4D magnetism and electricity

[PWrong]

I know there's already a topic similar to this, but I'll try to give it a better start.

I've just finished studying magnetism in physics. I don't know if anyone else has studied it, but it seems very strongly dependant on having three dimensions. Many of the laws of electromagnetism require three perpendicular vectors i.e. magnetic field, current and the force acting on the wire.

I found it interesting that these were actually three interchangeable aspects of the same force, and also that they were always perpendicular to each other, because we have three dimensions.

How do you think magnetism would work in more or less than three dimensions? I suspect that the electromagnetic force actually works in n different ways, where n is the number of dimensions. Therefore in 2D, magnetism wouldn't exist at all, only electricity and the "pushing" kind of force. In 4D, perhaps there would be two kinds of magnetism, or perhaps a new kind of electromagnetism altogether.

Alternatively, magnetic fields might just work differently in other dimensions. Maybe they oscillate around a wire in 2D and have some kind of spherindrical motion (like cylindrical, but with a spherinder) in 4D. Which is the more likely scenario?

[Euclid]

I know there's already a topic similar to this, but I'll try to give it a better start.

I've just finished studying magnetism in physics.

<<snip>>

How do you think magnetism would work in more or less than three dimensions? I suspect that the electromagnetic force actually works in n different ways, where n is the number of dimensions. Therefore in 2D, magnetism wouldn't exist at all, only electricity and the "pushing" kind of force. In 4D, perhaps there would be two kinds of magnetism, or perhaps a new kind of electromagnetism altogether.

<<snip>>

Stephen Hawking has (sort of) broached this topic, browse here.

[PWrong]

That article didn't mention electromagnetism at all. :? Did you mean to post that in the superstring thread?

I'd hoped for a slightly better response with this, but I guess 4D magnets don't really matter.

[Euclid]

That article didn't mention electromagnetism at all. :? Did you mean to post that in the superstring thread?

I'd hoped for a slightly better response with this, but I guess 4D magnets don't really matter.

Maxwell and Yang Mills fields ;-)

[PWrong]

I know Maxwell had something to do with light waves, but I've never heard of Yang Mill. Could you explain how they connect with the idea of magnetism in 4D?

[Euclid]

I know Maxwell had something to do with light waves, but I've never heard of Yang Mill. Could you explain how they connect with the idea of magnetism in 4D?

Yikes! If I could explain this (hence the long delay in response), I would be working on the Yang-Mills Millenium Problem instead of horsing around on this BBS. Well, since I probably won't be solving it anytime soon, let me just cheat and quote from the Clay Institute problem statement:

Successful use of Yang-Mills theory to describe the strong interactions of elementary particles depends on a subtle quantum mechanical property called the "mass gap:" the quantum particles have positive masses, even though the classical waves travel at the speed of light.

So we need to ask if EM has some relationship with higher dimensional spaces. Yang-Mills might explain that if the mass-gap question is answerable using a higher dimension.

[PWrong]

I'm not really trying to find a relationship between magnetism and extra dimensions. I'm just wondering how magnetism might work if our universe was 4-dimensional.

For instance, how could you apply the right-hand screw rule, or Lenz's law in 4 dimensions?

[Euclid]

I see.

EM propagates through space and we cannot see it (except for visible light) or feel it (except for IR wavelengths), but we can observe it's effects and measure it. We know a lot about it just from observation and when we develop a theory we can test it. So, in the same light (excuse the pun) we should be able to theorize how it would work in the fourth dimension.

Why not write a story about how A. Square experiences EM as opposed to how Sphere does? That could illuminate how it might work in 4D.