Bell Inequality Violation with Free Choice and Local Causality on the Invariant Set

Understand

Bell's Theorem requires any theory which obeys the technical definitions of Free Choice and Local Causality to satisfy the Bell inequality.

• Invariant set theory is a finite theory of quantum physics which violates the Bell inequality exactly as does quantum theory: in it neither Free Choice nor Local Causality hold, consistent with Bell's Theorem.
• However, within the proposed theory, the mathematical expressions of both Free Choice and Local Causality involve states which, for number-theoretic reasons, cannot be ontic (cannot lie on the theory's fractal-like invariant set $I_U$ in state space).
• Weaker versions of Free Choice and Local Causality are proposed involving only the theory's ontic states.