Macroscopic Simulation of Violation of Bell's Inequality

A macroscopic quantum model of a two-level system (the analogue of a half-spin particle) is described. The model is employed for simulating not only the system under study, but the measurement process as well. Single- and two-particle state models of a quantum system are constructed. The Einstein-Podolsky-Rosen paradox and Bell's inequality are discussed within the framework of the model.Comment: 20 page

Quantum mechanics without quantum logic

We describe a scheme of quantum mechanics in which the Hilbert space and linear operators are only secondary structures of the theory. As primary structures we consider observables, elements of noncommutative algebra, and the physical states, the nonlinear functionals on this algebra, which associate with results of single measurement. We show that in such scheme the mathematical apparatus of the standard quantum mechanics does not contradict a hypothesis on existence of an objective local reality, a principle of a causality and Kolmogorovian probability theory.Comment: 24 pages, no figures, Late

Quantum measurements and Kolmogorovian probability theory

We establish connections between the requirement of measurability of a probability space and the principle of complimentarity in quantum mechanics. It is shown that measurability of a probability space implies the dependence of results of quantum measurement not only on the properties of a quantum object under consideration, but also on the classical characteristics of the measuring device which is used. We show that if one takes into account the requirement of measurability in a quantum case, the Bell inequality does not follow from the hypothesis about the existence of an objective reality.Comment: 8 pages, no figures, Late

Algebraic-statistical approach to quantum mechanics

It is proposed the scheme of quantum mechanics, in which a Hilbert space and the linear operators are not primary elements of the theory. Instead of it certain variant of the algebraic approach is considered. The elements of noncommutative algebra (observables) and the nonlinear functionals on this algebra (physical states) are used as the primary constituents. The functionals associate with results of a particular measurement. It is suggested to consider certain ensembles of the physical states as quantum states of the standart quantum mechanics. It is shown that in such scheme the mathematical formalism of the standart quantum mechanics can be reproduced completely.Comment: 9 pages, no figures, Late

Quantum Teleportation

In the framework of an algebraic approach, we consider a quantum teleportation procedure. It turns out that using the quantum measurement nonlocality hypothesis is unnecessary for describing this procedure. We study the question of what material objects are information carriers for quantum teleportation.Comment: 17 pages, 5 figur

Quantum mechanics as a complete physical theory

We show that the principles of a ''complete physical theory'' and the conclusions of the standard quantum mechanics do not irreconcilably contradict each other as is commonly believed. In the algebraic approach, we formulate axioms that allow constructing a renewed mathematical scheme of quantum mechanics. This scheme involves the standard mathematical formalism of quantum mechanics. Simultaneously, it contains a mathematical object that adequately describes a single experiment. We give an example of the application of the proposed scheme.Comment: 13 pages, Latex, no figures. Version of the article publised in Theoretical and Mathematicl Physics, 132(3); 1262-1274 (2002

Causality and probabilistic interpretation of quantum mechanics

It is shown that probabilistic treatment of quantum mechanics can be coordinated with causality of all physical processes. The physical interpretation of quantum-mechanical phenomena such as process of measurement and collapse of quantum state is given.Comment: 10 pages. Submitted to "Theoretical and Mathematical Physics

Measurements and Mathematical Formalism of Quantum Mechanics

A scheme for constructing quantum mechanics is given that does not have Hilbert space and linear operators as its basic elements. Instead, a version of algebraic approach is considered. Elements of a noncommutative algebra (observables) and functionals on this algebra (elementary states) associated with results of single measurements are used as primary components of the scheme. On the one hand, it is possible to use within the scheme the formalism of the standard (Kolmogorov) probability theory, and, on the other hand, it is possible to reproduce the mathematical formalism of standard quantum mechanics, and to study the limits of its applicability. A short outline is given of the necessary material from the theory of algebras and probability theory. It is described how the mathematical scheme of the paper agrees with the theory of quantum measurements, and avoids quantum paradoxes.Comment: 42 pages, no figore

Quantum mechanics with the permitted hidden parameters

Within the framework of the algebraic approach the problem of hidden parameters in quantum mechanics is surveyed. It is shown that the algebraic formulation of quantum mechanics permits introduction of a specific hidden parameter, which has the form of nonlinear functional on the algebra of observables. It is found out that the reasoning of von Neumann and of Bell about incompatibility of quantum mechanics with hidden parameters is inapplicable to the present case.Comment: 9 pages, LaTex, no figures. Talk at "QFTHEP 2000" Tver, Russi

Quantum mechanics as the objective local theory

In the work it is shown that the principles "the objective local theory" and corollaries of the standard quantum mechanics are not in such antagonistic inconsistency as it is usually supposed. In the framework of algebraic approach, the postulates are formulated which allow constructing the updated mathematical scheme of quantum mechanics. This scheme incorporates the standard mathematical apparatus of quantum mechanics. Simultaneously, in it there is a mathematical object, which adequately describes individual experiment.Comment: 6 pages, no figures, Latex, talk at QFTHEP'2001 Moscow Russi