Time has more than one meaning, and these meanings are not clear enough and mostly confused. Now, let us examine how clocks tick in physical reality.

According to our discussions in previous chapters, elementary “particles” with mass are local deformation (strain) packages in the expanding space-time geometry, where the continuous expansion is confined in formations like knots or vortexes locally. Hence, there is a constant circulation (rotation) in the confinement volume (at constant speed of light).

Most simply, continuously “ticking” circulation in the confinement volume is the basis of the clock-ticks in physical reality, and time as the quantity of clock-ticks between two occurrences is dependent on the number of internal circulations in the confinement volume.

Let us immediately note that timeas clock-ticks is not a geometric distance towards time dimension. Clocks tick in physical reality, because of the dynamic action in the confinement volume; hence, timeas clock-ticks is the property of matter (knots and vortexes), and it is pointless to discuss quantity of clock-ticks in empty space or in a coordinate system, where there is no matter (knots or vortexes).

Because timeas clock-ticks is an internal property of an individual knot or vortex, its ticking rate can vary in different knots or vortexes in certain conditions (in relativistic cases). Fortunately, proper (physical) definition of timeas clock-ticks, which covers these variations, can easily be formulated.

In physical reality, spatial distance and clock-ticks are integrated concepts, which are interconnected by the constancy of speed of light. While light travels a certain spatial distance, the same length is circulated in the confinement volumes of matter, since both actions are the consequences of the expansion in space-time geometry.

As a result, the overall length taken by circulation is equal to the distance that light travels; and amount of circulations in the confinement volume is related to the tightness (radius) of the confinement volume.

Figure 6.10 Helical circulation in the confinement volume and the light cone

In fact, a concrete formulation of spatial distance metric automatically derives a proper formulation of timeas clock-ticks, considering the phenomenon of the constancy of speed of light (or the expansion character of space-time geometry).

In previous Section 6.1, we defined the standard spatial distance metric (unit distance) as the length of a full circulation in the confinement volume (such as electron’s). Hence, spatial distance between two points is described as the multiples of the spatial distance, which light travels during a single full circulation in the confinement volume.

We can concretely define quantity of clock-ticks as a function of distance, since we have a very concrete formulation of the spatial distance metric. Time, as quantity of clock-ticks, which is actually, what we measure as seconds, hours, etc., can simply be defined as below.

Since,

and,

then,

E 6.5

This equation gives the Time (quantity of clock-ticks as seconds) for any observer (based on the Compton wavelength of electron in its inertial frame) between two incidents (depending on the amount of circulations (Nrotations) between two incidents).

Practically, if we assume that a unit distance is equal to the Compton wavelength of electron, then any observer measures quantity of clock-ticks by dividing the distance light travels in that period by the wavelength of electron.

Time as defined above gives an exact formulation of the quantity of clock-ticks in any relativistic case. Variations in tightness of the confinement volume simply derive relativistic contractions in metrics. Please note that relativistic mass increase is also a consequence of the variation in the tightness of the confinement volume, since mass is a function of the tightness of the confinement volume as we discuss in Section 5.3. The detailed mechanism of time dilation and other relativistic variations will be discussed in following sections.

As a result, above formulation of the quantity of clock-ticks (as a function of the tightness of the confinement volume) is the concrete physical basis of Einstein’s imaginary “clocks”.

Interestingly, our formulation of timeas clock-ticks is very similar to our formulation of spatial distance. In fact, in Chapter 11, our Universal (Natural) Unit System fixes the incompatibility in SI units by assigning the constant speed of light as one (1); hence, both spatial distance and timeas clock-ticks join to become same kind of physical quantity. Moreover, since spatial distance metric and timeas clock-ticks are functions of the same property (tightness of the confinement volume), the ratio between these metrics is kept constant in any relativistic case; this phenomenon is known as the constancy of speed of light.

The following sections

6.4 Space-Time Interval

6.5 Simultaneity

6.6 Relativity

are related with formation of relativity phenomenon. Readers, who are not familiar with the concepts of relativity, may directly jump to the next chapter on “Fundamental Forces and Gravity”.