So I’m kind of curious about the Pauli exclusion principle. Umm, what causes it? Anyway to make a short story long I was interested since I’ve read about electron and neutron degeneracy pressure in regards to neutron stars. (Which basically causes a force to resist compression.) It was my understanding that there were only 4 forces in the universe so I figured Pauli exclusion must be caused by one or more of them. However when I tried reading about the underlying cause for this principle I didn’t see anything about any of the 4 fundamental forces and actually saw stuff about it being derived from some equations. So is PEP caused by the 4 fundamental forces or not?
What we call a “force” is subject to the limits of our own understanding of fundamental principles. We used to think electricity and magnetism were two different forces, but Maxwell figured out they were different manifestation of the same phenomenon. Eventually, physicists hope to have a “Theory of Everything” that will unite, well, everything under one explanation.
Having said that, the Pauli Exclusion Principle is best understood as a law of nature, like the conservation of energy. It’s not “caused” by anything-- it’s just the way it is. And a good thing, too, because we wouldn’t exist without it!
No, it’s not caused by the four forces.
There are two basic types of particles, Fermions and Bosons. Bosons have integral spin (0, 1, 2, etc.) and Fermions have half-integral (1/2, -1/2, 3/2, etc. (I don’t know of any fundamental particles with 3/2 spin.)). Electrons are Fermions.
As it turns out, when you get deep into the quantum mechanics of multiple particles, the QM field amplitude of the particles has a particular property that depends on spin. If you have a valid field amplitude for a number of Bosons (description of where particles are) of a single type, and you interchange two of the particles, you have the identical field amplitude, including the same sign. For Fermions, if you interchange two particles, the field amplitude is identical, except that it has the opposite sign. This means you can’t have two Fermions in the same state, since interchanging them will change the sign, so the only valid field amplitude is zero (if A = -A, A must be zero).
To summarize, you can’t have two Fermions in the same state, so you can only put two electrons in any given orbital of an atom (one with spin +1/2, and one with spin -1/2). Neutrons and Protons are also Fermions, so in a neutron star, the neutrons can’t all occupy one state, hence the neutron degeneracy pressure. They all have to have a distinct state.
For Bosons (like photons), since the sign doesn’t change, you can have two particles in the same state (e.g. lasers). Also, Helium 4 nuclei are Bosons, so you can make a Bose-Einstein condensate, where the nuclei all occupy the same state.
I think that ZenBeam’s explanation there is about as clear as you’re going to find.
But this has troubled me lately. Isn’t it a kind of hijack of the word “force” to say that there are fundamental kinds of force and that what happens according to the Pauli exclusion principle is, well, excluded? Or do we have to invoke several different fundamental kinds of “push” or “nudge” to compliment the “forces”?
Let’s say I began squeezing a ball of fermionic matter in my hand. As the ball got smaller and smaller, eventually the Exclusion Principle would come into play and I would feel resistance against my squeeze. Since my hand interacts with other matter primarily through the electromagnetic force, does that not mean the resistance I’d feel is ultimately electromagnetic?
Yes. It’s an EM force.
The way I’d put it is that the Exclusion Principle is more fundamental than any of the actual forces. It’s a general restriction on what any force can possibly do in quantum mechanics.
Thus when we say that the Exclusion Principle is acting against particles being forced together, what one actually means is that the electromagnetic or strong force[sup]*[/sup] is acting to preserve this restriction.
[sub]* Can’t offhand think of any natural examples that might involve weak or gravitational forces. They no doubt exist.[/sub]
It’s more like the fundamental nature of QM. Consider the energy levels of an electron in an atom. We don’t say there is a “force” that prevents non-allowed quantum states, we just say that they aren’t allowed. In the same way, fermions aren’t “allowed” to occupy the same quantum state.
I really don’t see how that contradicts what I said.
Maybe I misread your post, but it sounded like you were trying to rationalize there being a “force” involved. You mention the strong force, which is an attractive force, so it’s hard to imagine how that force would keep particles apart.
(my emphasis added). Is it true that they “aren’t allowed” or is it just Really Damn Difficult? Doesn’t gravitational force in a black hole overcome even that as the singularity is formed?
I’m no expert on Black Holes, but are they considered to be gravitational singularities? If we think of the Big Bang as the expansion from a singularity, I don’t expect we would find that the laws of physics, as we know them, would work at the level of the singularity.
I was responding to the OP’s puzzlement. Because physicists often do loosely express the effects of the Exclusion Principle as a force. My point was that, in doing so, we are actually adopting that as shorthand for the truth that a specific force is expressing the Exclusion Principle.
OK, this is what I’m not following. How is any force “expressing” the PEP?
I’ve never hear the PEP called a force, or likened to a force. Granted, it’s been quite a few years since I studied QM, but I just remember the PEP being an observed property of fermions.
FWIW, from the Wikipedia page on Exchange Interaction:
There is a bit of relevant discussion in the beginning of this post, where the question was:
to which I replied:
thanks for asking this!
And thanks everyone for answering. The discussion was very interesting. I really need to go back to school. I missed a lot way back then…
The Wiki article on Degenerate matter explains it as well as I’ve ever understood. In a white dwarf star the “force” is ultimately the electic repulsion between electrons. What’s different in degenerate matter is that the rules of quantum physics predict that the momentum of closely confined electrons will approach relativistic velocities, and thus their repulsion against each other will be much greater. IOW, the plasma becomes much more resistant to compression than classical physics would predict. An analogous situation exists with neutrons and the nuclear force in neutron-star matter.
Ultimately, the connection with the true forces is that it’s the forces which determine what the states are. Two fermions with all the rest of their quantum properties the same can’t be in the same location, but how close together can they be? Well, that depends on how close together two position states can be, and where the position states are depends on the potential, and what the potential is depends on the forces.