Considering our previous discussions on various meanings of concept of time, we can now formulate the exact physical definition of the concept of simultaneity.

In this section, we will directly introduce the definition of the concept of simultaneity like a self-evident postulate in order to limit the scope of this paper. In fact, the reasoning behind its definition can be traced all the way back to our previous definitions; but a closer examination at this point would prolong this paper too much.

Definition: Simultaneity

Same kind of knots or vortexes (elementary “particles” with mass) always have equal amount of circulations (Nrotations) in the same distance towards time dimension (Dtd) (in any relativistic cases).

Interestingly, according to our definition of simultaneity, there might be relative variations in the quantity of clock-ticks in simultaneous cases. We will examine relativistic transformations in the next section. We should emphasize that our concept of simultaneity is not about synchronization of clock-ticks or simultaneity of events. On the contrary, it describes the simultaneity of the amount of circulations in the confinement volume. In fact, it is the concrete physical mechanism, which does not vary in relativistic cases, while clock-ticks decrease relatively with acceleration or in gravitational fields. Additionally, the definition of simultaneity is essential for deriving gamma factor of Lorentz Transformation Equations (Section 6.6).

Below graph demonstrates that the (helical) confinement volumes of two vortexes, which are relatively in motion, have equal amount of circulations in the same distance interval towards time dimension. However, the accelerated confinement volume of the vortex in violet is tighter.

Figure 6.12 Inertial and accelerated helix both have same amount of Nrotations

Readers who are interested in the reasoning of our concept of simultaneity should examine the relation: Concept of mass is only dependent on the tightness of the confinement volume (since strain describes the stress) (Section 5.3), while spatial distance metric and time as clock-ticks depends on both the tightness of the confinement volume and Nrotations (Sections 6.1 and 6.3). Hence, Nrotations should be the same even in relativistic cases in order to keep the effect of (gamma) contraction the same for all.

This section treats simultaneity as a property of knots and vortexes. However, we should also note that the concept of simultaneity appears because of the expansion character in space-time geometry, where the expansion parameter defines and creates distinct time (as a dimension) states for a spatial location. Simply, we can also say that all simultaneous points in space-time are equally distant from the center of the curvature of space, or they have the same degree of the radius of curvature (ignoring gravitational fields).

Since, we have formulated the physical definition of the four-dimensional distance (the space-time interval, D4d); we can now suggest a geometric definition that describes the intrinsic circulating action in the confinement volume. In fact, Estring length is a crucial concept, being the basis of relativistic transformations.

Definition: Unit Estring length (or unit D4d)

Unit Estring length is the four dimensional length in space-time (D4d) of the helical path for a one full circulation in the confinement volume of a vortex (such as electron).

E 6.8

This definition is another interpretation of the simple version.

Definition: Simultaneity

Unit Estring length of same kind of knots or vortexes (accelerated or not) is constant.

Figure 6.13 Light cone and simultaneous circulations in confinement volume

- Four-dimensional length (D4d) that a photon travels between O and C in space-time is in orange.

- Estring length of the helical path in the confinement volume of an inert “particle” with mass between O and A is in red.

- Estring length of the helical path in the confinement volume of the same kind of “particle” (in a motion relatively to the inert one) between O and B is in violet.

All three four-dimensional lengths (Estring lengths) in Figure 6.13 are equal, and both confinement volumes have the same amount of circulations (Nrotations).

Now, we will discuss the formation of relativity and examine its mechanism in the smallest scale.

Please note that unit Estring length contracts in gravitational fields with the variation in radial obliquity angle (θ radial obliquity). We will discuss gravity deeply on Chapter 7 on “Fundamental Forces and Gravity”.