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I've been wondering, what causes the normal force to exist?

In class the teacher never actually explains it, he just says "It has to be there because something has to counter gravity." While I understand this is true, it never explains why. Whenever I ask anyone else they always respond in a similar way, saying "It has to be there, because the object is not accelerating", and this has become very frustrating.

So what is the cause of the normal force? From my reasoning, it has to be one of the four fundamental forces. (Gravity, electromagnetism, the weak force, or the strong force). It would seam to me that electromagnetism would make to most sense (electrons in the outer shells of atoms repelling each other),

However, just as I thought this had to be right, I read a thing online about "certain fundamental particles repelling each other when their wave functions overlap". I haven't studied quantum mechanics yet so I'm not really sure what to make of that.

If anyone could shed some light on this for me it would be much appreciated.

Qmechanic
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Ryan Stull
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  • Wow, your question seemed very simple and of elementary level. But you have done us to get think of something really interesting. Is the exclusion principle of fermions the main reason of this? or you can explain the normal force whit electromagnetism only? good question! – Anthonny Sep 24 '11 at 23:07
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    Hasn't this question already been asked? Someone should provide a link to the similar question (something about "standing on the ground", I can't immediately locate it) to avoid duplicates. – Chris Gerig Nov 19 '12 at 00:56
  • And it is indeed the EM force. – Chris Gerig Nov 19 '12 at 00:56
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    Possible duplicates: http://physics.stackexchange.com/q/1077/2451 and links therein. – Qmechanic May 17 '13 at 23:53

2 Answers2

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Assuming that by "normal force" you mean the one that acts against the force holding the object to the surface: it's electromagnetic. As a simple example, consider two interacting atoms. Basically, the force between these atoms arises from three sources:

  • The repulsion of their nuclei
  • The repulsion of the electron clouds
  • The attraction of each atom's nucleus to the other atom's electrons

If you graph the total potential energy of these contributions as a function of the atoms' separation, you get something that looks roughly like this:

Lennard-Jones potential graph
(source: wikimedia.org)

Knowing that force is the negative gradient of the potential energy, you can tell that the atoms experience a repulsive force when they are close together and an attractive force when they are further apart. The repulsive force gets larger the closer together the atoms are, essentially without limit, so no matter what force is pushing the atoms together, the system will reach some equilibrium point where the forces are balanced (except under certain extreme conditions that never occur on Earth). This illustrates how atoms are able to resist the forces pushing them together.

Obviously, the real story is much more complicated because real objects are made of molecules, and there are many different kinds of interactions going on.

Community
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David Z
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    Everything is irrelevant except the exclusion principle. – Ron Maimon Sep 24 '11 at 19:09
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    The exclusion principle comes into play only when you have a very high electron density. That happens in e.g. a white dwarf, but not in normal intermolecular interactions. – David Z Sep 24 '11 at 19:18
  • The exclusion principle is quite relevant to the stability of normal matter: just by applying it together with the uncertainty principle you can get the correct order of magnitude for the bulk modulus of metals (see section 3.4.2 here). Electromagnetic forces are relevant but "in the other direction" (after all solids are stable at zero pressure). If electrons were bosons, matter would not be stable (see theorem 3.2 here). – mmc Sep 24 '11 at 20:03
  • @David--- that's not true. The exclusion principle is important in the everyday solidity of matter too. – Ron Maimon Sep 24 '11 at 20:03
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    @mmc: the first link talks about the high-density limit, which doesn't apply to normal matter. I'll have to look at the second one, though. I definitely agree that the PEP plays a role in solid stability in that it keeps all the electrons from collapsing into the ground state, but I really seem to remember reading somewhere about how, given the atomic structure of matter, Coulomb repulsion produces the contact force. I guess I'll have to look for a source. – David Z Sep 24 '11 at 20:19
  • @David The section header says "high-density limit" because the high density limit of all matter is a degenerate Fermi gas. But metals are well approximated by a Fermi gas even at zero pressure and the bulk moduli appearing in table 3.2 for Li and Al match the "zero pressure" values. – mmc Sep 24 '11 at 20:44
  • @mmc: OK, but what about non-metals? – David Z Sep 24 '11 at 20:46
  • @David The repulsive part of interatomic potentials is generally attributed to the Pauli exclusion principle. A more quantitative analysis of the different "components" of the interaction between atoms and molecules can be seen here ($\Delta E^{rep}$ is the component of the binding energy due to the Pauli exclusion principle). – mmc Sep 24 '11 at 23:13
  • @David: Carl Sagan used to misattribute the repulsion to Coulomb effects, and other popularizers follow him, so this is probably what you remember. – Ron Maimon Sep 25 '11 at 03:50
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    @Ron: I don't think so; I wouldn't have trusted a popular science source on this. – David Z Sep 25 '11 at 06:55
  • David you are correct, you can see my elaboration in the other thread (entitled something along the lines of "standing on the ground") – Chris Gerig Nov 19 '12 at 02:38
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    @ChrisGerig I remember your elaboration in this thread. You were just asking us to take your word for it, as you didn't give any explanation (remember that I gave a lot of sources, FWIW). Please write a more detailed answer so we can address this issue properly (i.e. not by saying "I'm right!"). – mmc Nov 19 '12 at 12:18
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The normal force is not really due to any of the four force of nature. The forces of nature are not all the forces in the macroscopic sense, they are just the fundamental bosonic particles in a modern quantum field theory description.

