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

In the previous chapter, we treated space-time as a constantly and continuously expanding non-Euclidean geometry. In that geometry, circumference (closed spatial dimensions) expands proportionally with the increase in radius (time dimension) because of the logical principles. This process can be considered as early inflationary epoch.

Figure 5.2 Geometry of physical reality

However, when proportional increase in radius and circumference (the inflationary epoch) reaches a particular limit, we may assume that increase in circumference’s size (space) is decelerated and the expanding space is wrinkled. That wrinkling epoch is what we observe as Hubble’s expansion, and balancing interactions at this epoch will lead us to fundamental forces of physical reality.

We should mention at least a few points about the formation of the wrinkling epoch at an abstract level first, just before starting to relate our geometry to the concepts of physical reality.

It can be assumed that the expanding space wrinkles because of a pressure perpendicular to the spatial plane and the cause of this wrinkling can be visualized as such. Alternatively, we may also say that the increase in circumference’s size (space) is decelerated by a cause, which consists of tension (tensile stress) towards all spatial directions as if the circumference (space) is manacled at the largest scale.

Figure 5.3 Pressure or tension

In fact, the mechanism of wrinkling is based on local geometric formations; we will discuss this mechanism very soon. Let us immediately note that we do not imply a hidden universal manacle or a mysterious fifth force, and we do not claim that space can have such a stress resistance property.

However, let us assume that a stress mechanism creates a deformation on the expanding space-time geometry, and causes the expanding space to wrinkle universally. Please note that this stress mechanism is just an imaginary tool to help us discussing the nature of the deformation at the wrinkling epoch.

The deformation implied here is similar to the dimensional deformation of a physical body that is under stress, but here the expanding space contracts and wrinkles as if it is squeezed, and the increase in the circumference’s size decelerates.

Figure 5.4 Poisson’s contraction

Stress may deform the dimensions of a physical body (Poisson’s contraction); however, the stress mechanism here causes a mutual deformation on the expansion (the flux) in both spatial and time directions. Such a stress mechanism may collapse the expansion onto itself as if the expanding circumference (space) and the increasing radius (time dimension) are deformed.

However, wrinkling of the expanding space has a basic distinction from Poisson’s contraction. Here, the expansion and stress mechanisms are omnidirectional and isotropic. Hence, the deformation does not vary in different dimensions, and wrinkling does not occur in a specific direction like Poisson’s contraction. The expanding space wrinkles as a whole as if it is squeezed homogenously, and both space and time dimensions (circumference and radius) are deformed correspondingly.

Figure 5.5 The collapse

Consequently, the expanding space is contracted and wrinkled from the inflationary epoch to Hubble’s expansion. However, this metamorphosis does not mean that a static space is wrinkled or a Euclidean geometry is deformed like a sheet of paper. Here, the expansion of space is permanent, and it continues as if the expanding space wrinkles and increase in the circumference’s size decelerates.

In this paper, this epoch (deceleration of the increase in circumference’s size) will be referred to as the wrinkling epoch.

The important point here is that the deceleration of the increase in the circumference’s size (space) is not a reason to cancel the fundamental tendency to expand in the geometry of physical reality. After all, this expansion character is the result of balancing the geometric oppositeness, and it is only dependent on its own logical cause. Therefore, we are free to assume that the expansion (the flux) is permanent, constant, and continuous, even if increase in the circumference’s size (space) is somehow decelerated.

Readers may utilize the growing tree analogy in order to identify the difference between the expansion (growth of branches) and the increase in the circumference’s size (growth of the overall size of the tree).

Moreover, constancy of the expansion can be illustrated by an example of a balloon, which is squeezed while it is inflated. Although, overall size of the inflating balloon can be reduced by squeezing, expansion of the balloon’s surface would tend to continue by bulging out from available points, given that the causes of inflation (increasing inner pressure) and squeezing are independent (ignoring wall tension, elasticity of balloon wall etc.).

The graphic below visualizes the deformation in radius (time dimension), which is caused by our assumed global pressure mechanism.

Figure 5.6 Radius and deformed radius

Accordingly, the original radius (of the inflationary epoch) is no longer perpendicular to the circumference (space), and it has an oblique angle, since it is collapsed and warped under an assumed pressure mechanism. Hence, collapsed radius has a deformed path, and the expansion continues within this warped geometry fundamentally.

On the other hand, the wrinkled circumference has a new reduced radius. Eventually, it can be said that there appears a universal strain on the expansion, which expresses the ratio of the new reduced radius to the original perpendicular radius. In other words, this strain expresses the ratio of the decelerated increase in the circumference (space) to the original linear expansion. We will discuss the ratio of this strain in the following chapters. Additionally, we will examine that light follows the path of this warped radial direction in space-time, and it represents the direction of the expansion (the flux) in wrinkling epoch locally.

Essentially, we do not suggest that space (as a basic geometric concept) can have a capacity to resist force. In fact, such an assumption is not only unnecessary, but also problematic in many aspects, too. In following sections, we will examine this topic deeply. However, the critical point to note here is that the stress is formed on expansion, not the space, since the expansion has a logical cause to resist compression.

Moreover, our strain concept has a property of universality, too, because it is the comparison of two states of the entire circumference (space) at the universal scale. However, the expression universal does not imply that deformations on space-time during wrinkling epoch should be universally homogeneous.

In this paper, the strain formation on the expansion, discussed here, will be called as the universal strain on the expansion. However, please note that this formation is not called the deceleration of the expansion intentionally, because the expansion itself does not decelerate, but it just collapses onto itself.

Please note that the degree of strain (wrinkling) is exaggerated in all the graphics included in this paper, in order to help visualization.

Experienced readers may note that our concept, universal strain on the expansion is an interpretation of the space-time deformation (curvature) as formulated by The Theory of General Relativity. However, our paper clearly distinguishes the effect of the existence of a single matter quantum and the secondary effect of the lumping and gathering of matter. All details will be discussed in a complete chapter on “Fundamental Forces and Gravity”.

Considering above discussions, we may now say that, although, increase in the circumference’s size is decelerated; the expansion (the flux) constantly continues in locally collapsed areas. This tendency causes radius and circumference to expand on locally deformed (curved and twisted) paths by folding onto itself as if they locally wrinkle, ripple, buckle, bend, etc.

Figure 5.7 The inflationary epoch to Hubble’s expansion

In fact, those wrinkles/buckles form the quanta of matter and energy as mentioned in hypothesis. Moreover, the formation of those wrinkles/buckles is the reason of the universal strain on the expansion. Conversely, the opposite is also true; the quanta of matter and energy are local deformation (strain) formations on the expanding space.

Now, let us discuss formation of mass and energy and elaborate on them according to their basic characteristics.

We will not discuss the reason that triggered the wrinkling epoch at the beginning, here. However, it seems that vortex like formations of wrinkles are unavoidable in our spherical closed geometry, (which is known as hairy ball theorem), and those wrinkle vortexes form knots that decelerate the increase in circumference’s size reciprocally by locking the expansion to the local confinement volumes of mass.