Comment author:ctl
08 January 2012 10:43:03PM
4 points
[-]

I don't think his explanation for why a chair pushes back on your hand is quite right, either. I've mostly been told that material solidness comes from the Pauli exclusion principle, not electrostatic repulsion.

I don't know quantum mechanics, so I don't have a good perspective on the problem, but the electrostatic explanation has always seemed lacking to me. The electric charge in a neutral atom is fairly well-approximated by a symmetric sphere of negative charge with a bunch of positive charge at the center, so two atoms shouldn't experience much electrostatic repulsion until their electron clouds overlap. At which point [I've heard] the PEP should dominate the electrostatic force.

Both the Pauli exclusion principle and electrostatic repulsion contribute. There is a brief discussion of this on Wikipedia, which cites the work of Freeman Dyson.

A more rigorous proof was provided in 1967 by Freeman Dyson and Andrew Lenard, who considered the balance of attractive (electron-nuclear) and repulsive (electron-electron and nuclear-nuclear) forces and showed that ordinary matter would collapse and occupy a much smaller volume without the Pauli principle.[6] The consequence of the Pauli principle here is that electrons of the same spin are kept apart by a repulsive exchange interaction, which is a short-range effect, acting simultaneously with the long-range electrostatic or coulombic force. This effect is partly responsible for the everyday observation in the macroscopic world that two solid objects cannot be in the same place in the same time.

It would not surprise me if he just didn't want to start talking about quantum exchange interactions in response to an interview question about how magnets work. Electrostatic repulsion does count for some of the effect of solidity, so his answer wasn't wrong so much as incomplete. That was the point of his entire discussion: there are many different levels on which we can answer a "why" question.

Comment author:DanielLC
09 January 2012 03:15:26AM
*
0 points
[-]

The Pauli principle isn't a force at all. It's a symmetry, or at least a special case of one. Also, it has nothing to do what causes magnets to repel. If you violated the symmetry, magnets would still work.

Comment author:SilasBarta
09 January 2012 04:37:52AM
4 points
[-]

I'm not sure the distinction between a force and a symmetry is a useful one. Any use of "force" in modeling physics can be equivalently expressed via conservation of linear momentum, which itself is equivalent to the fact that the laws of physics are symmetric in translation (i.e. translation-invariant, i.e. have the same form when the origin of the coordinate system everything is expressed in is moved around).

Literally, for any force, you can say, "that's just the playing out of a necessary symmetry in the laws of physics".

Comment author:DanielLC
09 January 2012 05:29:07AM
2 points
[-]

Any use of "force" in modeling physics can be equivalently expressed via conservation of linear momentum

I don't see how. Either you're misunderstanding something, or you have a higher background in quantum mechanics than I do (I've had one in-depth class, and I've read the quantum physics sequence), and it works out like this for reasons I do not currently understand. Which is it?

In any case, force is clearly defined in the simplified version of quantum physics I've learned. It's the gradient of potential energy, which must be specified in the Schroedinger equation. The Pauli principle is not a force. It may be that force is always due to symmetry, in which case calling the Pauli principle a symmetry doesn't separate them at all, but the Pauli principle is still not a force.

Comment author:DanielLC
10 January 2012 12:18:50AM
-1 points
[-]

Conservation laws are not forces. There are hypothetical patterns of force that would not conserve these things, but the way things normally move is not the only one. For example, if there were no forces, all the conservation laws will still work.

Also, from what I understand, that's more a symmetry in the laws themselves, where the Pauli principle is a symmetry in the waveform being operated on.

Comment author:SilasBarta
09 January 2012 04:31:18PM
2 points
[-]

The Pauli principle is not a force in the sense that gravity is not force. Yes, you can distinguish between a "force" and the phenomenon responsible for the force (gravity vs gravitational force). What is the difference between these two statements?

1) That's not a force, it's the playing out of the fundamental symmetries in quantum physics, normally phrased here as the Pauli exclusion principle.

2) There's no force on that falling object in a vacuum, it's just following the geodesic dictated by the symmetries in General Relativity.

Comment author:Ronak
10 April 2013 03:29:46PM
0 points
[-]

PEP is not a force, in the sense that it's not 'dynamical:' it can't actually affect the Hamiltonian/Lagrangian of the world. And it's not a symmetry either, it's a consequence of the behaviour of 'fields' under rotations: see spin-statistics theorem.
(Explanation of the field business: modern physics postulates that at every point in space and time there are a certain number of degrees of freedom, and we call them fields and 'quantising' gives us particles - and particles are just spatially localised excitations when you don't look closely at them.)

