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arXiv:nlin/0407033

Base of nonlinear dynamics or Real Dynamics, Ideal Dynamics, Unpredictable Dynamics and "Schrodinger cat"

Oleg Kupervasser

Published Jul 14, 2004• 6 citations
arXivHTMLPDF

Abstract

In the paper paradoxes underlying thermodynamics and a quantum mechanics are discussed. Their solution is given from the point of view of influence of the exterior observer (surrounding medium) destroying correlations of system, or boundedness of self-knowledge of system in a case when both the observer, and a surrounding medium are included in system. Concepts Real Dynamics, Ideal Dynamics and Unpredictable Dynamics are entered. Consideration an appearance of a life is given from the point of view of these three Dynamics.

DOI
10.48550/arxiv.nlin/0407033

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In the paper paradoxes underlying thermodynamics and a quantum mechanics are discussed. Their solution is given from the point of view of influence of the exterior observer (surrounding medium) destroying correlations of system, or boundedness of self-knowledge of system in a case when both the observer, and a surrounding medium are included in system. Concepts Real Dynamics, Ideal Dynamics and Unpredictable Dynamics are entered. Consideration an appearance of a life is given from the point of view of these three Dynamics.
The paper discusses the basic paradoxes of thermodynamics and quantum mechanics. The approaches to solution of these paradoxes are suggested. The first one relies on the influence of the external observer (environment), which disrupts the correlations in the system. The second one is based on the limits of self-knowledge of the system in case of both the external observer and the environment is included in the considered system. The concepts of Real Dynamics, Ideal Dynamics, and Unpredictable dynamics are introduced. The phenomenon of Life is contemplated from the point of view of these Dynamics.
Statistical classical mechanics and quantum mechanics are developed and well-known theories that represent a basis for modern physics. Statistical classical mechanics enable the derivation of the properties of large bodies by investigating the movements of small atoms and molecules which comprise these bodies using Newton's classical laws. Quantum mechanics defines the laws of movement of small particles at small atomic distances by considering them as probability waves. The laws of quantum mechanics are described by the Schrödinger equation. The laws of such movements are significantly different from the laws of movement of large bodies, such as planets or stones. The two described theories are well known and have been well studied. As these theories contain numerous paradoxes, many scientists doubt their internal consistencies. However, these paradoxes can be resolved within the framework of the existing physics without the introduction of new laws. To clarify the paper for the inexperienced reader, we include certain necessary basic concepts of statistical physics and quantum mechanics in this paper without the use of formulas. Exact formulas and explanations are included in the Appendices. The text is supplemented by illustrations to enhance the understanding of the paper. The paradoxes underlying thermodynamics and quantum mechanics are also discussed. The approaches to the solutions of these paradoxes are suggested. The first approach is dependent on the influence of the external observer (environment), which disrupts the correlations in the system. The second approach is based on the limits of the self-knowledge of the system for the case in which both the external observer and the environment are included in the considered system. The concepts of observable dynamics, ideal dynamics, and unpredictable dynamics are introduced. The phenomenon of complex (living) systems is contemplated from the point of view of these dynamics.
The modern classical statistical physics, thermodynamics, quantum mechanics and gravity theory are developed and well-known theories. The described theories are developed and well studied for a long time. Nevertheless, it contains a number of paradoxes. It forces many scientists to doubt internal consistency of these theories. However, the given paradoxes can be resolved within the framework of the existing physics, without introduction of new laws. Further, in this paper we discuss the paradoxes underlying classical statistical physics, thermodynamics, quantum mechanics, and non-quantum and quantum gravities. We suggest the approaches to solution of these paradoxes on basis universal arrow of time. The first one relies on the influence of the external observer (environment), which disrupts the correlations in the system and results in time arrows alignment. The basis of the second one is the limits of self-knowledge of the system in case of the observed system; the external observer and the environment are included in the considered system. We introduce the concepts of observable dynamics, ideal dynamics, and unpredictable dynamics. We contemplate the phenomenon of complex (living) systems from the point of view of these dynamics. Perspectives of practical use of Unpredictable systems for artificial intellect are considered. c Chapter 1. The Universal Arrow of Time: Classical Mechanics. Abstract: Solution of paradox for the entropy increase in reversible systems. Statistical physics cannot explain why the thermodynamic time arrow does exist un- less very special and so it postulates unnatural initial conditions. However, we are ready to state that statistical physics is able to explain why the thermodynamic time arrow is
Many phenomena in the observable macroscopic world obey nonlinear evolution equations while the microscopic world is governed by quantum mechanics, a fundamental theory that is supposedly linear. In order to combine these two worlds in a common formalism, at least one of them must sacrifice one of its dogmas. Linearizing nonlinear dynamics would destroy the fundamental property of this theory, however, it can be shown that quantum mechanics can be reformulated in terms of nonlinear Riccati equations. In a first step, it will be shown that the information about the dynamics of quantum systems with analytical solutions can not only be obtainable from the time-dependent Schrödinger equation but equally-well from a complex Riccati equation. Comparison with supersymmetric quantum mechanics shows that even additional information can be obtained from the nonlinear formulation. Furthermore, the time-independent Schrödinger equation can also be rewritten as a complex Riccati equation for any potential. Extension of the Riccati formulation to include irreversible dissipative effects is straightforward. Via (real and complex) Riccati equations, other fields of physics can also be treated within the same formalism, e.g., statistical thermodynamics, nonlinear dynamical systems like those obeying a logistic equation as well as wave equations in classical optics, Bose- Einstein condensates and cosmological models. Finally, the link to abstract "quantizations" such as the Pythagorean triples and Riccati equations connected with trigonometric and hyperbolic functions will be shown.
The dynamical and information aspects of the behaviour of complex physical systems are considered. In classical physics the information coupling appears in the interaction of nonlinear systems with stohastic behaviour when a small external perturbation may greatly alter the paths of a classical system in phase space. In quantum systems the information coupling to the environment appears in measurement processes when the coherence of the wave function of a quantum object is destroyed and corresponding information appears in the external environment. These processes can be described in terms of the collapse of wave functions. Numerous examples of the collapse are considered, including those leading to the classical behaviour of macroscopic bodies with the information coupling to a nonequilibrium environment. The Einstein–Podolsky–Rosen paradox is discussed in detail together with its possible role in the processes of information transfer over a distance.
The resolutions to the paradox of Schrödinger’s cat engendered by three major perspectives on quantum mechanics—quantum logic, the many worlds interpretation, and the Copenhagen interpretation—are discussed. The core of each perspective is revealed in the process. Each resolution to Schrödinger’s cat has a counterpart which solves the logical paradox known as the unexpected hanging. The rather striking parallels serve to emphasize several points. First, the quantum paradox is an epistemological and not a physical one. Second, the three interpretations mentioned, unlike some others, are faithful to this understanding. And third, the pitfalls in these two paradoxes have a somewhat universal character.