# Why is the Pauli Exclusion Principle not a force?

• I
That you don't understand it does not mean nobody understands it.
Indeed it does not. This is a straw man argument, since I never used my own non-understanding as an argument.
Now if you understand anything more than Pauli did, please share.

bhobba
Mentor
Now if you understand anything more than Pauli did, please share.
Well there was this guy, Nicholas Burgoyne, that came up with something Pauli didn't, an actual rigorous proof of the spin statistics theorem:
http://www.sjsu.edu/faculty/watkins/spinstats11.htm

He wasn't the only one either.

Thanks
Bill

PeterDonis
Nugatory
Mentor
The truth is that nobody understands the PEP.
We have the famous spin statistics theorem
Now if you understand anything more than Pauli did, please share.
Well there was this guy, Nicholas Burgoyne, that came up with something Pauli didn't, an actual rigorous proof of the spin statistics theorem:
http://www.sjsu.edu/faculty/watkins/spinstats11.htm
This thread is in some danger of drifting into matters of personal taste. The spin-statistics theorem is a deep and important result, and the mathematical formalism of modern quantum field theory is far cleaner and more rigorous than the collection of brilliant intuitions that birthed quantum mechanics decades ago. We, favored by both time and hindsight, do indeed understand some things differently and better than Pauli did. But do we have a "satisfactory" explanation of the exclusion principle?

There's an element of personal taste in what it takes to be satisfied, and that's not going to be settled by argument.

(Please.... try not to make more work for your underpaid and underappreciated mentors.... we have enough to do without having to moderate arguments that aren't advancing anyone's understanding).

Carrock, PeterDonis, Demystifier and 1 other person
The connection between spin and statistics has been proved
so we know that it is indeed half integer spin that implies increased repulsion.
Yet my gut feeling is that there is something important missing.
There is a force, as V50 argues, but there is no force field, no force carrier.

bhobba
bhobba
Mentor
Yet my gut feeling is that there is something important missing. There is a force, as V50 argues, but there is no force field, no force carrier.
Yes it does SEEM strange.

As Nugatory points out its purely a matter of taste what you read into that.

Thanks
Bill

Summing up, when I hit a hammer on a nail, the hammer exerts a force to the nail.
This force is transmitted by the PEP, which is not a force.
That may be correct but is very counterintuitive and deserves further study.

Last edited:
Nugatory
Mentor
Summing up, when I hit a hammer on a nail, the hammer exerts a force to the nail.
This force is transmitted by the PEP, which is not a force.
That may be correct but is very counterintuitive and deserves further study.
Indeed it is, and this may be true of force transmission in general.

It's a lot easier to describe the force that A exerts on B than to describe the the mechanism by which that force is transmitted. It's been this way for a long time too - ask a seventeenth-century student of natural philosophy or a 21st-century layperson how it is that the hammer blow affects the nail, and you'd get an answer that reduces to "because they're solid objects and solidity means they can't both occupy the same space at the same time".

Last edited:
Truecrimson and bhobba
The PEP says that a doubly occupied fermion state is equal to zero. That in itself is merely math. You could have two fermions approaching the same state, and their combined state approaching zero, and it would be valid as a mathematical statement. The physics comes in when you mention the empirical fact that matter doesn't approach zero; that it has measures, such as total energy, that evidently do not decrease. In other words, the question isn't why the hammer and the nail remain separate from each other, but why they don't fade from existence when they touch.

If a possibility of two fermions approaches the same state and thus decreases in norm, then another possibility must increase in norm to compensate. So there is a "force", in the generalized sense of a conserved quantity being transferred. Something transfers an amount of norm from one possibility to another. But what? Has anyone attempted to describe interactions at this level?

Khashishi
With forces, you can overcome some force with greater force. For example, the Coulomb force between two protons could be overcome by the strong force.The Pauli exclusion principle is absolute. The Pauli exclusion principle cannot be overcome by greater force. Two electrons are not allowed to overlap in phase space, which is different than saying they repel.

There are several other differences. Forces are essentially a gradient in some potential, and so they have a direction. PEP has no direction. It's just a restriction.

The PEP does keep you from falling into your chair or sliding between atoms or slipping off. Without PEP, Earnshaw's theorem would prevent stable arrangements of charges in your butt and the chair. Actually, without PEP, all molecules would collapse.

The PEP applies only to identical fermions. So the restriction that a phase space domain is occupied by a fermion can be "overcome" by changing the fermion's identity.

For example, it would be theoretically possible that one of an atom's electrons gets hit by a proton, and they change into a neutron which goes into the atom's nucleus, and a neutrino which is emitted. Then where that electron was, there's room for another electron to take its place.

bhobba
Mentor
The chair thing is definitely coulomb force. PEP plays a role in determining the electro structure but that isn't what is holding you up.
Thats a common misconception - but its wrong as discovered by Dyson:
https://en.wikipedia.org/wiki/Electron_degeneracy_pressure

The reason its not a force is, as you stated, its really a symmetry thing that prevents electrons being in the same state.

Thanks
Bill

Demystifier, vanhees71 and Simon Bridge
Simon Bridge
Homework Helper
Thats a common misconception - but its wrong as discovered by Dyson:
https://en.wikipedia.org/wiki/Electron_degeneracy_pressure
That was a while ago - thanks for correcting it here. I was confusing models.
Note: we usually advise to avoid taking wikipedia's word for things, the Dyson Paper on the stability of matter is here:
http://scitation.aip.org/content/aip/journal/jmp/8/3/10.1063/1.1705209

There's another discussion on these forums:
https://www.physicsforums.com/threads/matters-solidity.15605/ ... some of the respondents may benefit from reviewing the argument though.

