size of kaluza-klein dimensions

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size of kaluza-klein dimensions

Postby PWrong » Sun Nov 05, 2006 4:18 pm

I was thinking about kaluza-klein theory again, and what might control the size of the extra dimensions. Kaluza Klein theory says that the universe has small extra dimensions that we can't see, kind of like a sheet of paper looks 2D, but actually has a small thickness.

Anyway, I was wondering, why does the thickness have to be constant? Imagine if the extra dimensions were being constricted by mass. In regions close to a star, they would be almost impossible to detect. But out in deep space, either interstellar, or if you want to be less extreme, intergalactic, they would be actually noticable. If you went out there, your atoms would gradually fall apart. Some physicists already believe gravity is "leaking" into extra dimensions. It might also explain some of the annoying things that require dark matter/energy. Any thoughts on this idea?
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Postby Nick » Sun Nov 05, 2006 8:28 pm

I always thought of Kaluza Klein theory as this:
Imagine a perfectly two dimensional piece of paper. That's the 2d world.
Now, imagine thin rolled up pieces of paper sticking up from the center of it. The thin piece of paper would be a small pocket of higher dimensional space.
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Postby PWrong » Mon Nov 06, 2006 1:22 am

My analogy was technically wrong. You have to embed the paper in 4D space to visualise it. A better example is the surface of a garden hose. From far away, it looks 1D, but close up you can see a second dimension.

My idea would be like a garden hose that bulges where there's no matter to constrict it, so the radius increases.
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Postby Hugh » Mon Nov 06, 2006 2:19 am

PWrong wrote:A better example is the surface of a garden hose. From far away, it looks 1D, but close up you can see a second dimension.

Closer still, you can see a third. I think if we went down to a small enough level we'd see at least a 4th. ;)
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Postby PWrong » Mon Nov 06, 2006 4:49 am

I'm talking about the surface of the hose. You need two numbers to specify the position of a point on the surface.
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Postby Hugh » Mon Nov 06, 2006 1:29 pm

PWrong wrote:I'm talking about the surface of the hose. You need two numbers to specify the position of a point on the surface.

If there are existing compactified dimensions, wouldn't you need more?
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Postby PWrong » Mon Nov 06, 2006 2:37 pm

I don't know what you mean. For the garden hose, there is one extended dimension, and one kaluza klein dimension. In the sheet of paper example, there's two extended, one small. In string theory, there's 3 extended, 6 curled up. In my idea, the 6 curled up dimensions start to come unfurled as you move away from regions of high gravity.
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Postby Hugh » Tue Nov 07, 2006 1:45 am

PWrong wrote:I don't know what you mean. For the garden hose, there is one extended dimension, and one kaluza klein dimension. In the sheet of paper example, there's two extended, one small. In string theory, there's 3 extended, 6 curled up.

Even if the higher dimensions are curled up, the particles that make up the hose would exist in that space, and have those higher dimensions themselves, as in this picture of a calabi-yau space.

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The surface of the hose might actually look like this:

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PWrong wrote:In my idea, the 6 curled up dimensions start to come unfurled as you move away from regions of high gravity.

If this were true, wouldn't the light from distant stars look more spread out than pinpoints?
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Postby PWrong » Sat Nov 11, 2006 2:46 pm

Even if the higher dimensions are curled up, the particles that make up the hose would exist in that space, and have those higher dimensions themselves, as in this picture of a calabi-yau space.

So you're saying that the hose has one extended dimension, one curled up dimension, and six dimensions that are even more curled up? That's true, but it's kind of irrelevent to the analogy.

PWrong wrote:
In my idea, the 6 curled up dimensions start to come unfurled as you move away from regions of high gravity.

If this were true, wouldn't the light from distant stars look more spread out than pinpoints?

I don't think so. I think light would be refracted by the extra dimensions, but I can't see why it would spread out. You'd need to do some maths to work out what actually happens.
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Postby Hugh » Sat Nov 11, 2006 4:57 pm

PWrong wrote:So you're saying that the hose has one extended dimension, one curled up dimension, and six dimensions that are even more curled up? That's true, but it's kind of irrelevent to the analogy.

I'm just trying to understand it all myself. If I think that each individual particle that makes up the hose, has all those dimensions on a very tiny scale, but we look at it from a macro scale, we don't see those higher dimensions, but they are actually still there.

If a point is specified on the surface of the hose, it would, in reality, on a micro scale, have to be specified in all of the existing dimensions.
PWrong wrote:I think light would be refracted by the extra dimensions, but I can't see why it would spread out. You'd need to do some maths to work out what actually happens.

Agreed. :)
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Postby PWrong » Sun Nov 12, 2006 9:24 am

If a point is specified on the surface of the hose, it would, in reality, on a micro scale, have to be specified in all of the existing dimensions.

Yes, that's true of a physical hose, but it's also true of the whole universe.
We can conceive of a hose-shaped universe that has one large dimension, a single curled up dimension, and nothing else. The inhabitants of this universe would think they are line segments, but they could actually be 2D blobs.
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Postby Hugh » Sun Nov 12, 2006 12:25 pm

PWrong wrote:We can conceive of a hose-shaped universe that has one large dimension, a single curled up dimension, and nothing else. The inhabitants of this universe would think they are line segments, but they could actually be 2D blobs.

Similarly, this might possibly be true for us, thinking we're only 3d, yet actually being higher dimensional ourselves.
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