Magnetism

[swirl gyro]

I'm wondering how magnetism would work in 4D. Ok like, what would the field be shaped like around a simple loop of electricity? There wouldn't be poles, would there?

[PWrong]

I started a post like this in the general forum a while back. We didn't get very far with the idea. It's difficult to visualise a thin wire in 4D, with invisible lines of force around it. The magnetic field has to rotate around a single axis, but there's three other axes, so I don't know how it would work.

I do think you would get magnetic poles though. You could use a "hyperblock" (like a tetracube, but longer in one direction). This could be magnetised just like a 3D magnet.

A 3D magnet is equivalent to a block of soft iron with an electrified coil of wire wrapped around it. That might give us some clue as to the 4D magnetic field around a wire.

Unfortunately, I have no idea how you would wrap a wire around a 4D shape. It seems like there would be more than one way to do it. Anyone have any idea?

[Keiji]

Only planar shapes can be wrapped around 4D axles.

[PWrong]

Hmm. I forgot that. Why is that exactly?

Maybe 4D electricity is planar then. That doesn't make sense, electrons should move in lines.

[Keiji]

You cannot wrap a line around a flunar axle just as you cannot wrap a point around a realmar axle. :wink:

[PWrong]

That's what I thought at first, but you can't wrap a point around a square either. Then again, I suppose you could wrap a 0-sphere (which is just two points) around a square, but not a cube.

The 2D analogue of a 1-D coil wrapped around a cube would be a square with two sides covered in points. It seems like you wouldn't be able to cover 4 of the 6 faces of a cube with a 0-D coil, without changing the radius.

It all depends on what you mean by "wrap", of course. If a line can't wrap around an object, what can it do?

For an axle of any dimension, and a string, or 1-sphere, of arbitrary length. I'll suggest that the following is true. I'm not sure, someone can tell me if I'm wrong. You can put a large circle in the string, put the axle through the circle, and then tighten the knot. Then with the string left over, you make another circle, and do it again. And so on. The problem is you can only cover 4 sides/faces/cells in this manner. So you can wrap a square entirely, or wrap a cube with the front and back faces remaining, or wrap a tetracube with the front, back, apos and zapos cells remaining.

Unfortunately, that kind of wrapping won't produce the same magnetic field as a 4D magnet. Maybe electricity should move through planes. But if you wrapped a planar wire around a flunar axle, would the electricity generate the correct magnetic field?

I haven't looked at the geometry forum much, but it seems like problems like this can only really be solved using vectors and maths notation, since we can't actually visualise the objects.

[PWrong]

Wait, I did make a mistake. You can't tie knots in tetraspace, so the coil would fall apart. So planar wires it is. That makes it confusing. Does anyone know how electricity moves through a flat sheet of metal?

More importantly, how can a simple electric circuit work with a sheet instead of wires? You'd need a linear battery, for one thing.

[Keiji]

Does anyone know how electricity moves through a flat sheet of metal?

Each electron would move linearly. When they bump into each other or the edge of the metal, they bounce. So, as a whole they would appear to move in a plane toward one direction. :wink:

[PWrong]

Ok, that's what I guessed. So a plane connected to a linear battery would be similar to a bunch of linear wires placed close together in a plane, and each with their own battery. The magnetism would be the same as well.

Ok, I think I can visualise this now. Imagine a hypercube, with one cell behind another. Now think of it as exactly what it looks like, a cube inside a larger cube, just for a while. I'll call the cubes "inside" and "outside" to reflect this.

Imagine wrapping a sheet of metal around each of these two cubes, leaving the top and bottom faces uncovered. One of the vertical edges has a linear battery to create a planar circuit. Electricity flows around anti-clockwise. According to traditional magnetism, a magnetic field should flow up, through the top face of the cube. Now with both cubes together, the magnetism flows up through the top cell of the hypercube.

I think I can now figure out the different magnetic fields for a cubindrical, spherindrical and duocylindrical coil.

[PWrong]

I haven't had any luck visualising it, but I learnt something about magnetism which makes it seem a bit less arbitrary.

When an electron spins around an atom, it effectively acts as a tiny electric loop, and creates a magnetic field. When atoms are aligned so that electrons can quickly pass from one to the other, like in a circuit, the magnetic fields so that they affect the alignment of the atoms around them, so the overall effect is the circular magnetic field. So the first thing we need to understand is the magnetic field of a 4D atom. Ideas anyone?