In this chapter, we will 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 previous chapters, we have discussed that space-time is a closed geometry, which fundamentally expands. However, our expanding geometry was wrinkled and collapsed onto itself, and increase in its circumference’s size (space) was decelerated.

Let us develop our previous example of a balloon so that we can visualize this new state of balance. Imagine a balloon (or more properly, a spherical plastic bag) that isolates its interior volume from the exterior, and whose inner pressure is almost the same with its outer pressure. That balloon would have almost zero wall tension. This example represents our basic expanding geometry, which also contains no stress or energy of any kind.

Figure 7.1 Photo of an inflating balloon

We can pinch and tug at the balloon’s surface and tie knots on its surface. Now, in this new state, the circumference of our balloon decreases, as some of its surface is knotted locally. Although knots tend to relax, they cannot do so, prevented by the tying nature of knots in their inner structure. Therefore, they behave like tension springs, which decrease the overall circumference. There also appears a tension on the wall of our balloon, because the decrease in its circumference increases its inner pressure. There is a mutual relation between the wall tension, pressure inside the balloon and quantity of knots. Additionally, there appear local wrinkles oriented around those knots on the surface of our balloon, as knots deform the balloon’s surface geometry.

Figure 7.2 Photo of a knot on balloon

Stress relations on our balloon example resemble fundamental forces of Nature. However, there are very important differences that we should immediately emphasize. Our space-time geometry expands fundamentally; it is not static like our balloon example. Additionally, our geometric structure is not in a medium like atmosphere that causes pressure difference between in and out as in our balloon example. Its fundamental tendency to expand is dependent only on its logical cause. Moreover, plain space in our geometry is not able to contain such properties of mechanical stress, wall tension etc. like a balloon’s complex molecular wall. We may only suggest that expanding space wrinkles (strained) when there is stress on the expansion.

Our balloon example may not be perfect, but it signifies the mutual relationship between the knots, the wrinkles around them, and their effect on the overall size of the circumference. It also reflects this paper’s philosophical viewpoint. The balanced system in our balloon example is indivisible. If a part of the balloon like a single knot is cut out and extracted from the system, the balanced stress relations in both the whole system and the extracted knot will cease to exist. Nature is also an indivisible complete structure like the balanced system in our balloon example. In Nature, all elements interact with the wholeness, and they are dependent on the state of balance in the wholeness. This is similar to the knots in our balloon example, where inner stress of knots both effects and depends on the pressure and the wall tension of the balloon. In Nature, energy and mass form an almost stable state, which is in equilibrium as in our balloon example.

(There is an interesting discussion on how mutual relations in the wrinkling epoch compel and limit formation of three independent spatial dimensions. We will skip this discussion now, but let us note that knots cannot exist in a space with more than three dimensions.)

In this chapter, we will detail elements of the perfect equilibrium in the wrinkling epoch (Hubble’s space) and describe how the expansion is universally strained in an almost stable state.