How can we demonstrate two particles can not occupy a same position at a same time?

Re: How can we demonstrate two particles can not occupy a same position at a same tim

There is actually loophole recently where you can have two fermi particles occupy the same space, but only in a special condition... doesn't quite answer your question, but it relates to the black hole horizon. I will try and find the paper for you. I found it quite interesting myself.

 

Re: How can we demonstrate two particles can not occupy a same position at a same tim

As you say, the total wave function is anti-symmetric (note that in general it cannot be factored into a spatial and a spin part). That means that you have a zero amplitude for two Fermions having the same spatial AND spin coordinates at the *same time*. If either of those differs, there is no need for the wave function to vanish. In particular, this implies that two Fermions can occupy the same position in space--as long as they have different spin coordinates.

In fact, this actually happens even in the case of electrons with their singular Coulomb repulsion. For example, in molecules and solids opposite spin electrons have a non-zero and actually quite high probability of sitting right on top of each other.

 

Re: How can we demonstrate two particles can not occupy a same position at a same tim

Mix? Electrons can pass through the nucleus. It is also possible for an electron to be absorbed by a proton, though this doesn't happen very often.

 

Re: How can we demonstrate two particles can not occupy a same position at a same tim

The do mix. There is a finite probability of finding an electron inside the nucleus.

"Fall into nuclei" doesn't really mean anything. As I said, an electron can be found in the nucleus on occasion. It just doesn't stay there. During the collapse of a massive star in the supernova process, it becomes energetically favorable for electrons to "combine" with protons and form neutrons. That is pretty much what I would consider electrons "falling" into the nucleus if I understand your meaning correctly.

 

Re: How can we demonstrate two particles can not occupy a same position at a same tim

Just the exclusion principle and electromagnetic repulsion. The weak interaction doesn't manifest as a "force".

Bosons don't have orbitals as far as I know. But this is only because they aren't electrically charged and don't have an atom to have orbitals in. They are still described by a wave function however.