An Axiomatic Basis For Quantum Mechanics Derivation Of Hilbert Space Structure
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| Author | : G. Ludwig |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 255 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 3642700292 |
This book is the first volume of a two-volume work, which is an improved version of a preprint [47] published in German. We seek to deduce the funda mental concepts of quantum mechanics solely from a description of macroscopic devices. The microscopic systems such as electrons, atoms, etc. must be detected on the basis of the macroscopic behavior of the devices. This detection resembles the detection of the dinosaurs on the basis offossils. In this first volume we develop a general description of macroscopic systems by trajectories in state spaces. This general description is a basis for the special de scription of devices consisting of two parts, where the first part is acting on the second. The microsystems are discovered as systems transmitting the action. Axioms which describe general empirical structures of the interactions between the two parts of each device, give rise to a derivation of the Hilbert space structure of quantum mechanics. Possibly, these axioms (and consequently the Hilbert space structure) may fail to describe other realms than the structure of atoms and mole cules, for instance the "elementary particles". This book supplements ref. [2]. Both together not only give an extensive foundation of quantum mechanics but also a solution in principle of the measuring problem.
| Author | : G. Ludwig |
| Publisher | : Springer |
| Total Pages | : 0 |
| Release | : 2011-11-17 |
| Genre | : Science |
| ISBN | : 9783642700316 |
This book is the first volume of a two-volume work, which is an improved version of a preprint [47] published in German. We seek to deduce the funda mental concepts of quantum mechanics solely from a description of macroscopic devices. The microscopic systems such as electrons, atoms, etc. must be detected on the basis of the macroscopic behavior of the devices. This detection resembles the detection of the dinosaurs on the basis offossils. In this first volume we develop a general description of macroscopic systems by trajectories in state spaces. This general description is a basis for the special de scription of devices consisting of two parts, where the first part is acting on the second. The microsystems are discovered as systems transmitting the action. Axioms which describe general empirical structures of the interactions between the two parts of each device, give rise to a derivation of the Hilbert space structure of quantum mechanics. Possibly, these axioms (and consequently the Hilbert space structure) may fail to describe other realms than the structure of atoms and mole cules, for instance the "elementary particles". This book supplements ref. [2]. Both together not only give an extensive foundation of quantum mechanics but also a solution in principle of the measuring problem.
| Author | : Günther Ludwig |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 252 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 3642718973 |
In the first volume we based quantum mechanics on the objective description of macroscopic devices. The further development of the quantum mechanics of atoms, molecules, and collision processes has been described in [2]. In this context also the usual description of composite systems by tensor products of Hilbert spaces has been introduced. This method can be formally extrapolated to systems composed of "many" ele mentary systems, even arbitrarily many. One formerly had the opinion that this "extrapolated quantum mechanics" is a more comprehensive theory than the objec tive description of macrosystems, an opinion which generated unsurmountable diffi culties for explaining the measuring process. With respect to our foundation of quan tum mechanics on macroscopic objectivity, this opinion would mean that our founda tion is no foundation at all. The task of this second volume is to attain a compatibility between the objective description of macrosystems and an extrapolated quantum mechanics. Thus in X we establish the "statistical mechanics" of macrosystems as a theory more compre hensive than an extrapolated quantum mechanics. On this basis we solve the problem of the measuring process in quantum mechan ics, in XI developing a theory which describes the measuring process as an interaction between microsystems and a macroscopic device. This theory also allows to calculate "in principle" the observable measured by a device. Neither an incorporation of consciousness nor a mysterious imagination such as "collapsing" wave packets are necessary.
| Author | : Günther Ludwig |
| Publisher | : Springer |
| Total Pages | : 264 |
| Release | : 1987-06-26 |
| Genre | : Science |
| ISBN | : 9783540175407 |
In the first volume we based quantum mechanics on the objective description of macroscopic devices. The further development of the quantum mechanics of atoms, molecules, and collision processes has been described in [2]. In this context also the usual description of composite systems by tensor products of Hilbert spaces has been introduced. This method can be formally extrapolated to systems composed of "many" ele mentary systems, even arbitrarily many. One formerly had the opinion that this "extrapolated quantum mechanics" is a more comprehensive theory than the objec tive description of macrosystems, an opinion which generated unsurmountable diffi culties for explaining the measuring process. With respect to our foundation of quan tum mechanics on macroscopic objectivity, this opinion would mean that our founda tion is no foundation at all. The task of this second volume is to attain a compatibility between the objective description of macrosystems and an extrapolated quantum mechanics. Thus in X we establish the "statistical mechanics" of macrosystems as a theory more compre hensive than an extrapolated quantum mechanics. On this basis we solve the problem of the measuring process in quantum mechan ics, in XI developing a theory which describes the measuring process as an interaction between microsystems and a macroscopic device. This theory also allows to calculate "in principle" the observable measured by a device. Neither an incorporation of consciousness nor a mysterious imagination such as "collapsing" wave packets are necessary.
