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First you learn about the PEP, but it is very subtle, because it only applies for the same type of fermions. So in the case of an electron and an up quark it does not apply. Then you learn about overlapping wavefunctions.

https://en.wikipedia.org/wiki/Pauli_exclusion_principle

So for simplicity, in an otherwise empty universe, if there is an electron and an up quark, they will feel EM attraction and will move towards each other, and eventually occupy the same space. I seem to fail to find a physical law that would prevent that from happening.

So the question is basically whether (in an otherwise empty universe) there is a physical law that would prevent them from occupying the same space, that is preventing their wavefunctions to completely overlap.

Question:

1.Can an electron and an up quark occupy the same space?

Árpád Szendrei
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  • They will orbit each other, and may lose energy by emitting photons, reducing their energy until they achieve some lower energy state. Just like an electron and proton would, but with different charge. – Jon Custer Nov 28 '20 at 16:57
  • This question got me thinking. I'm wondering what "occupies the same space" means, and I don't have an easy answer. Can be found by measurement to be at the same coordinate at the same time? Obvious difficulties with that. I hope someone can help define the concept. – garyp Nov 28 '20 at 19:56
  • @garyp you are correct, and I was not able to define it anyway, only to say "the wavefunctions completely overlap", or "the spatial distribution of the particle that is described by the wavefunction becomes identical". – Árpád Szendrei Nov 28 '20 at 22:17

1 Answers1

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Yes they can - to the extent that position means anything in quantum mechanics. But they still have to obey the uncertainty principle. If you were to pin them down to a similar spatial location at some point in time then there would be a large uncertainty in their momenta.

This wouldn't be any different in principle to the situation of an electron and a proton in a hydrogen atom. There is some small probability that the electron is within $10^{-15}$m of the proton. See Why do electrons occupy the space around nuclei, and not collide with them?

ProfRob
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  • Thank you so much! I just think in case of a proton, there are down quarks, with EM charge repelling the electron (though they are in confinement), and though the whole proton is EM neutral, the electron might feel the down quarks repelling EM force as it comes very close to the down quark. – Árpád Szendrei Nov 28 '20 at 19:14