On the EPR-chameleon experiment

We construct a family of classical deterministic dynamical systems (triples formed by a state space, an initial distribution, a dynamics) parametrized by pairs of vectors $(a,b)$ in the unit circle in $\Bbb R^2$. The systems describe pairs of particles and the dynamics is strictly local, i.e. the dynamics $T^{(j)}_a$ of particle $j=1,2$ depends only on one of the two unit vectors, but not on the other. To each particle one associates a family of $\pm 1$--valued observables $S^{(j)}_a$ ($j=1,2$), also parametrized by vectors $a$ in the unit circle in $\Bbb R^2$. Moreover we assume that, if observable $S^{(j)}_a$ is measured on particle $j=1,2$, then the dynamics of this particle will be $T^{(j)}_a$ (chameleon effect). (...)