Fermions are weird about each other in a standoffish way. Integer-spin particles are weird about each other in a ‘stand uncomfortably close while talking’ kind of way.
Fermions are weird about each other in a standoffish way. Integer-spin particles are weird about each other in a ‘stand uncomfortably close while talking’ kind of way.
It’s not really communication. They ‘know’ because they become part of the same wave function. The wave function of the system is
|psi1 psi2> ± |psi2 psi1>
Note that if the ± is a plus, then exchanging psi1 and psi2 yields the exact same equation. If it’s a minus, you get a negative sign out front. Electron systems have a negative sign because of the spin statistics theorem (I don’t understand that part, so you can look it up if you want—it involves field theory iirc) Now, if electrons are exactly the same (indistinguishable), then exchanging them will yield the exact same wave function, leading to
|psi1 psi2> - |psi2 psi1> = |psi2 psi1> - |psi1 psi2>
The only solution here is |psi1 psi2> - |psi2 psi1> = 0
But recall that |psi1 psi2> - |psi2 psi1> describes the system as a whole. So this system is prohibited by quantum mechanics, and there’s no way for two electrons to have indistinguishable states (be in the same place at the same time).
So the way I “understood” the spin-statistics theorem is that it’s basically this:
A given particle with a given intrinsic spin has a direct relationship to a collection of the same particles as a consequence of quantum math. Yeah. Just “it’s related.”
Proving that math is really freaking difficult and you need to use relativistic quantum field theory. I think it was Richard Feynman who said “We apologize for the fact that we cannot give you an elementary explanation.”
Actually when I graduated there was another professor (can’t remember his name) who was discussing his frustration with how they still can’t explain it without all of QFT steps.
Basically, this is where the shared attitude of “the more you know about quantum physics, the more confusing it becomes.”