In this chapter, we discuss how our expanding space geometry generates basic physical concepts of mass and energy.

In previous Section (5.2), we discussed the universal strain on the expansion and the wrinkling epoch, and we assumed as if it has been caused by a global stress mechanism. However, there is no global stress or a fifth force like a universal manacle, which squeezes the expanding space.

In fact, knot-like local formations effect the expansion; matter behave like tension springs that locks the wrinkling epoch, and cause the expanding space to collapse onto itself universally. The intrinsic structure of the knot prevents the knot from unknotting, because the fundamental tendency of expansion in the volume within the knot compresses itself. Therefore, knots lock the expansion locally.

Consequently, formation of these knots (formation of matter) is the reason that the expanding space has wrinkled from its inflationary epoch to the current observable Hubble’s expansion state.

This deduction simply means that total amount of energy in knots (total matter content in the universe) and the ratio of the universal strain on the expansion (rate of the Hubble’s constant) are related to each other.

Additionally, stable confinement volumes can only be formed in special conditions, when energy content of the package matches the ratio of the universal strain on the expansion.

We will detail the relationship between the knots and overall space-time geometry in Chapter 7 “Fundamental Forces and Gravity”.

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

Strain packages like knots can be visualized like a tension spring that resists becoming longer and thinner in space-time. Hence, the confinement volume of that knot needs additional stress (curvature and torsion) to accelerate in space-time (become longer and thinner in space-time).

The extra tightening in the confinement volume (by acceleration) can be visualized by a system, where transverse section of a material contracts under tensile stress (Poisson’s contraction); stress content of such a system can be measured by the contraction on its transverse section.

According to the formulation above, kinetic energy and energy of inertial mass are indistinguishable concepts, as definition of mass covers both of those concepts. The confinement volume contracts in relativistic cases; hence, this formulation intrinsically describes relativistic transformations. We will formulate in the next chapter how decrease in the confinement volume causes relativistic mass increase.

Figure 5.10 Inertial and accelerated helix

In Chapter 6, we will formulate the mathematical relation between the confinement volume and quantity of clock-ticks. Simply, formation of the confinement volume (knots) generates concepts of both mass and time (as quantity of clock-ticks). It is very important that without such knots in space-time, it is completely meaningless to mention time as quantity of clock-ticks. (Similarly, nautical speed unit, “the knot” is originated on knots.) Radius of the confinement volume may vary (tighten) by acceleration or gravity. Hence, quantity of clock-ticks and energy content varies relatively too.

We mentioned before that the stress in strain packages can be directed towards either radial (time) direction or spatial directions. Force fields (excluding gravity) are such wrinkles towards spatial direction. It is obvious that this paper treats mass and force field as very similar concepts and considers force field (spatial wrinkles) to be as real as mass. Simply, mass is a strain on radial (time) direction, and force field is a strain on spatial direction. Additionally, these strain packages affect the whole space geometry, and they are affected from the whole. This process can be likened to those knots on surface of a balloon. We will discuss relations of these concepts and detail the perfect dynamic balance in Nature on Section 7.12.

This paper considers concept of mass and energy as a local jam, a deformation in expanding geometry, instead of an independent property of a “point particle”. In other words, matter can be visualized as a chain of knot-like geometric deformations similarly like knittings on continuous space-time geometry, instead of a heap of point “particles” whose locations are uncertain.

Wrinkles might be wavier and indented in some locations like those wrinkles on human skin. However, existence of wrinkles as a whole and existence of crests and troughs in certain locations are different concepts. In general meaning, stress cannot be measured directly, but its existence can be deduced logically, and its magnitude can be measured by its consequences (amount of strain). Wrinkles and their stresses (energy contents) are physically REAL, but practically, it can be said that (vertical) deformation EXISTS at a location at a time, while crests and troughs flow within the expansion.

Eventually, this paper assumes the entire strain package, whose vertical deformation is defined by the wave function, as the basic constituent of physical reality. In fact, quantum mechanics itself proves that Nature is not formed of classical “particles". In Chapter 8 on “Quantum Mechanics”, we will discuss why Nature seems to be formed of point “particles”, which have wave like properties.

The relation that we discussed here between the formation of matter and space-time geometry leads to important and observable predictions on Nature. It would be unfair to neglect those predictions, which would also provide us with a better understanding of the subject. “Observable Predictions” are discussed in the next section.