# Where does a normal force come from?

Being more specific, let's say i place an object on top of a table, this will result on the table applying a normal force on the object.

My question is: Why does this force exists? Is it because of the existence of eletrical forces between the table and the object that makes a "repulsion", or even because the object "deforms" the structure of the table and the intramolecular forces are trying to "fix it" (make the table, that is a solid, go back to it's normal structure, that way aplying a force)?

• If you are not willing to accept various high-level hand waving then you have to get right down to it and deal with the complexity of inter-molecular forces. But don't say I didn't warn you. physics.stackexchange.com/q/1077 – dmckee Jun 16 '18 at 17:07

## 3 Answers

It's not exactly electrical or intra/inter-molecular forces as you conjecture in your question. Rather, it's ultimately exchange forces, e.g., https://en.wikipedia.org/wiki/Exchange_interaction. As two macroscopic objects get close (really close) together, the electron shells surrounding their respective atoms begin to affect each other. And two electrons (because they're fermions) can't simultaneously occupy the same state (be in "the same place at the same time", colloquially), better known as the Pauli Exclusion Principle, https://en.wikipedia.org/wiki/Pauli_exclusion_principle (link added after I noticed @Qmechanic edited that Tag into the original question:)

So as you try to push the macroscopic objects together, thus forcing too many electrons into the available atomic shell states, the overall multi-particle state describing that collection of electrons (determined by the Slater determinant, e.g., https://en.wikipedia.org/wiki/Slater_determinant) necessarily gives zero probability for finding any two electrons in the same state. And that gives rise to the macroscopic effect/semblance of a "force", preventing the macroscopic objects from being "in the same place at the same time".

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Another effect involving exchange forces (unrelated to the op's question about normal forces, per se, but perhaps more generally physically interesting) is the Bose-Einstein condensate, https://en.wikipedia.org/wiki/Bose%E2%80%93Einstein_condensate

Here, a gas of bosons is supercooled so that most of the constituent "particles" all fall into the lowest-energy state. And that's possible because bosons aren't subject to the Pauli exclusion principle, so a large collection of them can all occupy that same state. And then this macroscopic collection exhibits some remarkable quantum properties that you'd expect to only be observable at the microscopic level.

But, now, you couldn't prepare such a remarkable condensate comprised of fermions, like electrons, for exactly the same reason discussed above --- except for https://en.wikipedia.org/wiki/Fermionic_condensate#Fermionic_superfluids where fermions are paired together so that each pair of fermions acts like a boson.

An interesting video discussing all this is at http://learner.org/resources/series213.html Click the [vod] link along the right-hand side of Program 6. Macroscopic Quantum Mechanics The second half of this video interviews Deborah Jin (and some of her grad students), who produced the first-ever fermionic condensate, discussing the physics involved. (Unfortunately, the video's from 2010, and a more recent issue of Physics Today carried Jin's obit, also discussing her accomplishments.)

• @Nat not "basically", i.e. and e.g. are both abbreviations for Latin phrases that mean exactly what you wrote – Kyle Kanos Jun 16 '18 at 18:00
• @Nat (and at-KyleKanos), Gee, guys, this is fun:). And just for the record (though I have no idea why on Earth we'd want a record about any of this:), I did mean "for example". That is (just to get an i.e. in there), there are many, many web pages about exchange forces and about the Slater determinant, and I was just illustrating one each among those many. The op should google these terms himself for more or less mathematical/technical discussions. – John Forkosh Jun 16 '18 at 18:12
• @Nat please don't edit the post just to remove my wikipedia cites. I rolled it back. It's completely clear from the op's question that he isn't already familiar with these terms. So he needs some explanation. And I just gave him some cites, and he can ask followup questions if he has any interest or further questions about those concepts. But his profile tells nothing about his background, whereby I didn't want to bother trying to explain them, since I have no idea how to pitch such a discussion. Or if the op's even interested at all. – John Forkosh Jun 16 '18 at 18:21
• @Nat Oh, sorry. I mistakenly thought it had something to do with this eg, ie stuff. – John Forkosh Jun 16 '18 at 18:26
• Without electromagnetism the exchange forces would do nothing here. The electrons and nuclei wouldn't hold together, and the table would simply be a bunch of unbonded particles, which wouldn't make any normal force. So it's wrong to deny the electromagnetic nature of the normal force. – Ruslan Jun 16 '18 at 20:45

Essentially the same thing is happening when you place an object on a table as when you hang the object from a spring. Equilibrium is reached when the spring is extended enough for it to provide an upward force on the object equal to the pull of gravity on the object. [There may be oscillations before equilibrium is reached.] The table is also deformed when you place an object on it, though you don't notice the deformation unless you have special measuring equipment (or the table is rickety).

The forces involved in the deformation of both the spring and the table are fundamentally electromagnetic.

I am only putting this as an answer because I do not have the reputation to comment. If you listen to Feynmans lectures, he lists several examples of experimental outcomes that have been, to a great order of accuracy, successfully predicted by Quantum Electrodynamics (QED). Newton's Laws can be derived from the basic assumptions of QED.

• So I guess if you want the most fundamental reason why there is a normal force, go study QED – pmac Jun 16 '18 at 18:09

## protected by Qmechanic♦Jun 16 '18 at 19:38

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