_{1}

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The goal is to define Quantum Gravity Value by combination between our new concept about physics energy behaviour [1] and Einstein relativity’s Theory [2]. Our theory is based on the existence of a relationship between energy and vacuum! So it can be considered that the energy is a function of the vacuum ratio (v). Therefore, we can say that vacuum ratio constitutes a part of space-time. With simple mathematical formula, we can easily obtain the equation of the Energy Vacuum. This gives us the distribution of the energy Vacuum (E) into two parts are inversely proportional from our vacuum energy diagram, the effective energy that the sole responsible for Curvature of space-time fabric, and the lost energy that the responsible of the Gravitational waves [3]. From these equations, we can find that the relationship with Energy and Vacuum ratio is linear which are compatible with Quantum Mechanics laws and Maintains the energy conservation principle. It is also observed that the equations obtained through our theory are Combining relativity and Quantum Mechanics into one continuum. If we take the equations of our theory, we can easily obtain from Curvature of Space-Time Fabric, the Gravity value equation which equals to the square root of energy multiply times the square of the vacuum ratio. On other hand, a curvature matrix and a Time Dilation’s Circle are proposed, which gives us a new method to facilitate the calculations of the parameters involved in the Space-Time Curvature.

Energy (E) is one of the obsessions of humanity concerns since antiquity. The feasibility of formulating the Singularity of Nature was enunciated by Einstein’s mathematical formula, demonstrating the equivalency of energy and mass ( E = m ∗ c 2 ) [

The relation of the Space-Time Fabric to a Cosmic Energy impact during their interaction is very complex (_{L}) responsible for resultant Gravitational Waves:

E = E ′ + E L (1)

Our theory is based to consider the space-time fabric as element volume of a fluid [

E = f ( v ) (2)

When Space-Time Fabric extend in the unknown matter (or dark matter), a high proportion of the Energy impulse is transferred to the porous unknown matter. In this case we will consider that the energy is a function of degree of saturation of unknown matter (S) instead of the vacuum ratio Equation (3).

E = f ( S ) (3)

Without unknown matter, the physical displacement of the Space-Time skeleton (pothole) is the main mechanism of Curvature. During the displacement process (

E ′ = E ⋅ v (4)

On the other hand, it is also known that damping (amortization) occurs at infilling of vacuum by energy, which manifests itself as a decrease in the vacuum ratio as a function of time. When the damping (attenuation) in the system exceeds a critical value (v = 0%), there is a starting in the Gravitational waves as a function of time. Given the Equation (2), we deduce the Equation (5):

E p = E ⋅ ( 1 − v ) (5)

Space-Time Fabric interaction to Cosmic Energy in saturated Space-Time Fabric with unknown (or dark) matter is different and of course more complex (

E ′ = E ⋅ S (6)

Moderate levels of energy impulse could cause the displacement of previously vacuum areas in the Space-Time Fabric without unknown matter, Saturation means that these cavities are filled with vacuum matter and that the displacement would be inhibited by unknown matter (vacuum matter) resistance to curvature. However, the really saturated Space-Time Fabric may have few percent of the total vacuum non-occupied by unknown matter. In this condition, the intensity of the Gravitational Waves would be greatly increased due to the low bulk of vacuum matter, but the impact energy still ensure the curvature of the Space-Time Fabric due to the reduction of the rest vacuum volume. Given the Equation (3) we deduce the Equation (7):

E p = E ⋅ ( 1 − S ) (7)

As mentioned above, the curvature of the rest vacuum volume has a significant effect on the behaviour of saturated Space-Time Fabric with unknown matter under energy impact. It is accepted that unknown matter contains tiny vacuum pockets enclosed in vacuum volume. An accurate assessment of the volume of vacuum pockets trapped in unknown matter is difficult affect the curvature (displacement) of vacuum-matter mixtures and thus significantly alter the process of generating vacuum matter energy. It is therefore essential to take into account the curvature of the vacuum -matter mixture, instead of the curvature of pure matter. Similarly, based on the Equation (3), determining the energy of the vacuum -matter mixture is as follows Equation (8):

E a m = E m ⋅ S + E a ⋅ ( 1 − S ) (8)

where; E_{am} is the energy of the vacuum-matter mixture, E_{a} is the energy of the vacuum, therefore the lost energy is the energy of the vacuum Equation (9):

