On a Surprising Oversight by John S. Bell in the Proof of his Famous Theorem

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Christian, Joy
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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, after reviewing an oversight by Bell, in the Corollary below we derive the Bell-CHSH inequality by assuming only that Bob can measure along vectors b and b' simultaneously while Alice measures along either a or a', and likewise Alice can measure along vectors a and a' simultaneously while Bob measures along either b or b', without assuming locality. The violations of the Bell-CHSH inequality therefore only mean impossibility of measuring along b and b' (or along a and a') simultaneously.