It is not easy for practicing physicists to keep track of the ongoing philosophical debate concerning the "reality'' of the entities they manipulate or the "objective validity'' of the results of their work. In addition, the role of the observer and the theory of the measuring process seem to be themselves controversial. Therefore it may be appropriate to present an interpretation of quantum mechanics which corresponds to the perspective of most practicing physicists, although the author makes no claim to possessing any particular knowledge of the literature in this domain. The final four sections present some more specific descriptions of the concepts used, so that they may also serve for more philosophical discussions.
It is not easy for practicing physicists to keep track of the ongoing philosophical debate concerning the "reality'' of the entities they manipulate or the "objective validity'' of the results of their work. In addition, the role of the observer and the theory of the measuring process seem to be themselves controversial. Therefore it may be appropriate to present an interpretation of quantum mechanics which corresponds to the perspective of most practicing physicists, although the author makes no claim to possessing any particular knowledge of the literature in this domain. The final four sections present some more specific descriptions of the concepts used, so that they may also serve for more philosophical discussions.
This tome is a formal presentation of the unsharp observable approach to quantum mechanics using the positive operator valued (POV) concept of an observable. It is intended for philosophers and mathematicians as well as physicists. This is a very formalistic book. There are, however, portions that should be read by all experimentalists performing quantum mechanical studies as well as graduate students completing their first graduate year quantum mechanics course. If we interpret quantum mechanics as making statistical predictions on the results of states prepared in identical fashions, we will often find that the observed probabilities are nearly, but not exactly, the expected 1 or 0 for measurements that are expected to always give the same result. Hence, rather than demanding sharp measures with probabilities of exactly 1 or 0, quantum mechanics allows a reasonable interpretation of unsharp results of nearly 1 or nearly 0. As the authors point out in chapter II, POV measures and the associated unsharp measures are not essential for an interpretation of quantum mechanical results. However, more sharp variables, and hence a larger Hilbert space, will be needed than are required by the unsharp approach. Also, the theoretical interpretation will often not be as straightforward with only sharp observables. As I have previously stated, all graduate students, both those of a theoretical and those of an experimental bent, should read parts of this book (after they have completed a normal introduction using sharp variables). They should at least read the first chapter which explains the unsharp variable measure concept as well as giving some examples, one of which is the Stern - Gerlach experiment. In chapter VII, the last chapter, the Stern - Gerlach experiment photon polarization and other quantum optical experiments and wave-particle duality experiments for photons are examined in detail using the POV formalism. This would also be an excellent chapter for all graduate students to read. Some sections may send them back to some of the intermediate chapters, hopefully to peruse in greater detail. The intermediate chapters contain the formal development of the POV formalism and compare it to the normal method. There is also a brief introduction to measurement theory using unsharp observables. As the authors state, this is not intended to be a complete solution to the problem of measurement theory. The next two chapters deal with uncertainty and phase space formalism as considered by the unsharp observables. Philosophers of physics and mathematicians will find this an excellent introduction to the POV formalism and the distinction between sharp and unsharp measurements. Many texts will gloss over both the philosophical and mathematical consequences inherent in the full statistical formalism of quantum mechanics. This monograph is not, by the authors' admission, a full treatment of quantum measurement theory. Also, although in the introduction the authors discuss the importance of applying quantum mechanics to individual objects, this book mainly considers the interpretations as statistical measures. There is little attempt to deal with the quantum mechanical interpretations of the behaviour of a single particle. That is, questions about measurements on a single particle or the interpretation of the wavefunction for a single particle are not fully covered. The authors claim that the POV approach is also the best for individual systems, but do little in applications. The major example given is in the last chapter where they consider interference measurements for single photons. They might have referenced more of the current alternative approaches to measurement theory of single particle wavefunctions. The readers of this journal will be disappointed, but not surprised, that the covariant nature of observables is restricted almost entirely to the Galilei group. The only Poincare group material is the example of photon localization in the last chapter. This is a reflection of the great difficulty of applying the special or the general theories of relativity to the Hilbert space formalism.
This novel text directly addresses common claims and misconceptions around quantum mechanics and presents a fresh and modern understanding of this fundamental and essential physical theory. It begins with a non-mathematical introduction to some of the more controversial topics in the foundations of quantum mechanics. For those more familiar with the theoretical framework of quantum mechanics, the text moves on to a general introduction to quantum field theory, followed by a detailed discussion of cutting-edge topics in this area such as decoherence and spontaneous coherence. Several important philosophical problems in quantum mechanics are considered, and their interpretations are compared, notably the Copenhagen and many-worlds interpretations. The inclusion of frequent real-world examples, such as superconductors and superfluids, ensures the book remains grounded in modern research. This book will be a valuable resource for students and researchers in both physics and the philosophy of science interested in the foundations of quantum mechanics.