E L = E a = E ⋅ ( 1 − S ) (9)

If we take all the equations from 1 to 9 above we can easily obtain the Energy Vacuum Diagram (

In Space-Time Fabric without unknown matter, the graph of the Gravitational Waves Intensity is divided into four parts (Very Strong, Strong, Low & Limited and Low Gravitational Waves Intensity) as shown in

We proposed a relationship to predict the Space-Time Fabric Curvature is as follows [

D = v E (10)

where; D is the Interacted depth of curvature of Space-Time Fabric (Z = ∞), E(%) is the cosmic Energy to be interacted, and v (from 0% to 100%/ or 0 to 1) is vacuum ratio that is fundamentally characterised the Space-Time Fabric volume.

If we apply our theory in Space-Time Fabric without unknown matter, given Equation (10), we get Equation (11) [

D = f ( E , v ) (11)

If we apply our theory in saturated Space-Time Fabric with unknown matter, given Equation (10), we get Equation (12) [

D = f ( E , S ) (12)

Similarly, for the previous equation, we propose the following equality [

v = S (13)

When finishes Interaction between a Space-Time Fabric’s element volume and Energy, finding a crater which represent Space-Time Curvature (or Gravity from Einstein Relativity) (

Δ V = e ⋅ ∫ 0 D V ⋅ d D (14)

where, V is the total volume of the Space-Time Fabric’s element, A is the surface/or area of the Interacted Energy, ∆H is the height of the crater (Space-Time Curvature), e is the vacuum ratio (v) and D is the Interacted depth of curvature of Space-Time Fabric mentioned in Equation (10) above.

After development of Equation (14) and introducing Equation (11) we deduce Equation (15) [

v = Δ H E (15)

after development of Equation (14) and introducing Equation (11) we deduce Equation (15) [

Which implies the Equation (16):

Quantum Gravity = Δ H = E ⋅ v 2 (16)

We found an empirical relationship between the height of the crater (Space-Time Curvature) and interacted depth determined by Equation (17), where we introduce the proposed coefficient K (

D = K ⋅ Δ H , K = x ⋅ v − 1 (17)

x = 6.67 ⋅ v (18)

As illustrated in

If we take all assuming that indexes and components are linearly dependent we can easily obtain a curvature matrix, which clearly illustrates that three basic components are the diagonal and the other three main index properties compose the rest of the matrix:

( X X X Y X Z Y X Y Y Y Z Z X Z Y Z Z ) = ( T C c O C R C c C C g O C R C g E ) Curvature Matrix

v | v < 0.3 | 0.3 < v < 0.5 | 0.5 < v < 0.8 | v > 0.8 |
---|---|---|---|---|

x | 2 | 3 | 5 | 7 |

Nature of Space-Time Fabric typically display complex concept as a result of missing theory about its interaction with cosmic Energy. A key aspect for the selection of representative Space-Time Fabric parameters is to consider Knowledge of its properties. This nature is based on our theory to determine this characteristics (curvature index Cc, Anti-gravity index Cg, Vacuum ratio v, Over curvature ratio OCR) of the Space-Time Fabric; by using these curvature parameters, it is possible to determine the Curvature (gravity), Times dilation, and amount of interacted Energy etc. While the rigorous selection of Space-Time Fabric parameters requires a deep understanding and proper knowledge of its behaviour. Parameters such as OCR, Cc and Cg play a key role on Curvature and Interacted Energy predictions.

Curvature index (Cc) and Anti-gravity index (Cg) obtained from our theory are necessary in calculation for Space-Time Fabric curvature. In our hypothesis, we have been looking for a possible relationship between Cc and Cg indices and general characteristics of Space-Time Fabric. One of these parameters is over curvature ratio (OCR). In this study, the effect of OCR and vacuum ratio (v) on Cc and Cg indices, was proposed (Figures 9-13). Thus, The hypothesis indicate that Cc and Cg indices were influenced by OCR and v, and, a linear relationship between them should be observed. Increasing values of (v) will decrease Cc and Cg values. On the contrary, when OCR increases, Cc and Cg values would also increase. It is possible to say that the Cc and Cg values are influenced by the same parameters. Therefore it can be concluded that the amount of Curvature depends on the Anti-gravity index, and that the amount of Curvature (C) is proportional to the Anti-gravity index (Cg) (

