scholarly journals GENERALIZATION OF CLASSICAL STATISTICAL MECHANICS TO QUANTUM MECHANICS AND STABLE PROPERTY OF CONDENSED MATTER

2004 ◽  
Vol 18 (26n27) ◽  
pp. 1367-1377 ◽  
Author(s):  
Y. C. HUANG ◽  
F. C. MA ◽  
N. ZHANG
Keyword(s):  
Quantum Mechanics ◽  
Statistical Mechanics ◽  
Uncertainty Principle ◽  
Classical Limit ◽  
Condensed Matter ◽  
Superposition Principle ◽  
Classical Mechanics ◽  
Eigenvalue Equation ◽  
Quantum Uncertainty ◽  
Classical Statistical Mechanics

Classical statistical average values are generally generalized to average values of quantum mechanics. It is discovered that quantum mechanics is a direct generalization of classical statistical mechanics, and we generally deduce both a new general continuous eigenvalue equation and a general discrete eigenvalue equation in quantum mechanics, and discover that a eigenvalue of quantum mechanics is just an extreme value of an operator in possibility distribution, the eigenvalue f is just classical observable quantity. A general classical statistical uncertain relation is further given, and the general classical statistical uncertain relation is generally generalized to the quantum uncertainty principle; the two lost conditions in classical uncertain relation and quantum uncertainty principle, respectively, are found. We generally expound the relations among the uncertainty principle, singularity and condensed matter stability, discover that the quantum uncertainty principle prevents the appearance of singularity of the electromagnetic potential between nucleus and electrons, and give the failure conditions of the quantum uncertainty principle. Finally, we discover that the classical limit of quantum mechanics is classical statistical mechanics, the classical statistical mechanics may further be degenerated to classical mechanics and we discover that merely stating that the classical limit of quantum mechanics is classical mechanics is a mistake. As application examples, we deduce both the Schrödinger equation and the state superposition principle, and deduce that there exists a decoherent factor from a general mathematical representation of the state superposition principle; the consistent difficulty between statistical interpretation of quantum mechanics and determinant property of classical mechanics is overcome.

scholarly journals Decoherence: the view from the history and philosophy of science

2012 ◽  
Vol 370 (1975) ◽  
pp. 4594-4609 ◽  
Author(s):  
Amit Hagar
Keyword(s):  
Quantum Mechanics ◽  
Statistical Mechanics ◽  
Philosophy Of Science ◽  
Condensed Matter ◽  
Condensed Matter Physics ◽  
Methodological Issues ◽  
Classical Statistical Mechanics ◽  
Spin Bath ◽  
History Of ◽  
Philosophical Importance

We present a brief history of decoherence, from its roots in the foundations of classical statistical mechanics, to the current spin bath models in condensed matter physics. We then analyse the philosophical importance of decoherence in three different foundational problems, and find that its role in their solutions is less than that commonly believed. What makes decoherence more philosophically interesting, we argue, are the methodological issues it draws attention to, and the question of the universality of quantum mechanics.

scholarly journals CLASSICAL LIMIT OF THE TRAJECTORY REPRESENTATION OF QUANTUM MECHANICS, LOSS OF INFORMATION AND RESIDUAL INDETERMINACY

2000 ◽  
Vol 15 (09) ◽  
pp. 1363-1378 ◽  
Author(s):  
EDWARD R. FLOYD
Keyword(s):  
Quantum Mechanics ◽  
Statistical Mechanics ◽  
Classical Limit ◽  
Correspondence Principle ◽  
Classical Mechanics ◽  
Information Loss ◽  
Equivalence Classes ◽  
Trajectory Representation ◽  
Heisenberg Uncertainty ◽  
The Relationship

The trajectory representation in the classical limit (ℏ→0) manifests a residual indeterminacy. We show that the trajectory representation in the classical limit goes to neither classical mechanics (Planck's correspondence principle) nor statistical mechanics. This residual indeterminacy is contrasted to Heisenberg uncertainty. We discuss the relationship between residual indeterminacy and 't Hooft's information loss and equivalence classes.

