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 R-2. The systems describe pairs of particles and the dynamics is strictly local, i.e. the dynamics T-a((j)) of particle j = 1, 2 depends only on one of the two unit vectors, but not the other. To each particle one associates a family of +/-1-valued observables S-a((j)) (j = 1, 2), also parametrized by vectors a in the unit circle in R-2. Moreover we assume that, if observable S-a((j)) is measured on particle j = 1, 2, then the dynamics of this particle will be T-a((j)) (chameleon effect). Using these ingredients we prove that the dynamics and the initial distributions of the given systems can be chosen in such a way that, if the observable S-aj((j)) is measured on particle j = 1, 2, then the EPR correlations - cos(a(1) - a(2)) are reproduced. This theoretical construction is then used to realize the following experiment: a central computer S (source) sends the same signal to two local computers A and B. After receiving the signal A (resp. B), chooses one vector a (resp. b) in the unit circle in R-2 and computes the value of the corresponding observable S-a((1)) (resp. S-b((2))). These value. bare uniquely defined by the deterministic dynamics and the choices are independent of one another. The local computers send back to the central one the results of the evaluation of these +/-1-valued functions and the central computer evaluates the empirical correlations according to the usual statistical rules. As a result the EPR correlations are reproduced with very good approximation and the Bell inequality is violated by a classical, macroscopic deterministic system performing purely local choices. The program to run the experiment is available from http://volterra.mat.uniroma2.it.