How does quantum mechanics fit into logic?

Quantum mechanics states that we cannot know the position and the velocity of objects with an infinit degree of accuracy. There is inherently some degree of uncertainty in determining a particles position and speed. Therefore, we can only determine the probability of events and the effects they will have. The curious thing about quantum mechanics is that the probabilities of finding a particle's position and speed can combine constructively and destructively very similar to the interference paterns of waves. The paterns created by this interference are directly observable. So it is tempting to associated a physical nature to these probability waves because the mere probability of what might happen has a physical effect on what actually does happen.

The famous example is the double split experiment where if the path of a particle is obstructed by a thin wall with only one slit for the particle to pass through before striking a far wall, then the particle could strike anywhere on the far wall. However, if we put two slits in the obstructing wall, there will be some places in the far wall that the particle will not strike where it would strike if there were one slit. Why does the second slit prevent the particle from striking some places on the far wall? It would seem as though the particle somehow knows that there is a second slit even though it can only pass through one of the slits. This behavior is exactly described by the interference patern of waves.

In the deterministic world view, particles have an exact position and velocity and its trajectory can be calculated to exact positions in the future. Then all the interactions that will ever take place have been predetermined by events in the past, and there is no possibility of changing the future. But in the probabilistic world view of quantum mechanics, the exact position and velocity of particles do not exist in nature. At such small scales the question as to whether the particle exists at a precise location cannot be answered true or false but only with a 0% to 100% measure of certainty. And so there is a question as to whether the universe is consistent with the absolute certainty of logical deduction at its most fundamental levels.

But even at this sub-atomic level of quantum mechanics, no one denies that there is a cause for evey effect that's observed. And no one denies that everything that happens has an effect. Thus, no one is denying the premise-conclusion nature of cause and effect which is how logic is applied to reality. It is only that we don't know the precise cause that we cannot know the precise effect. We don't know exactly where a particle is and where it is going; so we cannot predict with certainty.

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