scholarly journals An analysis on Quantum mechanical Stability of Regular Polygons on a Point Base Using Heisenberg Uncertainty Principle

2021 ◽  
Vol 9 (10) ◽  
pp. 74-79
Author(s):  
Anurag Chapagain
Keyword(s):  
Quantum Mechanics ◽  
Uncertainty Principle ◽  
Stability Problem ◽  
Classical Mechanics ◽  
Quantum Mechanical ◽  
Heisenberg Uncertainty Principle ◽  
Heisenberg Uncertainty ◽  
Degree Of Stability ◽  
The Stability ◽  
Heisenberg's Uncertainty Principle

Abstract: It is a well-known fact in physics that classical mechanics describes the macro-world, and quantum mechanics describes the atomic and sub-atomic world. However, principles of quantum mechanics, such as Heisenberg’s Uncertainty Principle, can create visible real-life effects. One of the most commonly known of those effects is the stability problem, whereby a one-dimensional point base object in a gravity environment cannot remain stable beyond a time frame. This paper expands the stability question from 1- dimensional rod to 2-dimensional highly symmetrical structures, such as an even-sided polygon. Using principles of classical mechanics, and Heisenberg’s uncertainty principle, a stability equation is derived. The stability problem is discussed both quantitatively as well as qualitatively. Using the graphical analysis of the result, the relation between stability time and the number of sides of polygon is determined. In an environment with gravity forces only existing, it is determined that stability increases with the number of sides of a polygon. Using the equation to find results for circles, it was found that a circle has the highest degree of stability. These results and the numerical calculation can be utilized for architectural purposes and high-precision experiments. The result is also helpful for minimizing the perception that quantum mechanical effects have no visible effects other than in the atomic, and subatomic world. Keywords: Quantum mechanics, Heisenberg Uncertainty principle, degree of stability, polygon, the highest degree of stability

scholarly journals General Quantum Theory: II ----Measuring & Identical Theorems, Origins & Classifications of Entanglements and Solution to Crisis of Wave Collapse

2021 ◽  
Author(s):  
C. Huang ◽  
Yong-Chang Huang ◽  
Yi-You Nie
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Quantum Theory ◽  
Statistical Mechanics ◽  
Particle System ◽  
Square Root ◽  
Classical Statistical Mechanics ◽  
Wave Particle Duality ◽  
Wave Collapse ◽  
Modern Physics

This paper derives measurement and identical principles, then makes the two principles into measurement and identical theorems of quantum mechanics, plus the three theorems derived earlier, we deduce the axiom system of current quantum mechanics, the general quantum theory no axiom presumptions not only solves the crisis to understand in current quantum mechanics, but also obtains new discoveries, e.g., discovers the velocities of quantum collapse and entanglement are instantaneously infinitely large. We deduce the general Schrȍdinger equation of any n particles from two aspects, and the wave function not only has particle properties of the complex square root state vector of the classical probability density of any n particles, but also has the plane wave properties of any n particles. Thus, the current crisis of the dispute about the origin of wave- particle duality of any n microscopic particles is solved. We display the classical locality and quantum non-locality for any n particle system, show entanglement origins, and discover not only any n-particle wave function system has the original, superposition and across entanglements, but also the entanglements are of interactions preserving conservation or correlation, three kinds of entanglements directly give lots of entanglement sources. This paper discovers, one of two pillars of modern physics, quantum mechanics of any n particle system is a generalization ( mechanics ) theory of the complex square root ( of real density function ) of classical statistical mechanics, any n particle system’s quantum mechanics of being just a generalization theory of the complex square root of classical statistical mechanics is both a revolutionary discovery and key new physics, which are influencing people’s philosophical thinking for modern physics, solve all the crisises in current quantum theories, quantum information and so on, and make quantum theory have scientific solid foundations checked, no basic axiom presumption and no all quantum strange incomprehensible properties, because classical statistical mechanics and its complex square root have scientific solid foundations checked. Thus, all current studies on various entanglements and their uses to quantum computer, quantum information and so on must be further updated and classified by the new entanglements. This and our early papers derive quantum physics, solve all crisises of basses of quantum mechanics, e.g., wave-particle duality & the first quantization origins, quantum nonlocality, entanglement origins & classifications, wave collapse and so on.Key words: quantum mechanics, operator, basic presumptions, wave-particle duality, principle of measurement, identical principle, superposition principle of states, entanglement origin, quantum communication, wave collapse, classical statistical mechanics, classical mechanics

