How Do Curled Up Dimensions in String Theory Affect Matter and Space?

[chingomorph]

i was recently reading "the elegant universe" by bryan greene and i found a problem. first, how can there be, as i understand it, a curled up dimension at every point in space? the curled up dimentions don't touch, i presume, so there must be some space in between them, which i don't think is in accordance with the rest of the theory. also, space is symmetrical, namely matter doen't change as it travels or is translated through space. so how does matter travel through the curled up dimentions without somehow changing? finally, what keeps the curled up dimentions from moving? is there some force in between them, or do they in fact touch?

there is probably a rather simple explenation to these questions and i would appreciate it if someone could help. i was a firm believer in string theory until these problems came up. thanks.

 

[Sojourner01]

I don't know string theory, but I always felt that the 'curled up dimensions' analogy was a very ropey description of a topology problem that's actually very unique. Treating dimensions as 'objects' that can 'touch' just sounds...wrong.

My interpretation is that what the analogy means is that field gradients in these dimensions are so steep that relative to the three (four?) expanded dimensions, it's unrealistic to be able to move far enough to be noticeable in projection.

Consider a flat sheet of paper with a movable point on it. Look at it from some distance, at an arbitrary viewing angle. If you move the point on the paper you can perceive, from your point of observation, movement in the two-dimensional projection of the paper into your eyes. Now take the paper and roll it up very tightly into a tube - almost infinitely tight, in fact. For the point, nothing has changed, it's still free to move anywhere on the paper. For you observing from a distance though, moving the point parallel to the circular path enclosing the tube won't look like anything at all; whereas moving perpendicular to this same path i.e. up and down the tube, will look much the same as before.

Of course this could be completely wrong. Anyone who knows better, please do correct me.