The Mysterious Two-Valuedness of Spin Quantum Mechanics

Once Schrödinger in 1926 had formulated his partial differential equation for the Hydrogen atom with one electron with an eigenvalue spectrum in full agreement with observation, the next challenge was the Helium atom with two electrons: How to generalise from one to many electrons? 

The way to to do this was not clear and the simplest option was followed: Make a formal mathematical generalisation with a stroke of a pen, just add a new 3d spatial coordinate for each new electron to form Schrödinger's multi-dimensional wave equation in $3N$ spatial dimensions (plus time) for an atom/molecule with $N$ electrons, and then seek to live with that equation. 

For the Helium atom with two electrons this gives a six-dimensional wave equation, with the ground state appearing as having minimal energy.  But what is the electron configuration of that state? The idea then came up, from the success for the Hydrogen atom, to view the ground state of Helium to be composed of two spherically symmetry Hydrogen-type wave functions with the electrons so to speak on top of each other.  To make that possible in view of the Coulomb repulsion between electrons, Wolfgang Pauli suggested to assign the electrons different values of "spin" as "spin-up" and "spin-down" and then postulate a Pauli Exclusion Principle PEP proclaiming that two electrons with different "spin" can share spatial domain. 

The ground state of Helium was thus declared to be a $1S^2$ state with two identical spherically symmetric electron charge distributions with different spin, which gave a rough fit with observation. 

Pauli himself viewed PEP to be a mistake, but the physics community happily adopted the idea of a two-valuedness of quantum mechanics in the form of "spin-up" and "spin-down", which is now firmly implanted in Standard Quantum Mechanics StdQM.

In RealQM, as an alternative to the formal generalisation of StdQM into many electrons, the two-valuedness of Helium takes a different form as a split of the two electrons to be restricted to half-spaces meeting at a plane through the kernel. This a physical split of charge distribution to be compared with the formal split of StdQM into "spin-up" and "spin-down".

In RealQM the separating plane gives the charge distribution a direction in space, which is lacking with only "spin-up" and "spin-down".

The previous post takes up possible physical effects of the RealQM electron split in the form of diamagnetism. 

RealQM presents a physical origin to the observed two-valuedness of He, which is independent of any PEP. There is no PEP in RealQM because it serves no need, and so can be dispensed. 

Pauli would have been very satistfied with this message, but quantum mechanics has continued to cling to PEP as the correct expression of two-valuedness. 

Since all atoms have an innermost shell of two electrons, RealQM for any atom carries a form of two-valuedness, which is not based on two-valued spin.

RealQM with electrons split into two half-spaces gives a ground state energy which fits better with observations than the $1S^2$ configuration with split spin. Does that say anything?