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In https://arxiv.org/abs/1409.5158, the author concludes that Bell tests cannot refute local realism, because they employ a wrong analysis. He says:

"The quantum joint prediction cannot be recovered in an experiment with separated (marginal) measurements, just as for classical probability. Quantum mechanics correctly applied does not predict a violation of the CH inequality. The correct quantum mechanics prediction for an EPRB experiment must use the marginals (via reduced density matrices) and not the joint distribution. The source distribution in an EPRB experiment may be a joint one, but joint statistics cannot be recovered because the experiment yields only separated (marginal) measurements. A well-developed statistical field of study decomposes correlated joint distributions into the marginals plus an additional function called a copula. There would be no need for this field if any arbitrary joint distribution could be recovered through its marginals. Therefore, we cannot and do not apply the quantum joint prediction to EPRB experiments."

Also in https://arxiv.org/abs/1309.1153 he mentions:

"Most importantly, quantum mechanics is shown to be compatible with local realism, by means of correct handling of separated systems. We cannot use the joint probability formula for cases of separated measurements; instead we use the marginals (partial traces or reduced density matrices) together with whatever priors we have from an understanding of the system. Specification of what are separated measurements is delicate but has been adequately addressed here. If we accept this small reinterpretation of quantum mechanics, nonlocality is eliminated. The experiments when correctly interpreted confirm the local realist position. Nonlocal entanglement is seen to be an error."

Another error he claims to have found is the application of Luder's rule to the EPR problem in https://arxiv.org/abs/1607.01808. Here he says:

Lüders’ rule was developed for the treatment of ensembles [6], so its application to individual projection events is already problematic. Furthermore, by blindly applying Lüders’ rule to physical scenarios for which it is not validly applicable, such as EPR, nonlocality is in effect simply postulated by fiat, whereas Lüders’ rule is in reality not only incorrect for EPR, but is not needed to account for experiments correctly designed and analyzed. Prediction using Lüders’ rule is not a unique necessary quantum mechanical calculation for EPR. Alternative quantum mechanical calculations giving different results are available and required.

I can't be convinced that all physicists have been making such basic mistakes for decades. Can anyone illuminate this case in a clear and rigorous way?

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    $\begingroup$ I have not carefully read his arguments so maybe he has a subtle point. However, arxiv has plenty of crackpot papers so don't assume the author is credible by default :) $\endgroup$ – nr2618 Jan 29 at 21:19
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The correct quantum mechanics prediction for an EPRB experiment must use the marginals (via reduced density matrices) and not the joint distribution. The source distribution in an EPRB experiment may be a joint one, but joint statistics cannot be recovered because the experiment yields only separated (marginal) measurements.

The way I understand it, this is just a very basic misunderstanding of how quantum mechanics works. There is not much to argue about: quantum mechanics predicts correlations between the different parties, and that is what is measured.

The reduced density matrices are what determines the local statistics that each one of the two parties observes when ignoring the correlations between them. Bell's theorem is about the correlations between the observations, so it does not relate to the reduced density matrices but requires the use of the full entangled quantum state.

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