It wasn't the relation between T-duality and the idea of a "bounce" I was addressing. I was correcting the idea that T-duality allows the possibility that the universe may in some sense be both contracting and expanding. I'll get to the relation between T-duality and the pre-big bang or "bounce" scenario below. Also, one can imagine that certain dimensions might expand while others do something else, but again, this has nothing to do with T-duality, and in fact can even be considered independently of SMT (String/M-theory).Originally posted by Mentat
Another question: What is the string explanation for the Big Bang? I had always thought that this t-duality was what was used to explain the postulated "bounce" effect, but now I see I was mistaken in that, so it leaves this question open again.
Firstly, T-duality (which as I've explained relates theories on large and small tori) is just one type of a web of dualities that relate different descriptions of the same physical systems in SMT.Originally posted by Mentat
So, basically, t-duality is just the duality that unifies some of the different string theories, by creating a symmetry between the physics of higher and lower tori...aren't those higher tori what "branes" are, or is that a different concept also?
We'll suppose that spacetime has p noncompact spatial dimensions and one compact dimension given as a circle of radius R. D-branes appear in connection with T-duality as it applies to open strings. The T-duality transformation
(1) R → R′ = α′/R
produces a different but physically equivalent description in which open string endpoints can't move in the compact direction, now of radius R′, but only in the spatial hyperplane extended in the p noncompact spatial directions. However the rest of the string can move in all p+1 spatial dimensions.
Such hyperplanes are actually autonomous objects in their own right, D-branes. Their definition is in fact as surfaces upon which open strings end. Their dynamics are described by the compact components of the massless excitations of open strings whose endpoints live on them. Thus these massless excitations of open strings are in the T-dual picture physically equivalent to fluctuations of the D-branes on which they end.
This picture is greatly enriched by charging open string endpoints with U(n) gauge degrees of freedom and introducing a corresponding flat gauge field background for them to interact with. In this case, the spacetime coordinates of D-branes become noncommuting quantities suggesting that spacetime itself is quantized, but it's true meaning is currently a mystery. It's really in the full supersymmetric theory that D-branes have been so important in identifying the different dualities by which the many nonperturbative results have been established.
The space of inequivalent theories under the T-duality transformation (1) are thus given by R ≥ α′½ suggesting that the string scale α′½ represents in string theory a minimum observable length i.e. an ultraviolet cutoff, and there's considerable circumstantial evidence that it is. In particular, space-time singularities are expected to be avoided (or at least reinterpreted) in any geometric model of gravity which is compatible with string theory. In other words, in quantum string theory, relativistic quantum mechanics should solve the singularity problems in much the same way as non-relativistic quantum mechanics solves the singularity problem of the hydrogen atom, by keeping the electron and the proton a finite distance apart.
As a result, string theory allows us to formulate scenarios in which the universe can be sensibly said to "smoothly" pass or "bounce" from a collapsing to an expanding phase. In this way, string theory gives us a rationale for asking what there was before the big bang, and in no other currently available framework can such a question be meaningfully asked.
If you'd like more detail on any of this stuff, don't hesitate to ask.