On the physical meaning of the EPR–chameleon experiment

The physical meaning of the EPR–chameleon experiment proposed in [1, 2], in which the EPR correlations are reproduced by local, independent, deterministic choices is reexamined. In addition we extend the mathematical model of [1, 2] by showing that the dynamics considered there is effectively the reduced dynamics of a fully reversible evolution. We also propose a new protocol, more directly corresponding to real experiments, in which the local computers only send back to the central one the results of the evaluation of ±1–valued functions. The program to run the experiment is available from the WEB-page: http://volterra.mat.uniroma2.it. 1 Physical interpretation of the experiment The present paper extends and clarifies the result of the EPR–chameleon experiment, proposed in [1, 2]. The goal of the experiment is (i) to construct a classical, deterministic, reversible, dynamical system which reproduces the EPR correlations by local choices; (ii) to use this model to give an experimental proof of the fact that macroscopic systems with the above mentioned characteristics can violate Bell’s inequalities for principle and not for contingent reasons. We do not pretend our model to be a hidden variable model for the EPR experiments. Our goal is to prove that Bell’s statement [3]: “... the statistical predictions of quantum mechanics are incompatible with local predetermination ...” is theoretically and experimentally unjustified if by ”statistical predictions of quantum mechanics” we mean the EPR correlations and by ”local predetermination” the possibility of reproducing these correlations by a classical deterministic macroscopic system subject to local choices. The main hidden mathematical assumption in Bell’s argument was pointed out in [4] (cf. [1] for a survey) where the nonkolmogorovian character of the EPR correlations was first noticed and the crucial role played by conditional probability emphasized. In [5] (cf. also [1, 2]) von Neumann’s measurement theory was extended to include in it the two basic conditions of locality and causality and the physical principle which allows to exploit Bell’s hidden mathematical assumption was individuated in the “chameleon effect”: the dynamics of a system may depend on the observables we want to measure (or, more generally, on the local environment). For such systems what you measure is a response to an interaction and therefore, when dealing with them, one should not speak of platonic (i.e. in principle unobservable) things [email protected] [email protected] [email protected]