vektruscen said:
'These 6 dimensions are compacted to such a degree that they cannot be seen.'
Are they within our universe? How big are they? What goes on inside of them?
As I understand things, the way that string theorists like to think about the extra six dimensions is as a "
Calabi-Yau manifold". This is a particular mathematical way of describing the geometry of a space which is "curled up" in the way that the extra dimensions in string theory are believed to be curled up. Each Calabi-Yau manifold gives a different way of "curling". I think string theorists have some preferred way of visualizing these Calabi-Yau manifolds, but I'm not sure.
When we say the dimensions are "curled up" we mean that they loop back on themselves, so that the dimension has a "size" and if you travel the distance of that size you come back to where you started. The "size" of these dimensions would have to be absolutely tiny, like on the scale of the Planck length. So movements in these dimensions would make no difference to us. However
althoughthese extra six dimensions are of no interest to macroscopic objects like us, since
the equations of string theory behave differently depending on the details of the background geometry, the choice of calabi-yau manifold causes string theory to behave slightly differently.
There is also a version of string theory with "large extra dimensions". Here "large" means, like, as big as a centimeter. In this case our four dimensions are embedded in a larger space, but everything in our four-dimensional space is somehow "stuck" on the 4D manifold (except gravitons, which at least in some versions of this idea can leak out of the manifold into the "bulk"). I do not *think* this version of the theory is as popular as the version with small curled-up extra dimensions (?), but you hear about it sometimes because there is a
specific side effect if it is true, which means it would be potentially possible to see evidence of it at the LHC.
