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Reading the paper by Lieb "The stability of matter", it is clear from the start that quantum mechanics is absolutely necessary to solve this problem. However, I assume this question was thought of before the birth of Quantum Mechancis. If so, what were the main hypotheses? It seems unsolvable from a classical perspective, and therefore it could be a historically relevant pathway to the formation of Quantum Mechancis. However, I have never seen it mentioned in any historical perspective. So what solves this apparent "paradox"?

Alternative link: The stability of matter, Elliott H. Lieb (1976)

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    $\begingroup$ This belongs on HSM.SE. $\endgroup$
    – J.G.
    Nov 2, 2022 at 16:12
  • $\begingroup$ @J.G. the fact of it being on topic for another SE site doesn't necessarily make it off-topic here. (It may or may not be - I'm not to date with current Physics.SE policy. But if it's on topic here it may well get better answers than it would on HSM.) $\endgroup$
    – N. Virgo
    Nov 3, 2022 at 3:16
  • $\begingroup$ Related meta post. $\endgroup$
    – Qmechanic ♦
    Nov 3, 2022 at 5:14

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It wasn't an issue before Geiger, Marsden, and Rutherford discovered that the mass and positive charge of atoms was almost entirely contained in a tiny nucleus. Before that, the assumption was that the volume of condensed matter reflected the volume of whatever stuff its constituent atoms were made of. This seems a reasonable, commonsense assumption, which is why the Rutherford result was such a surprise.

Before the discovery of the nucleus, the Plum Pudding model was the most advanced model of atoms, with the "pudding" occupying the volume.

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According to Dalton's atomic theory (invented 1803) atoms were defined to be indivisible, i.e. not consisting of any subparticles. Therefore, at this time, the question why atoms are stable didn't arise.

This theory worked fine until the experimental discoveries that atoms consisted of sub-particles:

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