A relativistic formula

[Dubbelosix]

Now we move onto the second part of the essay. A modified Schrodinger equations. By convention correction where we should use the reduced version of h. we rectify it and it's done simple enough by distributing 1/2π, by doing so we learn that Schrodingers potential is embedded in the probability space

we will write out the full equation to tomorrow.

Edited April 29, 2021 by Dubbelosix

[Dubbelosix]

Today we are going back to the semi classical gravity equation and unify it with the Schrodinger equation

i[a^2, b^2] ∂h/ ∂t ψ = B N/N_0  ψ 

Where B is a notation for an object with units of energy x Planck constant

Edited April 29, 2021 by Dubbelosix

[Dubbelosix]

First and foremost we need to correct this equation properly for the uncertainty in the commutator. It's a matter of convention that the Planck constant be the reduced version

[a^2,b^2] ≥ h/(2π) 

remember.... In order to correct the dimensions, the Planck constant has been absorbed with an energy term as B

i[a^2, b^2] ∂h/ ∂t ψ ≥ B N/N_0  ψ 

since the operators have to Hermitian quadratic observables, it follows from the Schrodinger Roberton Walker inequalities that 

a^2, b^2  ≥ |1/2<{a,b}> - <a><b>|^2

+ |1/2<{a,b}> |^2

Where this <{a,b}> is the anticummutator respectively written as

<{a,b}> = ab +ba

 

by doing this, the quantum gravity wave equation is now completed with the unavoidable uncertainty laws. It is semi classical  in that respect. 

 

 

 

 

Edited April 29, 2021 by Dubbelosix

[Dubbelosix]

Now, if a^2 and b^2 are interpreted as Hermitian matrices respective to the derivatives of position of s complete three geometry.of space R^3 and b^2 as that if time then we now have a unifying principle, it's not new, but it's new the way it written here. It is the energy uncertainty principle where space and time are the variables in consideration E^2(X) and E^2(t)
Likewise, any time we do this. We always associate the wave function as a function of space and time as a prerequisite ψ (X,t)

When I find the time to plug In Schrodingers potential from.his famous equation, we'll also investigate it under the Dirac equation obeying the Clifford algebra containing all the "juicy stuff" of spinning systems associated to the Dirac energy Hamiltonian.

Edited April 29, 2021 by Dubbelosix

[Dubbelosix]

Now let's unify everything.

i/(2π)[a^2, b^2] ∂h/ ∂t ψ (X,t)

= - ħ/2m[a^2, b^2]∇^2 ψ (X,t)

≥ B N/N_0  ψ (X,t)

(iff) [a^2, b^2] =0 then (ab +ba = 0) which is the Clifford algebra with

a^2 = 1

b^2 = 1

as unitary matrices. Using Schrodingers wave equation we find the final full equation as

i/(2π)[a^2, b^2] ∂h/ ∂t ψ (X,t) = - h^2/(4πm)[a^2, b^2]∂^2/ ∂x^2 ψ (X,t) + V ≥  B N/N_0  ψ (X,t)

where V is the Schrodinger potential.

 

[Dubbelosix]

And that concludes the final theory.

[Dubbelosix]

Since I am the inventor the equation, I would like to name it, 

"the Schrodinger-Wigner-Dirac localisation equation."

Edited April 29, 2021 by Dubbelosix