The present volume is the fifth in a series of six, presenting a selection of the previously unpublished lecture notes of David Hilbert on the foundations of mathematics and natural science, roughly spanning the period from 1890 to 1933. Hilbert's Lectures and his personal interactions with the 'Hilbert circle' exercised a profound influence on the development of twentieth century mathematics and physics. The lecture notes presented, spanning virtually the whole of Hilbert's teaching career, document his intense engagement with the ideas of some of the central figures of modern science and make possible a detailed understanding of the development of his foundational work in geometry, arithmetic, logic, and proof theory, as well as in the theory of relativity, quantum mechanics and statistical physics. The lectures contain more philosophical, foundational and methodological remarks than does Hilbert's published work. Some of the individual volumes also reprint key published works of Hilbert when these are centrally relevant to the unpublished work presented. – Volume 5 has three parts, dealing with General Relativity, Epistemological Issues, and Quantum Mechanics. The core of the first part is Hilbert’s two semester lecture course on ‘The Foundations of Physics’ (1916/17). This is framed by Hilbert’s published ‘First and Second Communications’ on the ‘Foundations of Physics’ (1915, 1917) and by a selection of documents dealing with more specific topics like ‘The Principle of Causality’ or a lecture on the new concepts of space and time held in Bucharest in 1918. The epistemological issues concern the intricate relation between nature and mathematical knowledge, in particular the question of irreversibility and objectivity (1921) as well as the subtle question whether what Hilbert calls the ‘world equations’ are physically complete (1923). The last part deals with quantum theory in its early, advanced and mature stages. Hilbert held lecture courses on the mathematical foundations of quantum theory twice, before and after the breakthrough in 1926. These documents bear witness to one of the most dramatic changes in the foundations of science. M.-M. V.

This book presents contributions (242) by many of today's leading quantum physicists, philosophers and historians, including three Nobel laureates, this comprehensive A to Z of quantum physics provides a lucid understanding of the key concepts of quantum theory and experiment. It covers technical and interpretational aspects alike, and includes both traditional topics and newer areas such as quantum information and its relatives. The central concepts that have shaped contemporary understanding of the quantum world are clearly defined, with illustrations where helpful, and discussed at a level suitable for undergraduate and graduate students of physics, history of science, and philosophy of physics. All articles share three main aims: (1) to provide a clear definition and understanding of the term concerned; (2) where possible, to trace the historical origins of the concept; and (3) to provide a small but optimal selection of references to the most relevant literature, including pertinent historical studies. Also discussed are the often contentious philosophical implications derived from quantum theory and its associated experimental findings. This compendium will be an indispensable resource for all those seeking concise up-to-date information about the many facets of quantum physics. – Contents: Preface. - Alphabetical Compendium of Terms. - English-German-French Lexicon of Terms. - Author Biographies. M.-M. V.

This book presents an encyclopedic treatment of conceptual quantum mechanics as seen from a very up-to-date point of view. It explores the nature of quantum entanglement and quantum information and their role in the quantum world. Their relations to a number of key experiments and thought experiments in the history of quantum physics are considered, as is a range of interpretations of quantum mechanics that have been put forward as a means of understanding the fundamental nature of microphysics - the traditionally accepted domain of quantum mechanics - and in some cases, the universe as a whole. In this way, the book reveals the deep significance of entanglement and quantum information for our understanding of the physical world. – Table of contents : – Chapter 1, Superposition, Entanglement, and Limits of Local Causality; – Chapter 2, Quantum Measurement, Probability, and Logic; – Chapter 3, Interpretations of Quantum Mechanics; – Chapter 4, Information and Quantum Mechanics; – Chapter 5, Appendix. M.-M. V.

There is no sharp dividing line between the foundations of physics and philosophy of physics. This is especially true for quantum mechanics. The Author proposes a treatise devoted to the foundations of quantum physics and the role that causality plays in the microscopic world governed by the laws of quantum mechanics. There is no sharp dividing line between physics and philosophy of physics. This is especially true for quantum physics where debate on its interpretation and the status of the various entities postulated has raged in both the scientific and philosophical communities since the 1920s and continues to this day. Although it is readily granted that quantum mechanics produces some strange and counter-intuitive results, it is argued in Quantum Causality that quantum mechanics is not as weird as we might have been led to believe. – The dominant theory of quantum mechanics is called Orthodox Quantum Theory (also known as the Copenhagen Interpretation). Orthodox Quantum Theory is a ‘theoretical tool’ for making predictions for the possible results of experiments on quantum systems and requires the intervention of an observer or an observer’s proxy (e.g. a measuring apparatus) in order to produce predictions. Orthodox Quantum Theory does away with the notion of causality and denies the existence of an underlying quantum realm. – The Causal Theory is not well known within the physics community and many physicists who do know of it are generally dismissive in their attitudes. This is a historical legacy inherited by the majority of the physics community from the most influential founders of quantum mechanics, Niels Bohr and Werner Heisenberg. They both denied the independent existence of a quantum level of reality and declared that causality does not apply to quantum events. – Quantum Causality shows that the Causal Theory of Quantum Mechanics is a viable physical theory that provides realistic explanations for quantum phenomena. Much of what is argued for in this book will be controversial but, at the very least, these arguments will likely engender some lively debate on the various issues raised. – Chapter 1, General Introduction; – Chapter 2, Preliminaries; – Chapter 3, The Causal Theory of Quantum Mechanics; – Chapter 4, Energy and the Wave Field; – Chapter 5, Energy-Momentum Transfer and the Quantum Potential; – Chapter 6, The Exclusion Principle; – Chapter 7, Conclusions. M.-M. V.