Pauli's Exclusion Principle Can someone tell me how Pauli's Exclusion Principle gives stability to matter? I know two electrons cannot occupy the same energy state so that is why we cannot squeeze bulk matter after a limit and this principle is responsible for keeping us from collapsing into the ground while standing.But my question is, if that is so we should not be able to dive into water, but we can. Why? And why cant electrostatic repulsion be responsible for it? Owing to the fact that we are made made up of electrons and so is everything surrounding us so that could be one major possibility, I guess?
Is Pauli's Exclusion Principle necessary for explaining that?
 A: I'll try to give a qualitative view.  There are an array of forces working together at various distances and strengths that stabilize bulk matter.  The Pauli Principle could probably be considered to be one of the lowest fundamental levels.
The Pauli Exclusion Principle is often confused with the cause of macroscopic effects like being responsible for atoms or molecules not occupying the same space, but that is not really the full picture.  Atoms and molecules after all are mostly empty space.  The exclusion principle is only partly responsible for why macroscopic scale matter can't be in the same place at the same time.
And the stability of electrons themselves in an atom are unrelated to the Pauli Exclusion Principle which is strictly about quantum states of fermion matter.  In this respect fermion matter must occupy some finite volume.  The electrons of each atom cannot all fall into the lowest-energy orbital and must occupy successively larger shells cannot be squeezed too closely together.
Andrew Lenard considered the balance of attractive (electron–nuclear) and repulsive (electron–electron and nuclear–nuclear) forces and showed that ordinary matter would collapse and occupy a much smaller volume without the Pauli principle.  But this doesn't mean you can't compress bulk matter with millions of atoms and molecules tighter together you just have to overcome the other repellent forces first.  While the Pauli Principle sets the ultimate limits on all the bits that are fermions.
A: In every day situations, for example in the "diving into water" scenario, the leading actor is the electromagnetic repulsion. The Pauli exclusion principle is not important at macroscopic scale (of course macroscopic objects are made of atoms, so in some sense is important even here).
Anyway, if the density is high enough, the Pauli exclusion principle can be fundamental: just think about neutron stars. In these stars the degeneracy force from the fermions opposes to the gravity that tends to collapse the star.
