Peter Mittelstaedt - Böcker

The main theme of this book is the idea that quantum mechanics is valid not only for microscopic objects but also for the macroscopic apparatus used for quantum mechanical measurements. The author demonstrates the intimate relations that exist between quantum mechanics and its interpretation which are induced by the quantum mechanical measurement process. Consequently, the book is concerned both with the philosophical, metatheoretical problems of interpretations and with the more formal problems of quantum object theory. The consequences of this approach turn out to be partly very promising and partly rather disappointing. On the one hand, it is possible to give a rigorous justification of some important parts of interpretation, such as probability, by means of object theory. On the other hand, the problem of the objectification of measurement results leads to inconsistencies which cannot be resolved in an obvious way. This open problem has far-reaching consequences for the possibility of recognising an objective reality in physics.

The book is concerned with the laws of nature and in particular with the laws of physics. The authors discuss three important questions: First, whether the observed regularities are based on strict "laws of nature" that hold rigorously and without any exception. Second, what we call a "law of nature" is studied by comparing this concept with invariance principles, causality principles, teleological principles and means of predicting future events. Finally, on the basis of these investigations the authors treat the ambitious and intricate third question, why the laws of nature hold. Are there rational reasons for this largely unexplained phenomenon? This book addresses students as well as researchers. It will be an excellent reference for those interested in the philosophical foundations of the natural sciences.

The book is concerned with the laws of nature and in particular with the laws of physics. The authors discuss three important questions: First, whether the observed regularities are based on strict "laws of nature" that hold rigorously and without any exception. Second, what we call a "law of nature" is studied by comparing this concept with invariance principles, causality principles, teleological principles and means of predicting future events. Finally, on the basis of these investigations the authors treat the ambitious and intricate third question, why the laws of nature hold. Are there rational reasons for this largely unexplained phenomenon? This book addresses students as well as researchers. It will be an excellent reference for those interested in the philosophical foundations of the natural sciences.

The amazing accuracy in verifying quantum effects experimentally has recently renewed interest in quantum mechanical measurement theory. In this book the authors give within the Hilbert space formulation of quantum mechanics a systematic exposition of the quantum theory of measurement. Their approach includes the concepts of unsharp objectification and of nonunitary transformations needed for a unifying description of various detailed investigations. The book addresses advanced students and researchers in physics and philosophy of science. In this second edition Chaps. II-IV have been substantially rewritten. In particular, an insolubility theorem for the objectification problem has been formulated in full generality, which includes unsharp object observables as well as unsharp pointers.

Professor Peter Mittelstaedt is a physicist whose primary concern is the foundations of current physical theories. This concern has made him, through his prolonged, incisive and detailed examinations of the structures and overall characteristics of these theories, into a philosopher of physic- of contemporary physics, to be precise, of relativistic theories of space and time, and of the logic of quantum mechanics, in particular. The present book, which expounds his main ideas in these matters, has seen four editions (in German), each including newer results - as indeed does the present translation: see the author's 1975 preface to the English translation. Perhaps this is the place to repeat the author's chief problem and mention his own approach, even though they are expounded in his Intro­ duction. How close is Mittelstaedt to Kant's understanding of science? We are at liberty to choose a framework for thought - a logic and a method­ ology - prior to experience (in the classic sense, to think a priori); yet we choose a framework so as to fit our empirical findings. How is this done? How may it be understood and justified? This is obviously the question of all philosophies that evolve from, and are in reaction to, Kant's system.

In 1936, G. Birkhoff and J. v. Neumann published an article with the title The logic of quantum mechanics'. In this paper, the authors demonstrated that in quantum mechanics the most simple observables which correspond to yes-no propositions about a quantum physical system constitute an algebraic structure, the most important proper­ ties of which are given by an orthocomplemented and quasimodular lattice Lq. Furthermore, this lattice of quantum mechanical proposi­ tions has, from a formal point of view, many similarities with a Boolean lattice L8 which is known to be the lattice of classical propositional logic. Therefore, one could conjecture that due to the algebraic structure of quantum mechanical observables a logical calculus Q of quantum mechanical propositions is established, which is slightly different from the calculus L of classical propositional logic but which is applicable to all quantum mechanical propositions (C. F. v. Weizsacker, 1955). This calculus has sometimes been called 'quan­ tum logic'. However, the statement that propositions about quantum physical systems are governed by the laws of quantum logic, which differ from ordinary classical logic and which are based on the empirically well-established quantum theory, is exposed to two serious objec­ tions: (a) Logic is a theory which deals with those relationships between various propositions that are valid independent of the content of the respective propositions. Thus, the validity of logical relationships is not restricted to a special type of proposition, e. g. to propositions about classical physical systems.

