  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. Conventional hidden-variable theories satisfying only these weaker
definitions still obey the Bell inequality. However, invariant set theory,
which violates the Bell inequality, satisfies these weaker definitions. It is
argued that the weaker definitions are consistent with the physical meaning
behind free choice and local causality as defined in space-time, and hence that
Free Choice and Local Causality are physically too strong. It is concluded that
the experimental violation of the Bell inequality may have less to do with free
choice or local causality \emph{per se}, and more to do with the presence of a
holistic but causal state-space geometry onto which quantum ontic states are
constrained.

Quantum Physics