Do physicists ever expect to be able to derive the fundamental constants of nature from theory? For example, if string theory or some other theory unites the four forces, would the theory be considered complete if it relies on these measured constants, or would a true theory of everything (TOE) require that these constants come out of the theory itself?
A physical theory needs many experimental inputs - form of equations and constants in them. A theory claiming to be able to calculate all constants in its equations is mathematics, not physics. A recent take on it is presented by S. Weinberg here.
In this case, opinions diverge.
Some people claim that only two constants are needed: the speed of light $c$ and the string length $\lambda_s$.
Other think that you also need $h$.
You might want to have a look at: http://arxiv.org/abs/physics/0110060
The following constants might vanish (e.g., place-dependent behaviors along a dimension, built-in identifiers that assign access along a string [ push-forward ], carrier-entropy) or transform--as in a qubit (a decision) flinching characteristically from dimensional memory, where the amount of the flinch is just the carriernormal length--when the initial interior entropy & the final exterior curvature are equivalent: (1) the inertia (here to be the expected mass of the up quark; (2) the fundamental curvature=1/the Planck length; (3) dV sub E,G (electrical, gravitational work rate beyond the exterior mass on the Total Universe (the canonical sum of all current universe's [ tensor and/or Higgs fields? ]); (4) -1/qubit which approaches the inertia at our current Universe observable edge; (5) a Total Count times the carrierhole coupling constant such that all events approach all decisions (the current Universe is an event; and (6) the 8 lower and 8 upper dimensions but still normalized to 11?