The background for this book was a shift of interest among experimental physicists that began approximately 20 years ago. The shift was from quantum measurements on large ensembles of microscopic quantum objects, to experiments of very high precision on single, macroscopic objects. This shift was accompanied by developments in the “culture” of such measurements and the invention and elaboration of new experimental methods. In parallel with these experimental developments, there was a noticeable increase of theoretical interest in the foundations and interpretation of quantum theory, and even in attempts to revise its foundational principles. Although these efforts have not produced any significant changes in the fundamental structure of quantum theory, they have revealed a rather large number of “blank spots” and unsolved problems, to which the founders of quantum physics had paid no attention. A reasonable number of the blank spots have been filled in during the past decade. The reader has probably noticed that this book can be divided into two parts. In the first (chapters I―VII and XI), the authors have tried to present the modern approach to the quantum theory of measurement. This part can be regarded as a tutorial appendix to textbooks for advanced undergraduate or graduate-level courses in quantum mechanics, where little attention is usually paid to measurement theory.
The background for this book was a shift of interest among experimental physicists that began approximately 20 years ago. The shift was from quantum measurements on large ensembles of microscopic quantum objects, to experiments of very high precision on single, macroscopic objects. This shift was accompanied by developments in the “culture” of such measurements and the invention and elaboration of new experimental methods. In parallel with these experimental developments, there was a noticeable increase of theoretical interest in the foundations and interpretation of quantum theory, and even in attempts to revise its foundational principles. Although these efforts have not produced any significant changes in the fundamental structure of quantum theory, they have revealed a rather large number of “blank spots” and unsolved problems, to which the founders of quantum physics had paid no attention. A reasonable number of the blank spots have been filled in during the past decade. The reader has probably noticed that this book can be divided into two parts. In the first (chapters I―VII and XI), the authors have tried to present the modern approach to the quantum theory of measurement. This part can be regarded as a tutorial appendix to textbooks for advanced undergraduate or graduate-level courses in quantum mechanics, where little attention is usually paid to measurement theory.
In the standard, textbook treatment of quantum mechanics, the contact with experiment is described in terms of probabilities for obtaining this, that, or another result, when identical experiments are performed on a huge number ( ensemble ) of identical objects. Such an ensemble description was adequate during the first half century of quantum theory, because the technology of that era was incapable of making a measurement without destroying or severely changing the measured object (photon, atom, …). In recent years, however, advances in technology and technique have made possible repetitive quantum measurements on a single quantum object, with each measurement influencing the object only minimally. Such measurements cannot be analyzed using solely the ensemble theory. Additional theoretical concepts are needed. The purpose of this book is to describe the methods and theory of such measurements (as well as the more elementary theory of ensembles of measurements). This book is written for two types of readers: those who have had only a little previous contact with quantum mechanics, and those who have had much. Readers of the first type are presumed to understand atomic physics at a qualitative level. The unstarred sections of this book offer such readers an overview of the present state-of-the-art of quantum measurements on single objects and prospects for the future, as well as an elementary overview of the theory of such measurements.
Although there are many textbooks that deal with the formal apparatus of quantum mechanics (QM) and its application to standard problems, none take into account the developments in the foundations of the subject which have taken place in the last few decades. There are specialized treatises on various aspects of the foundations of QM, but none that integrate those topics with the standard material. This book aims to remove that unfortunate dichotomy, which has divorced the practical aspects of the subject from the interpretation and broader implications of the theory.The book is intended primarily as a graduate level textbook, but it will also be of interest to physicists and philosophers who study the foundations of QM. Parts of it could be used by senior undergraduates too.
This book is an up-to-date introduction to the quantum theory of measurement, a fast developing field of intense current interest to scientists and engineers for its potential high technology applications. It is also a subject of importance to students for its central role in the foundations of quantum mechanics. Although the main principles of the field were elaborated in the 1930s by Bohr, Schrödinger, Heisenberg, von Neumann and Mandelstam, it was not until the 1980s that technology became sufficiently advanced to allow its application in real experiments. Quantum measurement is now central to many ultra-high technology developments, such as squeezed light, single atom traps, and searches for gravitational radiation. It is also considered to have great promise for computer science and engineering, particularly for its applications in information processing and transfer. The book contains a pedagogical introduction to the relevant theory written at a level accessible to those with only a modest background in quantum mechanics. It then goes on to discuss aspects of the design of practical quantum measurement systems. This book is essential reading for all scientists and engineers interested in the potential applications of technology near the quantum limit. It will also serve as an ideal supplement to standard quantum mechanics textbooks at the advanced undergraduate or graduate level.
Although it is 70 years old, there are still areas of quantum theory which are open to interpretation. This book deals with such interpretational problems, and in particular with the issue of the measurement process. The main theme is whether quantum mechanics can be viewed as a (semantically) complete theory, namely as a theory capable of describing not only the physical object under observation but also the measuring instruments used to detect the properties of that physical object. The problematic aspects arise from the fact that the measuring instruments themselves behave as classical physical systems. Thus, we are faced with the open problem of the transition from the quantum to the classical, or more explicitly, the problem of why the composition of many quantum micro-objects gives rise to classical macro-objects. This book goes carefully, exhaustively, and deeply into the interpretational problems of quantum mechanics induced by the measurement process. The solution of many relevant issues, as well as the problems that remain unsolved, emerge clearly. The discussion itself is self-contained and the technical parts are reader-friendly. This book is of value to graduate students and researchers who have an interest in the physical, mathematical, and philosophical foundations of quantum mechanics.
The topics of this book are the mathematical foundations of non-relativistic quantum mechanics and the mathematical theory they require. The main characteristic of the book is that the mathematics is developed assuming familiarity with elementary analysis only. Moreover, all the proofs are carried out in detail. These features make the book easily accessible to readers with only the mathematical training offered by undergraduate education in mathematics or in physics, and also ideal for individual study. The principles of quantum mechanics are discussed with complete mathematical accuracy and an effort is made to always trace them back to the experimental reality that lies at their root. The treatment of quantum mechanics is axiomatic, with definitions followed by propositions proved in a mathematical fashion. No previous knowledge of quantum mechanics is required. This book is designed so that parts of it can be easily used for various courses in mathematics and mathematical physics, as suggested in the Preface. The book is of interest to researchers and graduate students in functional analysis, who can see how closely an important part of their chosen field is linked with quantum mechanics, and also to physicists, who can see how the abstract language of functional analysis brings unity to the apparently distinct approaches employed in quantum theory.
The important changes quantum mechanics has undergone in recent years are reflected in this approach for students. A strong narrative and over 300 worked problems lead the student from experiment, through general principles of the theory, to modern applications. Stepping through results allows students to gain a thorough understanding. Starting with basic quantum mechanics, the book moves on to more advanced theory, followed by applications, perturbation methods and special fields, and ending with developments in the field. Historical, mathematical and philosophical boxes guide the student through the theory. Unique to this textbook are chapters on measurement and quantum optics, both at the forefront of current research. Advanced undergraduate and graduate students will benefit from this perspective on the fundamental physical paradigm and its applications. Online resources including solutions to selected problems, and 200 figures, with colour versions of some figures, are available at www.cambridge.org/Auletta.