(See Part 1 here. Also I am going to suspend the limit of three comments per post for this series of posts because it is a topic that benefits from back and forth discussions.)
It looks like I may have not been sufficiently precise in my first post, leading to some confusion, so I am going to take a slight detour from my series of posts on this topic to address an issue that came up in the comments about the nature of the probability and statistics that is used in quantum theory and how it differs from what we use in everyday life, in particular, the nature of the uncertainty in predicting outcomes. (As always with quantum mechanics, since the phenomena involved are invisible to our senses and often counter-intuitive, we have to use analogies and metaphors to try and bring out the ideas, with the caveat that those never exactly represent the reality.)
Let’s start with classical statistics that we use in everyday life in a situation where the results of a measurement are binary. Suppose that we want to know what percentage of a population has heights less that five feet. If we measure the height of a single person, that will be either more or less than five feet. It will not give us a probability. How do we find that? We take a random sample of people and measure their heights. From those results, we can calculate the fraction of people less than five feet by dividing the number in that category by the size of the sample. That fraction also now represents the probability that if we pick any future person at random, that person will be shorter than five feet. When we pick a random person, we do not know which category they will fall into but we do know that it will be either one or the other. What we also believe is, that in the classical world, each person’s height was fixed before we measured it. We just did not know it beforehand.
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