Stability of Matter: Basic Math vs Miracle

1. Recent posts have discussed the fundamental problem of Stability of Matter SM, including stability of single atoms and collections of atoms as bulk matter, maybe the most fundamental problem of all of physics. 

With the help of chatGPT I have learned about the heroic work by Dyson-Lenard and Lieb-Thirring to mathematically prove SM within Standard Quantum Mechanics StdQM and Density Functional Theory DFT, which boils down to very intricate book-keeping to prevent collapse of potential energy to minus infinity by local accumulation of electron charge densities. The main difficulty to handle is the overlap in StdQM/DFT of electron wave functions with global support. The proof is lengthy and complicated and not easy to follow. It is not part of text books/courses in QM, even if completely fundamental. 

It is natural to ask how it can be so difficult to prove SM within StdQM/DFT, when SM is such a basic property of the physics modled by StdQM? Does real physics also have to handle intricate bookkeeping to avoid collapse?

Or is the proof difficulty of SM within StdQM/DFT yet another indication that there is something seriously unphysical with StdQM connecting to the difficulty of giving StdQM a physical meaning? Seems so.

On the other hand SM within RealQM directly follows from the stability of the Hydrogen atom with potential energy dominated by kinetic energy using the additive form of RealQM with a global wave function as a sum over one-electron wave functions with local non-overlapping supports. 

RealQM is a physical model with SM safely mathematically built in. StdQM is an unphysical model with SM basically a mathematical miracle. SM with RealQM could be essential part of even introductory texts/courses in QM.

According the chatGPT, SM is by physicists viewed as "settled" once and for all by Dyson et al, and it is not meaningful to teach the proof since it is so difficult and and non-illuminating. The advice to students appears to be to just accept SM and not ask about any justification. Seems a bit strange...

Summary:

1. StdQM in 1926 faces a fundamental problem: Prove Stability of Matter.
2. No progress towards solution until 1966 when Dyson-Lenard gives a dense 26-article page proof in the form of "awful mathematics" according to Dyson. 
3. Lieb-Thirring compresses the proof into a 3-page article 1975, which is then expanded into the 300 page book Stability of Matter in 2005.
4. The problem is viewed to be "settled" and there is nothing more to say according to chatGPT in 2025. The proof is not part of text-books on QM.   

This is a typical progression as concerns fundamental problems in StdQM: 1. State problem as fundamental (interpretation, measurement, complementarity...). 2 Realise that the problem cannot resolved. 3. Claim that there are solutions, but very difficult to understand. 4 Decide that the fundamental problem as been "settled" and that there is noting more to say. 5. Declare that it is sufficient to know that the problem has been solved and that asking for why is not part of physics education.