Newton’s classical physics and its underlying ontology are loaded with several metaphysical hypotheses that cannot be justified by rational reasoning nor by experimental evidence. Furthermore, it is well known that some of these hypotheses are not contained in the great theories of Modern Physics, such as the theory of Special Relativity and Quantum Mechanics. This book shows that, on the basis of Newton’s classical physics and by rational reconstruction, the theory of Special Relativity as well as Quantum Mechanics can be obtained by partly eliminating or attenuating the metaphysical hypotheses. Moreover, it is shown that these reconstructions do not require additional hypotheses or new experimental results. In the second edition the rational reconstructions are completed with respect to General Relativity and Cosmology. In addition, the statistics of quantum objects is elaborated in more detail with respect to the rational reconstruction of quantum mechanics. The new material completes the approach of the book as much as it is possible at the present state of knowledge. Presumably, the most important contribution that is added to the second edition refers to the problem of interpretation of the three great theories of Modern Physics. It is shown in detail that in the light of  rational reconstructions even realistic interpretations of the three theories of Modern Physics are possible and can easily be achieved.

Newton’s classical physics and its underlying ontology are loaded with several metaphysical hypotheses that cannot be justified by rational reasoning nor by experimental evidence. Furthermore, it is well known that some of these hypotheses are not contained in the great theories of Modern Physics, such as the theory of Special Relativity and Quantum Mechanics. This book shows that, on the basis of Newton’s classical physics and by rational reconstruction, the theory of Special Relativity as well as Quantum Mechanics can be obtained by partly eliminating or attenuating the metaphysical hypotheses. Moreover, it is shown that these reconstructions do not require additional hypotheses or new experimental results. In the second edition the rational reconstructions are completed with respect to General Relativity and Cosmology. In addition, the statistics of quantum objects is elaborated in more detail with respect to the rational reconstruction of quantum mechanics. The new material completes the approach of the book as much as it is possible at the present state of knowledge. Presumably, the most important contribution that is added to the second edition refers to the problem of interpretation of the three great theories of Modern Physics. It is shown in detail that in the light of  rational reconstructions even realistic interpretations of the three theories of Modern Physics are possible and can easily be achieved.

In 1936, G. Birkhoff and J. v. Neumann published an article with the title The logic of quantum mechanics'. In this paper, the authors demonstrated that in quantum mechanics the most simple observables which correspond to yes-no propositions about a quantum physical system constitute an algebraic structure, the most important proper­ ties of which are given by an orthocomplemented and quasimodular lattice Lq. Furthermore, this lattice of quantum mechanical proposi­ tions has, from a formal point of view, many similarities with a Boolean lattice L8 which is known to be the lattice of classical propositional logic. Therefore, one could conjecture that due to the algebraic structure of quantum mechanical observables a logical calculus Q of quantum mechanical propositions is established, which is slightly different from the calculus L of classical propositional logic but which is applicable to all quantum mechanical propositions (C. F. v. Weizsacker, 1955). This calculus has sometimes been called 'quan­ tum logic'. However, the statement that propositions about quantum physical systems are governed by the laws of quantum logic, which differ from ordinary classical logic and which are based on the empirically well-established quantum theory, is exposed to two serious objec­ tions: (a) Logic is a theory which deals with those relationships between various propositions that are valid independent of the content of the respective propositions. Thus, the validity of logical relationships is not restricted to a special type of proposition, e. g. to propositions about classical physical systems.

The theory of quantum mechanical measuring process has been a subject of increasing research interest during recent years. The revival of interest in it was encouraged during the 1980's due to the advances on the formal and conceptual structures of quantum mechanics, accompanied with new experimental possibilities and technological demands, as well as due to new ideas on the interpretation of the theory. This proceedings is devoted to reviewing the present situation on quantum measurement theory and discussing the related philosophical implications.

The theory of quantum mechanical measuring process has been a subject of increasing research interest during recent years. The revival of interest in it was encouraged during the 1980's due to the advances on the formal and conceptual structures of quantum mechanics, accompanied with new experimental possibilities and technological demands, as well as due to new ideas on the interpretation of the theory. This proceedings is devoted to reviewing the present situation on quantum measurement theory and discussing the related philosophical implications.

Symposium on the Foundations of Modern Physics 1993 is the fourth in a series of conferences held in Joensuu, Finland, in the years 1985, 1987 and 1990 and is devoted to offering discussions on foundational problems of quantum mechanics and other fundamental physical theories, taking into account new experimental developments. The surveying of the progress with respect to fundamental questions of the quantum theory of measurement forms the guiding line of thought of the present Symposium, the main themes discussed being: the interrelation of quantum measurement and irreversibility; the physics of information (concerned with questions of information processing and quantum noise); quantum interference and mesoscopic quantum effects (searching for the micro-macro borderline); and the quantum-classical relationship (the need for classical pointer and their realisation).