Now looking in The Elements Beyond Uranium, Seaborg & Loveland, 1990, pages 76-77, they discuss what atoms look like from the relativistic Dirac Equation. And here this book states in various passages that the torus is a usual shape (a doughnut is a torus) :
(a) ..." a doughnut (p3/2, m = 3/2)"
(b) ... " the highest m value for a given j always has a doughnut shaped distribution"
(c) ... "States of intermediate m are multi-lobed toroids."
So it is looking better all the time for the idea that the torus is the building block geometry of atoms, where we stack toruses onto more toruses. In this manner a sphere shape is just the stacking of 3 or more individual toruses where the middle torus is larger than the other two.
I posted in sci.physics a few minutes ago:
deriving both Schrodinger and Dirac Equations from Maxwell Equations #1727 Atom Totality 5th ed
I thought it best to repost how the Maxwell Equations derive both Schrodinger and Dirac Equations.
Deriving Schrodinger Eq from Maxwell Eq Alright the Schrodinger Eq. is easily derived from the Maxwell ?Equations. In the Dirac Equation we need more than two of the Maxwell ?Equations because it is a 4x4 matrix equation and so the full 4 ?Maxwell Equations are needed to cover the Dirac Equation, although ?the Dirac Equation ends up being a minor subset of the 4 Maxwell ?Equations, because the Dirac Equation does not allow the photon to be ?a double transverse wave while the Summation of the Maxwell Equations ?demands the photon be a double transverse wave. ?But the Schrodinger Equation:
ihd(f(w)) = Hf(w) where f(w) is the wave function
The Schrodinger Equation is easily derived from the mere Gauss's laws ?combined and without magnetic monopoles.
?These are the 4 symmetrical Maxwell Equations with magnetic ?monopoles:
div*E = r_E
div*B = r_B
- curlxE = dB + J_B
curlxB = dE + J_E
Now the two Gauss's law of Maxwell Equations standing alone are ?nonrelativistic and so is the Schrodinger Equation.
div*E = r_E
div*B = 0 ?____________
div*E + div*B = r_E
this is reduced to
k(d(f(x))) = H(f(x))
Now Schrodinger derived his equation out of thin air, using the Fick's ?law of diffusion. So Schrodinger never really used the Maxwell ?Equations. The Maxwell Equations were foreign to Schrodinger and to ?all the physicists of the 20th century when it came time to find the ?wave function. But how easy it would have been for Schrodinger if he ?instead, reasoned that the Maxwell Equations derives all of Physics, ?and that he should only focus on the Maxwell Equations. Because if he ?had reasoned that the Maxwell Equations were the axiom set of all of ?physics and then derived the Schrodinger Equation from the two Gauss ?laws, he would and could have further reasoned that if you Summation ?all 4 Maxwell Equations, that Schrodinger would then have derived the ?relativistic wave equation and thus have found the Dirac Equation long ?before Dirac ever had the idea of finding a relativistic wave ?equation.
Deriving Dirac Eq from Maxwell Eq
Alright, these are the 4 symmetrical Maxwell Equations with magnetic ?monopoles:
div*E = r_E div*B = r_B - curlxE = dB + J_B curlxB = dE + J_E
Now to derive the Dirac Equation from the Maxwell Equations we add ?the lot together:
div*E = r_E div*B = r_B - curlxE = dB + J_B curlxB = dE + J_E ?________________
div*E + div*B + (-1)curlxE + curlxB = r_E + r_B + dB + dE + J_E + J_B
Now Wikipedia has a good description of how Dirac derived his famous ?equation which gives this:
(Ad_x + Bd_y + Cd_z + (i/c)Dd_t - mc/h) p = 0
So how is the above summation of Maxwell Equations that of a ?generalized Dirac Equation? ?Well, the four terms of div and curl are the A,B,C,D terms. And the ?right side of the equation can all be conglomerated into one term and ?the negative sign in the Faraday law can turn that right side into ?the negative sign.
Now why is the derivation of the Dirac Equation by the AP-Equation ?important? Well, it is important for many reasons, not only that all ?of Quantum Mechanics is packed inside of the Maxwell Equations. But the important implication is that all the forces of physics are ?just the one force of EM, or commonly called Coulomb force. That means ?the Strong Nuclear force is a Coulomb force of a chemical bonding in ?the nuclei of atoms, and the Weak Nuclear force is EM also, and the ?gravity force is EM-gravity of magnetic monopoles which can only ?attract and never repel.