I don't think it is a force, but I might be wrong. The Pauli exclusion principle is not a true principle, in the sense that we don't need to "accept it" as a fact (as opposed to the principle of inertia, for instance). I would rather call it a "theorem", since it can be derived from Quantum Field Theory, the unification of Quantum Mechanics with Special Relativity. So I guess that you will find the answer in QFT.

Pauli exclusion principle is a crude approximation of the more general principle that states that particles are not discernable.

Actually, in the Bohmian interpretation of quantum mechanics you can indeed interpret it as a force. But in the standard picture,  there is no such picture!

Yes; there is.  This is the force responsible for the repulsive component of the interatomic helium (He-He) potential and other inert systems (Ne, Na, Ar, ... ).  As the electronic clouds surrounding two He (3He or 4He) nuclei begin to overlap strongly, a very strong repulsive force results, thanks to the Pauli exclusion principle.  This is the underlying physics behind the short-range, strongly-repulsive part of the binary potential (the other part being the long-range, weakly-attractive Van der Waals' force).  The resulting potential is very familiar in atomic and molecular physics, and constitutes a major input in many-body calculations for the corresponding fluids.  In fact, this 'Pauli-exclusion-force' is so strong that it persists almost intact even in the liquid (where the corresponding potential is several orders of magnitude greater than typical liquid energies, as typified by the chemical potential).

For references, please consult the fairly rich literature on He-He, Ne-Ne, Na-Na, Ar-Ar and similar other, potentials.

There are 4 known fundamental forces: Electromagnetic, gravitational, strong nuclear, weak nuclear. If the Pauli Principle were due to a force, which one would it belong to? What would be the boson carrier of this force?

I think that there is no force involved, the Pauli Principle just emerges from QFT.

To support the fact that the Pauli Principle is not due to a force, remember that it not only means that two fermions cannot occupy the same location, it also means that they cannot occupy the same state! You can choose any basis of the Hilbert space, the Pauli Principle states that one cannot put two fermions in the same basis state. What kind of force could prevent this?

In view of Dr. Rousseau's perceptive remarks, I would like to add to my previous answer, if I may, the following notes.

Consider an ideal Fermi gas.  As you know, although the interparticle interactions are negligible, you will still have a 'statistical potential' which arises solely  from the statistics -- in this case, from the Fermi-Dirac statistics; i.e., from Pauli's exclusion principle.  This 'potential' is an overall repulsive central potential, as derived from the two-particle reduced density matrix.  In contrast, in an ideal Bose gas, the statistical potential is an overall attractive central potential; no Pauli exclusion principle operates here.  Thus, although the exclusion principle is not a force, it does give rise to a repulsive 'effective' force, as manifested by the repulsive statistical potential.  It would be interesting, in light of Dr. Rousseau's remarks, to dig deeper into the origin of this effective force (for example, in terms of specific exchange 'particles', to use quantum-field-theoretic language, tracing it back to one of the four established forces).  Who knows?!

Read About neutron star. Specially how simply degeneracy pressure can hold an entire star.

Has anybody here read a recent paper on test of violation of Pauli exclusion? See http://arxiv.org/abs/1501.04462

http://arxiv.org/abs/1501.04462

Very good question Rousseau.

It does look like PEP gives rise to a force when seen from a space-time perspective. But it is more general than mere force in the Newtonian sense. It is better to ask "if we can have a repulsive potential corresponding to PEP", since potential is more fundamental than force.

Of course, In terms of force it can be classified as something that does not fall in any of the four known fundamental category of forces.

Regards,

Rajat.

I believe that this question and the answers demonstrate that the force is an ill defined concept in physics. It is well defined in classical mechanics, being the measure of the deviation from the free, non-accelerating motion. But it looses its clarity in quantum mechanics where the idea of interaction is generalized to entanglement, e.g. entanglement needs no energy-momentum exchange. The Pauli principle driven exchange interaction (a wrongly chosen word) acts on plane wave states in an ideal gas, showing the peaceful coexistence of the free motion and the entanglement which appears as an interaction. It is another story that the indistinguishability of the gas particles, the very source of the entanglement, somehow hides this kind of entanglement in physical observables.

I agree Aleksei, except about two minor points.

1. "entanglement is not a kind of interaction" It depends on what we mean by "interaction". One possibility, interaction = exchange of energy-momentum comes from classical physics. Another possibility is to identify interaction with the emergence of correlation. Pooyan's original question is about force and I believe that this concept is closer to the second way of defining interaction. But I suspect that we are talking here about words, not facts.

2.You mention that the (anti)symmetrization of the physical states of undistinguishable particles is not entanglement. Again, what is entanglement? If it is defined by physical measurements then you are right. But if it is defined by the non-factorisablity of the density matrix then it is the other way around. Consider two anyons in 2+1 dimensional space-time. Their exchange statistic phase, a real number between 0 and 2 pi, characterizes the state and influences the expectation values of observables. Such an effect of non-factorizablility, the exchange interaction (using again such a wrongly chosen, historical word)  is easily observable.

Another part of the argument: You mention correctly, that the non-factorisable structure of the state remains the same in time, therefore there is no need of any force. Take the example of the Coulomb interaction in temporal gauge, A0=0. Gauss' law, the remnant of the Mawell equation for A0 is a constraint: If it is satisfied by the initial condition then it remains to be satisfied forever. Nevertheless there is a force, corresponding to it.

Dear Janos and Aleksei,

What is the most general definition of an interaction? Exchange of a particle, of energy, momentum, charge? Is that enough general? Don't we have effects that don't match this definition?

There is no doubt that Pauli's exclusion principle behaves as a repulsion force. In nuclear physics it is taken in consideration as part of the potential energy, in the Schrodinger equation. I mean, besides the nuclear force there is also the Pauli repulsion between identical fermions.

Shouldn't we seek a more general definition for force? I am not sure, I just ask.

Dear Dr. Wechsler,

You are right: Pauli's exclusion principle does manifest itself as a repulsive force.  In this context, I have already mentioned the 'statistical potential' and, in a previous answer, the interaction between a pair of inert atoms (He, Ne, Ar, ...).  This interaction can be represented by a potential function V(r) [r being the interatomic separation] whose short-range, highly-repulsive component arises from Pauli's principle as the electronic clouds surrounding the  nuclei of the two interacting atoms begin to overlap strongly.  The corresponding central force at any r is simply the negative of the gradient at this point. [The long-range, weakly-attractive component is a Van der Waals' force arising from exchange of long-wavelength phonons; and the minimum in between the two components represents equilibrium where the force involved is zero.]

Maybe the concept of force (and that of field) should be reconsidered at some junction; but not on the present count.  One needs more compelling motives for doing so.

Kindest regards.

One way to look at this question is to consider the point of view that all "forces" are an observer's interpretation of quantum entanglement. Then, since identical particle exclusion rules (Pauli's being a particular case applicable to atomic electrons) are statements of entanglement, it is reasonable to consider the exclusion rule as a "force". However, IMO, it is better to think simply in terms of entanglement and forget "forces" and accept that there is nothing particularly special about identical particle exclusion rules. Entanglement limits possible state and that is all there is.