[Physics] Why does the Pauli exclusion principle not apply to bosons

Question

The Pauli exclusion principle states that two fermions cannot have the same quantum state simultaneously, but why does this not apply to bosons with whole integer spins?

Answer 1

This is a legitimate question but one for which you probably won't get any real, satisfying answer rather than just "because that's how nature works".

You can "derive" the impossibility for two fermions to have the same quantum numbers from the requirement for many-fermion states to be antisymmetric with respect to the exchange of any two particles, that is, $ \lvert \psi_1 \psi_2 \rangle = - \lvert \psi_2 \psi_1 \rangle,$ and show that there is a connection, given by the spin-statistics theorem, between spin and symmetry of the wavefunction, so that half-integer spin particles must be antisymmetric like in the above case. But then again, this is not really an answer to the "why" question, as it is just an equivalent way to formulate the exclusion principle.

Said in other words, there are no underlying or "deeper" principles or theories that can "explain" Pauli's principle from other more foundamental assumptions (yet?). When in physics you start asking a "why" question (like, why do magnets attract each others?), eventually you will inevitably find yourself in this situation, where the only possible answer you are left with is: "because that's how things work".