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If two or more identical fermions cannot occupy the same quantum state simultaneously, then shouldn't the entire universe have no two identical fermions in the same quantum state at any given time?

Intuition tells me this isn't true, so how do you define the boundaries for a quantum system in which the Pauli exclusion applies?

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    $\begingroup$ Being in the same quantum state includes being in the same place. More precisely if I have two wavefuctions which are the same shape but translated relative to each other they represent different quantum states and so the exclusion principle does not prevent two electrons from having those two wavefunctions simultaneously. $\endgroup$ – By Symmetry Apr 10 '18 at 0:39
  • $\begingroup$ If there is a spin up electron in the ground state of hydrogen, I can only have one more electron in the ground state of hydrogen and it must be spin down. That doesn't mean I can't put other electrons into the ground state of other hydrogen atoms. $\endgroup$ – PaulisDontExcludeMe Apr 10 '18 at 1:07
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    $\begingroup$ Possible duplicate of Pauli principle for particles very far apart from each other $\endgroup$ – Stéphane Rollandin Apr 10 '18 at 11:18