electricity, magnetism, other?

[alkaline]

In the third dimension, energy waves contain an electric component and a magnetic component.

http://en.wikipedia.org/wiki/Electromagnetic_wave

Thus in the fourth dimension, there must be a third component of energy waves. What should it be called? And what should the energy waves be called?

[moonlord]

Why does is have to have a third component?

[Nick]

The only way we can know for sure is if we knew how many there were for both 2d and 1d as well; then we can draw a pattern.

[PWrong]

Thus in the fourth dimension, there must be a third component of energy waves.

I suggested "tetric field" in an earlier thread, but I never really liked that name. Anyway, I think it's more sensible to represent the 4D magnetic field by a 2D tensor field, instead of having two 1D vector fields.
In nD, we can use either an (n-2) tensor field (the "classical" magnetic field), or it's duel, which is always a 2D tensor field (a bi-vector). The two fields are always perpendicular.
Since very few people here know how to work with tensors, it might be possible to describe them using a pair of vectors. But that's not the same as having three separate fields.

I haven't thought about EM waves using tensors, but I guess it would be pretty simple. You have the electric field oscillating in one direction, and the (classical) magnetic field perpendicular to the electric field and the direction of motion. I do know that Maxwells equations are the same in any dimension (if you replace the cross product with ^*).

[moonlord]

Therefore, the magnetic part would cover a plane and not a line... Right?

[PWrong]

Therefore, the magnetic part would cover a plane and not a line... Right?

Well, not exactly. Actually it was misleading to call it a 2D tensor field. It's really a 4D field of bivectors. You can think of a bivector as a pair of vectors, or as a little segment of a plane. Bo and I have been representing them with the i^j notation, but I don't know if that's the right way to do it.

In 3D, the magnetic field is a vector field. It covers the whole realm, but it consists of vectors, which are like a little segment of a line. There's a little arrow at every point. http://mathworld.wolfram.com/VectorField.html

If you think of a vector field as streamlines, then you can think of the 4D magnetic field as being a family of 2D surfaces. For instance, the field around a straight wire is a series of concentric spheres. That's probably easier to visualise, but it might be misleading.

[moonlord]

Yeah, I got it.... I hope...