**6. Non-realizable relativistic theories**

Since there are two pillars of modern physics one is dealing with very small particles of Schrödinger's quantum mechanics [6] and the other is dealing very large object of Einstein's relativistic theories [2], yet both of them are timeless (t = 0) or time independent principles since both of them were developed within a nonphysically realizable paradigm. Firstly we see that Einstein's special theory of relativity was developed on an empty space paradigm as depicted in **Figure 9**.

In which we see that it is not a physically realizable paradigm by virtue of temporal exclusive principle. Nevertheless Einstein's special theory can be developed with Pythagoras theorem as given by,

$$
\Delta \mathbf{t}' = \Delta \mathbf{t} / \left[ \mathbf{1} \text{--} (\mathbf{v}/\mathbf{c})^2 \right]^{1/2} \tag{20}
$$

where v is the velocity of a coordinate system and c is the speed of light. Since within empty space paradigm it has no time and has no direction, Einstein's special theory of Eq. (20) shows no sign of relativistic direction. Although the implication is relative-directional similar to the kinetic energy equation it has no sign of direction, but the equation implies that the energy is on the same direction of the velocity vector v. From which we see that scientists have frequently treated special theory as a relativistic-directional independent, which is due to the empty space paradigm. The question is that why we made those trivial mistakes? The answer is that, since scientists are mathematicians, they can implant virtual time on a piece of paper as they wish. But not knowing the background of that piece had have been assumed as an empty subspace for centuries.

On the other hand, if Einstein's special theory is developed within a temporal (t > 0) subspace as depicted in **Figure 10**. For example, derivation can start at time t=t1 with a light emitter of S, where t is the time of the background temporal (t > 0) space. With reference to the diagram, we see that it will take a section of time Δt (i.e., t = t1 + Δt) for beam 1 to reach position 1, which is a subsection within Δt <sup>0</sup> (i.e., Δt < Δt 0 ) for light beam 2 before reaches position 2. Since v�Δt is a

#### **Figure 9.**

*Shows where Einstein's special theory of relativistic mechanics was developed from an empty space paradigm. In which we see a coordinate system (X' Y*<sup>0</sup> *Z') is translating at a constant speed with respect to a stationary coordinate system (X, Y, Z).*

sub-distance of v�Δt <sup>0</sup> before the moving particle reaches position 2, it will take beam 2 an additional section of c <sup>Δ</sup>t″ =c(Δ<sup>t</sup> <sup>0</sup> – Δt) to reach position 2 simultaneously when the particle arrives. Therefore we see that the duration at static position 1 is actually Δt <sup>0</sup> <sup>=</sup> <sup>Δ</sup>t + <sup>Δ</sup>t″, instead of just <sup>Δ</sup>t as shown in the special theory of relativity [i.e., Eq. (20)], from which we see that the moving particle has "no" section of time-gain relative to the static position 1, since time at position 1 and 2 are "the same" (t = t2 = t1 + Δt 0 ) when moving particle reaches position 2. In which the duration at position 1 is actually Δt <sup>0</sup> <sup>=</sup> <sup>Δ</sup>t + <sup>Δ</sup>t″, instead of <sup>Δ</sup>t as shown in the special theory of relativity. Thus we see that Einstein's special theory of relativity fails to exist within our temporal (t > 0) universe. In other words Einstein's special theory of relativity is a timeless (t = 0) theory which is only existed within an empty space, which has no time and no space. From which we see that it is the background of that piece of paper inadvertently that had have treated it as an empty timeless (t = 0) space.

Nevertheless what is the physical significant of Einstein's special theory of relativistic to what? In view of the temporal (t > 0) paradigm of **Figure 10**, we see that it is the relativistic theory of distance as given by,

$$\mathbf{d}\_{\mathbf{r}} = (\mathbf{c} - \mathbf{v}) \cdot (\Delta \mathbf{t}' - \Delta \mathbf{t}'') = (\mathbf{c} - \mathbf{v}) \Delta \mathbf{t} \tag{21}$$

where dr is a relativistic distance between position S of the light source and position 1 of a moving particle both simultaneous reach position 2. From which we see that light beam has traveled a extra distance of (c – v) Δt more than the particle traveled. Thus we see that Einstein's special theory of relativity is relative to distance within our temporal (t > 0) subspace, instead of relative to time since we cannot change time. That means that particle and the light beam arrived position 2

*Temporal (t > 0) Space and Gravitational Waves DOI: http://dx.doi.org/10.5772/intechopen.99474*

#### **Figure 10.**

*Shows the same relativistic mechanics model is embedded within a temporal (t > 0) subspace. S is the light source and P is a particle in motion at a constant velocity of v, c is the velocity of light.*

at the same time which is the same time at position 1, at position 2, at position S and the same time at everywhere within our universe. In which we see it has no time-gain or time-loss of the traveling particle.

Nevertheless when velocity of the moving particle approaches the speed of light (i.e., v ! c), we have a relative distance dr ! 0. This is by no meant that time is running behind or ahead the pace of time. For which we see that it is the speed of light travels with time, and it is not the speed of light changes the pace of time.

