How could so much matter, or "all" in fact, have been concentrated in a smaller universe without being in the actual same place? Why did this not result in undercutting the Planck Length or violating the Pauli exclusion principle?

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    $\begingroup$ See e.g. "Did the Big Bang happen at a point" and "Does black hole formation contradict the Pauli exclusion principle" on Physics.SE. $\endgroup$ – David Moles Jul 3 '20 at 21:46
  • $\begingroup$ @BenCrowell adding the links would be helpful. $\endgroup$ – ProfRob Jul 4 '20 at 0:43
  • $\begingroup$ Broadly, it matters not at all how so much matter might have earlier been concentrated in a smaller universe, nor anything else. If it helps, a Big Bang might be as close as we could imagine to the opposite of infinity. It's called a "Big Bang" and not just a "Big Beginning/Start/(whatever)…" because "Bang" is the operative word. Whatever might have gone before, in our universe that "bang" meant it had enough energy propelling it outwards to overcome anything else. If that should hurt Planck or Pauli, can you show the maths? $\endgroup$ – Robbie Goodwin Jul 4 '20 at 21:54

The Pauli Exclusion Principle forbids two indistinguishable fermions occupying the same quantum state. It does not prevent them getting arbitrarily close together so long as they have very different momentum states.

The big bang model relies on classical General Relativity. When we go back to scales where quantisation of space might become important (i.e. Planck length scales, corresponding to the first $\sim 10^{-43}$ s of the universe) then GR needs to be replaced by some quantum theory of gravity (which we don't have).

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    $\begingroup$ So, we don't know? We know normal rules won't apply but we don't know which do? $\endgroup$ – Mast Jul 3 '20 at 8:50
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    $\begingroup$ @Mast Yes, there are limits to knowledge. $\endgroup$ – ProfRob Jul 3 '20 at 9:35
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    $\begingroup$ @Mast pretty much the usual situation in science (not only physics). $\endgroup$ – fraxinus Jul 3 '20 at 13:14
  • $\begingroup$ @RobJeffries And realistically, there are many more limits than knowledge -- our knowledge is like the rational numbers in a sea of real ones ;-). We can get close, sometimes. $\endgroup$ – Peter - Reinstate Monica Jul 3 '20 at 17:42
  • $\begingroup$ Did fermions even exist during the very early phases of the Big Bang? I suppose I should ask that on Physics.SE... $\endgroup$ – PM 2Ring Jul 4 '20 at 4:59

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