The Probabilistic Roots of the Quantum Mechanical Paradoxes

The goal of any mathematical investigation on the foundations of a physical theory is to clarify to what extent the mathematical formalism of that theory is uniquely determined by some clearly and explicitely stated physical assumptions. The achievement of that goal is particularly relevant in the case of the quantum theory where the novelty of the formalism, its being far away from any immediate intuition, the substantial failure met, for many years, by any attempt to deduce the quantum formalism from plausible physical assumptions, intersected with the never solved problems concerning the interpretation of the theory. That with quantum theory a new kind of probability theory was. involved, was clear since the very beginnings of quantum mechanics (cf. [28]), even if it was not so clear which of the axioms of classical probability had to be substituted, which physically meaningful statement had to replace it, how and if a physically meaningful statement could justify the apparently strange quantum mechanical formalism. The lack of clear answers to these questions had a tremendous impact on the process of interpretation and misinterpretation of quantum theory.