The first postulate characterizes the granularity of quantum mechanics: the fact that a finite number of possibilities exists. The second characterizes its indeterminacy: the fact that there is always something unpredictable that allows us to obtain new information. When we acquire new information about a system, the total relevant information cannot grow indefinitely (because of the first postulate), and part of the previous information becomes irrelevant, that is to say, it has no effect anymore upon predictions of the future. In quantum mechanics, when we interact with a system, we don’t
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