Now, I have discussed some issues on the “Spontaneous Symmetry Breaking” (SSB).
1. The SSB for quarks arises from three lower tier SSBs.
a. ED (SSB) --- energy dimension symmetry breaking. V (zero energy) and A (non-zero energy)
b. GD (SSB) --- singularity point symmetry breaking. Singularity point and a loop
c. ID (SSB) --- internal structure symmetry breaking. A loop and a line.
And, these three SSBs (ED, GD and ID) form a space-time sheet as the lower tier for the quark tier. With the principles of the Linguistics Manifesto (http://www.chinese-word-roots.org/cwy.htm ),
i. This space-time sheet is the source of SSB for the quarks.
ii. The quarks arise from a similarity transformation from its lower tier, its space-time sheet.
This quark space-time sheet is described in detail by the Prequark Chromodynamics ( http://www.prequark.org/ ).
2. The SSB for ED, GD and ID arise from a new number theory.
In this new number theory, the geometric “point” on the number line is an “information agent” which has the self-awareness and is conscious of all other points in the number line. In fact, every number “point” houses infinite numbers. For example, the point for the number “3”, it houses
b. “1/3” via a loop (operation)
c. “square root 3” via a loop of “square root”
d. “3 square” via …
e. etc. to …
All those numbers above reside in the “point 3”. That is, the point “3” sucks other numbers in via a “loop”. Thus, the point “3” is the “node point” of many, many loops, with every loop as a pathway to pinch a number into the point “3”.
With the understanding of this new number theory, the symmetry breaking of a singular geometric point into a loop, then into a line, becomes an innate and spontaneous process.
Yet, there is a big question. While a singular geometric point has an infinite internal structure, how can a “single” space-time sheet arise from those infinite possibilities? Why are these series of SSBs producing only “one” certain pathway? There are only three generations of quarks, absolutely not 4 nor 5. The quark color dimension is a Ternary charge, not Binary nor Unitary.
Tienzen (Jeh-Tween) Gong