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Merging Quantum Mechanics With General Relativity

Quantum Mechanics General Relativity Quantum Gravity

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#1 VictorMedvil

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Posted 10 October 2019 - 12:12 AM

Let's Start with Einstein's Field Equation General Form.

einsteinfieldeq.jpg

 

Now in order to merge this with Quantum Mechanics via space coordinates we must solve the equation for Radius® which is 

 

-2(8πGTuv/CΛguv + Ruv)/guv  = R 

 

Now R can be switched for (X,Y,Z) as  R2 = ∇= d2/dx2 + d2/dy2 + d2/dz2

 

Thus -2(8πGTuv/C - Λguv + Ruv)/guv  = Einstein Field Equation

 

Next is the Schrodinger equation which can be solved for the Laplace operator coordinates as well.

 

b949bac25131eaca08d626812362ac03.jpg

Which can be solved for ∇ as

 

-(2m(iħ(dΨ/dt) - VΨ)/Ψħ)1/2 Quantum Mechanics 

 

Then a merging equation which fuses GR with QM can be made that is

 

download.png

 

2Quantum Mechanics  - ∇2Einstein Field Equation  = dS2(x,y,z)

 

OR

-(2m(iħ(dΨ/dt) - VΨ)/Ψħ) + (2(8πGTuv/C - Λguv + Ruv)/guv) = dS2(x,y,z)

 

This Yields a Theory of Quantum Gravity directly from Schrodinger's Equation and the Einstein Field Equations.


Edited by VictorMedvil, 10 October 2019 - 01:09 AM.


#2 OverUnityDeviceUAP

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Posted 10 October 2019 - 12:44 AM

Let's Start with Einstein's Field Equation General Form.
einsteinfieldeq.jpg

Now in order to merge this with Quantum Mechanics via space coordinates we must solve the equation for Radius® which is

-2(8πGTuv/C4 - Λguv + Ruv)/guv = R

Now R can be switched for (X,Y,Z) as R2 = ∇2 = d2/dx2 + d2/dy2 + d2/dz2

Thus -2(8πGTuv/C4 - Λguv + Ruv)/guv = Einstein Field Equation

Next is the Schrodinger equation which can be solved for the Laplace operator coordinates as well.

b949bac25131eaca08d626812362ac03.jpg
Which can be solved for ∇ as

-(2m(iħ(dφ/dt) - Vφ)/φħ)1/2 = Quantum Mechanics

Then a merging equation which fuses GR with QM can be made that is

download.png

2Quantum Mechanics - ∇2Einstein Field Equation = dS2(x,y,z)

OR
-(2m(iħ(dφ/dt) - Vφ)/φħ) + (2(8πGTuv/C4 - Λguv + Ruv)/guv)2 = dS2(x,y,z)

This Yields a Theory of Quantum Gravity directly from Schrodinger's equation and the Einstein Field Equations.

I'm pretty sure it doesn't work that way. First of all because QM and GR are more than a Schrodinger equation and one of Einstein's field equations, secondly they aren't compatible in most all situations in which they can be applied so it's not a matter of of putting them both into one equation.

Edited by OverUnityDeviceUAP, 10 October 2019 - 12:45 AM.


#3 VictorMedvil

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Posted 10 October 2019 - 12:53 AM

I'm pretty sure it doesn't work that way. First of all because QM and GR are more than a Schrodinger equation and one of Einstein's field equations, secondly they aren't compatible in most all situations in which they can be applied so it's not a matter of of putting them both into one equation.

 

They seem mathematically compatible in this example here, what do you mean not compatible?



#4 OverUnityDeviceUAP

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Posted 10 October 2019 - 01:14 AM

They seem mathematically compatible in this example here, what do you mean not compatible?

How would you apply it?

How would you apply it to a quantum chemistry problem.

How would it be used any differently than the Schrodinger equation for mapping atomic orbitals?

Edited by OverUnityDeviceUAP, 10 October 2019 - 01:17 AM.


#5 VictorMedvil

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Posted 10 October 2019 - 01:22 AM

How would you apply it?

How would you apply it to a quantum chemistry problem.

How would it be used any differently than the Schrodinger equation for mapping atomic orbitals?

 

It just includes the gravity of the orbital is the only difference with the GR Terms being the (1/(2(8πGTuv/C - Λguv + Ruv)/guv n(n-1)))2 


Edited by VictorMedvil, 10 October 2019 - 01:52 AM.


#6 VictorMedvil

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Posted 10 October 2019 - 01:46 AM

Someone Pointed out this needs a correction, I messed up as R is scalar curvature which the Scalar Curvature of 4-D  Minkowski space is given by R = −n(n − 1)/r2

n = 4 as the space is 4 dimensional for Hyperbolic space or Minkowski space.

(1/(2(8πGTuv/C - Λguv + Ruv)/guv n(n-1)))2 = r = Einstein Field Equation

 

so, 

 

2Quantum Mechanics  - ∇2Einstein Field Equation  = dS2(x,y,z)

 

OR

 

-(2m(iħ(dΨ/dt) - VΨ)/Ψħ) - (1/(2(8πGTuv/C - Λguv + Ruv)/guv n(n-1)))4  = dS2(x,y,z)

 

Which furthermore, you cannot divide by guv thus I will take the inverse matrix guv-1 which  guv guv-1  

 

Untitled.png

 

Thus Corrected versions 

 

(1/(2(8πGTuv/C - Λguv + Ruv)guv-1/n(n-1)))2 = r = Einstein Field Equation

 

and

 

-(2m(iħ(dΨ/dt) - VΨ)/Ψħ) - (1/(2(8πGTuv/C - Λguv + Ruv)guv-1 n(n-1)))4  = dS2(x,y,z)


Edited by VictorMedvil, 10 October 2019 - 03:07 AM.




Also tagged with one or more of these keywords: Quantum Mechanics, General Relativity, Quantum Gravity