Either a discrepancy has been made with one of the equations, or an equation I have noted has set a constant to 1. The reason why I think this goes as following:

I take us to recall two equations of interest for me this time around:

[math]\frac{\partial V}{\partial r} = \frac{1}{e} \frac{\partial U(r)}{\partial r} \mathbf{J}[/math]

[math]\mathbf{B} = \frac{1}{mc^2 r}(\frac{\Phi}{c^2})\frac{\partial v}{\partial t} \mathbf{J} \approx \frac{1}{mc^2 r}(\frac{1}{c^2} \frac{c^2}{4 \pi G})\frac{\partial v}{\partial t} \mathbf{J} = -\frac{1}{mc^2 r}\frac{1}{4 \pi G}\frac{\partial v}{\partial t} \mathbf{J}[/math]

Since both

[math]\mathbf{E} \equiv \frac{\partial V}{\partial r} = \frac{1}{e} \frac{\partial U(r)}{\partial r} \mathbf{J}[/math]

and the Sciama gravielectric field is

[math]\mathbf{E} = (\frac{\Phi}{c^2})\frac{\partial v}{\partial t}[/math]

and (actually may still hold to be approximate if the gravitational permittivity and permeability relationships hold, which they seem to do). Plug our new relatonship in

[math]\mathbf{B} = \frac{1}{mc^2 r}\frac{1}{e} \frac{\partial U(r)}{\partial r} \mathbf{J} \cdot \mathbf{S} = \frac{1}{mc^2 r}\frac{\partial V}{\partial r} \mathbf{J}[/math]

Crucially what it shows more important though, is that the spin orbit coupling has derivatives which rely on the former equation to be an approximate to a more fundamental underlying theory involving the gravitational permeability and permittivity. The fact our terms could match the usual Maxwell equation only seems to varify that the Sciama definition of the field was related to those constants from the first place a certain fact it seems, he seemed to have missed about his theory.

[math]\approx \frac{1}{mc^2 r}(\frac{1}{c^2} \frac{c^2}{4 \pi G})\frac{\partial v}{\partial t} \mathbf{J} = -\frac{1}{mc^2 r}\frac{1}{4 \pi G}\frac{\partial v}{\partial t} \mathbf{J}[/math]

Notice, the former results in the gravimagnetic spin orbit weak coupling! Now, something strange has popped out of the equation, which I think has been a result of Sciama's application of cgs units to the Newton constant [math]G[/math]. Not sure yet, will need to investigate it, because the normal gravielectric field is

[math]\mathbf{E} = \frac{\partial V}{\partial r} = \frac{1}{e}\frac{\partial U}{\partial r}[/math]

Which means the first equation is at odds with the dimensions...

[math]\frac{\partial V}{\partial r} = \frac{1}{e} \frac{\partial U(r)}{\partial r} \mathbf{J}[/math]

I wonder how this happened, unless the previous equation has set a Planck constant equal to 1. I'll find the answer to this soon.

**Edited by Dubbelosix, 11 April 2018 - 06:50 AM.**