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

Abstract

Bell inequalities are usually derived by assuming locality and realism, and therefore experimental violations of Bell inequalities are usually taken to imply violations of either locality or realism, or both. But, after reviewing an oversight by Bell, here we derive the Bell-CHSH inequality 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 observed violations of the Bell-CHSH inequality therefore simply verify the manifest impossibility of measuring along the directions b and b' (or along the directions a and a') simultaneously, in any realizable EPR-Bohm type experiment.