We present a model that allows one to build structures that evolve continuously from classical to quantum, and we study the intermediate situations, giving rise to structures that are neither classical nor quantum. We construct the closure structure corresponding to the collection of eigenstate sets of these intermediate situations, and demonstrate how the superposition principle disappears during the transition from quantum to classical. We investigate the validity of the axioms of quantum mechanics for the intermediate situations.

According to Zurek, the emergence of a classical world from a quantum substrate could result from a long selection process that privileges the classical bases according to a principle of optimal information. We investigate the consequences of this principle in a simple case, when the system and the environment are two interacting scalar particles supposedly in a pure state. We show that then the classical regime corresponds to a situation for which the entanglement between the particles (the system and the (...) environment) disappears. We describe in which circumstances this factorisability condition is fulfilled, in the case that the particles interact via position-dependent potentials, and also describe in appendix the tools necessary for understanding our results (entanglement, Bell inequalities and so on). (shrink)

Many argued (Accardi and Fedullo, Pitowsky) that Kolmogorov's axioms of classical probability theory are incompatible with quantum probabilities, and that this is the reason for the violation of Bell's inequalities. Szabó showed that, in fact, these inequalities are not violated by the experimentally observed frequencies if we consider the real, “effective” frequencies. We prove in this work a theorem which generalizes this results: “effective” frequencies associated to quantum events always admit a Kolmogorovian representation, when these events are collected through different (...) experimental setups, the choice of which obeys a classical distribution. (shrink)

This paper consists of two parts. Firstly, we shall clarify the connections existing between Clauser-Horne's inequalities and the conditions established by Pitowsky expressing the Kolmogorovian nature of a probability vector. We shall discuss afterwards three possible interpretations of the experimental violation of these inequalities.

We show how trajectories can be reintroduced in quantum mechanics provided that its spatial continuum is modelled by a variable real number (qr-number) continuum. Such a continuum can be constructed using only standard Hilbert space entities. In this approach, the geometry of atoms and subatomic objects differs from that of classical objects. The systems that are non-local when measured in the classical space-time continuum may be localized in the quantum continuum. We compare trajectories in this new description of space-time with (...) the corresponding Bohmian picture. (shrink)

As was mentioned by Nicolas Lori in his (Found Sci, 2010 ) commentary, the definition of Information in Physics is something about which not all authors agreed. According to physicists like me Information decreases when Entropy increases (so entropy would be a negative measure of information), while many physicists, seemingly the majority of them, are convinced of the contrary (even in the camp of Quantum Information Theoreticians). In this reply I reproduce, and make more precise, some of my arguments, that (...) appeared here and there in my ( 2010 ) paper, in order to clarify the presentation of my personal point of view on the subject. (shrink)

According to the so-called Quantum Darwinist approach, the emergence of "classical islands" from a quantum background is assumed to obey a (selection) principle of maximal information. We illustrate this idea by considering the coupling of two oscillators (modes). As our approach suggests that the classical limit could have emerged throughout a long and progressive Evolution mechanism, it is likely that primitive living organisms behave in a "more quantum", "less classical" way than more evolved ones. This brings us to seriously consider (...) the possibility to measure departures from classicality exhibited by biological systems. We describe an experimental proposal the aimed at revealing the presence of entanglement in the biophotonic radiation emitted by biological sources. (shrink)

According to the so-called Quantum Darwinist approach, the emergence of “classical islands” from a quantum background is assumed to obey a principle of maximal information. We illustrate this idea by considering the coupling of two oscillators. As our approach suggests that the classical limit could have emerged throughout a long and progressive Evolution mechanism, it is likely that primitive living organisms behave in a “more quantum”, “less classical” way than more evolved ones. This brings us to seriously consider the possibility (...) to measure departures from classicality exhibited by biological systems. We describe an experimental proposal the aimed at revealing the presence of entanglement in the biophotonic radiation emitted by biological sources. (shrink)