As I understand the situation, string theory really has made no connection to reality yet. We don't seem to be able to calculate anything from string theory and confirm those calculations with observation. Or have I misunderstood? For example, we cannot even calculate the mass of a particle yet. Hatfield's book, QFT for points particles and strings, page 485, writes, "We know that all observable particles are not massless, and that the world at ordinary energies is not supersymmetric. Therefore, it is impossible to do true phenomenology from perturbation theory alone. (When we mentioned that some candidate vacuum states gave reasonable phenomenology, the supersymmetry breaking effects had to be added by hand.)" However, we find equations for the mass squared operator on page 513 of Hatfield eq 20.52 and also in Zwiebach's, First Course in String Theory, page 163 eq 9.82 for classical relativistic strings, page 232 eq 12.173 for quantum relativistic open strings, page 255 eq 13.48 for quantum relativistic closed strings, and page 265 eq 13.99 for supersymmetric strings. These are put in terms of the number operator defined in Zwiebach, page 233 eq 12.174. Are these in the general, non-perturbative form that Hatfield speaks of? Is there anything we can learn about the dependence of the mass on, say, frequency and mode number from these equations?