I am not a physicist, but I am very much into popular science, especially string theory. I would like to know if it is conceivable that string theory might be able to get rid of the randomness apparent in quantum processes.
For example, radioactive decay, could this process be related to the particular phases of the vibrations of the strings composing the particle? Can it be that decay occurs when a certain constructive interference occurs between the strings?
No, it's not possible. The reason is that string theory is a quantum theory. That means it includes all of the properties of quantum theory among its basic assumptions. That includes the Born rule, which relates wavefunctions to stochastic probabilities ("randomness") when measurements are made. Because string theory includes quantum randomness as an assumption, it can never hope to explain it.
This is true of almost all theories in modern physics. Quantum mechanics is seen as so basic and fundamental that it needs no explanation.
