String Theory is the dominant approach right now, and it has some success already, but the question is whether it will develop to the stage where we can actually solve problems that can be tested observationally.If we can’t bridge the gap between this ten dimensional theory and anything that we can observe, it will grind to halt.
In most versions of string theory, the extra dimensions above the normal three are all wrapped up very tightly, so that each point in our ordinary space is like a tightly wrapped origami in six dimensions. We see just three dimensions, the rest are invisible to us because they are wrapped up very tightly.
If you look at a needle, it looks like a one dimensional object from a long distance, but really it’s three dimensional.
Likewise, the extra dimensions could be seen if you looked at things very closely. Space on a very tiny scale is grainy and complicated–its smoothness is an illusion of the large scale.
That’s the conventional view in this string theories.
An idea which has become popular in the last two or three years is that not all extra dimensions are wrapped up–that there might be at least one extra dimension that exists on a large scale. Raman Sundrun and I (Lisa Randal) have developed this idea in our work on branes.
According to this theory, there could be other universes, perhaps separated from us by just a microscopic distance; however that distance is measured in some fourth spacial dimension, of which we are not aware. Because we are imprisoned in our three dimension, we can’t directly detect these other universes.
Lisa Randal on Theories of the Brane
The Universe, Edge.org