# Is pauli exclusion principle a force

Dropout
If it takes energy to squeeze matter, then its a force at work right?

And what is spin? I can put the quantized nature of spin in the back of my mind for a moment, but what the heck does spin do?

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Gold Member
If it takes energy to squeeze matter, then its a force at work right?
The standard term used is "pressure", specifically "degeneracy pressure", when dealing with the Pauli exclusion principle. You are right that pressure essentially means that work must be done to compress something, and that is also associated with forces. It's an unusual force though, because it is a kind of community property, and most forces are pairwise interactions between particles. I suppose it's all in how you treat it-- I tend to avoid taking the labels of physics too seriously. Your question is actually an excellent example of why that is good to avoid, but maybe someone else can find a way to answer it more directly by couching it in a more general mathematical framework. Chances are, however, if they do they will not be answering the question you intend!

And what is spin? I can put the quantized nature of spin in the back of my mind for a moment, but what the heck does spin do?
It tracks a conserved quantity, angular momentum, and also describes the symmetry of a system under rotations. There are deep connections between those, and if you ask a mathematical physicist you will probably get a very complete and very difficult answer! You may need to specify the specific situation you are trying to understand, and the answer will be, "the concept of spin helps you organize the behaviors you will see in that situation". General enough? But the point is, one can only be general when talking about "what is"-- it's not a function that physics is perfectly constructed to perform (check out the "wave/particle duality" thread to see what I mean)!

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Dropout
Well I read that spin creates a magnetic momentum of an electron particle. I also read that magnetism can be explained away by special relativity although I really hate special relativity but I will concur with that conclusion.

But if magnetism is explained away by special relativity then that electron particle would have to have velocity. Maybe velocity in a tiny tubular extra dimension? Ok forget I said that.

Spin is a magnetic moment of an electron particle, how fast would the electron particle have to travel to create the exact magnitude of that magnetic moment, classically speaking. Speed of light?

Also, is that magnetic moment randomly oriented with the 3 spatial dimensions, all 360 degrees?

Gold Member
Also, is that magnetic moment randomly oriented with the 3 spatial dimensions, all 360 degrees?
It's randomly oriented, yes, but it's also quantized-- if you measure the spin in some direction, it has to come out certain values separated by integers.

lbrits
Spin is a magnetic moment of an electron particle, how fast would the electron particle have to travel to create the exact magnitude of that magnetic moment, classically speaking. Speed of light?

Also, is that magnetic moment randomly oriented with the 3 spatial dimensions, all 360 degrees?

Well, I wouldn't agree that special relativity "explains away" magnetism, but you can read my response to your other thread on that. But you are a bit right when you think that the electron's spin comes from "internal" degrees of freedom. This is indeed the picture when we talk about single electrons, but quantum field theory talks about electrons as excitations of an electron field, and that field simply has spin (look up on the Dirac equation if you want).

Back to your first question. I think the first poster covered it well, but I'd just like to add that it is analogous to the "pressure" of an ideal gas of non-interacting particles. But for fermions, the available room of each particle goes down significantly as the density increases, because they have to avoid other particles (because of Pauli exclusion), so the pressure goes up. Put differently, you can almost think of the PV = nRT relation, but where V behaves in a complicated way as a function of n.**

**This is only a picture. Don't take the formula too seriously.

Gold Member
I'd just like to add that it is analogous to the "pressure" of an ideal gas of non-interacting particles.
That's a good point, pressure for a bunch of particles just means there's a momentum flux through any imaginary surface, so there doesn't need to be any forces, and degeneracy pressure is just like that too. What brings a force in is the implication that if we are going to compress this gas and do work on it, we are going to need some boundary that can contain the particles, i.e., that can exert a force on them. So the "force" that the OP is asking about really doesn't come from the pressure itself, it comes from whatever we are using to force the contraction of the gas. The pressure force may then be seen as the action/reaction pair of whatever real force is being used to accomplish the compression.

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