What causes Paulis Exclusion Principle?

Question

Currently I'm taking an astrophysics class and has now come across electron degeneracy. As far as I understand, the reason why white dwarfs and such, does not collapse, is due to this, meaning that the electrons are so close together in the core, that the Pauli exclusion principle prevents them from getting closer, even though the gravitational pressure is so high.

My question is: What force makes this possible? The Coulomb force? Is it just something you have to come to terms with, that no fermion can be in the same state, or is there actually a force that makes sure this does not happen?

Thanks in advance.

To understand Pauli's exclusion principle, I recommend Wouter's answer here: https://physics.stackexchange.com/q/69241/ — jinawee, Oct 10 '14 at 18:49
It follows from the indistinguishability of similar particles (which follows directly from Heisenberg's uncertainty principle), & the spin-statistics theorem. Section 61 here might help http://books.google.ie/books?id=J9ui6KwC4mMC&lpg=PP1&pg=PA227#v=onepage&q&f=false — bolbteppa, Oct 10 '14 at 22:10
Closely related: Is Pauli-repulsion a “force” that is completely separate from the 4 fundamental forces? — John Rennie, Oct 11 '14 at 09:30

score 12 · Accepted Answer · answered Oct 10 '14 at 18:16

It's a force like no other. It is fundamentally a quantum property and there is no classical way to think of it (at least to my knowledge). That's just how the universe is, and we haven't understood any deep reason "why" it should be that way. Mathematical consistency seems to dictate it.

It comes down to the observation that there can be some objects such that when you swap any two of them, the "wavefunction" (which describes the configuration, and can be squared to give the probability) picks up a negative sign. So when two of them sit on top of each other, the wavefunction of having A and then B is the negative of the wavefunction of having B and then A. The only mathematically consistent way to have this happen is for the wavefunction to be zero for any such configuration, which means that has zero probability of happening. We call such particles fermions.

Since electrons have spin $\frac{1}{2}$, the spin-statistics theorem tells us that they must behave like fermions.

And that is how I know it yes :) But it's just a funny thing to think about, that fermions just obey mathematics. That's why I asked this question. What is happening in the physical sense. But ofc, if we don't know, that is enough answer for me :)
Thank you. — Denver Dang, Oct 10 '14 at 18:58
And yet, that can't be all there is to it. Zero probability events can and do happen. — bright-star, Oct 25 '16 at 16:54
@bright-star well they do, but their frequency is exceedingly smaller than that of events with positive probability in the same event space. — Ruslan, Dec 21 '16 at 06:00

What causes Paulis Exclusion Principle?

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