- #26

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My point is, from what one reads every day in popular science articles and what one sees being asked on forums, it is not at all clear to the majority that Bell's theorem does not imply spooky action at a distance, quite the contrary, and this confusion was started by Bell.It's on the other hand clear that Bell's theorem does not imply spooky action at a distance

There are several aspects (no pun intended) of Bell's theorem that the majority fail to understand. Firstly, that a "hidden variable theory" is not merely the supposition that the measurements are determined by hidden unknown properties of the particles, it also includes a requirement that the experimental averages and correlations be recoverable from the set of hidden variable values by means of standard Kolmogorov probability. Unfortunately many physicists think you can just integrate or average over any sort of mathematical structure - you can't. Even in simplified versions of Bell's theorem where counting arguments are used, there is an erroneous assumption that averaging counts over any sort of structure will result in the same averages and correlations obtained in experiment - it doesn't. (For example, arrange the natural numbers as follows 1,3,2,5,7,4,9,11,6,13,15,8.... whoa!! picking an odd number from the set of natural numbers is "obviously" twice as likely as picking an even ... except it isn't.)

Another point is that Bell's theorem supposes the confusingly named counterfactual definiteness, which does not simply mean that an experiment not performed can be assigned a definite outcome, but that such outcomes can be treated equally with actual experimental outcomes when averaging or calculating correlations, something which relates back to the point about the ability to recover experimental averages from hidden parameters - it doesn't work with counterfactual values of incompatible observables.