The normal force is due to the Pauli exclusion principle almost exclusively. This is because electrons have the property that two electrons cannot be in the same quantum state. Two electrons can't be at exactly the same point.

But you might be thinking, "two point particles in three dimensions can't ever be at the same point, it's infinitely improbable!" In quantum mechanics, the particles are spread out in a wavefunction, and the condition that they can't be at the same point means that wherever their spread-out-ness overlaps, the wavefunction is zero. The wavefunction is in 6 dimensions for 2 particles, so it is hard to visualize, but the zeros appear on the diagonal part, where the two positions for the particle coincide.

When you bring two objects to touch, the electron wavefunctions are squeezed together, and the average scale of variation increases slightly, because of the exclusion. The rate of change of the wavefunction is the momentum of the electron, and as you push them closer, it costs energy. This is the source of the normal force. It would not exist if electrons were elementary bosons.

Ron Maimon
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    +1 But you also need attractive forces to get condensed matter. It's difficult to get normal forces from an ideal Fermi gas :-) – mmc Sep 24 '11 at 20:12
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    @mmc: you are right, but I was taking electrostatic attraction for granted. The surprise is that even when only electrons and protons feel a mutual force, you get stable matter. – Ron Maimon Sep 24 '11 at 20:12
  • So you need to have both electromagnetic interaction and the Pauli exclusion principle in order to have to Normal force? – Ryan Stull Sep 27 '11 at 14:48
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    @Ratz: you need the attractive electrostatic interaction between electrons and nuclei to keep the elctrons from flying off the nuclei. Other than that, you only need the exclusion principle. – Ron Maimon Sep 27 '11 at 18:48
  • @Ratz, this is false. The main cause of the normal force is the electrostatic, not Pauli exclusion. The latter is on too small of a scale. You can double check this with a ton of legitimate professors if you do not believe me. – Chris Gerig Nov 19 '12 at 00:54
  • @ChrisGerig: I have checked for myself, a long time ago, and you are wrong. There is a sense in which you are right, in that the "electrostatic energy" contributions in some calculation method is big and another contributions smaller, but this is not the correct way to compare contributions. The net neutrality of atoms, assuming they are classical charge distributions, leads to exactly zero electrostatic force at long distance. The small entanglements lead to London attractions. The way to show that it's Pauli is to replace electrons with bosonic spinning electrons, and then matter collapses. – Ron Maimon Nov 19 '12 at 03:10
  • You are wrong. No repeating. – Chris Gerig Nov 19 '12 at 03:31
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    @ChrisGerig: Ok--- here's a question. Suppose I had two different types of electrons, duplicate the electron field and have two electron fields with the same mass and charge, just they are distinguishable. Suppose you now brought some electron-1 matter into contact with electron-2 matter. Would they repel? Even for a short time? What do you think happens? The only difference here is zero Pauli force. I can tell you, but please work it out. I am not wrong, I know this from reading the classic literature and also indepedently working it out myself, I am not citing authority (I never do). – Ron Maimon Nov 19 '12 at 04:09