Samantha- Your background introduction is beautifully clear and spot-on. Please consider coming to study physics at UIUC. Your teacher sounds amazing as well.
As for your question, it's too hard for me, so I'll forward it to a string theorist. I'm sure the answer is that SR emerges as correct on spacetime scales large compared to the Planck scale in regions which are intrinsically flat, but I'm not sure what the limits are on that conclusion. Certainly if there are some other extended dimensions you can get effects which would never show up in plain SR. There may be other symptoms as well, which I hope we'll both soon learn about.
I guess what we're talking about here is an example where spacetime is S^1xR. There is a frame in which space is S^1 and time is R (the reals). The best way to think of this is as a 'compactification' of flat spacetime, RxR. We regard the circle S^1 as R/Z (reals mod integers), which means if we take a coordinate x along R, we regard a point x and a point x+2\pi m R as equivalent (for m an integer and R the radius of the circle).
This compactification breaks the Lorentz invariance of the 'covering space' RxR. To see this, start in the frame that I was discussing above, but impose the identification (x,t) ~ (x+2\pi R, t). If we boost to another frame, this identification becomes
(x',t') ~ (x',t') + 2\pi R (\gamma,v\gamma)
where v is the velocity of the frame (in units c=1). Note that (\gamma, v\gamma) is a unit spacelike Lorentz vector (which in the origin frame was just (1,0)). Thus, to specify the compactification, we have to select a fixed unit spacelike Lorentz vector, and this is where the notion of a 'preferred frame' comes from.
In string theory, what often happens is that we soup up this example to include extra large flat dimensions (that are not compact). So spacetime might be of the form S^1xR^3xR (compact direction, space, time). The 5-dimensional covering space has 4+1 Lorentz symmetry, but the compactified space has only 3+1 Lorentz symmetry (one can still boost along the large flat directions) -- one spatial direction is distinguishable from the other 3).
(published on 01/25/2010)