By questioning the validity of some of our basic concepts, such as space, object, and causality, quantum physics contributes quite decisively to the dramatic changes now taking place in our world picture.This book is addressed not only to physicists at an early stage in their careers (the first or second year graduate student) but also to philosophers, as well as to all the senior physicists interested in the interpretation problem. Beginning with a chapter that could be described as ?philosophy for physicists,? it presents an in-depth analysis of present-day quantum mechanical concepts, an analysis of physicists and philosophers alike. Specifically, it first offers an extensive critical analysis of such topics as the Einstein, Podolsky, Rosen reality criterion, nonseparatability, the quantum measurement riddle, decoherence theory, consistent histories approaches and ontologically interpretable theories. All this then naturally leads to philosophical questions concerning, in particular, intersubjective agreement and the limit of realism. And a thorough examination of this whole material finally leads to the view that distinguishing between empirical reality and a veiled man-independent reality yields an acceptable answer to the perplexing question of how to interpret quantum physics. Veiled Reality offers nonspecialists, including students in physics, philosophy and the history of science, an accessible perspective on basic problems in the foundations of physics.
Complementarity and Deconstruction: Plotnitsky's Analysis and Beyond Makoto Katsumori Akita University The philosophical thought of the modern physicist Niels Bohr (1885–1962), which revolves around the concept of complementarity, has long been a major subject of historical and philosophical inquiry. Many prior studies of Bohr's complementarity, however, seem to be limited by the fact that they largely proceed within the conceptual frames of the "mainstream" philosophy of science. This being the case, his radical questioning of traditional scientific and philosophical notions—such as the unambiguity of concepts and words—has not been adequately addressed, insofar as these notions are uncritically presupposed by the commentators themselves. In other words, Bohr's thought has often been interpreted under certain tacit premises of scientific rationality that are precisely of the kind targeted by his epistemological critique. In recent years, however, there have emerged new approaches to Bohr's idea of complementarity that place it in different, less conventional, philosophical contexts. Among the most notable of these is Arkady Plotnitsky's endeavor to connect Bohr's complementarity with Jacques Derrida's project of deconstruction. In the present article, based on my recent doctoral dissertation,1 I take up this contribution by Plotnitsky as a suitable point of reference from which to [End Page 435] explore anew Bohr's thought with its radical philosophical implications. After outlining Bohr's complementarity argument and Plotnitsky's reading thereof (in the first and second sections, respectively), I will examine a series of problems that seem to face, or to be left unsolved by, Plotnitsky's account (in the third section). This critical appraisal will finally lead me to sketch a new interpretive approach of my own (in the fourth section), which both extends and delimits the intersections between complementarity and deconstruction. As regards the historical development of Bohr's complementarity, I will largely restrict myself to the period between 1927 and 1950, in which the most crucial of his innovative ideas seem to have been presented. I. Bohr's Idea of Complementarity In his 1927 lecture delivered in Como, Italy, entitled "The Quantum Postulate and the Recent Development of Atomic Theory," Niels Bohr introduced the concept and framework of complementarity as a pivotal idea in his interpretation of quantum theory. From then on, he continually developed the idea of complementarity with regard not only to quantum theory but to other fields of knowledge as well. In what follows, I will first outline his complementarity argument in its "early" period, stretching from 1927 to the mid-thirties,—or, more precisely, until just before his 1935 debate with EPR.2 Bohr starts by noting that "our usual description of physical phenomena is based entirely on the idea that the phenomena concerned may be observed without disturbing them appreciably."3 This notion of physical phenomena as undisturbed by observation underlies all of classical physics and is still maintained in the theory of relativity. However, Bohr continues, a new situation has arisen with the development of quantum theory, specifically with "the so-called quantum postulate, which attributes to any atomic process an essential discontinuity, or rather individuality, completely foreign to the classical theories"; this "individuality" implies that "any observation of atomic phenomena will involve an interaction with the [End Page 436] agency of observation not to be neglected" (PWNB, 1: 53–54.). In more specific terms, any observation aimed at space-time coordination brings about an exchange of momentum and energy with the measuring rods and clocks. It is crucial here that this interaction between the object and the instrument of observation is not simply unavoidable, but "uncontrollable," which represents a "feature of irrationality" brought into the description of nature (PWNB, 1: 68, 91). For insofar as the measuring instruments are to fulfill their purpose, the interaction itself cannot be taken into account, and thus the magnitude of the disturbance always remains unknown. It follows, in Bohr's view, that "an independent reality in the ordinary physical sense can neither be ascribed to the phenomena nor to the agencies of observation...
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.
Abstract The conceptual foundations of quantum mechanics have been the object of intense interest and debate for both physicists and philosophers ever since the birth of the theory. Providing a coherent and comprehensive interpretation of the non-relativistic quantum algorithm has proved to be an ongoing challenge, and the vast literature on the subject is a testament to both the perennial fascination of the problem and to the absence of any durable consensus about how best to understand the theory.