How can a dimension be small ?

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how can a dimension be "small" ?

Sorry, I'm not much of a physicist. I have read that extra dimensions may be "small" and curled up. Since height, width, and depth appear to be limitless, I am having a hard time understanding what small means when applied to dimensions. I suspect it has something to do with our 3 spacial dimensions being "flat".
 

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  • #2
Hurkyl
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Imagine that you went forward in a straight line for 100 meters and discovered that you are now in the exact same place you started.

Loosely speaking, that's what "curled-up" means.


Now, imagine you only have to go 1.6*10-35 meters before you return to the place where you started. That's "small".
 
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OK, but

small and curled up could be contained in any of our 3 spatial dimensions. In this case the dimension itself is small and curled up, correct?
 
  • #4
Hurkyl
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In principle, a universe with 3 spatial dimensions could have them all be small and curled-up, but a brief observation proves that this is not the case for our universe. :smile:
 
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Image that your friend is 0,00000000000000000000000000000000001m high:D
 
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Sorry, I'm not much of a physicist. I have read that extra dimensions may be "small" and curled up. Since height, width, and depth appear to be limitless, I am having a hard time understanding what small means when applied to dimensions. I suspect it has something to do with our 3 spacial dimensions being "flat".
Height, width, and depth actually do appear to be limited. Or at least, there is a smallest possible length, based on the Planck length, which is very small indeed. The idea is that anything smaller would collapse into a mini black hole and dissappear. This result is due to Max Planck, who showed in the early part of last century that certain problems involving black body radiation went away if you assumed a minimum possible length. This minimum length has been generalized to a minimum possible time, the Planck time, and a minimum possible energy, the Planck energy.
 
  • #7
DaveC426913
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Height, width, and depth actually do appear to be limited. Or at least, there is a smallest possible length, based on the Planck length, which is very small indeed. The idea is that anything smaller would collapse into a mini black hole and dissappear. This result is due to Max Planck, who showed in the early part of last century that certain problems involving black body radiation went away if you assumed a minimum possible length. This minimum length has been generalized to a minimum possible time, the Planck time, and a minimum possible energy, the Planck energy.
Well yes, but that's not the same as having a small upper limit, which is what the OP is asking about.
 
  • #8
DaveC426913
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Hurkyl's respone is what you should concentrate on.

The size of a dimension is defined by how much freedom you have to move in it before you "wrap around".

Imagine an ant walking on a gardenhose; The ant's universe is 50 feet long in one dimension but only 2 inches in another. The ant's travel is unbounded, yet he does not have complete freedom of movement.

One theory of the universe is that length, width and depth are not infinite but will wrap around over billions or trillions of light years.
 

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