It isn't our ignorance of Nature that is questioned. It is the nature of Nature to act unpredictably:
We have implied that in our experimental arrangement (or even in the best possible one) it would be impossible to predict exactly what would happen. We can only predict the odds! This would mean, if it were true, that physics has given up on the problem of trying to predict exactly what will happen in a definite circumstance. Yes! physics has given up. We do not know how to predict what would happen in a given circumstance, and we believe now that it is impossible—that the only thing that can be predicted is the probability of different events. It must be recognized that this is a retrenchment in our earlier ideal of understanding nature. It may be a backward step but no one has found a way to avoid it.
No one has figured a way out of this puzzle. So at the present time we must limit ourselves to computing probabilities. We say "at the present time," but we suspect very strongly that it is something that will be with us forever—that it is impossible to beat that puzzle—that this is the way nature really is. The Feynman Lectures on Physics, Vol. 3, pp. 1-10,1-11.
Feynman has summed up the essence of quantum mechanics in surprisingly simple terms:
A philosopher once said, "It is necessary for the very existence of science that the same conditions always produce the same results." Well they don't! —Richard P. Feynman (1965)
Here again is Richard P. Feynman saying unmistakably that the essential nature of physical law is entirely probabilistic:
Philosophers have said that if the same circumstances don't always produce the same results, predictions are impossible and science will collapse. Here is a circumstance—identical photons are always coming down in the same direction to the piece of glass—that produces different results. We cannot predict whether a given photon will arrive at A or B. All we can predict is that out of 100 photons that come down, an average of 4 will be reflected by the front surface. Does this mean that physics, a science of great exactitude, has been reduced to calculating only the probability of an event, and not predicting exactly what will happen? Yes. That's a retreat, but that's the way it is: Nature permits us to calculate only probabilities. Yet science has not collapsed. — Richard P. Feynman, QED: The Strange Theory of Light and Matter (1985), 19.
You can find truly startling illustrations of quantum mechanics in The Foundation of Molecular and Quantum Creationism.
It appears that an inescapable conclusion to be drawn from mainstream quantum theory is that methodological naturalism isn't science.
http://www.everythingimportant.org/video/Richard_Feynman_naturalism.flv
Newton begat physics, and physics begat Lagrangian mechanics and Lagrangian mechanics begat Hamiltonian mechanics and Hamiltonian mechanics begat quantum mechanics. Then quantum mechanics repudiated methodological naturalism.



