**5. Nature of gravitational waves**

Strictly speaking there are "two" dominant energies that associated with mass M before big bang explosion as given by,

$$\mathbf{E'} = \mathbf{G}\_0 \mathbf{M}/\mathbf{r} \tag{5}$$

$$\mathbf{E} = \begin{pmatrix} \mathbb{W} \end{pmatrix} \mathbf{Mc}^2 \tag{6}$$

where E' represents the gravitational energy induced by mass M, and E is the thermo-nuclei energy due to mass M annihilation. Since physically realizable paradigm guarantees her solution would be physically realizable, but either Eq. (5) and Eq, (6) are not physical realizable. Firstly there are timeless (t = 0) or time independent equations, as most of the laws and principles do. Secondly there are not temporal (t > 0) equations yet since mass M does not change with time [i.e., or temporal (t > 0)]. In which we see that everything existed within a temporal (t > 0) space has to be temporal (t > 0). Thus from physical reality standpoint, the existence mass M it has to be temporal (t > 0) [i.e., M(t)]. Which means that M(t) changes naturally with time and exist within positive time domain. For which

Eq. (5) and Eq. (6) can be written in temporal (t > 0) formulas as given by, respectively,

$$\mathbf{E}'(\mathbf{t}) = \mathbf{G}\_0 \ \mathbf{M}(\mathbf{t})/\mathbf{r}, \mathbf{t} > \mathbf{0},\tag{7}$$

$$\mathbf{E}\left(\mathbf{t}\right) = \left(\mathbb{W}\right)\mathbf{M}(\mathbf{t})\,\mathrm{c}^2, \mathbf{t} > \mathbf{0},\tag{8}$$

where t > 0 denotes that equation is complied with the temporal (t > 0) condition (i.e., exists within the positive time domain (t > 0). E' (t) is the gravitational equation, E(t) is the thermo-nuclei energy equation, and M(t) is a temporal (t > 0) mass.

In view of thermo-nuclei Eq. (8) one might wonder where the (1/2) factor comes from since it is different from Einstein's energy Eq. E = Mc<sup>2</sup> . For which I will show in a in Section 6 Einstein's energy equation is physically significantly correct that energy and mass are equivalent, but it is "not" physically realizable within our temporal (t > 0) universe. It is because Einstein energy Eq. E = Mc<sup>2</sup> was derived from his special theory of relativity, but his special theory was developed within a non-physically realizable empty space. Since E = Mc<sup>2</sup> and E = (½)Mc<sup>2</sup> shares identical physical significance that energy and mass are equivalent, but E = (½)Mc<sup>2</sup> was based on kinetic energy standpoint where velocity of light is the current physical limit.

However, it is the induced gravitational energy E'(t) that had had never been a component included within the big bang explosion that I am concerned [3]. For which we start with the total potential energy due to induced gravitational field of Eq. (7), as referenced to point of interest "m" the overall gravitational energy induced by mass M(t) can be "approximated "by,

$$\mathbf{E}''(\mathbf{t}) \approx -\mathbf{G}\_0 \left( 4/3\pi \right) (\mathbf{r}\_0)^2, \mathbf{t} > \mathbf{0} \tag{9}$$

this shows that total gravitational energy E"(t) decreases as mass M(t) annihilates. From which we see that a huge amount of gravitational energy releases instantly soon after M(t) annihilated. In other words an intense "divergent" gravitational shock waves releases almost simultaneously with thermo-nuclei explosion, within a newly created expanding universe as depicted in **Figure 8**.

Since Eq. (7) and Eq. (8) are not time varying equations, strictly speaking they "cannot" implement directly within the temporal (t > 0) space unless they were reconfigured into time-varying partial differential forms, as given by [4, 5],

$$\frac{\partial E^{\prime\prime}(\mathbf{t})}{\partial t} \approx -K \frac{\partial \mathcal{M}(t)}{\partial t} = [\nabla \cdot \mathcal{S}^{\prime}(t)], \mathbf{t} > \mathbf{0} \tag{10}$$

$$\frac{\partial E(\mathbf{t})}{\partial t} \approx -\left(\frac{\mathbf{1}}{2}\right) \mathbf{c}^2 \frac{\partial M(t)}{\partial t} = [\nabla \cdot \mathbf{S}(t)], \mathbf{t} > \mathbf{0} \tag{11}$$

where **K=(**4/3)π G0 (r0) 2 , <sup>∇</sup>� represents a divergent operator, S″(t) and S(t) are the respective gravitational and thermo-nuclei energy vectors and (t > 0) denotes that equation is subjected to the temporal (t > 0) constraint. In other words equation only exists in the positive time domain or equivalently temporal (t > 0).

