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

At last, we can start to discuss real physical concepts. First, we will examine the exact meaning of energy and mass.

Put simply, both matter and energy are local deformations (strain packages like wrinkles, buckles, bends, etc) that are formed on the wrinkling epoch of the expanding space. The expansion is confined or compressed into locally deformed areas correspondingly with the formation of the universal strain on the expansion. These strain packages form quanta of matter and energy, and they have an extra intrinsic tendency to expand.

In other words, strain packages are formed where the expansion is limited and is not able to expand freely, therefore the expansion flows in self-collapsed and deformed paths locally. Consequently, in all meanings, energy is the local compression or confinement on the expansion (the flux).

Our concept of formation of energy is very similar to Hooke’s law, which relates the elastic material deformation (strain) to stress. According to Hooke’s law, potential energy stored in a spring increases with the increase in deformation:

E 5.1 (x is the distance the spring is elongated by, and k is the spring constant)

Similarly, our concept of energy indicates a strain - stress relation. Hence, energy content of any kind of strain formation in space-time geometry (quantum of matter or energy) is related to the magnitude of the compression or the tightness of the confinement on the expansion.

We should immediately note a critical point here. It would be incorrect to visualize the concept that has been suggested above, like a complex molecular system having elastic deformations and stress. Local tiny deformations like wrinkles would be suspicious logically on static and plain space-time geometry in reality (even if it would be managed mathematically). Here, the expansion is under stress, not the space or static geometry itself. In a case, where the expansion (the flux) is under stress, space keeps on expanding in local confined volumes as if it wrinkles or as if bulged out areas of our balloon keeps on expanding.

Additionally, deformations like wrinkles, buckles, etc. do not have a reason to contain energy by themselves on a plain geometry. It is not possible to claim that a curved line or a wrinkled sheet of paper has energy because it is deformed. Local strain packages on our geometry also do not have energy because they contain wrinkles, buckles, bends, etc. These deformations (magnitude of strain) indicate the magnitude of the stress on that region. Strain packages have energy because there is confinement or compression on the expansion.

In fact, it is very important to notice that both matter and energy is formed because space-time geometry tends to expand constantly and continuously in any case, because of its logical principles. These strain packages have an intrinsic tendency to expand, which is against the compression or confinement that forms them.

Moreover, those strain packages are not in static locations in space; the geometry of space-time expands constantly and constantly. As a result, strain packages also flow within the expansion on the space.

As a result, the tightness of the confinement or the compression determines the magnitude of the energy in that strain package. If the magnitude of the compression is higher in a strain package, then the size of the package is smaller, and it has increased tendency to expand in a tighter area. Quantity of all energy forms, including the potential of force fields or kinetic energy (of elementary particles) is simply the tightness of strain packages; we will soon present its mathematical formulation. In fact, this situation is a well-known phenomenon; energy of a photon is only dependent on the tightness of its wavelength.

E 5.2 (h is the Planck constant, c is the constant speed of light, and λ is the wavelength of the energy package)

Strain packages (quantum of electromagnetic radiation), whose stress is also directed in spatial directions, can be visualized as spatial wrinkles. They consist of both normal stress and torsion. Mathematically, they are deformations on expanding geometry, which have varying curvature and torsion (of curves). There is a mutual relation between the curvature and torsion, which support each other. We will detail versions of this relationship afterwards. Simply, such strain packages (spatial wrinkles) form electromagnetic interaction.

In fact, the direction of the stress in electromagnetic radiation is exactly the original direction of the radius (time dimension) in the inflationary epoch, which now has an oblique angle with the spatial plane, because of the collapse in the wrinkling epoch (Section 5.2).

On the other hand, stress of strain packages is not supposed to scatter towards spatial directions; they can be directed perpendicularly towards the spatial plane (directed towards time dimension) and form matter.

Mass is also a form of energy, which has an intrinsic tendency to expand. However, its stress (tendency to expand) is specifically on the radial direction (towards time dimension perpendicular to spatial plane).

Simply, elementary “particles” with mass are circulating packages of energy. Mathematically, the simplest elementary “particle” with mass (electron) has a helical-like deformation with a constant curvature and torsion. Hence, the expansion is localized into a strain package by circulating with a constant curvature and mass is formed.

The difference between the quantum of energy and the quantum of mass can be visualized by examining the difference between water waves and whirlpools. While water waves diffuse and interfere with each other, whirlpools have constant locations and two of them cannot be in the same location at the same time. However, unlike a whirlpool, there is no flowing medium (of a substance) in reality, but the constant and continuous expansion of space is confined into local volumes.

Two basic mechanisms form localized strain packages having mass. These two mechanisms both compress and confine the expansion into the local confinement volumes, but they are formed of completely different mechanisms.