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This section presumes that the reader has worked through the preceding sections and chapters.
 
   
 

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10.1. Basic Classification of Elementary Particles

10.3. Quantization

 

10. Formation Principles of Elementary Particles

 

10.2. Geometric Deformations: Curvature and Torsion

 

Actually, local deformations (bends, folds, twists, crossings) suggested by Geometric Generalization may show some similarities with the dimensional complexity of the superstring theory. On the other hand, according to the Geometric Generalization, it is possible to define certain basic geometric deformations (instead of adding fictitious dimensional parameters). As a result, elementary “particle” (strain package) classifications can be deducted according to the variations of those deformations.

 

In fact, these three-dimensional geometric deformations can be described mathematically according to their curvature and torsion (of curves).

 

Curvature is the amount by which a geometric object deviates from being flat. For a curved line, it is the degree of the deviation from a straight line, or for a curved surface, it is the degree of the deviation from being planar. In other words, curvature is the degree by which a geometric object bends (at a location, at a time).

 

Torsion measures the departure of a curve from a plane, or it measures how sharply a curve twists.

 

According to our final generalization of laws of Nature, all existence (geometric deformations) flow the equivalent distance towards time dimension. Hence, strain packages (elementary “particles”) can be compared according to their curvature and torsion (for each spatial dimension) within an equivalent Estring length (the four-dimensional arclength). Fortunately, parametric coordinates of the geometric object are not essential to make such a comparison.

 

Different kinds of strain packages (elementary “particles”) have different formations and degrees of curvature and torsion:

Photons have an oscillating curvature and torsion with any degree.

Electrons (leptons in general) have a constant curvature and torsion (helical like) in all spatial directions (curvature and torsion of electrons change with acceleration or in gravitational fields).

Protons (hadrons in general) have a different curvature and torsion in each spatial direction, which cause crossings, and form knot-like strain packages on expanding geometry (curvature and torsion of protons vary with acceleration or in gravitational fields).

 

Practically, curvature in space-time geometry causes electricity phenomenon (pressure and tension effect), and torsion causes magnetism (rotation effect).

 

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10.1. Basic Classification of Elementary Particles

10.3. Quantization

 

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