# If the earth has gravity, why don't we all collapse to the center?

I'm sorry if the answer is obvious for you guys, but why don't we all (including buildings, road, people, the ground) collapse to the center of the earth because of gravity? Is it because we have velocity, just like the earth not falling to the sun (or electrons not falling to the protons)? But that analogy doesn't sound right because those involve wide empty space.

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## 5 Answers

While there is some truth to all the answers presented, I think there is something important that has been missed.

It is not just electromagnetism, it really is a quantum mechanical effect. The Pauli exclusion principle for the spin-$\frac{1}{2}$ electrons says that two electrons with the same spin state cannot occupy the quantum orbital state. So when two atoms are pushed together by, for example, gravity, is therefore essentially a quantum mechanical effect that prevents the electrons from occupying the same space that results in a distortion of the quantum mechanical wavefunction. The energy it takes to create this distortion is what then results in the electromagnetic repulsion.

As @Vineet and others say, there are only 4 forces in nature and only gravity and electromagnetism have a long range. So it has to be the stronger electromagnetic force that opposes gravity, but it is the quantum mechanical Pauli exclusion principle that causes the distortion of the wavefunction that results in the electromagnetic force.

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+1: good that someone said it. – Ron Maimon Oct 23 '11 at 18:00

Well, if you run over a sufficiently deep hole, you WILL fall to center. So why don't you fall to the center anyway? Because there already is something thats blocks the space - namely "the earth". As most of it is either heavier than you are (so switching places would need energy to lift the it up) or at least is solid and sticks together, it's on you to stay on the outside of the ball. If the matter below you is light and doesn't "stick together" tough, you will fall as deep as possible to the center (i.e., until you hit something that again is solid and/or heavier than you are). In case of a hole this lighter material is air, in case of, for example, the ocean it is water. In both cases you "fall" to the ground, that is, towards the center of the earth.

So why does matter block us at all, why can't we go through walls or fall THROUGH the ground to the center of the earth? The answer is: elektromagnetic forces between the atoms of the matter. They prevent the atoms from colliding.

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-1: the answer is not electromagnetic forces in any way. It's all exclusion forces. Bosonic electrons would collapse to sit on top of each other in a small sphere at the center of the Earth, where the radius would be determined by the exclusion of the Fermionic nuclei. – Ron Maimon Oct 23 '11 at 17:59

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Why should they do that? They repell each other much more electromagnetically than they attract gravitationally. – mcandril Oct 23 '11 at 19:12

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Because the attraction to the nuclei balances out the repulsion, the attractive force with the nucleus is equal to the repulsive force of the electrons, and you gain by mushing the electrons closer to other nuclei. The nuclei and bosonic electrons clump together in a volume which doesn't grow proportionally to their number. Fermionic electrons occupy a volume proportional to the number. You can see this already in one atom, solving for Bosonic electron orbitals. This is a famous problem of the stability of matter, and it was solved in the 1960s, and Freeman Dyson was involved in this. – Ron Maimon Oct 23 '11 at 19:29

## A simple framework of the fundamental forces suggests the following explanation

The second of your guesses is the correct one. The reason we do not fall to the center of the Earth is the same reason you don't fall to the floor when you sit down in a chair; the electrons in your body repel the electrons in the chair.

More specifically, there is an electron cloud around each atomic nucleus. When two atoms get close to each other, the repulsion between their respective clouds keeps them apart. Meanwhile, the attraction between the cloud and the nucleus keeps each individual atom together.

From this view, the explanation superficially makes sense.

## However...

As pointed out in the comments below, this explanation is not the one given by modern quantum theory. According to quantum mechanics, particles with half-integer spins follow the Pauli exclusion principle and cannot occupy the same quantum states simultaneously. Because electrons, protons, and neutrons are all fermions, they are excluded from occupying the same states and it is this that prevents you from falling through the chair. To figure out why the Pauli exclusion principle holds, it is necessary to get deeply into quantum mechanics and solid state physics. I am not an expert in either so I'll leave that up to those more capable than myself.

It should be noted that the correction to my original answer is not a trivial one. It isn't just the framework of the two views that changes, the predictions made by them also change. A fantastic example of the difference can be seen in superconductivity. In this phenomenon, electrons join together to form Cooper pairs. These pairs of fermions are bosons and so do not obey the exclusion principle. As a consequence, they can travel through superconducting material (made up of electrons and protons) without resistance despite the Coulombic attraction and repulsion.

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why don't the nucleus in our body attract the electrons of the chair? And if there is such a strong repulsion why aren't we floating? – Louis Rhys Sep 29 '11 at 6:37

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You better not dig into explanations such as "those electrons repel other electrons", because solid state physics is much more complex, and those arguments are, simply speaking, incorrect. For instance two dipoles do attract each other, although some particles in one dipole repel others in another dipole. It's impossible even to explain why single atom has its size. Not to mention molecules, and why some electronic configurations have lesser energy than the others. – valdo Oct 23 '11 at 11:58

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-1: The repulsion forces between electrons are not responsible for this in any way. It's only exclusion. – Ron Maimon Oct 23 '11 at 17:58

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@AdamRedWine: I'll remove the downvote--- sorry, but this misconception is repeated endlessly. It happened here several times. The reason is because Carl Sagan used this explanation in Cosmos, and the degree to which popularization texts are repeated is never determined by accuracy, but by how popular the meme becomes. – Ron Maimon Oct 23 '11 at 18:48

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@Adam, no problem, leave it as is. I apologize for my inappropriate comment. – FrankH Oct 24 '11 at 1:40
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To add to the previous answers, note that the universe has four major forces. Of these, gravity and electromagnetism dominate the macroscopic level. Between these two forces, electromagnetic forces are orders of magnitude stronger than gravitational forces, mainly because of the small value of the Gravitational constant $G$. So, when you sit on a chair, there are two forces playing tug of war, the gravitational force of the earth pulling you towards center, and the electromagnetic forces between the electrons in you and the chair which keeps you apart (one is attractive and other is repulsive).

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This is not true. It's not electromagnetic forces, but electron forces--- exclusion principle forces--- that keep the chair stable. -1 – Ron Maimon Oct 23 '11 at 17:58
@RonMaimon..u mean pauli's exclusion?? That can only describe the degenerate electronic configuration...not the stabliliy of everyday matter! – Vineet Menon Oct 24 '11 at 6:31
it describes the stability of everyday matter, because this is a highly degenerate eletronic configuration in the external field provided by the nuclei. – Ron Maimon Oct 24 '11 at 7:16
i have read the answer by @FrankH, it seems to me that it explains the quantum origins to EM forces? Is it true?? Anyways thank for that info regarding stability of matter.. – Vineet Menon Oct 25 '11 at 5:44

Because the electromagnetic force, the force that keeps atoms together is much much much much more stronger then the gravitational force. So the only thing that the gravitational force can do given the mass of the earth (G = mg) is bring the atoms closer, but as we go down to the atom, the electromagnetic force overcomes the gravitational force and keeps everything as it is

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