The Unphysical Pauli Exclusion Principle

Here is a continuation of the previous post.

The foundation of modern atom physics is Quantum Mechanics QM in its text book formulation StdQM takes the form of Schrödinger's Equation SE formulated exactly 100 years ago. Solutions of SE are called wave functions which depend on $3N$ spatial variables for an atom with $N$ electrons, thus with a separate 3d Euclidean coordinate system for each electron, which connect to a common 3d coordinate system for Coulomb repulsion between electrons and Coulomb attraction between electrons and atomic kernel. 

All electrons thus have global presence or global support and so overlay in the common coordinate system. This does not fit with Coulomb repulsion and in fact is the root of the confusion surrounding the physical meaning of the wave function, which has never been settled.

To handle the difficulty with overlaying electrons the Wolfgang Pauli came up with the idea to assign electrons a two-valued 4th quantum number named spin-up and spin-down with the role to allow overlay of two electrons with different spin, and forbid overlay in case of equal spin. This would allow at most two electrons to overlay. This was coined Pauli's Exclusion Principle PEP, which is an ad hoc assumption without physics since spin-up and spin-down lack physics and in particular has nothing to with spinning in a classical sense. 

So QM is based on SE complemented by PEP. The trouble is that both SE and PEP lack physics. Both represent ad hoc inventions without clear physics. 

RealQM is an alternative to QM based on electron charge densities with non-overlapping supports in a common 3d coordinate system. In RealQM there is no role for PEP because no two electron overlay. The ad hoc non-physical assumption PEP has been replaced by a physical assumption of no overlay of electrons motivated by Coulomb repulsion.

RealQM has the form of classical continuum mechanics in 3d and so has polynomial complexity (is computable) while QM has exponential computational complexity (is incomputable).

Stability of matter is a direct consequence of the form of RealQM, but is very difficult to establish for QM.

Chemistry is based on molecules formed by atoms and electrons with support over the whole molecule in QM. Keeping track of spin is impossible, which makes QM for atoms useless for molecules. RealQM for atoms naturally extends to molecules again based on non-overlapping electron charge densities.