As we know that an equation is a language, a picture or even a video, from which we see that soon after the big bang explosion two divergent energies emerge from the exploding mass M(t) are illustrated in **Figure 8**, one is due to thermo-nuclei explosion and the other is from sudden releases (i.e., outward explosion) stored gravitational energy due to instantaneous mass M(t) annihilation. Although thermo-nuclei explosion is responsible mostly for the big bang creation [4, 5] for

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

**Figure 8.**

*Shows a composited diagram that our universe was created. The set of converged arrows represents a shrinking gravitational field. A set of outward arrows shows an outward energy explosion due to big bang. In which we also see that the boundary our universe is expanding at speed of light due to thermo-nuclei big bang explosion.*

which the boundary of our universe is expanding at the speed of light, but with a surge of gravitational waves as represented by a set of arrows diverges from the big bang explosion as can be seen in the figure. From which we see that a set of convergent arrows represents the collapsing gravitational field as the mass of M(t) reduces rapidly as big bang explosion started.

Since every subspace within our universe is created by an amount of energy ΔE and a section of time Δt, we see that it is the "necessary cost" for space creation, which includes our universe herself. For instance mass to energy conversion can be written in partial differential form as given by,

$$\frac{\partial E(t)}{\partial t} \approx -\left(\frac{1}{2}\right)c^2 \frac{\partial M(t)}{\partial t}, \mathbf{t} > \mathbf{0} \tag{12}$$

In which we have ignored the stored gravitational energy due to mass M(t), since thermo-nuclei energy is much greater than the induced gravitational energy from mass M(t) [i.e., E(t) > > E"(t)], where t > 0 denoted that equation is subjected to temporal (t > 0) condition or exists only in the positive time domain t > 0. By which the "total" amount of energy due to big bang explosion can be approximated by,

$$
\Delta \mathbf{E}(\mathbf{t}) \,\,\Delta \mathbf{t} \approx (\mathbb{W}) \,\,\mathbf{M}\_0 \,\, \mathbf{c}^2 \tag{13}
$$

where M0 represents the total mass and c is the speed of light. Since ΔE(t) Δt is equivalent to a temporal (t > 0) subspace. In this case we see that our universe changes with time [i.e., temporal (t > 0)].

For example if we let t = 0 which is at the time equals to 14 BLY (i.e., billion light years) after the big bang, the amount of energy ΔE and the section of time Δt = 14 BLY that created our universe is given as,

*Gravitational Field - Concepts and Applications*

$$
\Delta \mathbf{E}(\mathbf{t} = \mathbf{0}) \left(\Delta \mathbf{t} = \mathbf{1} \mathbf{4} \,\mathrm{BL} \mathbf{Y}\right) \approx \left(\mathbb{M}\right) \,\mathrm{M}\_0 \,\mathrm{c}^2 \tag{14}
$$

where t = 0 represents the instant present moment, after the big bang explosion 14 BLY ago which is the moment when big bang started to explode (i.e., 14 BLY ago). Nevertheless, Eq. (13) can be written as.

$$
\Delta \mathbf{E}\_{\mathbf{t}<0} \,\Delta \mathbf{t}\_{\mathbf{t}<0} \approx (\forall \mathbf{i}) \,\mathbf{M}\_0 \,\mathbf{c}^2 \tag{15}
$$

