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 the previous sections, we overviewed the basic points of electromagnetic fields. Now, let us examine electromagnetic interaction with more detail.

As we discussed in previous chapters, this paper formulates the concept of energy in its widest sense as the magnitude of confinement or compression on the fundamental tendency to expand. This paper’s concept of energy is an interpretation of Hooke’s law, which relates the strain to stress. Hence, energy content in all forms of irreducible units (rest mass of a “particle”, kinetic energy of a “particle”, energy of a photon etc.) is defined by the tightness of their confinement volumes or compression (wavelengths). Energy content of these units is inversely proportional to the length of their confinement or compression, and it is only a function of distance:

E 7.1 (Basic relation between energy and strain ignoring constants)

E 7.2 (h is the Planck constant, c is the constant speed of light, and λ is the wavelength of the energy package)

This was discussed in Section 5.3 with detail. The relation between kinetic energy (relativistic mass increase) and tightness of the confinement volume was discussed in Section 6.6. Additionally, Lorentz gamma factor was derived from the hypothesis on which this paper is based.

However, as we discussed in the previous section, spatial wrinkles (geometric strains) around the knots and the vortexes tend to cover the whole space without any limitation while space expands fundamentally. Energy of spatial wrinkles self-relaxes by extending and departing from the knot or vortex, and as a result, their wavelength increases constantly. In other words, if there is only one single knot on the balloon in our example, then we can say that the wrinkles caused by this single knot extend and cover the surface of whole balloon. In fact, in such a case, these wrinkles should not preserve any energy, because there is no local confinement of the expansion (except spatial closeness of the universe).

Space is full of matter. Therefore, these wrinkles cannot extend and cover the whole space freely without meeting another knot or vortex (charge). In such a case, we may assume that the extension of spatial wrinkles is intercepted and the expansion is compressed locally between charges. As a result, there appears energy, because two charges block and intercept spatial wrinkles to extend and relax, and strain exists between charges. Practically, spatial wrinkles behave like mechanical springs that exist between charges. The energy (stress) that is against the tightness of this interception (strain) is well known as the electric potential energy.

Although the electric potential energy is between charges, the stress that is produced by a knot is not directed towards radial directions from the knot. Instead, knots wrinkle the space, as if there is a stress in circumferential directions around themselves. In other words, potential difference between two points is the difference of the stresses between these points (similarly like differences in atmospheric pressure).

E 7.3 (k is the Coulomb’s constant and l is the distance between charges)

The magnitude of the electric potential energy is dependent on two parameters. Interestingly, another parameter appears as an addition to the tightness (length) of compression.

The first parameter that affects the magnitude of the electric potential energy is the distance between charges. This parameter is a result of the integral tendency to expand, which we discussed in previous chapters.

Spatial wrinkles (electromagnetic field) that appear around a knot do not have a structure that confines them like a knot, and they tend to extend continuously as an integral part of the expanding space.

The exact mathematical formulation of this extension is consistent with our hypothesis, and it is included in the derivation of the gamma factor from the Lorentz transformation equations. Simply, it can be said that the rate of the extension of wavelengths of spatial wrinkles is equivalent to the distance taken by rotation in the confinement volumes of those knots or vortexes (charges).

However, when the fundamental tendency of expansion in spatial wrinkles is intercepted and compressed between two charges, there appears electric potential energy, whose magnitude is dependent on the magnitude of the compression.

If the distance between two charges increases, the tendency to extend in spatial wrinkles decreases (as a ratio between the extension and the actual length). Simply, it means that the stress on the expansion between two charges decreases when distance increases. Practically, this argument is the reason why electric potential decreases with the distance between charges.

This phenomenon can be visualized mechanically. Imagine two helical springs with identical properties. Magnitude of force that is needed to compress these two springs to different lengths differs (Hooke’s law). However, according to Geometric Generalization, the case is slightly different in reality; springs (spatial wrinkles) do not have fixed lengths, but they tend to extend constantly.

The second parameter that affects the magnitude of electric potential energy is the density of spatial wrinkles (geometric strains) around the knot.

Stress is formed between two charges, because extension (diffuse) of spatial wrinkles is intercepted between them. However, if no wrinkles were formed by the knots, then there would be no stress too. Hence, the interaction between two charges is also dependent on the formation density of spatial wrinkles.

This density adjusts the strength of electric potential (in fact, the strength of electromagnetic interaction), and it is known as the (square root of) fine structure constant (electromagnetic coupling constant).

Fine structure constant is a unitless constant that appears in the equation of electric potential, and it cannot be removed by any natural unit system. In fact, the fine-tuning of the strength of electromagnetic interaction is a phenomenon that can be observed practically.

