In this section, we will present the formation of relativity phenomenon as a natural result of our geometric principles. Please note that we will discuss “The Exact Meaning of Relativity” in Section 9.3, and we will underline Einstein’s statement: "Relativity teaches us the connection between the different descriptions of one and the same reality”.

First, let us review our definitions of distancespatial, timeas clock-ticks, and mass.

In the previous sections, we discussed the physical basis of Einstein’s imaginary elements; “measuring rods” and “clocks”, and examined the physical definitions of distance, timeas clock-ticks, and mass.

We suggested that standard metrics of these concepts should be based on the tightness of the confinement volume of a certain type of elementary “particle”, such as that of electron’s. (We will detail the principles of standard metrics in Chapter 11 “The Universal Unit System”.) The tightness of the confinement volume is an expression of the Compton wavelength:

E 6.9

Our definitions of unit distancespatial and timeas clock-ticks are:

E 6.10

Mass of an elementary “particle” is defined as a function of its Compton wavelength (as a ratio to electron’s Compton wavelength).

E 6.11

Figure 6.14 Graph of definitions

On Figure 6.14

 - Estring of the inert “particle” with mass is in red, and

 - Estring of the same type of “particle”, which is accelerated relatively according to the inert “particle”, is in violet.

According to our definition of simultaneity, Estring lengths of both red and violet “particles” are equal, and both “particles” have the same amount of Nrotations in the same distance interval towards time dimension. Figure 6.14 above simply demonstrates this equivalency.

Since, violet “particle” is accelerated; its direction is more oblique in space-time. Consequently, the confinement volume of the accelerated violet “particle” is tightened and contracted because its Estring length is stretched during acceleration. Contraction in the accelerated confinement volume can be visualized mechanically, where transverse section of an elastic material contracts under tensile stress (Poisson’s contraction). Similarly, stress content in the accelerated violet “particle” increases, while strain in the expanding space-time geometry increases. (Mathematically, curvature and torsion increases in the violet “particles’ ” helical path.)

Above graph demonstrates that the radius of the confinement volume of the accelerated violet “particle” varies, and its variation can be calculated geometrically.

The contraction of the accelerated confinement volume has significant consequences: standard metrics in the accelerated frame relatively changes (contracts), as these metrics are based on the tightness of the confinement volume.

According to the inert one (red), quantity of clock-ticks of the accelerated one (violet) decreases in the simultaneous case. Hence, its mass (total energy content of the violet one) increases relatively. This conclusion is in accordance with the empirical results of Einstein’s relativity. We will derive the geometric contraction of the confinement volume, which can be seen on the graph above. The rate of the geometric contraction of the confinement volume exactly gives the gamma factor of Lorentz Transformation Equations. We will present three different geometric derivations of the gamma factor in this section.

However, this paper has more to add to Einstein’s Theory of Relativity. It suggests that the standard distance metric (unit distance) on the accelerated frame also contracts relatively as opposed to Einstein's theory, which proposes that a restricted length contraction takes place.

It is very important that timeas clock-ticks and distancespatialmetrics contracts together with the same proportion. Such a mechanism always ensures the constancy of speed of light for relative observers by ensuring the constant relation between timeas clock-ticks and distancespatial metrics.

Above derivation of postulates of special relativity (constancy of speed of light) and derivation of gamma may be accepted as one of the theoretical verifications of the Geometric Generalization.

In fact, our definition of timeas clock-ticks exactly explains the decrease in the quantity of clock-ticks (time dilation) in relativistic cases, and it suggests a concrete mechanism that allows comparison between relative observers. Eventually, the contraction of the confinement volume behaves like a built-in gamma factor indicator.

Considering the delicate nature of the subject, interested readers may wish to study additional discussions on links below.

6.6.4 Time dilation

6.6.5 Reconstruction of N.D. Mermin’s light clock experiment

The links below present mathematical derivations of the Lorentz gamma factor from the geometric contraction of the confinement volume.

6.6.6 Derivation of the Lorentz gamma factor (basics)

6.6.7 Derivation of the Lorentz gamma factor (simple version)

6.6.8 Derivation of the Lorentz gamma factor (full version including time dimension)

Next chapter is a major one that discusses “Fundamental Forces and Gravity”.