For more information on this very interesting question, look up “hidden variables”. This was the idea (much favored by Einstein, among others) that the apparent randomness in quantum mechanics was an illusion, and that there were physical variables governing these processes that we just couldn’t observe (whether because of our technological limitations, or inherently). For instance, an atom of carbon-14 might have some sort of “clock” inside of it, and when the clock wound down to 0, the atom would decay. The current time on that clock would then be a hidden variable.
Unfortunately, there are some serious problems with hidden variable models. Bell found that, for some experiments, any physical model dependant on local hidden variables would produce results different from those predicted by quantum mechanics, and when the experiments are actually performed, the results match QM, not hidden variables. The results can still be explained using nonlocal hidden variables (that is to say, they can “communicate” with each other faster than light), but many physicists find such models distasteful, since then you have to invoke some sort of censorship to keep the FTL communication from being used in a non-hidden way.