There remains much confusion in the physics community regarding the meaning of the so-called experimental "violations" of Bell inequalities. But there shouldn't be.

As is well known, Bell derived his inequalities by considering four incompatible experiments in any possible world, classical or quantum. What I have demonstrated in this paper, however, is that his tacit assumption of compatibility of the manifestly incompatible experiments is the ONLY assumption needed to derive the Bell-CHSH type inequalities. Therefore such inequalities have nothing to do with the issues of locality and realism. Here is a slightly more accurate conclusion from my paper:

To summarize our Corollary, Bell inequalities are usually derived by assuming locality and realism, and therefore

violations of the Bell-CHSH inequality are usually taken to imply violations of either locality or realism, or both. But

we have derived the Bell-CHSH inequality above by assuming only that Bob can measure along the directions b and b′

simultaneously while Alice measures along either a or a′, and likewise Alice can measure along the directions a and a′

simultaneously while Bob measures along either b or b′, without assuming locality. The violations of the Bell-CHSH

inequality therefore simply confirm the impossibility of measuring along b and b′ (or along a and a′ ) simultaneously.

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