I had a inspiration with how to merge QM and GR this time across the Riemann Curvature/Ricci Tensor, there was a previous attempt in the (http://www.sciencefo...ral-relativity/)thread which the definition I used for the trace of Scalar Curvature in 4-D time-space was not accepted as exact enough, however I can use one of the exact definitions of Riemann Curvature and still merge them into a Quantum Gravity Equation.

First as always we started with the fundamental equation of quantum mechanics being the Schrodinger Equation then reverse solve it for ∇^{2 }= d^{2}/dx^{2} + d^{2}/dy^{2} + d^{2}/dz^{2}.

Which

Solves as -(2m(iħ(dΨ/dt) - VΨ)/Ψħ)^{1/2 }= ∇_{Quantum Mechanics}

Now for General Relativity the defintion of the Reimann Curuvature I will be using is

R(X,Y)Z = ∇_{X}∇_{Y}Z - ∇_{Y}∇_{X}Z - ∇(x,y)Z where X = u ,Y = v , Z = W

Now Einstein's General theory of Relativity is as follows

Now we must solve that equation for R_{uv }or R_{xy }which solved for the Ricci Tensor is R_{uv} = (8πG/C^{4})T_{uv }+ (1/2)Rg_{uv }+ **Λg _{uv} which is also **R

_{xy}= (8πG/C

^{4})T

_{xy }+ (1/2)Rg

_{xy }+

**Λg**

_{xy}Now we can take that entire equation and substitution that in for R(X,Y)Z being the same as R

_{uv}or R

_{xy , }so (8πG/C

^{4})T

_{uv }+ (1/2)Rg

_{uv }+

**Λg**= ∇

_{uv }_{X}∇

_{Y}Z - ∇

_{Y}∇

_{X}Z - ∇(x,y)Z , now we must solve that for ∇(x,y)Z which is the same as saying ∇(x,y,z). then -((8πG/C

^{4})T

_{uv }+ (1/2)Rg

_{uv }+

**Λg**+ ∇

_{uv }_{Y}∇

_{X}Z - ∇

_{X}∇

_{Y}Z) = ∇(x,y)Z and also equals -((8πG/C

^{4})T

_{uv }+ (1/2)Rg

_{uv }+

**Λg**+ ∇

_{uv }_{Y}∇

_{X}Z - ∇

_{X}∇

_{Y}Z) = ∇

_{General Relativity}

Lastly, ∇_{General Relativity }- ∇_{Quantum Mechanics }= ∇_{Quantum Relativity}

_{Or}

_{ }-((8πG/C^{4})T_{uv }+ (1/2)Rg_{uv }+ Λg_{uv }+ ∇_{v}∇_{u}W - ∇_{u}∇_{v}W) + (2m(iħ(dΨ/dt) - VΨ)/Ψħ)^{1/2 }= ∇_{Quantum Relativity}

_{or }

**-((8πG/C ^{4})T_{uv }+ (1/2)Rg_{uv }+ Λg_{uv }+ ∇_{v}∇_{u}W - ∇_{u}∇_{v}W) + (2m(iħ(dΨ/dt) - VΨ)/Ψħ)^{1/2 }= (**d

^{2}/dx

^{2}+ d

^{2}/dy

^{2}+ d

^{2}/dz

^{2})

^{1/2}

**Edited by VictorMedvil, 17 May 2020 - 11:21 AM.**