Fractal Torus 4 - Grain of Salt
I want to critique some of the calculations in the previous essays on EVO physics.
Lorentz Force
First we have the magnetic field out at the circle of electrons. As we approach the circle of electrons, the strength of the B-field rapidly increases, because we are getting close to the circle current which is creating all the magnetic field in the first place. See Fig. 1. This will serve to greatly increase the inward force, hence lowering the requirements for high speeds.
This would seem to make everything more stable, but, as pointed out in Part 3, what is more likely is that the electrons will break up into various spirals. In other words - my search for a self-stabilized current flow leads us directly to an unstable current flow.
Electrostatic Repulsion
As I looked more into the electrostatic repulsion term, I found several different derivations, including one that had a ln(N_e) term, which would increase the repulsive term by about 30x. Without working through how this might balance with the increased Lorentz force just mentioned, it only says to me that the system has additional instabilities.
Relativistic Corrections
The only term directly affected by relativistic correction is the mass. From the very first calculations here, it was clear that the required speeds of the electrons are in the relativist realm. Putting in the larger effective mass will push the required speeds very close to the speed of light. How does this balance with the resultant increased Lorentz force? The equations become what is called “implicit”, which means they can only be solved with numeric approximations. I tried several methods and could not get the answers to converge.
Conclusion
This line of analysis is done for now. I am convinced that a self-stabilizing current system is automatically at the edge of multiple instabilities. It could blow apart or snap into a 3-level fractal torus, and my toolbox cannot walk through that.
Thanks to any who have made it all the way to here.
Noble effort - this kind of stability considerations sounds a lot like John Wheeler's (1911-2008) comments on GEONs.
https://youtu.be/LarJgZOOL_U?si=gZDCpjbAvoosSzO5
Neither physicist, nor mathematician, but the calcs. or rather the torus reminds me of "The Cosmic Wheel", eternally spiralling and as we are thrown out to the edges of it we must make our way to the central axis about which is said;
"The axle at the centre of the wheel is the innermost core of consciousness which cannot be expressed in language."
Never stops anyone from trying... sounds like a challenge tbh.
They say the closer one moves to the centre of the wheel, the less suffering one feels. At the very centre, there is absolute stillness and no motion. The conscious experience of time is related to how rapidly the wheel spins, or how far away from the centre one’s mind is focused.
Pretty specific philosophical framework. Not saying it can't be done. But yes, good luck.