Foundations And Interpretation Of Quantum Mechanics

The aim of this book is twofold: to provide a comprehensive account of the foundations of the theory and to outline a theoretical and philosophical interpretation suggested from the results of the last twenty years.There is a need to provide an account of the foundations of the theory because recent experience has largely confirmed the theory and offered a wealth of new discoveries and possibilities. On the other side, the following results have generated a new basis for discussing the problem of the interpretation: the new developments in measurement theory; the experimental generation of ?Schr”dinger cats?; recent developments which allow, for the first time, the simultaneous measurement of complementary observables; quantum information processing, teleportation and computation.To accomplish this task, the book combines historical, systematic and thematic approaches.

Authored by an acclaimed teacher of quantum physics and philosophy, this textbook pays special attention to the aspects that many courses sweep under the carpet. Traditional courses in quantum mechanics teach students how to use the quantum formalism to make calculations. But even the best students - indeed, especially the best students - emerge rather confused about what, exactly, the theory says is going on, physically, in microscopic systems. This supplementary textbook is designed to help such students understand that they are not alone in their confusions (luminaries such as Albert Einstein, Erwin Schroedinger, and John Stewart Bell having shared them), to sharpen their understanding of the most important difficulties associated with interpreting quantum theory in a realistic manner, and to introduce them to the most promising attempts to formulate the theory in a way that is physically clear and coherent. The text is accessible to students with at least one semester of prior exposure to quantum (or "modern") physics and includes over a hundred engaging end-of-chapter "Projects" that make the book suitable for either a traditional classroom or for self-study.

This comprehensive volume gives a balanced and systematic treatment of both the interpretation and the mathematical-conceptual foundations of quantum mechanics. It is written in a pedagogical style and addresses many thorny problems of fundamental physics. The first aspect concerns Interpretation. The author raises the central problems: formalism, measurement, non-locality, and causality. The main positions on these subjects are presented and critically analysed. The aim is to show that the main schools can converge on a core interpretation. The second aspect concerns Foundations. Here it is shown that the whole theory can be grounded on information theory. The distinction between information and signal leads us to integrating quantum mechanics and relativity. Category theory is presented and its significance for quantum information shown; the logic and epistemological bases of the theory are assessed. Of relevance to all physicists and philosophers with an interest in quantum theory and its foundations, this book is destined to become a classic work.

It may tum out that, like certain other phenomena studied by sociologists, bouts of interest in the foundations of quantum mechanics tend to come in 60-year cycles. It is hardly surprising that in the first decade or so of the subject the conceptual puzzles generated by this strange new way of looking at the world should have generated profound interest, not just among professional physicists themselves but also among philosophers and informed laymen; but this intense interest was followed by a fallow period in the forties and fifties when the physics establishment by and large took the view that the only puzzles left were the product either of incompetent application of the formalism or of bad philosophy, and only a few brave individualists like the late David Bohm dared to suggest that maybe there really was something there after all to worry about. As Bell and Nauenberg, surveying the scene in 1966, put it: "The typical physicist feels that [these questions 1 have long ago been answered, and that he will fully understand how if ever he can spare twenty minutes to think about it. " But gradually, through the sixties and seventies, curiosity did revive, and the last ten years or so have seen a level of interest in foundational questions, and an involvement in them by some of the leading figures of contemporary physics, which is probably unparalleled since the earliest days.

Quantum mechanics is an extraordinarily successful scientific theory. But more than 100 years after it was first introduced, the interpretation of the theory remains controversial. This Element introduces some of the most puzzling questions at the foundations of quantum mechanics and provides an up-to-date and forward-looking survey of the most prominent ways in which physicists and philosophers of physics have attempted to resolve them. Topics covered include nonlocality, contextuality, the reality of the wavefunction and the measurement problem. The discussion is supplemented with descriptions of some of the most important mathematical results from recent work in quantum foundations, including Bell's theorem, the Kochen-Specker theorem and the PBR theorem.

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.

This book studies the foundations of quantum theory through its relationship to classical physics. This idea goes back to the Copenhagen Interpretation (in the original version due to Bohr and Heisenberg), which the author relates to the mathematical formalism of operator algebras originally created by von Neumann. The book therefore includes comprehensive appendices on functional analysis and C*-algebras, as well as a briefer one on logic, category theory, and topos theory. Matters of foundational as well as mathematical interest that are covered in detail include symmetry (and its "spontaneous" breaking), the measurement problem, the Kochen-Specker, Free Will, and Bell Theorems, the Kadison-Singer conjecture, quantization, indistinguishable particles, the quantum theory of large systems, and quantum logic, the latter in connection with the topos approach to quantum theory. This work was published by Saint Philip Street Press pursuant to a Creative Commons license permitting commercial use. All rights not granted by the work's license are retained by the author or authors.

This volume provides a sample of the present research on the foundations of quantum mechanics and related topics by collecting the papers of the Italian scholars who attended the conference entitled “The Foundations of Quantum Mechanics — Historical Analysis and Open Questions” (Lecce, 1998). The perspective of the book is interdisciplinary, and hence philosophical, historical and technical papers are gathered together so as to allow the reader to compare different viewpoints and cultural approaches. Most of the papers confront, directly or indirectly, the objectivity problem, taking into account the positions of the founders of QM or more recent developments. More specifically, the technical papers in the book pay special attention to the interpretation of the experiments on Bell's inequalities and to decoherence theory, but topics on unsharp QM, the consistent-history approach, quantum probability and alternative theories are also discussed. Furthermore, a number of historical and philosophical papers are devoted to Planck's, Weyl's and Pauli's thought, but topics such as quantum ontology, predictivity of quantum laws, etc., are treated.