ryan
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Would you mind providing this evidence of hidden variables?
Since you claim to have overwhelming evidence of determinism, would you be able to use that knowledge to predict/determine - beforehand - which slit a single photon goes through and the known mechanism that causes it to go through that particular slit?
You cannot know, even after the event, which slit it went through. You may address the probabilities, though. It came all ways weighted by probability. Beforehand all you know is that it will go all ways weighted by probability. We can only predict a pattern after multiple trials. One trial? Random.
Oh yeah, I was thinking about what happens when detectors are in the slits, but then I guess that isn't really a probabilistic system anymore. It would act in a classical way because we eventually see the path it takes.