# Is Pauli-repulsion a “force” that is completely separate from the 4 fundamental forces?

You can have two electrons that experience each other's force by the exchange of photons (i.e. the electromagnetic force). Yet if you compress them really strongly, the electromagnetic interaction will no longer be the main force pushing them apart to balance the force that pushes them towards each other. Instead, you get a a repulsive force as a consequence of the Pauli exclusion principle. As I have read so far, this seems like a "force" that is completely separate from the other well known forces like the strong, electroweak and gravitational interaction (even though the graviton hasn't been observed so far).

So my question is: is Pauli-repulsion a phenomenon that has also not yet been explained in terms of any of the three other forces that we know of?

Note: does this apply to degenerate pressure too (which was explained to me as $\Delta p$ increasing because $\Delta x$ became smaller because the particles are confined to a smaller space (Heisenberg u.p.), as is what happens when stars collapse)?

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If you like this question you may also enjoy reading this Phys.SE post. – Qmechanic Nov 20 '12 at 19:42

The pauli exclusion principle is not a repulsive force. It applies to fermions. It says that two electrons cannot occupy an energy state in a potential well with exactly the same quantum numbers. They have to differ by at least one quantum number. It is the Pauli exclusion principle that organizes the electron shells filling them sequentially from low to higher energy levels in atoms, otherwise they would all pile up at the lowest energy level. Also the periodic table of elements filling the baryons in the strong potential well. It makes matter as we know it.

Yet if you compress them really strongly, the electromagnetic interaction will no longer be the main force pushing them apart to balance the force that pushes them towards each other. Instead, you get a a repulsive force as a consequence of the Pauli exclusion principle.

The above is a misunderstanding.

It is not a force, since at the particle level forces have carriers that are exchanged between particles so that momentum and energy change.

In your "compression" description there is a continuum and not a quantized state so the PEP does not apply. When one scatters an electron on an electron one can get very close until the exchange particle ( the photon in this case)

transfers enough energy in the center of mass system to start creating other elementary particles. The process is accurately described by quantum electrodynamics.

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But how does this explain degenerate pressure? The name implies that a force is acting. Would it actually mean that adding electrons to a small space would force them (PEP) into higher energy levels because all the ground states are occupied and thus they actually have a higher kinetic energy (and thus also a higher momentum which results in a higher pressure) – PatronBernard Nov 20 '12 at 20:38
I was not familiar with the term. It seems from the Wiki article that a potential well can be defined for a constrained volume, then this means that there are discrete energy states that will then be filled sequentially with the effects described en.wikipedia.org/wiki/Degenerate_pressure . This pressure is a collective effect not a one upon one fermion. – anna v Nov 20 '12 at 20:43
I just have difficulty understanding the apparent link between energy (levels) of the contained particles and the way they exert a force on the "walls" of the container. The whole explanation tells something about particles being forced in higher energy levels, and somehow this results in a higher pressure, but I have trouble seeing that link. – PatronBernard Nov 20 '12 at 22:40
@PatronBernard It is important to notice that in the case of, for instance, degenerate matter in a white dwarf there is an actual force (gravitation) trying to squeeze the electrons ever closer together. It is the tension between that force and the exclusion based limit on the number of low momentum electrons that can be in a particular volume that results in the electrons getting forced into high momentum states. The energy comes from gravity, not from the PEP. – dmckee Nov 21 '12 at 0:26
@annav: It is funny, but Dirac represented it as an "exchange interaction", via effective potentials depending on spins. And "exchange" here means exchange with fermions ;-) – Vladimir Kalitvianski Nov 21 '12 at 18:20
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