where t is bounded between - 14 BLY to 0 [i.e.,(� 14 BLY, 0)], and Δt increases proportionally from – 14 BLT to 0. In view of preceding equation we see that energy is conserved which is equals to the total equivalent energy of the big bang mass M0. From which we see that the section of time Δt = 0 means that no energy releases yet from mass M0 at exactly 14 BYL ago (i.e., t = �14 BLY). In other words our past time universes [i.e., ΔE **<sup>t</sup><<sup>0</sup>** Δt **<sup>t</sup><0**] can be treated as a time-independent universe from mathematical standpoint since time and physical substance are no longer there. And this is the past-time universes (or subspaces) were deterministic (or certainty) time-spaces which we normally used to predict the future universe (or subspace). And this is precisely why all our laws, principles, and theories were deterministic instead of non-deterministic or uncertainty. Yet from physically realizable standpoint, future prediction is supposed to be non-deterministic and uncertain. And this exactly why Einstein's general theory is deterministic instead of nondeterministic, which violates the nature of our temporal (t > 0) universe, where future is hard to predict.

But as time moves on forwardly from the present t = 0 into the future time domain (I.e., t > 0), our universe [i.e., ΔE(t > 0)Δt] is an indeterministic or uncertainty domain, for which we have the following expression after Eq. (13),

$$
\Delta \mathbf{E}\_{t>0} \,\,\Delta \mathbf{t}\_{t>0} \approx \left(\mathbb{W}\right) \,\mathbf{M}\_0 \,\,\mathbf{c}^2 \tag{16}
$$

which shows our universe [i.e. ΔE <sup>t</sup> <sup>&</sup>gt; <sup>0</sup> Δt <sup>t</sup> <sup>&</sup>gt; 0] changes with time and it does not change time. From which it is a mistake to treat our temporal (t > 0) universe as a deterministic universe, as Einstein's general theory did. From which we have seen that scores of fantasy time-traveling scenarios back to the past or to the future emerged.

Yet, it remains to be answered when the section of time Δt approaches to infinitely large (i.e., Δt ! ∞)? Or is our temporal (t > 0) universe having a life? As we accepted our temporal (t > 0) universe, then it would be the end of physical realizability as Δt ! ∞ that must be the end of our universe. But in view of energy conservation we see that when Δt ! ∞ then ΔE ! 0, we should have a finite energy preserved within a huge cosmological subspace within a vast temporal (t > 0) space that our universe was created as given by,

$$(\Delta \mathbf{t} \to \infty) \cdot (\Delta \mathbf{E} \to \mathbf{0}) = (\mathbb{W}) \text{ M}\_0 \text{ c}^2 \tag{17}$$

And this is the end of our universe at t ! ∞ at point of infinity, since time within the greater temporal (t > 0) space that had had supported the big bang creation of our universe has no beginning and has no end. But our universe has a beginning, but it has no end in time and in space. Similar to a wave created on a still water pond, it has the beginning, but it has no end from strictly speaking viewpoint.

Yet every subspace within our temporal (t > 0) universe, no matter how small it has a lowest limit by Planck constant. In which we see that the lowest limit for a tiniest particle within our temporal universe even at point of infinity (i.e., t ! ∞) Δt ΔE is still within the quantum limit as from current knowledge of science is given by, *Temporal (t > 0) Space and Gravitational Waves DOI: http://dx.doi.org/10.5772/intechopen.99474*

$$
\Delta \mathbf{t} \,\Delta \mathbf{E} = \mathbf{h} \tag{18}
$$

where h is the Planck's constant.

Nevertheless as from macroscopic standpoint every subspace no matter how big it is, it is currently limited by.

$$
\Delta \mathbf{t} \,\Delta \mathbf{E} = \begin{pmatrix} \mathbb{W} \end{pmatrix} \mathbf{M} \,\mathbf{c}^2 \tag{19}
$$

where M is the mass.

Nonetheless, every subspace, as well our universe, changes with time. But our universe and her subspaces "cannot" change the speed of time since time and subspace (i.e., substance) are coexisted. Thus every subspace within our universe has the "same" time speed. Since the universe as a whole run at "the same" pace of time. In which we see that if any subspace has a "different" pace of time it "cannot" exist within our universe, that includes the timeless (t = 0) subspace. The fact is that; those timeless (t = 0) and time-independent subspaces are virtual and "nonphysically" realizable subspaces. For which is "incorrect" to assume those virtual and non-physically realizable spaces as "inaccessible" subspaces within our universe as some scientists do.
