# (Alpha) Does an EM-Field contain a vorticity

So, it's not clear to me what vorticity means, other than what wikipedia tells me.

I know there is an analogy between fluid dynamics and gauge theory---essentially electromagnetism can be thought of as a fluid with no self-interaction*, it I recall/understand the analogy correctly. Given this, it's not clear how it could have any analogue of vorticity, which seems to require a fluid have some attraction to itself.

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* This comes, near as I can recall, from the fact that photons don't interact with each other. This is not true in other gauge theories, like QCD.

Check out http://en.wikipedia.org/wiki/Two-photon_physics. It's a bit of a trick, but we know that a photon can undergo pair production, and that Compton scattering is a photon-electron interaction. So you temporarily turn one photon into an electron-positron pair, let another photon interact with the electron, then shove the electron and positron back together, and voila, photon-photon interaction. Who's to know what really happened under the covers?

Has nothing to do with vorticity.

So, it's not clear to me what vorticity means, other than what wikipedia tells me.

I know there is an analogy between fluid dynamics and gauge theory---essentially electromagnetism can be thought of as a fluid with no self-interaction*, it I recall/understand the analogy correctly. Given this, it's not clear how it could have any analogue of vorticity, which seems to require a fluid have some attraction to itself.

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* This comes, near as I can recall, from the fact that photons don't interact with each other. This is not true in other gauge theories, like QCD.

I have a similar problem. I cannot work out the difference between a vorticity for instance, to one which is the viscosity. Is the viscosity the medium which moves the object, and vorticity is the object which moves in the medium?

I need help here:

note, it was mentioned in the OP.

I have a similar problem. I cannot work out the difference between a vorticity for instance, to one which is the viscosity. Is the viscosity the medium which moves the object, and vorticity is the object which moves in the medium?
Viscosity is a property of a fluid, not an object in and of itself, just like 'hard' is a property of an object not something which can exist in its own right.

Vorticity is vector, viscosity is a scalar, utterly different, though you have gotten vectors and scalars mixed up on the past.....

Its possible to reformulate the Navier Stokes equations to include explicit vorticity terms or to turn off viscosity but these can be done independently as they are two different terms in the equations. Viscosity is something you can set before solving the equations while vorticity is much harder to set, if at all possible, as it is explicitly dependent on the flow field $$\mathbf{v}$$, which you obtain by solving the equations. Inviscid flows can have vorticity and irrotational flows can have viscosity.

The fact you refer to properties of objects as objects (ie vorticity is a property of an object, the fluid, not an object itself) suggests you haven't quite wrapped your head around whatever it is you're looking at. For a change I have a slight amount of sympathy for you because I've been spending the last month pretty much trying to learn particular bits of fluid mechanics from scratch (half a lecture course 6 years ago isn't much to go on) and the physics of objects in fluids is a bitch. Just as GR is simplified if you assume a small test mass doesn't alter the gravitational field it moves through fluid mechanics is a lot easier if you assume objects in the flow don't alter the flow. If you can't make that assumption its a whole lot more unpleasant...

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Viscosity is a property of a fluid, not an object in and of itself, just like 'hard' is a property of an object not something which can exist in its own right.

Vorticity is vector, viscosity is a scalar, utterly different, though you have gotten vectors and scalars mixed up on the past.....

Its possible to reformulate the Navier Stokes equations to include explicit vorticity terms or to turn off viscosity but these can be done independently as they are two different terms in the equations. Viscosity is something you can set before solving the equations while vorticity is much harder to set, if at all possible, as it is explicitly dependent on the flow field $$\mathbf{v}$$, which you obtain by solving the equations. Inviscid flows can have vorticity and irrotational flows can have viscosity.

The fact you refer to properties of objects as objects (ie vorticity is a property of an object, the fluid, not an object itself) suggests you haven't quite wrapped your head around whatever it is you're looking at. For a change I have a slight amount of sympathy for you because I've been spending the last month pretty much trying to learn particular bits of fluid mechanics from scratch (half a lecture course 6 years ago isn't much to go on) and the physics of objects in fluids is a bitch. Just as GR is simplified if you assume a small test mass doesn't alter the gravitational field it moves through fluid mechanics is a lot easier if you assume objects in the flow don't alter the flow. If you can't make that assumption its a whole lot more unpleasant...

That's very, admirable of you. - Yes I am certainly finding it increasingly difficult wrapping my head round many of these concepts. I am not understanding them very well.