On the other hand, if we look once more into our balloon example, it can be seen that the amount of wrinkles around a knot is a function of the compression and torsion in that knot. Wrinkles around a knot increase in proportion to the increase of the intrinsic compression-torsion in that knot.

Additionally, in previous chapters, we have discussed that the knots (strain packages with mass) strains the expansion (the inflationary epoch to Hubble’s expansion), and similarly, there is a mutual relation between the energy content (confinement - compression) in knots and the ratio of the universal strain on the expansion (Hubble’s constant).

We will detail the exact meaning and formation of fine structure constant in another entire (next) section, since it is an extensive subject involving the relation between both local and universal stresses.

Another critical point with electromagnetic interaction is that the speed of the diffusing flow of wrinkles is constant for any relative observer. Relativity phenomenon has been discussed in Section 6.6, with details; however, we should emphasize here that propagation (extension) of our spatial wrinkles (strains) are a consequence of the fundamental expansion character of our geometry. In fact, spatial wrinkles follow the original radial (time) direction that is oblique in the wrinkling epoch.

Consequently, phenomenon of the constancy of the propagation speed is an outcome or a proof of our collapsed and wrinkled geometrical structure, which has a constant intrinsic universal expansion.

When charges accelerate or decelerate, the stress that they apply on the spatial wrinkle that is trapped between them varies, because the distance between those charges varies. In accordance with this variation, charges emit or absorb packages of spatial wrinkles (strain packages).

These packages of spatial strains (photons) contain a certain amount of energy (as a function of their wavelength), and they flow and propagate within the expansion. In fact, emitting and absorbing these strain (energy) packages causes charges to accelerate (or decelerate) as if there exists mechanical springs between them. As a result, spatial strains change the energy content of the charge (tightness of the confinement volumes of the knots or vortexes), by transferring their energy content.

This phenomenon is very well known as electromagnetic radiation, where photons are said to propagate with the constant speed of light.

Electromagnetic fields are diffusing and extending spatial wrinkles (strains) within our expanding space. They originate around vortex-like and knot-like formations. They appear and they diffuse because knot-like structures deform geometry around themselves (differently in circumferential and radial directions). These strains are formed of normal stress (electricity) and torsion (magnetism). Energy content in such an interception of the expansion towards spatial direction is dependent on two parameters: (a) the distance between charges (b) intrinsic ratio of compression in knots or vortexes (hence, the ratio of the universal strain on the expansion).

Eventually, electromagnetic interaction appears between charges, because in our geometric structure, space tends to expand fundamentally, even if it is wrinkled universally.

By electromagnetic interaction, energy content of a charge (a vortex or knot) is transferred to another charge by spatial strain packages. In other words, charges pull or push and apply force to each other, and transfer energy by spatial strain packages.

Consequently, these spatial strain packages seem to behave like waves; their crests and troughs (peaks and lows) interfere with each other. Intensity of a wrinkle formation can be transferred to a confinement volume to make it tighter and gain kinetic energy, or they can radiate freely as electromagnetic radiation.

In fact, interactions between knots and spatial strain packages explain most of the actions (except gravitational and nuclear) in Nature. Quantum Electrodynamics (QED) formulates this phenomenon. However, elements of this theory (like “point particles”, probability amplitudes, uncertainties) seem to be questionable, and they cannot be combined to obtain a coherent description of Nature as masters also noted.

We will deeply discuss Quantum Mechanics separately, in Chapter 8. However, now let us note that probability density describes the magnitude of the (vertical displacement) deformation (buckle, wrinkle) of a strain package at a location at a time, but not the probability of finding a “point particle” at a location at a time. Consequently, this paper accepts the soft volume of the entire strain package, which is described by the wave function, as the basic constituent of physical reality.

As a result, it is interesting that electric potential energy is also the resistance to the confinement or compression on the expansion just like other forms of energy. Stress on the expansion is directed either towards time dimension or towards spatial directions; but in both cases, it is a resistance against confining or compressing the expansion. This point of view suggests that electric potential energy and kinetic energy are equivalent in this manner. Both of them are the measure of extra local compression or confinement on the expansion. Additionally electric potential energy is also defined as function of distance (between charges) like all other forms of energy.

Essentially, one of the most important conclusions of this paper lies here. According to previous chapters, concept of “point particles” is already unnecessary. This section also states that electromagnetic interactions are not formed by exchange of virtual energy “particles” (like points). Nevertheless, strain packages in expanding geometry exist, and they flow between charges, whose peaks and lows are formulated by quantum mechanics. We will soon discuss quantum mechanics and its other aspects. Here, this point of view has a great significance, because it reinforces the notion that Nature is not a coincidence of scattered “particles”.