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i understand that the Pauli exclusion principle states that two fermions cannot occupy the same quantum state.

This question is not about a black hole. It is more about the singularity at moment of the big bang, that had every mass in the universe in a single point, that had no spatial extension.

The uncertainty principle states that it gives a fundamental limit to the limit with which certain pairs of properties of particles can be known.

I understand that a singularity has no spatial extension.

Question:

  1. Does a singularity (especially at the moment of big bang) violate the Pauli principle? So the principles were not in force before the Big Bang?
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closed as off-topic by Qmechanic Apr 26 '18 at 18:17

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  • $\begingroup$ I understand the big bang did not happen at a certain point in space. What I mean is I understand that the universe at the moment of big bang is considered a singularity right? I will edit my question with that. $\endgroup$ – Árpád Szendrei Apr 26 '18 at 18:05
  • $\begingroup$ The universe is probably infinite in size, and if it is, then it's always been infinite, from the very start of the Big Bang. Fermions didn't exist in the early moments of the BB, so Pauli exclusion wasn't relevant. $\endgroup$ – PM 2Ring Apr 27 '18 at 6:37
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A singularity does not violate the Pauli principle, because the composition of a black hole is fundamentally untestable. If two fermions fall into a black hole, maybe they annihilate, maybe they don't, but in the end you could never observe the inside of the black hole and see that it is made up of separate parts. And as the saying goes: if it's not testable (in principle), it's not physics.

Black holes can have spin, and so it might be possible for the entire black hole to in fact be fermionic, but that's not the same as having multiple constituent parts that are fermionic.

Your question is a great gateway to the discussion of what exactly happens to all the information about these pieces that have fallen into a black hole. See black hole complementarity and the "firewall" to read more about that.

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    $\begingroup$ Thank you. This question is not about a black hole though. It is more about the singularity before the big bang, that had every mass in the universe in a single point, that had no spatial extension. Is this true for that too? $\endgroup$ – Árpád Szendrei Apr 26 '18 at 16:12
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    $\begingroup$ Well, a singularity is a singularity, so I would say it is true for that as well. The key point is that at the big bang you didn't have all the particles that exist now compressed together. All the particles that exist now have been pair created from energy as the universe expanded. The assumption is that the reverse must be true for collapse into a black hole, where particles annihilate back into energy (stored as gravitation). $\endgroup$ – Martin Lichtman Apr 26 '18 at 16:25
  • $\begingroup$ You've hit on yet another quandry implied by all this, which is that most processes result in the pair creation of equal amounts of matter and anti-matter, and in the universe we see mostly matter. See baryon asymmetry. $\endgroup$ – Martin Lichtman Apr 26 '18 at 16:25
  • $\begingroup$ Although, the interior of a black hole is as you say can never experimentally be probed. String theory does model black holes by through D-Branes thus explaining Hawking entropy in the classical manner as the entropy of the ensemble of micro-states. $\endgroup$ – Mozibur Ullah Apr 26 '18 at 17:14

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