| Author | : R. I. G. Hughes |
| Publisher | : Harvard University Press |
| Total Pages | : 388 |
| Release | : 1989 |
| Genre | : Philosophy |
| ISBN | : 9780674843929 |
This important work provides an account of the philosophical foundations of quantum theory that should become a classic text for scientists and nonscientists alike. Hughes offers the first detailed and accessible analysis of the Hilbert-space models used in quantum theory and explains why they are so successful. He goes on to show how the very suitability of Hilbert spaces for modeling the quantum world gives rise to deep problems of interpretation, and makes suggestions about how they can be overcome.
| Author | : Kurt Engesser |
| Publisher | : Elsevier |
| Total Pages | : 821 |
| Release | : 2011-08-11 |
| Genre | : Mathematics |
| ISBN | : 008055038X |
Since its inception in the famous 1936 paper by Birkhoff and von Neumann entitled “The logic of quantum mechanics quantum logic, i.e. the logical investigation of quantum mechanics, has undergone an enormous development. Various schools of thought and approaches have emerged and there are a variety of technical results.Quantum logic is a heterogeneous field of research ranging from investigations which may be termed logical in the traditional sense to studies focusing on structures which are on the border between algebra and logic. For the latter structures the term quantum structures is appropriate. The chapters of this Handbook, which are authored by the most eminent scholars in the field, constitute a comprehensive presentation of the main schools, approaches and results in the field of quantum logic and quantum structures. Much of the material presented is of recent origin representing the frontier of the subject. The present volume focuses on quantum structures. Among the structures studied extensively in this volume are, just to name a few, Hilbert lattices, D-posets, effect algebras MV algebras, partially ordered Abelian groups and those structures underlying quantum probability. - Written by eminent scholars in the field of logic- A comprehensive presentation of the theory, approaches and results in the field of quantum logic- Volume focuses on quantum structures
| Author | : Jirí Blank |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 626 |
| Release | : 1999-04-23 |
| Genre | : Science |
| ISBN | : 9781563961427 |
Market: Mathematicians, researchers, teachers, and graduate students specializing in quantum physics, mathematical physics, and applied mathematics. "I really enjoyed reading this work. It is very well written, by three real experts in the field. It stands quite alone....The translation is remarkably good." John R. Taylor, University of Colorado Based on lectures delivered over the past two decades, this book explains in detail the theory of linear Hilbert-space operators and its uses in quantum physics. The central mathematical tool of this book is the spectral theory of self-adjoint operators, which together with functional analysis and an introduction to the theory of operator sets and algebras, is used in a systematic analysis of the operator aspect of quantum theory. In addition, the theory of Hilbert-space operators is discussed in conjunction with various applications such as Schrodinger operators and scattering theory.
| Author | : Wolfram Schommers |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 352 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 3642955703 |
Schommers introduces the foundations, mostly from a histori- cal point of view. Eberhard gives an introductory account of the Einstein-Podolsky-Rosen paradox and Bell's celebrated inequalities. D'Espagnat discusses realism andseparability and concludes that contemporary physics does not lead to a definite conception of the world. Eberhard shows how a model consistent with Bell's theorem can be constructed by ad- mitting faster-than-light action at a distance. Schommers discusses the structure ofspace-time and argues that physi- cally real processes do not take place in but are projected on space-time. Selleri discusses the idea that objectively real quantum waves exist and could in principle be detected.
| Author | : A. Blaquiere |
| Publisher | : Springer |
| Total Pages | : 356 |
| Release | : 2014-05-04 |
| Genre | : Science |
| ISBN | : 3709129710 |
| Author | : Jirí Blank |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 677 |
| Release | : 2008-09-24 |
| Genre | : Science |
| ISBN | : 1402088701 |
The new edition of this book detailing the theory of linear-Hilbert space operators and their use in quantum physics contains two new chapters devoted to properties of quantum waveguides and quantum graphs. The bibliography contains 130 new items.
