Bell Inequality Violation with Free Choice and Local Causality on the Invariant Set
Abstract
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 numbertheoretic reasons, cannot be ontic (cannot lie on the theory's fractallike 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 hiddenvariable 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 spacetime, 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 statespace geometry onto which quantum ontic states are constrained.
 Publication:

arXiv eprints
 Pub Date:
 March 2019
 arXiv:
 arXiv:1903.10537
 Bibcode:
 2019arXiv190310537P
 Keywords:

 Quantum Physics