On Local Interactions in EPR-Type Dynamics

F. Selleri

W. Michael Dickson

M. Hoffmann

Luigi Accardi, Kentaro Imafuku, Massimo Regoli

On September 27 (2001), as a side activity to the "Japan-Italy Joint workshop on: Quantum open systems and quantum measurement", the first; public demonstration of the dynamical EPR-chameleon experiment was performed at Waseda University in order to give an experimental answer to a long standing question in the foundations of quantum theory: do there exist classical macroscopic systems which, by local independent choices, produce sequences of data which reproduce the singlet correlations, hence violating Bell's inequality? The EPR-chameleon experiment gives an affirmative answer to this question by concretely producing an example of such systems in the form of three personal computers which realize a local deterministic dynamical evolution whose mathematical structure is very simple and transparent. In the experiment performed on September 27 the local dynamics used was not a reversible one because the interaction with the degrees of freedom of the apparatus was integrated out giving rise to an effective Markovian dynamics which, although mapping probability measures into probability measures, did not preserve the +/- 1-values of the spin (or polarization) observables. This feature was criticized by some of the partecipants and the following two questions arose: i) is it possible to prove that the Markovian evolution, used in the experiment, is indeed the reduced evolution of a bona fide reversible evolution? ii) if the answer to question (i) is affirmative, is it possible to reproduce the EPR correlations by simply considering empirical averages of +/- 1-values, as one does in usual EPR type experiments? An affirmative answer to these questions was given in the paper [AcImRe01] and it is briefly reviewed in what follows.

Arthur I. Fine

W. Michael Dickson

We now have under our belts several interpretations of quantum mechanics, each requiring, or anyhow advocating, some understanding of quantum probabilities. In the next two chapters, I will consider some connections among various interpretations of quantum probabilities and non-locality. I do so in the context of the well-known EPR–Bohm experiment, though it is worth emphasizing at the start that non-locality is very likely the rule rather than the exception for quantum-mechanical systems. Entanglement of systems occurs not only in the confines of a laboratory, but also in the course of quite typical interactions among quantum-mechanical systems. Nonetheless, the EPR-Bohm experiment shines a bright light on the phenomenon of non-locality, and is therefore the most useful context in which to explore the relation between probability and non-locality. In this chapter, I consider models of the EPR–Bohm experiment that deliver probabilities for the various outcomes given the initial state of the pair of particles. In the next chapter, I consider fully dynamical models, i.e., ones that provide a dynamics for the complete state of the pair of particles as well as probabilities for various outcomes based on these complete states. The EPR–Bohm experiment The EPR–Bohm experiment is well known, but some observations about it are important for later.