This section describes the balance in Nature between the smallest and the largest scales.
If we utilize our balloon example, we may say that each knot on the surface of our balloon decreases the overall circumference and increases the inner pressure of the balloon. (Pressure stays the same everywhere inside the balloon according to Pascal’s principle.) Moreover, we can also say that the magnitude of this effect is directly proportional to the surface area tied into a knot (ignoring the elasticity of balloon material).
In our expanding space-time geometry, this relationship differs from the balloon example. Yet, there appears a reciprocal balance:
- The expansion is locally confined into the knots, and the tightness of the confinement (local strain) describes the energy content of that elementary “particle” (Section 5.3).
- On the other hand, the increase in the overall circumference of the universe is decelerated (the inflationary state to Hubble’s expansion), because the expansion is knotted into local volumes against the universal strain on the expansion. This strain has a physical ratio, and its basics have already been presented (Section 5.4). Moreover, if the electromagnetic interaction is examined carefully, we can see that the ratio of the universal strain on the expansion appears in equations of electricity, which is known as the fine structure constant (Section 7.4).
The total energy in all knots in the universe determines the ratio of the universal strain on the expansion, analogously to our balloon example. Hence, the basic balance in Nature is between the total energy in the knots and the universal strain on the expansion. Please note that according to our previous discussions, our concept of energy covers all kind of energies like the energy of the rest mass, kinetic energy, heat energy, and other forms.
Moreover, gravity creates an additional mechanism that affects both sides of the universal balance. As we discussed previously, the mechanism of gravity at the smallest scale compresses the confinement volumes of the knots that are gathered to form heaps of matter. As a result, this additional compression mechanism increases the tightness of the heaped confinement volumes (or their energy content). Of course, this additional creation of energy is against the regional restraint on the expansion.
As a matter of fact, the Theory of General Relativity describes both the universal strain and the regional restraint on the expansion as the curvature (deformation) in space-time. It is natural to arrive at this conclusion, because General Relativity does not examine the mechanism of gravity at the smallest scale, or the mechanism in which the existence of matter affects space-time.
On the other hand, our paper clearly distinguishes the effect of the existence of a single knot (matter quantum) and the secondary effect of the lumping and gathering of matter. The existence of a single knot affects the universal strain on the expansion. As we discussed in Section 5.2, the universal strain on the expansion indicates the ratio of the decelerated increase in the circumference (space) to the original linear expansion, but it does not describe the distribution of deformation on the space-time. Naturally, the effect of a single knot is very slight, because the size of the knot and the size of the circumference of the universe hugely differ. Similarly, a tiny knot on a balloon’s surface has a very slight effect on the balloons circumference.
Figure 7.18 Photo demonstrating how a knot on a balloon deforms its shape
However, gravity as a secondary effect makes a distinction. The energy created by the mechanism of gravity comes from the compression caused by the gathering of knots, but not from the existence of individual knots. Moreover, the counter formation of this effect is the regional restraint on the expansion, which compresses and decreases the expansion. Hence, gravity changes the ratio of the universal strain on the expansion and deforms the rate of the expansion regionally.
Actually, both the universal strain and the regional restraint on the expansion are on the same side of the balance; they both describe the deformation (strain) at the universal scale. They may be referred to as negative energy, considering the energy of the local strain formations (the knots or vortexes) are positive.
As a result, the matter-energy content in the universe was not determined initially, and it was not scattered because of a mysteriously embedded energy potential. Instead, the matter-energy content in the universe was formed at the wrinkling epoch against the universal strain on the expansion, and it was increased by gravitational activities against the regional restraints on the expansion.
We may assume that the total energy content in the knots is equal to the energy content of the universal strain on the expansion, since they cause each other reciprocally. That is to say, the total energy-mass content in the universe equals zero by balancing the largest and the sum of the smallest. This paper first assumes that physical reality is a consequence of balancing the oppositeness in deviation from nothingness, and finally, concludes that the sum of its energy contents equals nothingness. Let us leave discussing the philosophical consequences of Geometric Generalization to further chapters, and finalize the energy conservation problem that we came across in the previous section.
According to the previous section, after the collision of two massive objects, the confinement volumes of the joined final mass undergoes further contractions as if additional energy is injected into the system (the universe). Now, we can concur that energy of the matter content in the universe has slightly increased after such a collision by gravity. Of course, the ratio of the strain on the expansion also increases contrarily. However, variation of this ratio (variation in fine structure constant or variation in Hubble’s constant) would not have practically observable consequences. This situation is similar to the effect caused by very tiny knots on the circumference of a huge balloon.