The reason its not a force is, as you stated, its really a symmetry thing that prevents electrons being in the same state.
Thanks.

bhobba
It says I can rent it for $4, but when I click on that, it says to join "DeepDyve" for$40 a month.

Where can I get the article without such a trick?

Everybody successfully taking quantum mechanics I understands the Pauli exclusion principle. I.
So anyone who is puzzled by PEP would fail "quantum mechanics I".
I do not support this approach.

Staff Emeritus
So anyone who is puzzled by PEP would fail "quantum mechanics I".
I do not support this approach.
Well, you should. If you don't understand Newton's laws, you should not pass Physics 1. If you don't understand what a derivative is or how to take one, you should not pass Calc 1. If you don't understand the Pauli Exclusion Principle, you should not pass QM 1.

Only if you define understanding the PEP as passing QM1.
What is taught is the starting point, but not the end point of understanding.
Consider what Erik Verlinde is doing. His aim is to understand gravity.
Did he fail his courses on GRT ? I don't think so.

vanhees71
Gold Member
I don't care about the requirements for passing QM 1. What I wanted to say is that anybody who has taken the introductory course lecture on quantum mechanics should have understood the Pauli principle. It's the statement that for fermions (bosons) the Hilbert space is the Fockspace of antisymmetric (symmetric) many-body states (antisymmetric (symmetric) meant with respect to exchanging two particles within the state) or said differently: Any physicist with a BSc is understanding the Pauli principle contrary to the belief expressed in the posting I was answering to.

I also don't know whether Verlinde failed a GR exam. I'd guess not ;-)).

Erik Verlinde understands gravity in this sense, but yet he searches an explanation of gravity.
In the same way I understand PEP, I know how to state it and use it and I know what its consequences are.
Still I miss an explanation of it.

vanhees71
Gold Member
Well, the explanation is that it describes the observations. That's the usual explanation science has to offer: It describes what's objectively observable in nature. A mathematical explanation why in spaces with dimension ##\geq 3## there are only bosons or fermions, while in 2D there are also anyons possible, can be found in the paper

M. G. G. Laidlaw and C. M. DeWitt, Feynman Functional Integrals for Systems of Indistinguishable Particles, Phys. Rev. D, 3 (1970), p. 1375.

dextercioby
There's not only the degeneracy pressure as an example of PEP manifesting as a force. There's also the exchange interaction.

Oh, never mind, it's already been said.

Huh? Since when is a description the same as an explanation?

Q: Explain how a car works.
A: You get in, turn the key, put your foot on the accelerator, and it moves.

vanhees71
Ken G
Gold Member
The connection between spin and statistics has been proved
so we know that it is indeed half integer spin that implies increased repulsion.
Yet my gut feeling is that there is something important missing.
There is a force, as V50 argues, but there is no force field, no force carrier.
I think what a lot of people miss about "degeneracy pressure" is that it is nothing other than completely mundane kinetic pressure. As such, it is no more of a force than gas pressure is-- when you take into account the kinetic energy enclosed, and treat what is inside as a fluid, then you have something in there that acts as a momentum flux. It doesn't even require collisions, only that fluid averages are appropriate. The reason you can tell the "degeneracy pressure" is actually nothing but mundane kinetic pressure is that it obeys P = 2/3 E/V for kinetic energy E contained in volume V, for any nonrelativistic monatomic particles.

So what is degeneracy doing, if it is not producing any "extra" pressure (as is so often erroneously claimed)? Simple-- degeneracy repartitions the kinetic energy in such a way that drastically lowers the ratio kT/E, ultimately all the way to 0 when the gas reaches its ground state. So degeneracy is all about the T given the E, and is nothing at all about P. The only reason there is an expression for "degeneracy pressure" is that there is an expression for the completely mundane kinetic pressure when degeneracy drives kT/E to 0. That's all "degeneracy pressure" in a gas ever meant-- it's not any special kind of pressure, it's just garden variety kinetic pressure.

Zarqon
nothing but mundane kinetic pressure is that it obeys P = 2/3 E/V
But if the gas is behaving non-classically, how can there be only one formula? If all the atoms are identical, isn't the behavior described by one of two entirely different sets of forumlas depending on whether the atomic spin is an integer?

Nugatory
Mentor
But if the gas is behaving non-classically, how can there be only one formula? If all the atoms are identical, isn't the behavior described by one of two entirely different sets of forumlas depending on whether the atomic spin is an integer?
This is a thread about the Pauli exclusion principle, so we're talking about a "gas" made up of particles with half-integral spin. The integral-spin case isn't under consideration here.

Collin237
Ken G
Gold Member
What is behaving differently is how the kinetic energy is partitioned among the particles-- you have a Fermi-Dirac distribution instead of the more familiar Maxwell-Boltzmann. But none of that affects the pressure-- that depends only on the kinetic energy content, and the volume, via P = 2/3 E/V. The problem is, often people like to track the temperature, and degeneracy alters kT/E dramatically. But if you simply track E instead of kT, you don't need to even know if the gas is fermionic or not-- you still know P from E and V, even if it gets called "degeneracy pressure" when kT/E is driven way down. It's just garden variety kinetic pressure if you know E and V, it makes no difference to P what the spin statistics are, or even if the particles are distinguishable or not. What's more, very often you do know E and V, such as when you apply the virial theorem to a star of given mass and radius, or more generally, when you know the P(V) function of some kind of containment vessel, and then you only need to read off V. You will then know the E of the gas, and will understand its pressure perfectly, without even knowing if it is fermionic or not. People have some strange ideas about "degeneracy pressure"! It's really a kind of limiting pressure at which point you should not be able to extract any more heat, but if you don't care what T is, you can always get P from E and V, that's why it's such a mundane form of pressure.

Last edited:
Mentz114 and Zarqon