EPR-Bohm Experiment Research Articles

Bell inequality violation in the framework of a Darwinian approach to quantum mechanics

A fundamental particle in physical space subject to conservation of momentum and energy, and characterized by its average mass and its position is methodologically supplemented with an information processor – a classical Turing machine – and a randomizer both defined on an information space localized on every particle. In this way the particle can be considered a generalized Darwinian system on which natural selection could act steering the evolution on the information space of the algorithms that govern the behaviour of the particles, giving rise plausibly to emergent quantum behaviour from initial randomness. This theory is applied to an EPR-Bohm experiment for electrons in order to analyse Bell inequality violation. A model for the entanglement of two particles has been considered. The model includes shared randomness – each particle stores its own randomizer and that of its partner – and the mutual transfer of their algorithms – sharing programs – that contain their respective anticipation modules. This fact enables every particle to anticipate not only the possible future configurations of its surrounding systems, but also those of the surrounding systems of its entangled partner. Thus, while preserving locality and realism, this theory implies outcome dependence – through shared randomness – and parameter dependence – through shared anticipation – for entangled states and, as a consequence, the violation of the Bell inequality in an EPR-Bohm experiment.

Frieden wave-function representations via an Einstein-Podolsky-Rosen-Bohm experiment

The appearance of the spin-1/2 and spin-1 representations in the Frieden-Soffer extreme physical information (EPI) statistical approach to the Einstein-Podolsky-Rosen-Bohm (EPR-Bohm) experiment is shown. In order to obtain the EPR-Bohm result, in addition to the observed structural and variational information principles of the EPI method, the condition of the regularity of the probability distribution is used. The observed structural information principle is obtained from the analyticity of the logarithm of the likelihood function. It is suggested that, due to the self-consistent analysis of both information principles, quantum mechanics is covered by the statistical information theory. The estimation of the angle between the analyzers in the EPR-Bohm experiment is discussed.

The Scope and Generality of Bell’s Theorem

I present what might seem to be a local, deterministic model of the EPR-Bohm experiment, inspired by recent work by Joy Christian, that appears at first blush to be in tension with Bell-type theorems. I argue that the model ultimately fails to do what a hidden variable theory needs to do, but that it is interesting nonetheless because the way it fails helps clarify the scope and generality of Bell-type theorems. I formulate and prove a minor proposition that makes explicit how Bell-type theorems rule out models of the sort I describe here.

Violation of Bell's Inequality and Postulate on Simultaneous Measurement of Compatible Observables

We discuss coupling of violation of Bell’s inequality and non-Kolmogorovness of statistical data in the EPR-Bohm experiment. We emphasize that nonlocalty and “death of realism” are only sufficient, but not necessary conditions of non-Kolmogorovness. There can be found other sufficient conditions of non-Kolmogorovness and, hence, violation of Bell’s inequality. We find one important source of non-Kolmogorovness by analyzing axiomatics of quantum mechanics. We pay attention to the postulate (due to von Neumann and Dirac) on simultaneous measurement of quantum observables given by commuting operators. This postulate is criticized as nonphysical. We propose a new interpretation of the Born-von Neumann-Dirac rule for calculation of the joint probability distribution for such observables. It gets a natural physical interpretation by considering conditional measurement scheme. We use this argument (i.e., rejection of the postulate on simultaneous measurement to motivate non-Kolmogorovness of the probabilistic structure of the EPR-Bohm experiment.

Epr-bohm experiment and Bell’s inequality: Quantum physics meets probability theory

Our main aim in this paper is to inform the physics community (and especially experts in quantum information) about investigations of the problem of the probabilistic compatibility of a family of random variables: the possibility of realizing such a family based on a single probability measure (of constructing a single Kolmogorov probability space). These investigations were started a hundred years ago by Boole. The complete solution of the problem was obtained by the Soviet mathematician Vorobiev in the 1960s. It turns out that probabilists and statisticians obtained inequalities for probabilities and correlations that include the famous Bell’s inequality and its generalizations.

Nonlocality as well as rejection of realism are only sufficient (but non-necessary!) conditions for violation of Bell’s inequality

In this review we remind the viewpoint that violation of Bell’s inequality might be interpreted not only as an evidence of the alternative – either nonlocality or “death of reality” (under the assumption the quantum mechanics is incomplete). Violation of Bell’s type inequalities is a well known sufficient condition of probabilistic incompatibility of random variables – impossibility to realize them on a single probability space. Thus, in fact, we should take into account an additional interpretation of violation of Bell’s inequality – a few pairs of random variables (two-dimensional vector variables) involved in the EPR–Bohm experiment are incompatible. They could not be realized on a single Kolmogorov probability space. Thus, one can choose between: (a) completeness of quantum mechanics; (b) nonlocality; (c) “ death of reality”; (d) non-Kolmogorovness. In any event, violation of Bell’s inequality has a variety of possible interpretations. Hence, it could not be used to obtain the definite conclusion on the relation between quantum and classical models.

EPR-Bohm Experiment and Interference of Probabilities

We demonstrate that the EPR-Bohm probabilities can be easily obtained in the classical (but contextual) probabilistic framework by using the formula of interference of probabilities.

Event Independence, Collective Independence, EPR‐Bohm Experiment, and Incompleteness of Quantum Mechanics

We analyse notion of independence in the EPR-Bohm framework by using comparative analysis of independence in conventional and frequency probability theories. Such an analysis is important to demonstrate that Bell's inequality was obtained by using totally unjustified assumptions (e.g. the Bell-Clauser-Horne factorability condition). Our frequency analysis also demonstrated that Gill-Weihs-Zeilinger-Zukowski's arguments based on "the experimenter's freedom to choose settings" to support the standard Bell approach are neither justified by the structure of the EPR-Bohm experiment. Finally, our analysis supports the original Einstein's viewpoint that quantum mechanics is simply not complete.

Determinism and locality in quantum systems

Models of the EPR-Bohm experiment usually consider just two times, an initial time, and the time of measurement. Within such analyses, it has been argued that ‘locality’ is equivalent to determinism, given the strict correlations of quantum mechanics. However, an analysis based on such models is only a preliminary to an analysis based on a complete dynamical model. The latter analysis is carried out, and it is shown that, given certain definitions of ‘locality’ and ‘determinism’ for completely dynamical models, locality implies, but is not implied by, determinism. Further, it is suggested that a local deterministic model has not been ruled out by Bell's theorem. It is suggested that such a model could naturally deny the independence of initial complete states from the settings of the apparatuses (a crucial assumption in the derivation of Bell's inequality).

Bell-type inequalities on tensor products of quantumlogics

The problem of Bell-type inequalities on tensor products of quantum logics is studied. To formulate the problem the definition of tensor product used for sum logics by Hudson and Pulmannova is generalized to arbitrary orthomodular lattices and the existence of such product for lattices describing the simplest EPR-Bohm experiment is shown. It is proved that Bell-type inequalities hold for all product states.