In this chapter, we will examine the meaning of the concept of distance in physical reality, beyond its meaning in abstract mathematics, and we will formulate exact definitions of different meanings of time, as a function of physical space. As a result, we will demonstrate how these definitions naturally derive the relativity phenomenon.

In previous chapters, we discussed that a closed and expanding space geometry is the basis of physical reality, and we suggested that quanta of energy and matter are geometric deformations (strains) that are formed against the universal strain on the expansion.

However, the wrinkled epoch of our expanding space has significant differences with an abstract Euclidean space. In our space geometry, the concept of distance also has different properties than the concept of distance in an abstract geometry, and other basic physical concepts of time and mass emerges as a function of the physical distance. As a result, these concepts are intrinsically connected to each other, whose relations are described by Einsteinian relativity.

Einstein’s theory of special relativity is based on two postulates:

- The speed of light is constant for all observers,

- The laws of physics are the same in any inertial frame of reference.

In fact, Einstein’s principle is not very different from Galileo’s except that it includes the postulate of constancy of speed of light, and formulates relativistic transformations at high speeds.

By following these postulates, Einstein formulated correct description of motion of relativistic objects and transformations between arbitrary coordinate orientations. These transformations are based on Lorentz gamma factor. On the other hand, although special relativity suggests mathematics for relativistic transformations, it does not suggest a full reason for the constancy of speed of light as a phenomenon.

Additionally, one of the fundamental assertions of Einstein's relativity is that lengths and time can be measured by a set of imaginary arbitrary elements called "measuring rods" and "clocks". Unfortunately, these elements do not have proper metrics based on physical reality, because Einsteinian relativity do not discuss what basic concepts of distance, time, and mass are, and how the relativistic mechanism is ensured in the smallest scale.

Our point of view agrees on Einstein’s conclusions and ensures transformations between arbitrary coordinate systems, but it also explains constancy of speed of light as a phenomenon, and explains the mechanism of relativity at the smallest scale.

Additionally, our hypothesis suggests that every observer is able to determine a concrete definition of the metric, which emerges as a property of the whole space geometry by observing its own state in smallest scale. In fact, this concrete definition is the physical formulation of Einstein’s “measuring rods” and “clocks”. As a result, the proper definition of the spatial metric explains the relativistic correlation between fundamental concepts like distance, time, and mass; and it generates the gamma factor as a variation of its intrinsic property.

In this chapter, we will directly present the physical definitions and concrete formulations of distance and time. Finally, these re-definitions will become the basis of the formulation of laws of Nature only if they are comprehended with the full meaning of Geometric Generalization, which is discussed in further chapters.

In this chapter, it will also be demonstrated as an example, how these re-definitions derive gamma of Lorentz Transformation Equations. Three different versions of the derivation are presented. Additionally, we will reconstruct N.D. Mermin’s “the light clock” experiment.

Please note that this chapter discusses formation of basic physical concepts, and derives relativistic transformations from these definitions. However, we will examine “The Exact Meaning of Relativity” in Section 9.3, and we will emphasis Einstein’s statement: "Relativity teaches us the connection between the different descriptions of one and the same reality”.