Quantum-mechanical correlations and Tsirelson bound from geometric algebra

The Bell–Clauser–Horne–Shimony–Holt inequality can be used to show that no local hidden-variable theory reproduce the correlations predicted by quantum mechanics (QM). It proved certain QM lead a violation of classical bound established inequality, while all correlations, and classical, respect (the Tsirelson bound). Here, we these well-known results depend crucially on assumption values physical magnitudes are scalars. More specifically, not scalars, but vectors elements geometric algebra G $$^{{\mathbf {3}}}$$ over R , makes it possible is violated respected, even given locality assumption.The result implies, first, origin geometrical, physical; and, second, does contradict if in .