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 4 on “The Basis of Physical Reality”, we presented a geometric principle, where closed spatial dimensions (space) isotropically expand like the surface an inflating balloon.

Figure 7.5 Geometry of physical reality

In Chapter 5, we discussed the deceleration in the increase of circumference’s size, and we noted that the relation between the circumference of the universe and the expansion seems to vary after the formation of knot-like structures (the universal strain on the expansion – wrinkling epoch).

Figure 7.6 The inflationary epoch to Hubble’s expansion

We also discussed the ratio of the universal strain on the expansion in Section 5.4. However, it seems the ratio of the universal strain on the expansion cannot be directly observed, since it is a universal constant that describes state of the balance in the universe. (E.g. Pascal’s principle, which states that the pressure stays the same at all points in a static fluid.)

In previous sections, we discussed that electromagnetic field is the flow of extending spatial wrinkles, which appears around the knot because knots deform (wrinkle) and change the standard ratio between the radius and circumference around itself.

Figure 7.7 Photo of a knot on a balloon and wrinkles around it

In fact, there is a significant correlation between the universal strain on the expansion and the formation density of the spatial wrinkles of electromagnetic fields. These two formations are connected to each other.

The universal strain on the expansion deforms the increase in the circumference’s size (space) as if dimensions of an elastic material contract under isotropic pressure. Actually, with the universal strain on the expansion (the inflationary epoch to Hubble’s space) both circumference of the universe (space) and radius (time dimension) is deformed in such a way that both space and time have the same amount of deformation (wrinkling - collapsing) isotropically in both time and all spatial directions.

Fortunately, it is possible to deduce the ratio of the universal strain on the expansion by studying the density of spatial wrinkles around knots.

The relation between the universal strain on the expansion and the density of spatial wrinkles (electromagnetic field) can simply be visualized: Suppose that there is a brittle body, which is under pressure. Pressure deformations (cracks) might be formed on that body (depending on the material characteristics of that body). Although stress cannot be measured directly and it is spread on the whole of pressured body, the amount of crack deformations implies the magnitude of the pressure.

Similarly, the ratio of the universal strain on the expansion does not vary locally; it is an isotropic global magnitude. However, like crack deformations, spatial wrinkles (electromagnetic field) appear around charges, because charges (like knots) strain the expansion by confining the expansion into local locked circulating volumes.

Therefore, we may assume that density of spatial wrinkles (electromagnetic field) and the ratio of the universal strain on the expansion (Hubble’s constant) are mutually related to each other. According to Geometric Generalization, density of spatial wrinkles is an indicator that describes the compression ratio on the expansion. If the ratio of the universal strain on the expansion increases (or Hubble’s constant decreases), the density of spatial wrinkles will increase as a direct consequence.

Interestingly, it is practically possible to measure the formation density of spatial wrinkles (of electromagnetic field) by checking the strength of electromagnetic interaction, where energy contents of knots are transferred to each other by spatial strain formations.

Readers, who followed this paper carefully, should be aware that this paper defines all forms of irreducible energy units (energy of a “particle” with mass, kinetic energy of a “particle” with mass, etc.) as the tightness of their volumes, where the expansion is confined or compressed. Energy of irreducible units is inversely proportional to the length of their confinement volumes, and it is only a function of distance.

E 7.4 (Basic relation between energy and strain ignoring constants, which appear in equations because of the maladjusted, human centric unit system.)

As it is well known, electric potential energy is also a function of distance, and it is inversely proportional with the distance between charges. However, energy of electric potential contains an additional constant, and it is rather different from the other forms of energy. This additional constant is permanent in the equation of electric potential unlike other constants, which can be removed from the equations by a proper Universal (Natural) Unit System (Chapter 11).

This constant ratio is a phenomenon, and it determines the strength of electromagnetic interaction. It is known as fine structure constant (electromagnetic coupling constant), and it is the ratio of two energies:

(a) the energy needed to bring two electrons from infinity to a distance of L against their electrostatic repulsion

E 7.5 Potential energy between two electrons at distance L
 (k is the Coulomb’s constant)

(b) the energy of a single photon with a wavelength 2πL.

E 7.6 Energy of a single photon
(c is speed of light, and h is Planck’s constant)

In fact, the (square root of) fine structure constant describes the formation density of spatial wrinkles (for per intrinsic circulations), and it indicates the compression ratio of the universal strain on the expansion (the inflationary epoch to Hubble’s space).

Fine structure constant varies at high energy levels. This phenomenon is to do with the interrelation between matter (the knots and vortexes) and overall space geometry, since quantum of matter is a local (confined) deformation (strain) package on expanding geometry. When (charged) knots or vortexes accelerate in space, spatial wrinkles that they cause on the expanding space also change. We will discuss other aspects of the relationship between matter and space-time (gravity) in the following sections.