gill1109 wrote:Joy Christian wrote:FrediFizzx wrote:FrediFizzx wrote:... So Bell ends up with the inequality,
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without any indexing. So the current argument by the Bell fans is that a, b and c don't have to happen all at the same time. But that is obviously wrong.
Back more on topic here. So if the pairs are independent like the Bell fans want to do, then the equality can be,
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which of course then we have a higher bound of 3 for the inequality.
Precisely. Without the assumption of "happen all at the same time", the stringent bound of 1 (or of 2 in the CHSH case) simply cannot be derived. That should be completely obvious even to a school child. And I suspect that Bell believers know this. So what can they do to fool the world? What they do is obfuscate this simple fact by invoking probability and statistics. In doing so they overplay (perhaps unwittingly) the EPR criterion of reality. See footnote 3 in my argument for a homely example: https://arxiv.org/pdf/1704.02876.pdf.
There is no assumption that different measurements are made at the same time. The assumption of Local Realism is that a random realisation of is formed. Then, *if* Alice chooses setting a, she gets to observe the outcome A(a,). Similarly for Bob. But Alice and Bob are free to choose any settings they like, or even, to do nothing at all - they can switch off the *detectors* and go home early and watch TV ...
Then there is the no-conspiracy assumption that the average value of A(a,)B(b,) over many, many hypothetical repetitions is the same - up to statistical variation - as the average value of A(a,)B(b,) over only those repetitions in which Alice did choose a, and Bob did choose b
This has nothing to do with local realism so not sure why you are even mentioning it. It is about some pretty simple mathematics. Is the "a" in P(a, b) the same "a" in P(a, c) and is the "b" in P(a, b) the same "b" in P(b, c) and is the "c" in P(a, c) the same "c" as in P(b, c)? Sure they are. So it is pretty simple to see that a, b and c all have to happen at the same time. If the 3 terms are independent (happen at different times), then the bound on the inequality is 3 not 1.
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