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.

If we examine the knots in our balloon example, we can realize that each knot deforms the surface around it, and it changes the amount of stress on the balloon’s elastic wall. Each knot changes the tensile stress on the balloon’s walls towards radial direction to itself. However, there also appear local wrinkles around a knot, as if there is a circumferential compressive stress around it, which relaxes and decreases the wall tension locally in circumferential directions. Most simply, electromagnetic fields resemble those wrinkles that appear around a knot on our balloon. We will now discuss the formation of electromagnetic fields according to this point of view. However, for the time being, we will refrain from discussing the mutual relation between the knots and the global structure of the balloon.

Figure 7.3 Photo of a knot on balloon representing electromagnetic field

In a very limited point of view, these wrinkles (strains) in our geometry have similarities with the stress deformations that appear in a complex body. At first, we may visualize these wrinkles as (longitudinal) stress waves. They are strains in fundamentally expanding geometry, and they consist of both normal stress (electricity) and torsion (magnetism). As we discussed in Section 5.2, these wrinkles are formed with the universal strain on the expansion.

Let us remind again that, the concept of stress in our geometry is rather different from mechanical stresses on our static balloon example. Here, there is no elastic medium like a balloon’s surface. In our geometric structure, wrinkles are formed on space that tends to expand fundamentally, but not on the surface of a static space. Moreover, energy magnitude of such a wrinkle depends on the size of the area where the expansion is confined or compressed (as an interpretation of Hooke’s law, which relates stress and strain).

On the other hand, our wrinkles do have crests and troughs (peaks and lows) too. Of course, these crests and troughs should not be simplified as transverse waves on a static medium. In fact, they indicate the magnitude of the deformation (curvature and torsion) at a location at a time in the expanding geometry.

Structure of our knots (the confinement volumes of mass) in our space-time geometry also has differences with those knots on our balloon example. Since the first chapter, it is clear that this paper does not consider the confinement volume like a static knot. The expansion in our knots and vortexes is constant, even though it can be locally tightened and confined in a volume. In fact, the expanding space is partially confined in those volumes. Therefore, wrinkles around the confinement volumes are also not static and do not have a constant length (wavelength). Because of the expansion (the flux), crests and troughs of those wrinkles flow and diffuse, and their wavelengths extend freely and relax, while the confinement volume also has the same dynamism internally. In fact, this active structure is described in our hypothesis.

In Chapter 5, we have discussed how the increase in the circumference (space) in our fundamentally expanding geometry has been decelerated universally and spatial plane has been wrinkled. In a point of view, the flow of strain wrinkles resembles winds, which is caused by air flowing from high pressure to low pressure. However, here, wrinkles extend and flow from areas where the expansion is compressed, to areas where this compression is relaxed. In fact, as we mentioned in Section 5.3, the confinement volumes of mass (electrons) are the vortexes of the flow of wrinkles in the expanding space.

Figure 7.4 Photo of a knot on a balloon and wrinkles around it

Here, we should open up a very critical point about the directions of the wrinkles. Wrinkle-like strains of electromagnetic field do not resemble water waves that circularly propagate from the center of oscillation. For water waves, the heights of the vertical displacements (crests and troughs) are equivalent at all points that are equidistant from the center. Crests of water waves propagate equivalently. However, these wrinkle-like strains, which form around the knots, have varying vertical displacements in equidistant points from the center. These wrinkle-like strains appear as if there is a stress in circumferential directions around the knot, but strain formation itself flows towards radial directions. The above photo of a knot on a balloon simply visualizes these kinds of strain formations (although this knot is a static structure).

When the complex structure of the wrinkle-like strains of electromagnetic field is combined with intrinsic circulations in confinement volumes, it results in much more complicated consequences. Further details of this subject are included in the scope of our next chapter on Quantum Mechanics.

Although, space-time is not a medium like air, the ratio of the universal strain on the expansion behaves as a feature like atmospheric pressure. In fact, variations in its ratio also form the basis of gravitation.

Please note that confined circulation in the knots or vortexes have a direction of rotation, which affect the structure of diffusing spatial wrinkles (strains). It can also be seen on the photo above that the folding direction of wrinkles on the balloon depends on the direction of the rotation in knot. Eventually, direction of the rotation (clockwise or counter clockwise) is the basis of the electric charge concept. However, this concept has a delicate nature that can easily be misunderstood; we will closely examine the formation of the electric charge in Chapter 10 on “Formation Principles of Elementary Particles”. Simply, electric charge is the property of the knot or the vortex, which describes the direction of the intrinsic circulation from the direction of time dimension (radial directions), where opposite directions are not equivalent. Electric charge is an invariant property for all observers. On the other hand, direction of rotation in space varies according to the location of the observer (behind or front). As a result, the electric charge is not related with the direction of rotation observed from spatial directions.

Most simply, diffusing flow of strains (spatial wrinkles) in our expanding geometry is the electromagnetic field. Their stress is directed towards spatial directions (original radial direction that is oblique in the wrinkling epoch). They appear around knot-like or vortex-like centers, where there is an intrinsic circulation in the strain formation (“particles” with electric charge). Like those wrinkles in our balloon example, electromagnetic fields (spatial wrinkles) extend and cover the whole space.

As we discussed the physical meaning of electromagnetic fields in our geometric structure, now we can start to discuss electromagnetic interaction. Later on, we will deduce the density of spatial wrinkles (strength of electromagnetic interaction). These additional discussions on electromagnetism are essential for the examination of both gravity and quantum mechanics.