In this chapter, we discuss fundamental forces and explain how and why they emerge. However, this chapter assumes that the reader has a basic knowledge on both fundamental forces and previous chapters of Geometric Generalization.

In Chapter 5, we have discussed that electrons are strain formations like vortexes, which emerge with the universal strain on the expansion. In other words, the expansion is confined in electrons locally, and electrons have a fundamental tendency to expand that is directed towards time dimension. However, this tendency reflects the ratio of the universal strain on the expansion. This point is important because it means that electrons cannot exist coherently without the universal strain on the expansion. Strain formation of electron has a helical-like structure, and they are not self-balanced. Therefore, energy of the rest mass of electron (tightness of its confinement volume) is dependent on the ratio of the universal strain on the expansion. Previous chapters of this paper discuss many aspects of this phenomenon.

In fact, the reason why a helical-like structure of an electron cannot be self-balanced is simple: helix has a constant curvature and torsion, and it does not form a knot, which can lock the intrinsic tendency to expand. Conversely, imagine you tie a knot on a rope; such a knot is formed of multiple bends and crossings in different directions.

Similarly, the knots on our geometry (e.g. protons) have a more complex structure. They have different deformations (bends, folds, etc.) towards different spatial directions. Readers may glance back at our balloon example in Section 7.1, in order to visualize the physical meaning of our knots.

This point of view has some similarities with the popular string theory, which suggests that elementary “particles” are excitation modes of elementary strings. However, this paper suggests that elementary “particles” are strain packages, which are a set of various local bends, folds, etc. in the fundamentally expanding space.

There are several different basic bends and folds, which can occur in different directions independently. Moreover, such basic deformations can be re-applied multiple times by forcing them to fold over themselves. Consequently, it is possible to produce many kinds of elementary “particles” by variations of these processes. We will discuss these in Chapter 10 on “Formation Principles of Elementary Particles”. However, let us note that each additional bend causes the confinement volume to be tighter, heavier, and more unstable. In fact, the only self-stable knot is proton.

Strain packages can form a complete knot that can locally lock the expansion in a confined volume. In fact, in the structure of our knots, the tendency to expand is confined by those strain formations, and intrinsic tendency to expand compresses itself in order not to expand. Therefore, knots have a resistance and an intrinsic consistency not to be open. This resistance (or consistency) is the strong force (and weak forces). The strong force indicates the strength of the fundamental tendency to expand indirectly.

If readers tried to tie a knot on a balloon’s surface, they would realize that knots on the surface of a balloon tend to unknot immediately. In fact, the stability of such a balloon knot depends on the friction resistance of balloon’s material. However, naturally, our space-time geometry does not have such a property like friction resistance. It is important to notice that the fundamental tendency to expand in the confinement volume (against the universal expansion) locks the knot. Analogously, a knot on balloons surface is stabilized only if the air confined in knot has the same pressure (/wall tension) with balloons overall inner pressure. Practically, this relation has a very important consequence; the knots of the same kind (elementary “particles”) always have exactly the same mass (ignoring relativistic cases), and the magnitude of that mass depends on the ratio of the universal strain on the expansion. Please note that we will examine the formation principles of elementary “particles” in Chapter 10.

Figure 7.8 Photo of a knot on balloon

Our photo of example balloon knot is imperfect, since the pressure in the volume at the end of the knot is not equal to balloon overall inner pressure.

Intrinsic structure of the strong force can also be visualized by a knot tied on a rope. Knot tied on a rope becomes tighter and stronger when it is pulled. Hence, knot resists being open more, when it is under more stress. In nature, any energy (tightness of a strain package) transferred to a knot makes its confinement volume tighter and causes it to have more kinetic energy.

The strong force has a very short range. In fact, its range can be considered as intrinsic consistency of the knot or the size of the knot.

The knots (like protons and neutrons) come together, and they form stable groups of knots, which are known as atoms. In fact, an atom should be considered as a complex single knot (like knitting), because (vertical) deformations (bends and folds) of individual knots in nucleus interfere partially.

These knots have a very important effect on the global size of the universe. We have discussed in Section 5.3, that the expanding space has wrinkled and collapsed onto itself, and matter (knots) behave like tension springs that lock the wrinkling epoch.

Strictly speaking, the intrinsic structure of the knot prevents the knot from unknotting, because the confined expansion in the knot compresses itself. Therefore, knots lock the expansion locally. Consequently, formation of these knots (formation of matter) is the reason that the expanding space is wrinkled from the inflationary state to current observable Hubble’s expansion state. This simply means that total stress in knots and the ratio of the universal strain on the expansion are related to each other.