6.  Deriving the Principles of Special and General Relativity:

The famous Michelson-Morley experiment in 1887 proved that light travels with the same speed regardless whether it was moving in the direction of the movement of the Earth or perpendicular to it (MICHELSON and MORLEY, 1991). This unexpected result initiated active research that eventually led to Special Relativity in 1905 (Einstein, 2005). The speed of light in vacuum is then considered the maximum speed which anything in the Universe can attain. Photons, or massless particles, propagate in vacuum at this terminal speed, regardless of the motion of the source or reference frame of the observer. However, even though this was confirmed by many experiments, there is yet no theoretical or philosophical account that could explain the reasons behind this constancy and invariance of the speed of light.

Logically, there are two cases under which a quantity does not increase or decrease when we add or subtract something from it. Either this quantity in infinite, or it exists in orthogonal dimension. As we have already introduced in sections 2 and 3 above, according to the Duality of Time postulate, both these cases are equivalent and correct for the absolute speed of light in vacuum, because it is the speed of creation which is the only real speed in nature, and it is intrinsically infinite (or indefinite), but the reason why we measure a finite value of it is because of the sequential re-creation process; so individual observers are subject to the time lag during which the dimensions of space are re-created. Moreover, since the normal time is now genuinely imaginary, the velocities of physical objects are always orthogonal onto this real and infinite speed of creation.

As demonstrated in Figure 5 and explained in section 5.1 above, one of the striking conclusions of the sequential re-creation in the inner levels of time is the fact that it conceives of only two primordial states: vacuum and void, whose spatial and temporal superposition is producing the multiplicity of intermediary states that appear in the cosmos as matter particles. Vacuum is the continuous existence in the inner levels of time, and void is the discrete existence in the outer level. These two super states, which correspond to  and  respectively, can be conceived as abstract extreme limits, but only a relative superposition of them can ever be observed or measured as relative events in space-time, or inner-outer time that is the complex-time discussed in section 5.

As the real time flows uniformly in the inner levels, it creates the homogeneous dimensions of vacuum, and whenever it is interrupted or disturbed, it makes a new dimension that appears as a discrete instance on the outer imaginary level which is then described as void, since it does not last for more than one instance, before it is re-created again in a new state that may resemble the previous perished states, which causes the illusion of motion, while in reality it is only a result of successive discrete changes. So the individual geometrical points can either be at rest (in the outer/imaginary time) or at the speed of creation (in the inner/real time), while the apparent limited velocities of physical particles and objects (in the total complex time, which forms the physical space-time dimensions) are the temporal average of this spatial combination that may also dynamically change as they are progressing over the outward ordinary time direction.

Therefore, the Universe is always coming to be, perpetually, in “zero time” (on the outward level), and its geometrical points are sequentially fluctuating between existence and nonexistence (or vacuum and void), which means that the actual instantaneous speed of each point in space can only change from  to , and vice versa. This instantaneous abrupt change of speed does not contradict the laws of physics, because it is occurring in the inner levels of time before the physical objects are formed. Because they are massless, this fluctuation is the usual process that is encountered by the photons of light on the normal outward level of time, for example when they are absorbed or emitted. Hence, this model of perpetual re-creation is extending this process onto all other massive particles and objects, but on the inner levels of time where each geometrical point is still massless because it is metaphysical, while “space” and “mass” and other physical properties are actually generated from the temporal coupling, or entanglement, of these geometrical points, which is exhibited only on the outward level of time.

Accordingly, the normal limited velocity, of physical particles or objects, is a result of the spatial and temporal superposition of these dual-state velocities of its individual points , thus:

                                                                                             (5)

Individually, each point is massless and it is either at rest or moving at the speed of creation, but collectively they have some non-zero inertial mass , energy , and limited total apparent velocity  given by this equation 5 above.

Consequently, there is no gradual motion in the common sense that the object leaves its place to occupy new adjacent places, but it is successively re-created in those new places, i.e. motion occurs as a result of discrete change rather than infinitesimal transmutation, so the observed objects are always at rest in the different positions that they appear in (see also Figure 5). This is the same conclusion of the Moving Arrow argument in Zeno’s paradox, which Bertrand Russell described as: “It is never moving, but in some miraculous way the change of position has to occur between the instants, that is to say, not at any time whatever.” (Haj Yousef, 2018).

This momentous conclusion means that all frames are effectively at rest in the normal (imaginary) level of time, and there is no difference between inertial and non-inertial frames, thus there is even no need to introduce the second principle of Special Relativity (which says that the laws of physics are invariant between inertial frames) neither the equivalence principle that lead to General Relativity. These two principles, which are necessary to derive Lorentz transformations and Einstein’s field equations, are implicit in the Duality of Time postulate and will follow directly from the resulting complex-time geometry as it will be shown in sections 6.1 and 6.3 below. Furthermore, it will be also shown in section 6.2 that this discrete space-time structure that results from the genuinely-complex nature of time is the only way that allows exact mathematical derivation of the mass-energy equivalence relation ().

In this manner, the Duality of Time postulate, and the resulting perpetual re-creation in the inner levels of time, can explain at once all the three principles of Special and General Relativity, and transform it into a quantum field theory because it is now based on discrete instances of dynamic space, which is the super-fluid state  that is the ground state of matter, while the super-gas state  is the ground state of anti-matter, which accounts for super-symmetry and matter-antimatter asymmetry as we shall discuss further in section 7.1. The other fundamental forces could also be interpreted in terms of this new space-time geometry, but in lower dimensions: , , and , while gravity is in .