An Axiomatic Basis for Quantum Mechanics: Volume 2 Quantum Mechanics and Macrosystems

ISBN-13: 9783642718991 / Angielski / Miękka / 2011 / 244 str.

G. Nther Ludwig; Kurt Just

Opis

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."

Spis treści

IX Further Structures of Preparation and Registration.- § 1 Transformations of Registration Procedures Relative to Preparation Procedures.- § 2 Composite System and Scattering Experiments.- § 3 Measurement Scatterings and Transportations.- X The Embedding Problem.- § 1 Classical Theories as Approximations to the Quantum Mechanics of Microsystems.- § 2 Macroscopic Systems and an Extrapolated Quantum Mechanics.- § 2.1 An Extrapolated Quantum Mechanics.- § 2.2 The Embedding of PTmin PTqexp.- § 2.3 General Consequences of the Embedding Theorem.- § 2.4 Partitioning of the Macroscopic Effects into Classes.- § 2.5 Dynamics.- § 2.6 Dynamically Determined Systems and Contracted State Spaces.- § 2.7 Disturbances by Measurements.- § 3 Examples for Approximate Embedding.- § 3.1 Imprecision Sets.- § 3.2 Embedding at Time Zero.- § 3.3 The Embedding of the Time Evolution.- § 3.4 A Heavy Masspoint.- § 3.5 The Boltzmann Distribution Function.- § 4 Intermediate Systems.- XI Compatibility of PTq with PTqexp.- § 1 Scattering of Microsystems on Macrosystems.- § 2 Preparation.- § 3 Registration.- § 4 Coupling of Preparation and Registration.- § 5 Macrosystems as Transpreparators.- § 6 The Problem of Embedding the Scattering Theory of Microsystems on Macrosystems in PTqexp.- § 7 The Problem of the Desired Observables and Preparators.- XII Special Structures in Preparation and Registration Devices.- § 1 Measurement Chains.- § 2 The Einstein-Podolsky-Rosen Paradox.- § 3 Microsystems and Time Direction.- § 4 Macrosystems and Time Direction.- § 5 The Place of Human Beings in Quantum Mechanics.- XIII Relations Between Different Forms of Quantum Mechanics and the Reality Problem.- § 1 Correspondence Rules.- § 2 The Physical Contents of a Theory.- § 2.1 Species of Structure.- § 2.2 Axiomatic Bases.- § 2.3 Laws of Nature and Theoretical Terms.- § 2.4 Norms and Fundamental Domain.- § 2.5 Empirical Laws and the Finiteness of Physics.- § 3 Intertheory Relations.- § 3.1 Restrictions.- § 3.2 Embedding.- § 3.3 Networks of Theories and the Various Forms of Quantum Mechanics.- § 3.4 Pretheories.- § 4 Physically Possible, Physically Real Facts and Physically Open Questions.- § 4.1 Hypotheses in a PT.- § 4.2 Classifications of Hypotheses.- § 4.3 Relations Between Various Hypotheses.- § 4.4 Bahavior of Hypotheses under Extension of the Observational Report.- § 4.5 The Mathematical Game.- § 4.6 Possibility, Reality, Open Questions.- § 4.7 Some Aspects of the Quantum Mechanical Game and the Role of Probability Theory in Physics.- § 4.8 Real Facts and the Reality of Microsystems.- § 4.9 The Real Domain of a PT.- List of Frequently Used Symbols (1).- List of Frequently Used Symbols (2).- List of Axioms.