Now, let us detail our space-time geometry, before discussing its logical cause.

According to the logical cause that we will soon discuss, the geometry of physical reality has a non-Euclidean three-dimensional space. In this geometry, spatial dimensions (space) are closed; hence, space is finite, although it is unbounded. In this geometry, there is a curvature in all spatial coordinates in all spatial directions.

The curvature, which is a consequence of the closeness, adds an additional dimensional parameter to this geometry. This parameter is the radius of the curvature of spatial dimensions, or it is the time dimension, which is perpendicular to the spatial plane (dimensions). Conversely, the radial direction on this geometry (time dimension) seems to be open-ended. Consequently, any arbitrary point on this geometry can be defined by both spatial and time coordinates.

This geometry cannot be defined on a standard static polar coordinate system. Here, circumference (closed spatial dimension) expands with the increase in radius (time dimension). Although, any arbitrary point on spatial plane is static, spatial plane itself expands continuously, and any arbitrary point flows towards time dimension perpendicularly to spatial dimensions. The expansion of space towards time direction is the most fundamental of physical reality, and it is a result of self-evident logical principles (e.g. the first four postulates of Euclid).

However, it is important to note that the flow of spatial coordinates towards time dimension is not a mechanic action that has energy content. More precisely, flow of expansion means that coordinates in radial (time) direction has sequential precedence, while all coordinates are equivalent in circumferential (spatial) directions (at a time).

Additionally, here, it is not possible to determine a rate of change, such as “speed of the flow” or “speed towards time”, because this flow is a complete process of the entire space, and it leaves out no comparable entity. The only factor that varies with the expansion of space is the increase in the radius of spatial curvature (time dimension).

Figure 4.2 Geometry of physical reality

Our geometry has the properties of two opposite geometries. In a sense, it is elliptic, because spatial dimensions are closed and they make great circles. In a way, it has a hyperbolic character too, because of the extension character, where the distance between two arbitrary points on spatial dimension increases constantly.

Simply, in our geometry, space is a three-dimensional sphere, which constantly expands. Readers may also visualize this geometry by an example of an inflating spherical balloon by leaving only one-dimension of the three spatial dimensions out.

The expansion of spatial dimension is omnidirectional and isotropic, which means that expansion continues in all directions equivalently. It is not easy to visualize this expansion in three dimensions. However, we will soon discuss in the following chapters why physical existence can exist only with three spatial dimensions.

We will also discuss space and time dimensions, and examine the various meanings of the concepts of distance and time in Chapter 6 on “Distance – Time – Relativity”.

Now, let us discuss the logical cause of this geometry.