There is the possibility that spacetime has more than 4 dimensions, and that the additional dimensions are curled up not at the Planck scale but at some larger scale. There has been some discussion that if these extra dimensions exist, then the LHC might produce microscopic black holes (which would presumably evaporate immediately). I'm interested in getting a broad overview of what this is about, and would be grateful if anyone could point me to a review paper or post any information here. Is there any physical motivation for assuming these extra dimensions? GUTs? What fixes the scale of these dimensions? Empirically, it presumably has to be less than the de Broglie wavelength corresponding to a TeV or something, since that's the scale we've probed already. Is there some theoretical motivation for fixing this scale at some value? Is there a hypothetical unification that occurs at some energy higher than the electroweak unification energy, which is ~100 GeV? In a classical theory, dimensions with wrapped-around topology violate Lorentz invariance (since there's a preferred frame in which the circumference has minimum Lorentz contraction). Would preexisting tests of Lorentz invariance have been blind to this, since it occurs in a dimension they can't detect? I'm not specifically interested in Planck-scale physics here, but as a side note, I assume that string theory somehow dodges this issue, since string theory has Lorentz invariance baked in; is there any elementary way of seeing that the Lorentz-violation argument above *doesn't* apply to string theory? Is there any reason for disliking the idea, other than "who ordered that?" If the LHC did produce microscopic black holes, would there be any clear experimental signature of that? Thanks in advance! -Ben [EDIT] Re the side-note about string theory -- if the circumference of a wrapped up Planck-scale dimension could be Lorentz contracted, it seems like you could make it Lorentz contracted by any amount you liked. You could contract it to 10^-100 of the Planck scale. Obviously that would be a problem, since there aren't supposed to be observable lengths below the Planck scale, are there?