Similarly relativistic distance of preceding equation can also be applied for relative velocity of two moving particles. For example two particles are moving at the same direction at different speeds v1 and v2, respectively. In view of Einstein's special theory is not a physically realizable theory within our temporal (t > 0) universe, and it is also incorrectly had have interpreted as directional-independent, as can be seen from Eq. (20). It is however should correctly treated special theory as a directional sensitive theory because of particle's velocity vector. From which we see that the relativistic distance between two particles on the "same direction" can be shown as,

$$\mathbf{d}\_{\mathbf{r}} = (\mathbf{v}\_1 \mathbf{-v}\_2)(\Delta \mathbf{t}' - \Delta \mathbf{t}'') = (\mathbf{v}\_1 \mathbf{-v}\_2)\Delta \mathbf{t} \tag{22}$$

Again we have seen that Einstein's special theory is a relativistic velocity equation instead a relativistic time theory.

Equivalently Einstein relativistic mass equation can be derived from his special theory as given by,

$$\mathbf{M} = \mathbf{M}\_0 \left(\mathbf{1} - \mathbf{v}^2/\mathbf{c}^2\right)^{-1/2} \tag{23}$$

where M is the effective mass (or mass in motion), M*<sup>o</sup>* is the rest mass, *v* is the velocity of the moving M and *c* is the speed of light. In other words, the effective mass of a moving particle increases at the same amount with respect to the relativistic time window (i.e., time dilation Δt 0 ) increases. Nevertheless as we had shown in preceding Einstein's special theory is not a physically realizable theory within our temporal (t > 0) universe, then relativistic mass equation is also not a physically realizable equation. But one of the famous energy Eq. E = mc<sup>2</sup> was derived based on the special theory. Then the legitimacy within our temporal (t > 0) universe is in question. Since E = mc<sup>2</sup> was based to Kinetic energy equation to legitimize the significant of the equation as shown by,

$$M = M\_0 \left( 1 + \frac{1}{2} \cdot \frac{v^2}{c^2} + \text{terms of order } \frac{v^4}{c^4} \right) \tag{24}$$

By multiply the preceding equation with the velocity of light c2 and noting the terms with the orders of v4 / c<sup>2</sup> are negligibly small, above equation can be approximated by,

$$\mathbf{M} \approx \mathbf{M}\_0 + \frac{1}{2} \mathbf{M}\_0 \mathbf{v}^2 \frac{1}{\mathbf{c}^2} \tag{25}$$

which can be written as,

$$(\mathbf{M} - \mathbf{M}\_0)\mathbf{c}^2 \approx \frac{1}{2}\mathbf{M}\_0\mathbf{v}^2\tag{26}$$

The significant of the preceding equation is that M-Mo represents an increased in mass due to motion, which is the kinetic energy of the rest mass Mo. And (M-Mo)c2 is the extra energy gain due to motion. Nevertheless what Einstein postulated, as I remembered, is that there must energy associated with the mass even at rest. And this was exactly what he had proposed,

$$\mathbf{E} \approx \mathbf{M} \mathbf{c}^2 \tag{27}$$

where E represents the total energy of the mass. In which we see that Energy and mass are equivalent but there are not equaled.

Since we had shown that Einstein's special theory of relativity exists only within empty space, from which we see his energy equation cannot be legitimized within our temporal (t > 0) universe. Yet energy and mass are equivalent is a wellaccepted physical reality but may not in exact form since science after all is approximated. In view of the legitimacy and Einstein's energy equation and comparison of the well accepted although empirical kinetic energy Eq. E = (1/2) m v<sup>2</sup> , where v is the velocity. Since velocity of light c is the current limit of science, it is justifiable to rewrite the energy equation in following form after kinetic energy equation as given by,

$$\mathbf{E} \approx (\mathbf{1}/2) \text{ Mc}^2 \tag{28}$$

In which we see that mass and energy are equivalent, and it has the same physical significant as Einstein's energy equation although Einstein's equruion has been illegimated. In view of preceding equation we see that energy and mass can be simply traded as given by,

$$\mathbf{E} \leftrightarrow \mathbf{M} \tag{29}$$

From which in princiole we can convert mass to energy or energy to mass. Nevertheless, one of the greatest theories that Einstein had had developed must his general theory of relativity as given by [2],

*Temporal (t > 0) Space and Gravitational Waves DOI: http://dx.doi.org/10.5772/intechopen.99474*

$$\mathbf{G}\_{\mu\nu} + \; \mathbf{g}\_{\mu\nu} = \begin{pmatrix} 8\pi \mathbf{G}/\mathbf{c}^4 \end{pmatrix} \mathbf{T}\_{\text{uv}} \tag{30}$$

where Gμν is the Einstein tensor, gμν is the metric tensor, Tu<sup>ν</sup> is the stress-energy tensor, is the cosmological constant, *G* is the Newtonian constant of gravitation, and *c* is the speed of light.

In view of general theory it is a point-singularity approximated deterministic equation, we see that Einstein's general theory is not a physically realizable principle since science is supposed not to be deterministic. For which it is impossible to predict future with deterministic general theory. Although we can change a section of time Δt but we cannot change the pace of time or even stop time. Strictly speaking all physically realizable theory must be temporal (t > 0). For which we see that degree of uncertainty increases as time moves further away from the point of absolute certainty (i.e., present instance t = 0). Thus we see that it is not the complexity of mathematic that Einstein had have used, it is the physically realizable paradigm that determines the physically realizable science. Nevertheless, Einstein's theory is a relativistic theory of distance but not a relativistic theory of time since we cannot change time.
