Eventually, formulization of gravitational effect describes the mutual relation between the smallest stress (in the knots) and the largest strain (in entire space-time). Naturally, these two concepts cannot be directly connected to each other without a balancing parameter.

Let us consider our balloon example again in order to visualize the relation between matter and space-time. This relation in the balloon example depends on both the surface area that is tied into a knot and the overall size of the balloon (elasticity of balloon’s wall is ignored). Therefore, it is necessary to know the ratio between the knot size and the balloon size in order to understand the effect of the knot to the balloon’s shape.

Figure 7.16 Photo demonstrating how a knot on a balloon deforms its shape

Similarly, matter seems to affect and deform space-time, because the expansion is confined locally. Hence, we may assume that there appears a gravitational constant in gravitational equations, which indicates the ratio between the size of the confinement volume (of a knot or a vortex) and the circumference of the universe.

Unfortunately, the current value of the gravitational constant (6.672×10^-11 m³s^-2kg^-1) does not reflect this proportion, since it is distorted by the current incongruous unit system (SI). Our Universal (Natural) Unit System, which will be discussed in Chapter 11, renders an automatic revision of the gravitational constant to 2.787 x 10^-46. The proper value of gravitational constant in our unit system indicates the ratio between the knot-vortex size and radius of curvature of the universe.

It is no coincidence that even in any incongruous unit system this value (2.787 x 10^-46) characterizes the ratio of the strength of gravitational effects. It is similar to the fine structure constant of electromagnetic interaction. It is the constant ratio of two energies:

(a) Gravitational potential between two electrons at a distance L

E 7.9 Gravitational potential between two electrons (G is gravitational constant)
Please note that practically, there is no such an interaction between two electrons.

(b) the energy of a single photon with a wavelength of L

E 7.10 Energy of a single photon
(c is speed of light, and h is Planck’s constant)

Strictly speaking, the strain caused by gravity is an equivalent quality to the strain in packages of electromagnetic radiation. Both of them are strain formations on the expansion. However, while strain packages of electromagnetic radiation are local strain formations (like wrinkles on our balloon example), gravity compresses and restrains the expansion globally in all spatial directions (like knots affecting and reducing the circumference of the balloon). In other words, the energy content of strain packages are confined in local (confinement) volumes against the universal strain on the expansion, where the same energy content of the knot is spread universally. Practically, the ratio of their strengths indicates the size (tightness) of the strain (energy) they form on fundamentally expanding space-time geometry.