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Paulovsk comments on [Transcript] Richard Feynman on Why Questions - Less Wrong Discussion
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I'm not a physicist, but when I looked into this, I found this well-written article:
The Stability of Matter: From Atoms to Stars
It goes into lots of detail of what's happening with a single hydrogen atom, then a large atom, then bulk matter. It doesn't require quantum physics knowledge from a reader, but it does require mathematical maturity, and isn't easy reading.
The short of it is that you're right, the Pauli exclusion principle is more important than electrostatic repulsion.
Thanks! I love docs like these, that take the a broad approach.