Exploring Classical Mechanics

2020 ◽  
Author(s):  
G. L. Kotkin ◽  
V. G. Serbo
Keyword(s):  
Quantum Mechanics ◽  
Statistical Mechanics ◽  
Classical Mechanics ◽  
Theoretical Physics ◽  
English Edition ◽  
Mechanical Part ◽  
Russian Edition ◽  
The Given

This book was written by the working physicists for students and teachers of physics faculties of universities. Its contents correspond roughly to the corresponding course in the textbooks Mechanics by L. D. Landau and E. M. Lifshitz (1976) and Classical Mechanics by H. Goldstein, Ch. Poole, and J. Safko (2000). As a rule, the given solution of a problem is not finished with obtaining the required formulae. It is necessary to analyse the results, and this is of great interest and by no means a mechanical part of the solution. The authors consider classical mechanics as the first chapter of theoretical physics; the methods and ideas developed in this chapter are literally important for all other sections of theoretical physics. Thus, the authors have indicated wherever this does not require additional amplification, the analogy or points of contact with the problems in quantum mechanics, electrodynamics, or statistical mechanics. The first English edition of this book was published by Pergamon Press in 1971 with the invaluable help by the translation editor D. ter Haar. This second English publication is based on the fourth Russian edition of 2010 as well as the problems added in the publications in Spanish and French. As a result, this book contains 357 problems instead of the 289 problems that appeared in the first English edition.

Uncertainty in quantum mechanics: faith or fantasy?

2011 ◽  
Vol 369 (1956) ◽  
pp. 4864-4890 ◽  
Author(s):  
Roger Penrose
Keyword(s):  
Quantum Mechanics ◽  
Quantum Measurement ◽  
Uncertainty Principle ◽  
Quantum Level ◽  
Diverse Range ◽  
Absolute Truth ◽  
Quantum Uncertainty ◽  
Level Of Activity ◽  
Heisenberg's Uncertainty Principle

The word ‘uncertainty’, in the context of quantum mechanics, usually evokes an impression of an essential unknowability of what might actually be going on at the quantum level of activity, as is made explicit in Heisenberg's uncertainty principle, and in the fact that the theory normally provides only probabilities for the results of quantum measurement. These issues limit our ultimate understanding of the behaviour of things, if we take quantum mechanics to represent an absolute truth. But they do not cause us to put that very ‘truth’ into question. This article addresses the issue of quantum ‘uncertainty’ from a different perspective, raising the question of whether this term might be applied to the theory itself, despite its unrefuted huge success over an enormously diverse range of observed phenomena. There are, indeed, seeming internal contradictions in the theory that lead us to infer that a total faith in it at all levels of scale leads us to almost fantastical implications.

scholarly journals Interpretive analogies between quantum and statistical mechanics

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
C. D. McCoy
Keyword(s):  
Quantum Mechanics ◽  
Statistical Mechanics ◽  
Quantum Measurement ◽  
Measurement Problem ◽  
Initial Conditions ◽  
Primitive Ontology ◽  
Quantum Measurement Problem ◽  
Classical Statistical Mechanics ◽  
Interpretive Strategies ◽  
Significant Application

AbstractThe conspicuous similarities between interpretive strategies in classical statistical mechanics and in quantum mechanics may be grounded on their employment of common implementations of probability. The objective probabilities which represent the underlying stochasticity of these theories can be naturally associated with three of their common formal features: initial conditions, dynamics, and observables. Various well-known interpretations of the two theories line up with particular choices among these three ways of implementing probability. This perspective has significant application to debates on primitive ontology and to the quantum measurement problem.

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