A Presupposition of Bell’s Theorem

The most prominent version of Bell’s theorem consists of the Bell-CHSH inequality and a quantum-mechanical example that violates it. The inequality is shown to rest on the non-trivial presupposition that the values of elementary spin quantities are scalars, and not, e.g., vectors. In the version considered, the theorem’s argument succeeds for scalars and fails for vectors. However, the reference to vector values can be motivated by the physics of spin. Hence, recognizing the presupposition suggests a critical reassessment of the theorem.