The rest of the forces, however, do come from symmetries called local gauge symmetries; roughly, since the wavefn is a complex no, change the phase by some amount which depends on the point and then requiring that physics be invariant under this. (Even gravity, though only in classical field theory as of now: it can be found by a Lorentz transformation by a different amount at every point.)

This explanation is horrible, so sorry; but on the bright side, the math is simple enough that you may actually understand wikipedia on these things.

It goes into lots of detail of what's happening with a single hydrogen atom, then a large atom, then bulk matter. It doesn't require quantum physics knowledge from a reader, but it does require mathematical maturity, and isn't easy reading.

The short of it is that you're right, the Pauli exclusion principle is more important than electrostatic repulsion.

Comment author:see
09 January 2012 05:05:14AM
4 points
[-]

I note Fyenman above is quoted as saying, "There's other forces involved, connected to electrical forces" in the context. One can quibble about how "connected" the Pauli exclusion principle is to electrical forces, but he is explicitly acknowledging there's more going on than just the immediate results of the electromagnetic force, in the midst of an extemporaneous explanation as to what's going on with magnets.

Comment author:Manfred
09 January 2012 07:28:41AM
*
2 points
[-]

It's mostly this stuff. Dispersion forces involve both pauli exclusion and the electric force, working in sweet harmony. Which is the one that actually pushes the heavy nuclei around and stops your hand? The electric force.

Comment author:DanielLC
09 January 2012 03:27:01AM
1 point
[-]

I have never been taught this in particular, but it seems unlikely that the Pauli exclusion principle could do it. It's a symmetry, not a force.

From what I understand, if you sent two fermions at each other, assuming they don't otherwise repel, they'd just pass through each other. The Pauli principle would merely guarantee that they do so at an anti-node. You'd never find them at the same spot. You also wouldn't find them at any other anti-nodes that appear along their trajectories, or more accurately, their joint trajectory in configuration space, or still more accurately, their joint waveform in configuration space. In any case, their momentum and energy would be completely unaffected by this.

The Pauli principle might be why electrons end up in a pattern in which they repel each other so well, but I don't see what else it can do.

If I'm wrong, please correct me, and send me somewhere where I can read more about how it works.

Comment author:TobyBartels
27 January 2013 11:55:17PM
0 points
[-]

The Pauli exclusion principle applies to all fermions, including both electrons and nucleons. The PEP for nucleons is what keeps neutron stars from collapsing (normally). But the PEP for electrons keeps electron clouds from overlapping (much).

## Comments (44)

BestI don't think his explanation for why a chair pushes back on your hand is quite right, either. I've mostly been told that material solidness comes from the Pauli exclusion principle, not electrostatic repulsion.

I don't know quantum mechanics, so I don't have a good perspective on the problem, but the electrostatic explanation has always seemed lacking to me. The electric charge in a neutral atom is fairly well-approximated by a symmetric sphere of negative charge with a bunch of positive charge at the center, so two atoms shouldn't experience much electrostatic repulsion until their electron clouds overlap. At which point [I've heard] the PEP should dominate the electrostatic force.

Can any physicists or physics students comment?

Both the Pauli exclusion principle and electrostatic repulsion contribute. There is a brief discussion of this on Wikipedia, which cites the work of Freeman Dyson.

I guess Feynman includes the Pauli principle as electric force. Remember, he got a Nobel prize for this stuff.

It would not surprise me if he just didn't want to start talking about quantum exchange interactions in response to an interview question about how magnets work. Electrostatic repulsion does count for some of the effect of solidity, so his answer wasn't wrong so much as incomplete. That was the point of his entire discussion: there are many different levels on which we can answer a "why" question.

*0 points [-]The Pauli principle isn't a force at all. It's a symmetry, or at least a special case of one. Also, it has nothing to do what causes magnets to repel. If you violated the symmetry, magnets would still work.

I'm not sure the distinction between a force and a symmetry is a useful one. Any use of "force" in modeling physics can be equivalently expressed via conservation of linear momentum, which itself is equivalent to the fact that the laws of physics are symmetric in translation (i.e. translation-invariant, i.e. have the same form when the origin of the coordinate system everything is expressed in is moved around).

Literally, for any force, you can say, "that's just the playing out of a necessary symmetry in the laws of physics".

I don't see how. Either you're misunderstanding something, or you have a higher background in quantum mechanics than I do (I've had one in-depth class, and I've read the quantum physics sequence), and it works out like this for reasons I do not currently understand. Which is it?

