xkcd #3027: Exclusion Principle
xkcd #3027: Exclusion Principle
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.
Not that I know much about this, but the Pauli principal always struck me as an observation rather than anything like an explanation. As an explanation it's extremely unsatisfying. "Why won't electrons occupy the same space?" "Well.. because of the Pauli principal". No.. that's not the reason, that's just restating what we observe. Glad to see physicists find it weird too (as is suggested in the comic)
It's a lot more complicated than that even.
Pauli Exclusion Principal is that two or more identical particles of half integer spin cannot occupy the same quantum state. So two electrons in an orbital must be made of a +1/2 and -1/2 spin. This is evidenced by observation, but the prediction was made long before that.
This is because the total wave function for fermions is antisymmetric (bosons, like the photon, are symmetric). It's sort of hard to describe how this works without paper and pen, but essentially there is different formula of solving a wave function. A symmetric wave function is a sum, and an antisymmetric wave function is a difference. The issue arises when you have two identical particles - symmetric functions can be any state as it results in a solution >0. If you have an assymetric function of two identical particles, the result is 0, which isn't a valid state.
The very uncomfortable part of physics is here: when we ask "why" the answer based on the math and the observation is quite literally "because that is the way math works." It's fundamental - just like x * 0 = 0.
But it's an outlier right? I guess that's why it's joked as an additional force in the comic, because even by "maths just describes reality" standards, it's weird. Like, it feels like a particle "knows" if the state is already occupied, and that's why it can't occupy it. But that implies some communication - the conveying of some force - else how does it "know"?
I gotta ask, what's with the three spaces between sentences?
Google keyboard weirdness. Maybe because I'm of an age where you put two spaces after a full stop. But then the keyboard is automatically adding one to be "helpful" because maybe people don't do that themselves anymore?
Also known as "things we shrug about" and say "maybe we'll understand these things one day."