The following may be a little on the technical side. It deals with some thoughts about physics that have been going through my head lately.

One of the most important open questions facing high-energy physics in the next century is to explain the curious experimental fact that at low energies, the universe appears to be a smooth manifold, with four large dimensions and a locally Minkowskian signature, i.e. three space dimensions and one time dimension.

None of these are obvious principles because we know that there are circumstances in which each of them are violated. At sufficiently high energies, manifold structure itself breaks down. The number of dimensions is, at this point, wholly unexplained; string theory prefers 10 or 11, and why 6 or 7 of these ought to roll up into very small dimensions while four remain very large is mysterious to say the least. Minkowskian signature may follow naturally out of whatever solves the first two problems, or it may not; physics with multiple time dimensions is very strange (imagine being able to go in a loop in the time plane!) and physics with zero time dimensions is, well, rather static. Even in the context of string theory, we know of several “ground states” of the theory that don’t look like manifolds at all, but like collapsed spacetimes that nonetheless have very nontrivial dynamics. (e.g., the Gepner point)

I believe this question can be summarized as “Explain 4.” (4 being the number of large dimensions. If you can explain that to reasonable satisfaction, you can probably explain the rest in the process)

(The following is somewhat more technical)

Conjecture: My sense is that some suitable improvement of string field theory (that takes supersymmetry and closed strings and so on into account) is correct and a good model of the “underlying system.” The [nonassociative] string field algebra would then encode, not just the macroscopic geometry of the universe, but the “stringy geometry” including all brane effects, etc. SFT on different algebras should correspond to perturbative string theory on different (classes of?) background spaces. There will be some “usual set” of string field algebras that correspond roughly to things that look like ordinary manifolds at long distances. Studying SFT on more general nonassociative (etc) algebras should give us a much clearer picture of what the possible kinds of spacetime (and other) can emerge in a physical context.

Of particular interest, a fuzzification of the string field algebra (i.e. an approximation of this algebra by a sequence of finite-dimensional algebras) could describe an approximately continuous spacetime at large distances, breaking down to a noncommutative spacetime at shorter distances, and could even have finite total entropy as required (cf. Tom Banks’ ideas) for our universe to have an approximately de Sitter shape on cosmological scales.

A full understanding of this system probably requires understanding not just SFT on a single algebra, but transitions between algebras. The simplest case of this will probably look like the “algebra-adding” rules one finds when noncommutative algebras emerge from putting multiple D-branes close to one another and looking at the dynamics of strings on their surface. In that situation, allowing the D-branes themselves to be dynamical objects means allowing transitions between algebras; a mathematically similar process (although not necessarily a physical one) will very likely happen in the SFT case.