Basic question about small curled dimensions in string theory.

[Azuma]

Hi,
I have no knowledge of ST but have a probably simple question.
I saw a program about how the extra dimensions of space in string theory are curled in on them selves. What I want to know is if they really are the same dimensions. Say for example if there are 11 dimensions and I would pick one , the sixth dimension and go into that dimension where it is curled up can I then travel to other curled up sixth dimensions ? Are they connected in the same way that the 2nd dimension of space is arranged like parallel lines while I am in this dimension ? Or are they all separate entities of dimension ?

to be clear when I talk about entering the sixth dimension I am not talking about as a human but in an imaginary way going into one particular instance of a curled dimension.

Does that make sense ?

 

[tom.stoer]

I am sure if I understand you problem correctly.

Take a rectangular piece of paper. Glue two opposite edges together to form a cylinder. Now one dimension is curled up to a circle, whereas the second dimension along the axis of the cylinder remains large. Now you have one small dimension (the circle) attached to one large dimension (the line along the axis of the cylinder). You can move freely along the small and along the large dimension. Even spirals around the cylinder are allowed

You can do similar things with more dimensions, if you like, but of course you can no longer visualize them. In addition in ST the shape of the small dimensions becomes much more complicated.

 

[Azuma]

Yeah I am talking about these small curled dimensions.
Somewhere inside the atom the little curled up dimensions are there all separate like bubbles, if i were to enter one bubble could i see inside all the other bubbles ?
Its similar to in normal space there is a direct line of sight through
out the whole 2nd dimension it is all connected (supposedly).

Or are these bubbles parallel dimensions with no connection between?

 

[haael]

All the additional dimensions are mixed together and we can't assign them numbers. Just as the "big" space - do we see coordinate system in nature? All small dimensions are "connected" with each other and with big dimensions.
If you were very small, you would just see 10D space, no matter what direction.

 

[Azuma]

okay that makes sense about all the dimensions being connected,
would you say that if i were really small and decided to move in dimension '8' i could keep moving in only that dimension and experience all of it, or would i have to move 'sideways' into another dimension to find the next 'piece' of dimension 8.

thanks.

 

[haael]

You could always move in any dimension. You could, i.e. move one angstrem in dimension '8', then change mind and start moving in dimension '6'. Any point in the Universe is equivalent, unless we live on some brane.

You cannot say, that you have experienced "all" of some dimension. It doesn't mean anything. Earth has two compactified dimensions. You can't say, that you have "discovered all longitude". You can still travel to any point on Earth from any other point and that's probably what you want to say.

 

[Azuma]

Thanks, I think that helps me clarify my question. I can compare these bubbles of dimension to planets and my normal concept of dimensions to being in outer space

if i walk around in dimension 2 on planet A and you walk dimension 2 on planet B we will never meet no matter how far we walk, because we are separated like parallel dimensions. However if we were in open space we could meet each other.

saying that I've realized that it is my lack of control over the dimensions other than dimension 2 that prevents me from experiencing 'all' of it'. Because if we were in open space we would likely need to move in the other two dimensions in order to meet.

i might have to think about this some more...

 

[tom.stoer]

I can compare these bubbles of dimension ...

Are you confused because you have seen drawings with these bubbles? Then have a look at may cylinder example; there are no bubbles (just circles if you cut the cylinder) and you can move freely in any direction, regardless if it's a "small" or a "large" direction or a mixture ...