Parameter | Curvature | Vacuum ratio, v (%) | Energy, E (%) | Curvature Index, Cc | Anti-gravity Index, Cg | Over curvature ratio, OCR |
---|---|---|---|---|---|---|

Equation | 0 - ∞ (infinity is a black hole) | 0 - 100 | =E' + E_{L} | =0.510(v − 0.33) | =0.15(v + 0.007) | =E'/E_{L} |

Our theory introduced the following factors as the main causes of Time Dilation (Td) according to Space-Time Fabric Curvature (

C = O C R ⋅ e i φ = e i ( C c ⋅ t + C g ⋅ X ) (19)

φ ( X , t ) = [ 0 ~ Δ H ] , M a x . Δ H = 2 π (20)

In order to carry more than one value and indices to represent the Time Dilation Circle, We used the complex number to explain the curvature characteristics of Space-Time Fabric. We can simply conclude that the final state equals the initial state multiply by the time dilation (Td) Equation (21).

φ ( X 1 , t 1 ) = φ ( X 0 , t 0 ) ⋅ T d (21)

The most determining factor for the credibility Time Dilation’s Circle is its ability to Contain all the characteristics and indices contributing to this phenomenon as illustrates

Is not there yet a complete theory linking Einstein’s relativity to quantum mechanics?! Our theory is based on the existence of a relationship between energy and vacuum! So, it can be considered that the energy is a function of the vacuum ratio E = f ( v ) . With simple mathematical formula we can easily obtain the equation of the Energy Vacuum E = E ∗ v + E ∗ ( 1 − v ) . This gives us the distribution of the energy Vacuum (E) into two parts are inversely proportional from our vacuum energy diagram, the effective energy ( E ′ = E ∗ v ) that the sole responsible for Curvature of space-time fabric, and the lost energy ( E L = E ∗ ( 1 − v ) ) that the responsible of the Gravitational waves. Therefore, we can say that vacuum ratio which has value from 0% to 100% (or from 0 to 1) is constitutes a part of space-time. From these equations, we can find that the relationship with Energy and Vacuum ratio is linear which are compatible with Quantum Mechanics laws and Maintains the energy conservation principle. It is also observed that the equations obtained through our theory are combining relativity and Quantum Mechanics into one continuum. If we take the equations of our theory, we can easily obtain from Curvature of Space-Time Fabric the Quantum Gravity value equation which equal to the square root of energy multiply times the square of the vacuum ratio (Quantum Gravity = E ∗ v 2 ). From the consequences, we have found after our theory that gravity is energy?! On other hand, our theory consists in considering Space-Time as element volume of a fluid or Continuous media, which gives us possibility for using finite element method (FEM) to resolve and simulate Space-Time Fabric Curvature according to Navier-Stokes equations. Energy Vacuum Diagram as theory can be given new and good explanations in physics about cosmic, quantum and relativity phenomenon, if will make laboratory experiments or cosmic monitoring.

The Interacted Energy consists of displacing Space-Time Fabric and increasing the time dilation. The effectiveness of this hypothesis was demonstrated by the results of the available propositions which verified by curvature matrix. In addition, this matrix gives us a new method to facilitate the calculations of the parameters involved in the Space-Time Curvature, which gives a great credibility to our hypothesis. Maybe our hypothesis about relationship between Indices involved in curvature cycle based on theoretical results caused by lack of equipments, but can be proved in future by experimental tests in order to compare them by our theory. Indeed, Time Dilation’s Circle is considering a good new tool to calculate, interpret and explain this phenomenon; moreover, maybe it can clarify us more other cosmological phenomenon in the future.

This work was supported and funded by the K.E.C Laboratory, Department of Engineering & Applied Science of K.E.C Laboratory, Jijel, Algeria, under the project number (PN): KEC.LAB.DEAS.ASTPHY.NCEERQGVP2018N007.

I would like to thank the researchers Dr. Maher Sawaf & Pr. Nidhal Guessoum for his researches and explanation lessons. Also; I would like to thank the Master Khelalfa Hocine & Khalil Agha for their help and support in all steps of this work.

The author declares no conflicts of interest regarding the publication of this paper.

Houssam, K. (2019) New Concept of Physics Energy Behaviour and Its Application in Cosmology to Define Gravity Value from Einstein’s Relativity. Journal of Modern Physics, 10, 1255-1270. https://doi.org/10.4236/jmp.2019.1010084