The Elegant Universe

by Brian Greene

Using light string modes to measure distances aligns with our conventional notion of length—the one that was around long before the discovery of string theory. It is according to this notion of distance, as seen in Chapter 5, that we encountered insurmountable problems with violent quantum undulations if sub-Planck-scale distances play a physical role. We once again see, from this complementary perspective, that the ultra-short distances are avoided by string theory. In the physical framework of general relativity and in the corresponding mathematical framework of Riemannian geometry there is a single concept of distance, and it can acquire arbitrarily small values. In the physical framework of string theory, and, correspondingly, in the realm of the emerging discipline of quantum geometry, there are two notions of distance. By judiciously making use of both we find a concept of distance that meshes with both our intuition and with general relativity when distance scales are large, but that differs from them dramatically when distance scales get small. Specifically, sub-Planck-scale distances are inaccessible.