Reconstructing The Energy-Stress Tensor

[Vmedvil2]

It is well known that Einstein's Energy Stress Tensor only accounts for electromagnetic stress upon the gravitational medium which does not account for the other forces of nature, so we are going to experiment with changing the T₀₀  section to account for the Strong Nuclear Force and Weak Nuclear Force in the Energy Density section of the Energy Stress Tensor.

 

 

First we must define what is Energy density which is Joules/Volume which are the units of Energy Density meaning any equation added to this Tensor must be in the form of Joules/Volume for the Strong and Weak Nuclear forces. Now gravity in energy is defined as E_g = E_EM + E_SNF + E_WNF meaning that the energy is equal to the combined energy of all the forces taking those divided by volume gives E_g/V = E_EM/V + E_SNF/V + E_WNF/V  which V = (4/3)πr³ , so by taking all the parts of the equation divided by the 3-D space we can arrive at that Energy Density is just Energy potential divided by volume. The electromagnetic Density is already solved as E_EM/ V= (1/2)(e₀E² + (1/u₀)B²)  Similar equations must be derived for the Strong and Weak Nuclear Forces for E_SNF/V and E_WNF/V. 

 

The Strength of Charged particles bound by the Strong Nuclear Force is E = Ke²/r where as the binding energy between two Neutral particles is U = U₀(r₀/r)e^-r/r0  we can create a any case for charged and neutral particles by adding these equations together  E_Charged + U_Neutral = Ke²/r + U₀(r₀/r)e^-r/r0   now the description for the Strong Nuclear Force is completed for charged and neutral particles. If the equation is divided by V = (4/3)πr³  ,we arrive at a energy density of (E_Charged + U_Neutral)/V = (3/4)(Ke²/r + U₀(r₀/r)e^-r/r0)/πr³ which can now be added to the Tensor making (E_EM + E_SNF)V = (1/2)(e₀E² + (1/u₀)B²) + (3/4)(Ke²/r + U₀(r₀/r)e^-r/r0)/πr³ which is a accurate Energy Density for the Electromagnetic and Strong Nuclear Forces which is not complete yet as the WNF needs to be added, but for now T₀₀ = (1/2)(e₀E² + (1/u₀)B²) + (3/4)(Ke²/r + U₀(r₀/r)e^-r/r0)/πr³  considering the Strong Nuclear Force and Electromagnetism.

 

 

The Weak Nuclear Force is a bit more tricky to get a energy density for as there is not a equation for the Energy of the WNF but it can be added as E_WNF = Σ₀^NΔE_Nucleon as a complex summation that counts the nucleon changes in energy via the weak nuclear force making this part of the equation like Gibb's Free Energy in enzyme reactions but counting for how many nucleons experience changes via the Weak Nuclear Force, as a energy density the equations is E_WNF/V = Σ₀^NΔE_Nucleon/(4/3)πr³  = (3/4)Σ₀^NΔE_Nucleon/πr³ . This gives a accurate description of the energy density of a particle decay at a given time by summing the particle changes which can be added to T₀₀  as T₀₀ =(1/2)(e₀E² + (1/u₀)B²) + (3/4)(Ke²/r + U₀(r₀/r)e^-r/r0 + Σ₀^NΔE_Nucleon)/πr³  which yields an equation that describes all the forces in the Energy Stress Tensor.

 

Unified General Relativity Energy Density

 

T₀₀ =(1/2)(e₀E² + (1/u₀)B²) + (3/4)(Ke²/r + U₀(r₀/r)e^-r/r0 + Σ₀^NΔE_Nucleon)/πr³

Edited January 7, 2020 by VictorMedvil

[Dubbelosix]

OK your dimensions look good, I just wish you would write it out in latex, I know I am not one to talk but I am using a pad which won't let me use certain characters at the moment.

[Vmedvil2]

OK your dimensions look good, I just wish you would write it out in latex, I know I am not one to talk but I am using a pad which won't let me use certain characters at the moment.

Welcome back dubbel, did you go fishing or something, I don't like latex the formatting of it annoys me.

Edited January 13, 2020 by VictorMedvil

[Dubbelosix]

No just a little a break.

[Vmedvil2]

This "Version" of the Energy-Stress Tensor isn't even wrong as explained by PeterDonis of the Physics Forums, Link = https://www.physicsforums.com/threads/energy-stress-tensor-question.983528/ , it just includes different sources of energy-stress as there are many "Versions" of the Energy-Stress Tensor dependent upon the forces present.

Edited January 25, 2020 by VictorMedvil