Physics doesn't directly try to answer questions about fundamental numbers with units (like mph) because you get completely different numbers if you switch units. So physics focuses on dimensionless ratios. These include ratios of masses of different particles, the ratio e2
/hc, where e is the unit charge, h is Planck's constant, and c is the speed of light, etc. Many of these, like e2
/hc (called the fine-structure constant), have c in them. So I'll translate your question to being about those ratios.
So with that warm-up, the answer is still sort of no. Many string theorists had great hopes that a fully developed version of the theory would generate a unique solution, in which all those dimensionless ratios would emerge. That's still conceivable, but it's not the consensus any more. Now it looks like string theory will generate a large number of solutions which are stable for very long times. Within that huge family of solutions, many different combinations of fundamental ratios could be found.
It's become increasingly popular to suspect that all the solutions exist, and that the particular values we find are set by a peculiar constraint: only special values are consistent with complex chemistry existing for long times. Domains with other values don't have anybody in them to ask "why?" This sort of argument is called "anthropic". I've talked with string theorists who find it to be an anti-scientific negation of the purpose of their life's work, and others who find it to be the natural interpretation of what's currently known.
(published on 06/02/2011)