# Mathematical form of the de facto repulsive "force" associated with the Pauli Exclusion Principle [duplicate]

One of the principles of General Relativity is that test objects follow a geodesic unless otherwise acted upon by a force. From this perspective, it is clear that physicists, consciously or unconsciously, view the Pauli Exclusion Principle (PEP) as a force, since it is intrinsically involved in the processes that prevent us, for example, from following a geodesic through the earth's surface. If this interpretation is considered incorrect, so be it.

There are other instances where physicists treat PEP as a force. Semantic arguments aside, PEP is in fact a repulsive phenomenon that that keeps fermions from occupying the same state. It behaves like a de facto force, and can be overcome by sufficient pressure. What is the mathematical form, in terms of $r$, of PEP repulsion? Have experiments been done to determine this?

Regarding the fall-off with $r$: note that one electron approaching another electron must "know" at some distance that it is being repulsed; the two electrons need not come in contact.

[Author's note: Since several readers claim this is a duplicate question, official forum guidelines require I explain why it is not. First, I see nowhere else the question as to the mathemetical form of the EFFECTIVE repulsive force f(r). Thus, the question is new on this forum. Second, whether PEP repulsion is a "true" force, a "fundamental" force, or a "pseudo" force is a matter of semantics, discussions of which do not answer the question. In any case, PEP repulsion is an EFFECTIVE force, and therefore in principle can be described by some function f(r), even if only statistically.]

• "it is clear that physicists, consciously or unconsciously, view the Pauli Exclusion Principle (PEP) as a force": nope: physics.stackexchange.com/questions/44712/… Dec 19, 2015 at 23:23
• en.wikipedia.org/wiki/Exchange_interaction "In physics, the exchange interaction (with an exchange energy, and exchange term) is a quantum mechanical effect that only occurs between identical particles. Despite sometimes being called an exchange force in analogy to classical force, it is not a true force, as it lacks a force carrier."
– user83548
Dec 19, 2015 at 23:24
• PEP is a quantum effect. GR is strictly classical. Dec 19, 2015 at 23:50
• The actual force involved is ultimately electromagnetic in nature, since really we're talking about chemical bonds. These bonds are responsible for the rigidity and finite bulk moduli of materials. The PEP plays a role in all this, of course (without it, you wouldn't get stable chemical bonds at all, at least not very interesting ones), but the PEP is not in itself a force. It's one component in a long, complicated explanation of how electromagnetism produces rigidity. Dec 20, 2015 at 4:07
• Also see Nature of the quantum degeneracy pressure where I make much the same argument this time involving the gravitational force. Dec 20, 2015 at 10:59