Bell's Inequality

Bell's theorem shows that no local hidden variable theory can reproduce quantum correlations. The inequality

$$|E(a,b) - E(a,c)| \leq 1 + E(b,c)$$

is violated by quantum mechanics: nature is either nonlocal, or measurement outcomes are not predetermined.

The standard framing assumes measurement outcomes are binary $\{-1, +1\}$ — spin up or spin down. But the act of measurement — the moment before the outcome resolves — is exactly the null state. The particle is not $\{\}_+$ or $\{\}_-$ until cross-composition happens, until two oriented contexts meet.

Bell violation in MMP terms: the assumption that particles carry predetermined $\{\}_+$ or $\{\}_-$ before measurement is the hidden variable assumption. MMP says no — they carry null $\{\}$, and the outcome is determined by which oriented void meets which. The order of $\circlearrowright$ matters:

$$\{\}_- \circlearrowright \{\}_+ \neq \{\}_+ \circlearrowright \{\}_-$$

The noncommutativity of $\circlearrowright$ is the Bell violation. You cannot assume a predetermined sign because the sign is produced by the meeting, not carried into it.