You have to really look at the Heisenberg uncertainty relation.
Position cannot be sharply determined if we know direction (angular momentum). Speed is problematic too. The state of an electron (or electrons) in the atoms isn't an eigenstate of the velocity (or speed) operator, so no way to nail down the speed precisely.
That being said, we chose to abbreviate momentum with rotation speed for our visualization. Reality includes coherence of the shells. They must effectively rotate together to produce coherent momentum and force the other terminal.
Thanks for linking that spin paper earlier - I'm reading it and it's interesting.
With respect to uncertainty of angmom vs position - I would expect the pontryagin dual of angmom (which would be affected by the H.U.P.) to be angular density distribution, not "position" as such. Do you have any information on this relationship?
Also, do you know what the energy eigenstates of electrons in the fermi band look like, and how those relate to velocity eigenstates? As I understand, fermi band electrons that carry electrical current are usually not bound to atoms, but in a much wider (space basis) state, which I would expect to be closer to momentum/velocity eigenstates.
Also, how literal are you claiming the OP is? I've never heard this "gearing" analogy before, and I'm wondering if it's highly metaphorical or if this reflects some actual physical process I'm just not familiar with.
Density distribution can be transformed to position with spherical shell slice processing from what i understand.
This visualization is an interpretation of all of the math we could get our hands on. Hopefully we get closer to what the atoms are actually doing. Quite literally, electron volt can be considered momentum, so we did our best to illustrate this...simplifying it to rotation speed. In all cases, we are trying to get closer to what the physical object atoms are doing to provide for the phenomenon.
For instance, ionization means delocalized surface of the atom in this illustration because we can't imagine the electron to be a bead that flies around magically and moves through the wire providing motive pressure, per se. So we use shell gearing instead as a rationalization that fits the math and makes more intuitive sense.
Our belief is that QM is absolutely correct in its descriptions but lacking in its interpretations. There is a lot of woo out there because of this.
If you know any other QM experts that would be willing to help us develop the model further, that would be great- can you PM me through the website?
Position cannot be sharply determined if we know direction (angular momentum). Speed is problematic too. The state of an electron (or electrons) in the atoms isn't an eigenstate of the velocity (or speed) operator, so no way to nail down the speed precisely.
That being said, we chose to abbreviate momentum with rotation speed for our visualization. Reality includes coherence of the shells. They must effectively rotate together to produce coherent momentum and force the other terminal.