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Annales de la fondation Louis de Broglie/Annales de la Fondation Louis de Broglie

Bridge from Classical to Quantum Theory of Open Systems

Yu. L. Klimontovich

Published Jan 1, 2001• 0 citations
OpenAlex

Abstract

The paper consists in a short survey of some results con- cerning the physical interpretation of the basic equations for quantum open systems. The concept of the continuous medium for quantum systems is intro- duced. From this point of view the question of completeness descrip- tion and the hidden parameters (scales) for the quantum open systems is considered. The Heisenberg uncertainty principle in the physics of open quantum systems is represented. The question: Is the consept of pure ensemble justifled in quantum mechanics is also discussed.

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From Classical to Quantum Theory of Open Systems

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The paper consists of a short survey of some results concerning the physical interpretation the basic equations for quantum open systems. The concept of a continuous medium for quantum systems is introduced. From this point of view the question of completeness description and the hidden parameters (scales) for quantum open systems is considered. The Heisenberg uncertainty principle in the physics of open quantum systems is represented. The question: Is the concept of "pure ensemble" justified in quantum mechanics is also discussed.

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The paper consists in a short survey of some results con- cerning the physical interpretation of the basic equations for quantum open systems. The concept of the continuous medium for quantum systems is intro- duced. From this point of view the question of completeness descrip- tion and the hidden parameters (scales) for the quantum open systems is considered. The Heisenberg uncertainty principle in the physics of open quantum systems is represented. The question: Is the consept of pure ensemble justifled in quantum mechanics is also discussed.
The paper consists of a short survey of some results concerning the physical interpretation the basic equations for quantum open systems. The concept of a continuous medium for quantum systems is introduced. From this point of view the question of completeness description and the hidden parameters (scales) for quantum open systems is considered. The Heisenberg uncertainty principle in the physics of open quantum systems is represented. The question: Is the concept of "pure ensemble" justified in quantum mechanics is also discussed.
In this paper we consider physical systems and the concept of their states in the context of the theory of fuzzy sets and systems. In section 1 we give a brief sketch on the fundamental difference between the theories of classical physics and quantum mechanics. In section 2 and 3 we introduce very shortly systems and their states in classical and quantum mechanics, respectively. Section 4 presents the concept of fuzzy systems. We propose to fuzzify the classical systems in section 5 and quantum systems in section 6. In section 7 we start to consider a fuzzy interpretation of the uncertainty principle.
When we are presented with apparently bizarre properties of microsystems governed by quantum mechanics (as in our discussion of the double-slit experiment in the previous chapter), we naturally ask whether it might be possible to find another theory, or at least another story to go with the equations, that would make more sense to us. We might seek a theory and a view of fundamental physical processes that would accord more with our classically based, everyday common sense. This typically takes the form of the question of the possibility of the existence of a more detailed description of atomic processes than that afforded by the wave function (that is, by the Copenhagen interpretation of the previous chapter). In this chapter we discuss some of the central interpretive problems of the Copenhagen version of quantum mechanics. Then, in the next two chapters, we look at the severe, general restrictions that are placed on any such completion of quantum mechanics and at one particular extension of quantum mechanics. First, though, we begin here with the struggle that ensued over the status of causality in quantum theory. THE COMPLETENESS OF QUANTUM MECHANICS Although the Heisenberg uncertainty principle (Section 20.4) and the lack of absolute predictive power are an inherent feature of quantum mechanics, there have been attempts to preserve an in principle completely deterministic structure for physics. Even classically, in a macroscopic sample of gas there are so many molecules that it would be hopeless, as a practical matter, to predict the future locations of all these molecules from Newton's laws of motion.
We attempt to contribute some novel points of view to the "foundations of quantum mechanics", using mathematical tools from "quantum probability theory" (such as the theory of operator algebras). We first introduce an abstract algebraic framework for the formulation of mathematical models of physical systems that is general enough to encompass classical and quantum mechanical models. After a short discussion on the properties of classical systems (realism and determinism), we move on to the study of a general class of quantum-mechanical models of physical systems and explain what some of the key problems in a quantum theory of observations and measurements are. In the last part of our essay, we attempt to elucidate the roles played by entanglement between a system and its environment and of information loss in understanding "decoherence" and "dephasing", which are key mechanisms in a quantum theory of measurements and experiments. We also discuss the problem of "time in quantum mechanics" and sketch an answer to the question when an experiment can be considered to have been completed successfully.
A survey is made of the hitherto proposed answers to the following crucial questions arising in the physical interpretation of the mathematical formalism of wave mechanics: (I) What is the meaning of the dynamical variables and of their eigenvalues? (II) What is the meaning of the wave function? (III) What is the nature and origin of Heisenberg's uncertainty relations? (IV) What is the nature of the systems dealt with by wave mechanics? Taking into account the interpretations that have been proposed in the last few years, a surprisingly large number of answers is found. The present situation in quantum mechanics is compared with similar crises in the past history of physics. The mere multiplicity of consistent interpretations of quantum mechanics is regarded as a warning against the dogmatic adherence to any one of them, to the exclusion of new possibilities.
Quantum mechanics, one of the most successful theories in the history of science, was created to account for physical systems not describable by classical physics. Though it is consistent with all experiments conducted thus far, many of its core concepts (amplitudes, global phases, etc.) can not be directly accessed and its interpretation is still the subject of intense debate, more than 100 years since it was introduced. So, a fundamental question is why this particular mathematical model is the one that nature chooses, if indeed it is the correct model. In the past two decades there has been a renewed effort to determine what physical or informational principles define quantum mechanics. In this paper, recent attempts at establishing reasonable physical principles are reviewed and their degree of success is tabulated. An alternative approach using joint quasi-probability distributions is shown to provide a common basis of representing most of the proposed principles. It is argued that having a common representation of the principles can provide intuition and guidance to relate current principles or advance new principles. The current state of affairs, along with some alternative views are discussed.