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[Alex K]

Alex, I have a question concerning the dimensions in SST.  My understanding is that most of them are found at the tiniest scales.  Does this mean they are in some way fractal, and if so, could you INFER something reasonable about some kind of super-dimension despite the observational breakdown at the event horizon of the BB singularity?  In other words, is there any possibility of unifying all the dimensions under a single principle or mathematical relationship, say it's turtles all the way down, and then extend that principle upward as well?

Or am I just talking out my ass?

The role of space in Superstring Theory is interesting and sometimes controversial. In the usual approaches to superstring theory, a smooth ten-dimensional spacetime is usually assumed as a starting point because the quantum theory of supersymmetric strings demands it for consistency. (This assumption of a smooth geometry as a starting point is sometimes criticized by proponents of more audacious approaches to quantum gravity such as loop quantum gravity, in which you basically take nothing for granted, which leads to horrible technical challenges.) Closed strings are actually nothing but gravitons and hence fluctuations of spacetime itself, and so, the presence of a closed string indicates a small fuzzy deviation from flat space. If you zoom in, you will find the string having loops and holes and twists of all sorts, corresponding to arbitrarily complicated deformations of space at small scales, and this could, I suppose, look as if space was fractal. However, I have never heard it claimed by real string theorists (I have only dabbled in string theory from a field theorist's perspective) that the spacetime they formulate their theory in has anything but exactly 10 dimensions, not some weird fractal dimension. Maybe that's because there is an intrinsic string length related to the planck length, and I would venture a guess that below this length, deformations of the string, and hence of spacetime as well, are strongly dampened, smoothing out the fluctuations of space at the smallest scales and ensuring a well-defined dimensionality. But I am not sure at all.

An amusing side note: in order to get rid of infinities in quantum field theory, Nobel laureates Martinus Veltman and Gerardus 't Hooft have invented a mathematical scheme that is now universally used in calculations called dimensional regularization, in which it is assumed as a mathematical trick, that the dimensionality of spacetime is some noninteger number d. Only after all calculations are done and observable quantities are expressed in terms of other observable quantities is the limit d->4 taken, and the infinities are gone. People have entertained the thought that maybe, nature actually has a noninteger number of dimensions close to 4, and that this is more than just a mathematical trick, but that is a complete pipe dream.

In recent years, string theorists have considered scenarios which are non-geometric, i.e. the quantum structure of the additional space dimensions is so weird that it cannot be expressed in terms of usual geometry. I know next to nothing about how that works, though.