Comment author:DanielLC
09 January 2012 03:15:26AM
*
0 points
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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
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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
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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
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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
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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.

## Comments (44)

Best*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.