​This book summarizes the results of research the authors have pursued in the past years on the problem of implementing Bell's notion of local causality in local physical theories and relating it to other important concepts and principles in the foundations of physics such as the Common Cause Principle, Bell's inequalities, the EPR (Einstein-Podolsky-Rosen) scenario, and various other locality and causality concepts. The book is intended for philosophers of science with an interest in the formal background of sciences, philosophers of physics and physicists working in foundation of physics.

This monograph identifies the essential characteristics of the objects described by current quantum theory and considers their relationship to space-time. In the process, it explicates the senses in which quantum objects may be consistently considered to have parts of which they may be composed or into which they may be decomposed. The book also demonstrates the degree to which reduction is possible in quantum mechanics, showing it to be related to the objective indefiniteness of quantum properties and the strong non-local correlations that can occur between the physical quantities of quantum subsystems. Careful attention is paid to the relationships among such property correlations, physical causation, probability, and symmetry in quantum theory. In this way, the text identifies and clarifies the conceptual grounds underlying the unique nature of many quantum phenomena.

Combining twenty-six original essays written by an impressive line-up of distinguished physicists and philosophers of physics, this anthology reflects some of the latest thoughts by leading experts on the influence of Bell's theorem on quantum physics. Essays progress from John Bell's character and background, through studies of his main work, and on to more speculative ideas, addressing the controversies surrounding the theorem, and investigating the theorem's meaning and its deep implications for the nature of physical reality. Combined, they present a powerful comment on the undeniable significance of Bell's theorem for the development of ideas in quantum physics over the past 50 years. Questions surrounding the assumptions and significance of Bell's work still inspire discussion in the field of quantum physics. Adding to this with a theoretical and philosophical perspective, this balanced anthology is an indispensable volume for students and researchers interested in the philosophy of physics and the foundations of quantum mechanics.

A conceptually and mathematically rigorous analysis of the common cause principle and its status in quantum theory.

This book is the most complete collection of John S Bell's research papers, review articles and lecture notes on the foundations of quantum mechanics. Some of this material has hitherto been difficult to access. The book also appears in a paperback edition, aimed at students and young researchers.This volume will be very useful to researchers in the foundations and applications of quantum mechanics.

John Bell, FRS was one of the leading expositors and interpreters of modern quantum theory. He is particularly famous for his discovery of the crucial difference between the predictions of conventional quantum mechanics and the implications of local causality, a concept insisted on by Einstein. John Bell's work played a major role in the development of our current understanding of the profound nature of quantum concepts and of the fundamental limitations they impose on the applicability of the classical ideas of space, time and locality. This book includes all of John Bell's published and unpublished papers on the conceptual and philosophical problems of quantum mechanics, including two papers that appeared after the first edition was published. The book includes a short Preface written by the author for the first edition, and also an introduction by Alain Aspect that puts into context John Bell's enormous contribution to the quantum philosophy debate.

This thesis is devoted to the systematic study of non-local theories that respect Lorentz invariance and are devoid of new, unphysical degrees of freedom. Such theories are attractive for phenomenological applications since they are mostly unconstrained by current experiments. Non-locality has played an increasingly important role in the physics of the last decades, appearing in effective actions in quantum field theory, and arising naturally in string theory and non-commutative geometry. It may even be a necessary ingredient for quantum theories of gravity. It is a feature of quantum entanglement, and may even solve the long-standing black hole information loss problem. “Non-locality” is a broad concept with many promising and fruitful applications in theoretical and mathematical physics. After a historical and pedagogical introduction into the concept of non-locality the author develops the notion of non-local Green functions to study various non-local weak-field problems in quantum mechanics, quantum field theory, gravity, and quantum field theory in curved spacetime. This thesis fills a gap in the literature by providing a self-contained exploration of weak-field effects in non-local theories, thereby establishing a “non-local intuition” which may serve as a stepping stone for studies of the full, non-linear problem of non-locality.

This textbook presents in a concise and self-contained way the advanced fundamental mathematical structures in quantum theory. It is based on lectures prepared for a 6 months course for MSc students. The reader is introduced to the beautiful interconnection between logic, lattice theory, general probability theory, and general spectral theory including the basic theory of von Neumann algebras and of the algebraic formulation, naturally arising in the study of the mathematical machinery of quantum theories. Some general results concerning hidden-variable interpretations of QM such as Gleason's and the Kochen-Specker theorems and the related notions of realism and non-contextuality are carefully discussed. This is done also in relation with the famous Bell (BCHSH) inequality concerning local causality. Written in a didactic style, this book includes many examples and solved exercises. The work is organized as follows. Chapter 1 reviews some elementary facts and properties of quantum systems. Chapter 2 and 3 present the main results of spectral analysis in complex Hilbert spaces. Chapter 4 introduces the point of view of the orthomodular lattices' theory. Quantum theory form this perspective turns out to the probability measure theory on the non-Boolean lattice of elementary observables and Gleason's theorem characterizes all these measures. Chapter 5 deals with some philosophical and interpretative aspects of quantum theory like hidden-variable formulations of QM. The Kochen-Specker theorem and its implications are analyzed also in relation BCHSH inequality, entanglement, realism, locality, and non-contextuality. Chapter 6 focuses on the algebra of observables also in the presence of superselection rules introducing the notion of von Neumann algebra. Chapter 7 offers the idea of (groups of) quantum symmetry, in particular, illustrated in terms of Wigner and Kadison theorems. Chapter 8 deals with the elementary ideas and results of the so called algebraic formulation of quantum theories in terms of both *-algebras and C*-algebras. This book should appeal to a dual readership: on one hand mathematicians that wish to acquire the tools that unlock the physical aspects of quantum theories; on the other physicists eager to solidify their understanding of the mathematical scaffolding of quantum theories.

Covering much of the recent debate, this ambitious text provides new, decisive proof of the reality of the wave function.

The new edition provided the opportunity of adding a new chapter entitled "Principles and Lessons of Quantum Physics". It was a tempting challenge to try to sharpen the points at issue in the long lasting debate on the Copenhagen Spirit, to assess the significance of various arguments from our present vantage point, seventy years after the advent of quantum theory, where, after ali, some problems appear in a different light. It includes a section on the assumptions leading to the specific mathematical formalism of quantum theory and a section entitled "The evolutionary picture" describing my personal conclusions. Alto gether the discussion suggests that the conventional language is too narrow and that neither the mathematical nor the conceptual structure are built for eter nity. Future theories will demand radical changes though not in the direction of a return to determinism. Essential lessons taught by Bohr will persist. This chapter is essentially self-contained. Some new material has been added in the last chapter. It concerns the char acterization of specific theories within the general frame and recent progress in quantum field theory on curved space-time manifolds. A few pages on renor malization have been added in Chapter II and some effort has been invested in the search for mistakes and unclear passages in the first edition. The central objective of the book, expressed in the title "Local Quantum Physics", is the synthesis between special relativity and quantum theory to gether with a few other principles of general nature.