>and so the probability must be different from P. Not if they interfere in just the right way to keep the probability the same as in P. I see a second problem

>and so the probability must be different from P. Not if they interfere in just the right way to keep the probability the same as in P. I see a second problem with this experiment - in the double slit experiment, there is one electron interfering with itself. If you released two protons at the same time, they'd interact with each other and change the probabilities, even classically.