It is commonly stated that there are four fundamental forces, or interactions, in nature. It is natural to consider which of those is responsible for the normal force we meet in elementary physics. What is the nature of the force exerted on a body by the floor on which it rests?

Of the four forces, the only one that seems relevant is the electromagnetic force, and I always assumed the repelling force in question is ultimately the EM one. The Wikipedia article on contact forces seems to agree:

Molecular and quantum physics show that the electromagnetic force is the fundamental interaction responsible for contact forces.

An alternative explanation is that the force results from Pauli's Exclusion Principle; however, reasonable as it may seem, it doesn't seem to answer the question of what force is actually at play here. The exclusion principle isn't a force, or at least it's not normally described as such.

I've recently come across a rather forcefully presented argument that states that the normal force is a macroscopic force that is not directly reducible to the EM force, or to any of the other forces; rather, it does indeed result from Pauli's Exclusion Principle by way of interaction of electron wave functions. The argument further claims that attempts to correct the Wikipedia article have met with the usual "source needed" objections, and that this topic is either misunderstood by or poorly covered in the standard texts.

(The argument can be found here).

Which way is it?

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    $\begingroup$ I think when particle physicists talk of four fundamental forces, the better word would be "interaction between the fundamental quantum fields" but I'm just surmising here: The fermion degeneracy pressure arises from the interaction of the particular fermion field in question with itself - I guess that is why it is not part of the four fundamental interactions. I'd like a straight answer to your question from a particle physicist too. $\endgroup$ Jul 22, 2013 at 6:46
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    $\begingroup$ possible duplicate of What does it mean for two objects to "touch"? $\endgroup$ Jul 22, 2013 at 7:00
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    $\begingroup$ The duplicate I've suggested may not be immediately obvious, but Terry's long and detailed answer to that question covers the relevant ground. Also Wouter's anser to physics.stackexchange.com/q/69241 gives an excellent description of how the exclusion force works. $\endgroup$ Jul 22, 2013 at 7:02
  • $\begingroup$ @JohnRennie and what of my surmising that the four forces would be better called the four interactions? I've always thought that the particle physicists are being slightly "poetic" when they use the same word for macroscopic forces. $\endgroup$ Jul 22, 2013 at 7:06
  • $\begingroup$ @JohnRennie, thanks for the link. So it seems that it is, indeed, Pauli's principle at work behind the normal force and that, indeed, this force isn't simply one of the "four fundamental" ones? So it is quite inaccurate to say that nature only has those four forces? $\endgroup$
    – Alon Amit
    Jul 22, 2013 at 7:09

1 Answer 1


Suppose you take two helium atoms and try to push them together. There will be a short distance repulsion and we'd normally describe this as the Pauli exclusion force, so it does indeed sound as if the exclusion principle generates a fundamental force.

However suppose one of the He atoms has both electrons excited to the $2s$ orbital (not physically likely, but this is just a thought experiment). This will clearly affect the exclusion force because the overlap of the He $1s$ and $2s$ orbitals is different to the overlap of two $1s$ orbitals. Indeed, is you push the two He atoms into the same space the overlap integral would go to zero and the exclusion force would disappear. Admittedly, there is an egregious amount of hand waving going on here but you get the basic idea.

So the force exists because the exclusion principle requires excitation of electrons out of the ground state as they are pushed together, and this costs energy. But it only costs energy because of the electromagnetic force responsible for binding the electrons into the He atoms in the first place. If you weakened the electromagnetic force then the exclusion force would also weaken and in fact disappear in the limit of the EM force going to zero.

This is why the exclusion force isn't a fundamental force. When you push the He atoms together the work you do is going into excitations of the EM field not excitations of some "Pauli field". The exclusion principle is a fundamental principle, but the fact that work is required is down to the electromagnetic force.


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