The Ad Hoc Invention of Spin by Pauli

The basic idea of Quantum Mechanics QM of giving a two-valued quality of spin as spin-up and spin-down of electrons, came from the need to explain the shell structure of atoms with $2n^2$ electrons in shell $n=1,2,3,...$ with the factor 2 accounting for the two values of spin. 

This led to the Pauli Exclusion Principle PEP allowing two electrons with different spin to occupy the same region of space in an atom, but not three. The two electrons of the Helium atom could then have identical overlapping spatial presence in agreement with the principle of QM of electrons as being identical and interchangeable. Without PEP the Helium atom would appear as a mystery, as well as other atoms.

Pauli received the Nobel Prize in Physics in 1945 for his PEP, but his Nobel Lecture expressed deep dissatisfaction with PEP, because it was an ad hoc invention without convincing physics with only purpose to explain an observed apparent factor 2. But the Nobel Committee resisted and gave him the Prize despite his protests. 

RealQM is an alternative to QM based on non-overlapping one-electron charge densities where there is no role for spin and PEP. The two electrons of Helium will thus be separated into two half-spaces meeting at a common dividing plane with continuity of non-zero charge density. This separation introduces a two-valued quality of geometric nature: one electron occupying one half-space and the other electron occupying the other half space, thus as electrons with identity from spatial occupation. RealQM explains the factor 2 in the shell structure, without resort to spin.

The presence of spin in QM was one of the aspects which made Schrödinger protest against unphysical  aspects of QM and leave the field he had created in 1926 with his model for the Hydrogen atom with one electron, since the generalisation by Born-Heisenberg-Dirac to many electrons took unphysical form. It did not help that he received the Nobel Prize in Physics in 1933 for his model. 

Today QM is viewed to be settled once and for all, but the protests of Pauli and Schrödinger are still as alive as ever. RealQM follows the spirit of Pauli and Schrödinger. 

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. The trouble still haunting modern physics is that the physical meaning of Schrödinger's equation is still hidden if any at all, despite intense efforts over 100 years.  

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, and maybe also an outermost, 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?