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.