Another confusion: How many measurements is "many"? Since quantum mechanics gives only statistical prediction, we actually need numerous measurements to verify the theory. But how many measurements will make it statistically meaningful? Let's say we want to verify the uncertainty principle, we make two measurements of the momentum and position. If the results of two measurements just happen to be the same, then the standard deviations are 0, it'll make delta x*deltap=0. Of course we can say only two measurements won't make the result statistical, but how many is "many"? 100, 1000, 10000? What's the criterion?