Electron Spin: Weak as Physics Strong by Theory

This is a continuation of previous post. ChatGPT informs that atoms can be divided into diamagnetic with paired electrons (no net spin) and paramagnetic with unpaired electrons (with net spin) with opposite non-zero reactions to a magnetic field. According to Standard Quantum Mechanics StdQM. 

But these effects/reactions are incredibly small and can only be observed in laboratory settings with very strong magnetic fields of 1-20 Tesla, while the Earth's magnetic field is about $10^5$ times weaker. The magnetic field gradient in the Stern-Gerlach experiment viewed as evidence of electron spin, is very steep about 10-100 Tesla/m. 

We learn that electron spin is manifested as a very small magnetic effect. Yet electron spin serves a fundamental role in StdQM by dividing matter into bosons like photons and fermions like electrons with different spin characteristics. 

In particular, Pauli's Exclusion Principle PEP for electrons/fermions is formulated in terms of spin allowing two electrons with different spin to share common space, which is forbidden/excluded for same spin. 

PEP serves a fundamental role in StdQM to theoretically explain the periodic table and chemical reactions. StdQM theory collapses without PEP. 

Electron spin has a very weak magnetic effect, much weaker than Coulombic attraction/repulsion between electric charges, but yet it governs the world of atoms and molecules according to StdQM theory.

We are thus led to the following apparent contradiction:: 

• Electron spin has a very weak physical effect, which according to theory is very strong.  

We compare with RealQM where electron spin has no role to play which goes along with a very small physical effect. There are also forms of DFT where spin has a minor if any role. 

Recall that science explaining a very large effect of something very small, like a tornado in Mexico from a butterfly flap in Amazonas, has a very difficult task. It requires a very precise mathematical model allowing to accurately simulate the far away effect of a butterfly flap to identify it as the true origin of the tornado. This is an impossible task. To use electron spin to explain the world of atoms and molecules faces a similar difficulty.