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Ken G said:If the universe is fundamentally probabilistic, then it is not fundamentally unitary in its time evolution. If I can prepare two particles as spin up, and do a sideways spin measurement, I can get left or right for different particles with equal probability, which we might regard as just fundamentally how the universe works. But since the initial states were superpositions of left and right, and the final states are one or the other, that's not unitary, if it's fundamentally probabilitistic. That does imply a lack of unitary evolution when you do an observation and only get one outcome.
I see what you mean. However, it's really not clear what it would "mean" to see superpositions, so the fact that we don't see superpositions is sort of a mystery, but doesn't really contradict any assumption about unitary evolution.
To "notice" that a system is in a superposition of states means that it's possible to make a decision based on whether the state is pure or not. But there is no way to do that. There is no way to make a machine that prints out "yes" if the system it observes is in a superposition of states and "no" otherwise.