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I'm trying to understand what's the physical meaning behind Pauli Exclusion Principle, why can't two electrons in the same orbital have the same quantum numbers? In particular, why do they have to have different spins?

I understand that the spin creates a magnetic field but I don't see why the magnetic fields would have to cancel out

randomdude
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  • I don't know if there is an easy answer to your question. The "correct" detailed answer is highly technical, I am afraid. Spin is a consequence of the world being relativistic. You can find some of the "technicalities" here: https://physics.stackexchange.com/questions/665328/emergence-of-spin-from-special-relativity. I would be lying if I said that I understand them properly, either. Or maybe I am misunderstanding your question and you only want to know "how" we are dealing with fermions properly if we just accept that they exist? – FlatterMann Mar 30 '23 at 18:31
  • Yes, I'm just trying to understand why the spins have to be opposite inside an orbital. From what i've read the electrons both create a magnetic field while spinning and the magnetic fields cancel out, but if they didn't what would happen? – randomdude Mar 30 '23 at 18:35
  • If the spins are parallel, then there is a net magnetic field and if that happens in an entire solid, then we are witnessing the wonderful world of permanent magnets, and that is a very complex sub-field of physics in itself. I would, by the way, refrain from adopting a mental model in which electrons are little spinning things that create magnetic fields. Spin is a symmetry of quanta that expresses itself as angular momentum at the macroscopic level. Going from spin to an actual macroscopic magnetic field involves thermodynamics in addition. – FlatterMann Mar 30 '23 at 18:46
  • So everything would be a magnet if this happened. Very interesting, thank you – randomdude Mar 30 '23 at 18:51
  • Under the right thermodynamic conditions (below the Curie point of the material), yes. If you want to think of the most simple case (T=0), then, yes. Materials in which the spins don't cancel have a net magnetic field. In single molecules this leads to the opportunity to do spin=spectroscopy experiments (electron spin resonance) and, if it's the nuclear spins rather than the electrons, then we can do nuclear magnetic resonance. – FlatterMann Mar 30 '23 at 19:02
  • There is a deep connection between Pauli’s exclusion principle and relativistic QFT’s which does not have a simple explanation. Check out the spin statistic theorem. Note that it is not related to the magnetic dipole moment. In fact, even if this is how spin is usually introduced, it is a rather separate concept. – LPZ Mar 30 '23 at 23:46

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