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Author Topic: Can extra dimensions be spherical?  (Read 2468 times)

Offline DoctorBeaver

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Can extra dimensions be spherical?
« on: 23/07/2008 18:56:43 »
In the literature I've been reading, they mention extra dimensions that are curled up into cylinders or Calabi-Yau manifolds.

I though the laws of physics were supposed to treat all directions as equal. So, if there is a force, or energy, causing the dimension to curl into a cylinder, why doesn't that force/energy act perpendicularly and cause it to collapse into a sphere or point?


 

Offline LeeE

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Can extra dimensions be spherical?
« Reply #1 on: 25/07/2008 01:01:01 »
They all tend to require closed spaces in the same way that an object in orbit around a planet, while following a straight (one-dimensional) line in curved space, defines a two dimensional area.

No idea about forces or energy causing dimensions to collapse because I'm not aware of any models describing exactly how/why this force or energy causes the 'curl' in the first place - it just seems to be an arbitrary rule that's required to make it all work.
 

Offline DoctorBeaver

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Can extra dimensions be spherical?
« Reply #2 on: 25/07/2008 08:27:01 »
Thanks LeeE
 

Offline LeeE

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Can extra dimensions be spherical?
« Reply #3 on: 29/07/2008 23:23:46 »
Actually, a thought came to me about this earlier today.  Energy/mass equivilence could be responsible for curling extra-dimensional spacetime via gravity, although it seems that it would have to be either directional, or not present in all the dimensions, to avoid total collapse:  If the curling energy was in the shape of a two-dimensional surface it might only have an effect in the dimensions where it has non-zero size.
 

Offline DoctorBeaver

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Can extra dimensions be spherical?
« Reply #4 on: 29/07/2008 23:37:10 »
If the curling energy was in the shape of a two-dimensional surface it might only have an effect in the dimensions where it has non-zero size.


For argument's sake, let's say the 2 dimensions are up/down & left/right. The top, bottom, left & right would all be pulled towards the centre. It still wouldn't curl into a cylinder.

The only way I can see that it could curl into a cylinder is if the top were pulled to the bottom and the 2 sides were unaffected - and that means that not all dirctions are treated equally. And even then, curling into a cylinder would imply some force acting from the centre to repel the surface so that it curled rather than compressed or crumpled.

Surely, curling into a cylinder would imply an almost magnetic type of force where the north & south poles would be attracted to each other but the sides would be unaffected. Gravity certainly doesn't act that way.
« Last Edit: 29/07/2008 23:39:17 by DoctorBeaver »
 

Offline LeeE

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Can extra dimensions be spherical?
« Reply #5 on: 30/07/2008 00:21:00 »
Ah - don't forget that the up/down & left/right is the shape of the energy causing the curling of the dimension, not the shape of the dimension itself.  It would be more like standing a coin upright on a sheet of paper, with the sheet of paper then wrapping itself around the coin.

It's all very debatable though - if it's the width of the sheet of paper that gets wrapped around the coin, is it reasonable to assume that it will occur along the entire length of the sheet?  It might just pinch the sheet into a cylinder in the region of the coin but leave it open at all other points.
 

Offline DoctorBeaver

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Can extra dimensions be spherical?
« Reply #6 on: 30/07/2008 08:14:43 »
Sorry, I misunderstood.

It's an interesting idea. I shall ponder on it for a while. Expect more stupid questions later!  :D
 

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Can extra dimensions be spherical?
« Reply #6 on: 30/07/2008 08:14:43 »

 

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