# Differentiating quantum mechanics and string theory

It was surprising to learn how difficult it is classify a theory as classical or quantum based on criteria (PDE, complex numbers, axioms, probabilities, Planck constant, and realism). Rreference, “What makes a Theory Quantum”, (What makes a theory "Quantum"?). My question, if String Theory were included in the comparison, how would the criteria differ and would there be a clear distinction? Thanks

• There isn't much of an issue classifying string theory as quantum since it uses the same formalism as every other quantum theory, path integrals and Hilbert spaces. – Slereah Apr 18 '18 at 14:29
• People doing loop quantum gravity call what they do a type of "canonical" quantum gravity, which I guess lays their claim to be doing the only natural generalization of quantum mechanics to include gravity. Of course I'm sure string theorists would disagree. – Ben Crowell Apr 18 '18 at 15:14
• The distinction between quantum and classical is very subtle, especially in string theory since there are, in a sense, two $\hbar$s: the string length squared, $\ell_s^2=\alpha'$, (which is the $\hbar$ of the 2d theory) and the string coupling constant, $g_s=e^{\Phi}$, with $\Phi$ the dilaton (which is the $\hbar$ in the spacetime theory). Furthermore, string dualities mix these two in surprising ways. E.g., summing string loops (all powers of $g_s$) can lead to a theory that looks classical from a spacetime viewpoint. – Wakabaloola Apr 18 '18 at 20:47
• Some related comments can be found in the popular science article: sns.ias.edu/ckfinder/userfiles/files/Reflections(3).pdf – Wakabaloola Apr 18 '18 at 20:47
• Thanks for the reference, which introduces string tension as a new fundamental constant analogous to the Planck constant. The new constant implies quantum mechanics (if I correctly understood Witten’s article). I was initially thinking that there might a “branch” of math or criteria which is unique to String Theory. This constant may be the key mathematical distinction. – Jim Johnson Apr 21 '18 at 15:20