Higgs.
In their extremities, distributed in 3 Generations, also say Families, 3 couples of matter and antimatter, e-/e +, µ – / µ +, t-/t +, generate their 48 subsets. Because, according to the Set theory: any set of 3 elements, here the electron, has 8 subsets.
Why these 3 generations of 2 connect each? For very simple reasons.
There are 3 generations because there are 3 charges of different colors, the red, the green, the blue: that of the generation electron, that of the generation muon, that of the generation tau. They appear in the previous picture which visualizes, by the triangles of G3, their 6 permutations, which they also mean, by their color, in the first compartment of every line of the table in 48 compartments.
In each of 6 permutations of the triangle, the summit is the invariant, and if 2 charges of color of the base switch around, it’s loke a reversal of the triangle, which thus inverts its direction of rotation. So the matter is transformed into antimatter, its opposite. And that is why every generation has 2 Branches.
The only difference between the matter and the antimatter is, indeed, their direction of inverse rotation. The experiment showed it: if by a magnetic field, we invert the direction of rotation of an electron, it is transformed into positron.
In the group G3, there are only 3 objects, here 3 charges of color, which thus make, successively all the permutations. That is why there is an interval of time between every permutation and the opposite, for example between the electron and the positron which, obviously, cannot turn simultaneously in inverse directions. What happens during this interval?
According to the process described in the page Visualization, 3 charges of color of the electron merge in a photon which makes the permutation by creating the positron.
The 6 lines of the table carry, each, 4 constituents of the universe: the quark, the antiquark, the electron and its complement, the neutrino. There are 3 quarks, because each carries one of 3 fundamental charges of color of the quantum chromodynamique.
Also, there are 3 antiquarks, because each carries the association of 2 complementary color charges of of the charge of the corresponding quark, to reconstitute the set of the 3 charges of color.
The superior line of the table, that of the 1st branch of the Family, contains 8 elements of the current matter, that of the 2nd branch contains 8 elements of the symmetric antimatter.
Built according to the same model, but more ancient, the following 2 Families, of ( µ ) and of ( τ ), are said fossils, their important masses, especially that of (τ), do they make, nevertheless, part of the » missing mass » of the universe?
So, the model of the universe would be a set of 3 elements, charges of color of the quantum chromodynamique, sometimes mixed: it is the photon, white, sometimes different: it is the electron, three-coloured, with its 6 permutations of 3 charges of color and their 48 subsets.
If each electron appears twice in the picture, it is because: any set is subset of itself. There is thus an electron-set at the beginning of every line, and an electron-subset in the 7th compartment of every line.