In any case, force is clearly defined in the simplified version of quantum physics I've learned. It's the gradient of potential energy, which must be specified in the Schroedinger equation. The Pauli principle is not a force. It may be that force is always due to symmetry, in which case calling the Pauli principle a symmetry doesn't separate them at all, but the Pauli principle is still not a force.

Indeed, conservation laws correspond to symmetries: http://en.wikipedia.org/wiki/Noether%27s_Theorem

That has a lot of explanatory power for why I linked Noether's Theorem the first time around.

I must have missed that. Sorry.

I must have missed that. Sorry.

Conservation laws are not forces. There are hypothetical patterns of force that would not conserve these things, but the way things normally move is not the only one. For example, if there were no forces, all the conservation laws will still work.

Also, from what I understand, that's more a symmetry in the laws themselves, where the Pauli principle is a symmetry in the waveform being operated on.

The Pauli principle is not a force in the sense that gravity is not force. Yes, you can distinguish between a "force" and the phenomenon responsible for the force (gravity vs gravitational force). What is the difference between these two statements?

1) That's not a force, it's the playing out of the fundamental symmetries in quantum physics, normally phrased here as the Pauli exclusion principle.

2) There's no force on that falling object in a vacuum, it's just following the geodesic dictated by the symmetries in General Relativity.

PEP is not a force, in the sense that it's not 'dynamical:' it can't actually affect the Hamiltonian/Lagrangian of the world. And it's not a symmetry either, it's a consequence of the behaviour of 'fields' under rotations: see spin-statistics theorem. (Explanation of the field business: modern physics postulates that at every point in space and time there are a certain number of degrees of freedom, and we call them fields and 'quantising' gives us particles - and particles are just spatially localised excitations when you don't look closely at them.)

The rest of the forces, however, do come from symmetries called local gauge symmetries; roughly, since the wavefn is a complex no, change the phase by some amount which depends on the point and then requiring that physics be invariant under this. (Even gravity, though only in classical field theory as of now: it can be found by a Lorentz transformation by a different amount at every point.)

This explanation is horrible, so sorry; but on the bright side, the math is simple enough that you may actually understand wikipedia on these things.

Gravity can be interpreted as a force. To my knowledge, the Pauli principle cannot.

I'm not a physicist, but when I looked into this, I found this well-written article:

The Stability of Matter: From Atoms to Stars

It goes into lots of detail of what's happening with a single hydrogen atom, then a large atom, then bulk matter. It doesn't require quantum physics knowledge from a reader, but it does require mathematical maturity, and isn't easy reading.

The short of it is that you're right, the Pauli exclusion principle is more important than electrostatic repulsion.

Thanks! I love docs like these, that take the a broad approach.

I note Fyenman above is quoted as saying, "There's other forces involved, connected to electrical forces" in the context. One can quibble about how "connected" the Pauli exclusion principle is to electrical forces, but he is explicitly acknowledging there's more going on than just the immediate results of the electromagnetic force, in the midst of an extemporaneous explanation as to what's going on with magnets.

*2 points [-]It's mostly this stuff. Dispersion forces involve both pauli exclusion

andthe electric force, working in sweet harmony. Which is the one that actually pushes the heavy nuclei around and stops your hand? The electric force.I have never been taught this in particular, but it seems unlikely that the Pauli exclusion principle could do it. It's a symmetry, not a force.

From what I understand, if you sent two fermions at each other, assuming they don't otherwise repel, they'd just pass through each other. The Pauli principle would merely guarantee that they do so at an anti-node. You'd never find them at the same spot. You also wouldn't find them at any other anti-nodes that appear along their trajectories, or more accurately, their joint trajectory in configuration space, or still more accurately, their joint waveform in configuration space. In any case, their momentum and energy would be completely unaffected by this.

The Pauli principle might be why electrons end up in a pattern in which they repel each other so well, but I don't see what else it can do.

If I'm wrong, please correct me, and send me somewhere where I can read more about how it works.

Pauli exclusion holds neutron stars and atomic nuclei apart. ie. much denser than atomic contact.

Even with the clouds overlapping, I think it's mostly electromagnetic. They are too sparse for exclusion to be significant.

To get any deeper, we would need someone who understands the source and mechanism of exclusion.

The Pauli exclusion principle applies to

allfermions, including both electrons and nucleons. The PEP for nucleons is what keeps neutron stars from collapsing (normally). But the PEP for electrons keeps electron clouds from overlapping (much).