The well known theoretical physicist and editor of the Journal of Mathematical Physics has written a handy book, with eight chapters devoted to the broader knowledge of and reflection about physical theories, notably quantum theory. After thinking about what is a physical theory, he addresses the problem of the state in quantum theory (a very central chapter of the book), the power of mathematics, the field - particle issue (the author pleads for the superiority of the field concept - the book is very indebted to Julian Schwinger's ideas), symmetry in physics, the problem of causality and probability, the five different arrows of time (from cause-effect ordering to the cosmological arrow), and finally turns to the presently quite often discussed relation of the quantum-mechanical description to reality. After one has learned that the author is not approaching the questions from a sharper historical point of view, and that he shares the prejudices of a mathematical physicist toward experiment, one thoroughly enjoys his elegant, competent and deep treatment. This reviewer wishes that every graduate student of physics should, at an early stage, read Newton's book (which could be done either at a stroke or piecewise) because it presents the essence of a great deal of modern physical theory in both a condensed and leisurely digestible form.
The well known theoretical physicist and editor of the Journal of Mathematical Physics has written a handy book, with eight chapters devoted to the broader knowledge of and reflection about physical theories, notably quantum theory. After thinking about what is a physical theory, he addresses the problem of the state in quantum theory (a very central chapter of the book), the power of mathematics, the field - particle issue (the author pleads for the superiority of the field concept - the book is very indebted to Julian Schwinger's ideas), symmetry in physics, the problem of causality and probability, the five different arrows of time (from cause-effect ordering to the cosmological arrow), and finally turns to the presently quite often discussed relation of the quantum-mechanical description to reality. After one has learned that the author is not approaching the questions from a sharper historical point of view, and that he shares the prejudices of a mathematical physicist toward experiment, one thoroughly enjoys his elegant, competent and deep treatment. This reviewer wishes that every graduate student of physics should, at an early stage, read Newton's book (which could be done either at a stroke or piecewise) because it presents the essence of a great deal of modern physical theory in both a condensed and leisurely digestible form.
It is very likely that most readers and authors of articles appearing in Classical and Quantum Gravity are interested in what might loosely be termed the philosophy of science. It is equally likely, with perhaps a few exceptions, that the research of these same readers and authors has not been influenced in the least by the work of professional philosophers of science. This is certainly the case for those of us who work in quantum field theory. One must therefore ask who the intended audience is for a book which purports to discuss the philosophical implications of quantum field theory. In the preface, the author states that there are two intended audiences for his book. The first is `other interested interpreters of physics' who wish to learn something about quantum field theory in as painless a way as possible. The second is for students of physics who are bogged down in the details of learning quantum field theory and cannot see the overall picture. I am not convinced that either audience will find this book to be of much use. There are two basic problems with this book. The first is that the quantum field theory in it is of the old-fashioned kind, and is not really representative of the way the subject is either taught or thought of today. The second is that there is not sufficient background material present to make this book suitable for a novice reader. For example, I wonder how much a reader who has not studied quantum mechanics in any depth will get out of a treatment which launches into Hilbert space and a discussion of states without much in the way of proper introduction. Any reader who is familiar with the workings of quantum field theory will find much to disagree with in this book. For example, the author tries to make a case that a Fock space description is better than talking about particle labels and restricting to symmetric or antisymmetric states. The reason claimed for this is that there are states in Fock space which are neither symmetric nor antisymmetric under particle interchange which must be discarded. (In the author's words, this introduces `surplus formal structure'.) However, in Fock space an equally arbitrary choice is made by focusing on relations among the creation and annihilation operators which involve only commutation or anticommutation relations. Although this is acknowledged by Teller, no satisfactory explanation is given as to why one procedure is any less arbitrary than the other. The book is incomplete in many ways, with many interesting points mentioned just in passing. For example, the discussion around the Newton--Wigner position operator would have been greatly enhanced by including more details, such as an explanation as to why quanta described by Newton--Wigner states seem to propagate at superluminal speeds. It is hard to believe that a reader who has not met the Rindler vacuum before would find Teller's discussion to be very informative. After being so critical of this book, I should mention a part which I did enjoy and would recommend to students of physics. This is the last chapter of the book which contains a discussion of renormalization theory. It is my experience that students often find renormalization theory confusing, and may find Teller's semiqualitative discussion illuminating.
The relation between Physics and Philosophy brings to mind the proverbial marriage of high drama; the parties do not approve of each other, but separated they cannot live. Philosophers find physicists shallow, and many physicists claim that they find philosophic speculations useless or worse. Mostly both display a lack of knowledge and understanding of the methods and goals of the other. A few researchers have tried to bridge this gap and explore the worlds of both parties. Michael Redhead has worked in this borderland, and when he retired from his chair in Cambridge, a symposium was arranged to honour him. The talks presented on this occasion are now published in a volume presenting much food for thought to both philosophers and physicists. The essays in this publication do not offer easy reading; not too many readers will have the preparation to penetrate the technical arguments offered. The authors are well acquainted with both philosophical argumentation and mathematical formalism, and, following the lead of Professor Redhead, they combine these in intricate and suggestive ways. Only a close reading can offer understanding of the points of view taken by the various authors. Browsing and mere reading defines the scenery, exploring it demands much more. Many of the nine essays included investigate the meaning of terms used loosely in physics contexts: locality, beables, symmetries and time in relativity. All essays utilize the mathematical structures of physics, but the approach is mainly philosophical; concepts like reality and metaphysics are applied. Some writings are more physical in their treatment of technical questions relating to modern quantum theory. Bohmian mechanics, localized quantum states and gauge symmetries are discussed in detail. It is, however, found that these present interpretational problems that are usually glossed over in purely physical treatments. For an old sceptic like myself, it is quite refreshing to find that many assertions, taken for granted in our textbooks, are indeed doubtful and offer conceptual or technical difficulties. This insight is what a philosophical analysis can offer the working physicist; future progress may well arise from such realizations. However, the results offered by philosophical analysis are usually found unsatisfactory; the hope that philosophy can suggest novel directions for the theory remains unfounded. Philosophers can learn that modern physics rests on a very shaky conceptual foundation. The theory has evolved by a combination of serendipity and opportunism. The beast that finally has emerged is neither well founded nor internally consistent. Its only merit is that it works. That offers the ultimate philosophical problem of modern physics. If the present book can help the philosopher to behold this challenging but overwhelming wilderness, then it serves a useful purpose indeed. But the prospective researcher has to learn to master the difficult language used by the natives, who are not always friendly. I enjoyed reading the book immensely, but the technical difficulty of the text made my understanding remain mostly superficial. I hope to have the time to return some of the essays, and look into the references and issues involved. The work is genuinely what it promises: a guide From Physics to Philosophy .
Quantum mechanics is one of the principle pillars of modern physics. It also remains a topic of great interest to mathematicians. Since its discovery it has inspired and been inspired by many topics within modern mathematics, including functional analysis and operator algebras, Lie groups, Lie algebras and their representations, principle bundles, distribution theory, and much more. Written with beginning graduate students in mathematics in mind, this book provides a thorough treatment of (nonrelativistic) quantum mechanics in a style that is leisurely, without the usual theorem-proof grammar of pure mathematics, while remaining mathematically honest. The author takes the time to fully develop the required mathematics and employs a consistent mathematical presentation to clarify the often-confusing notation of physics texts. Along the way the reader encounters several topics requiring more advanced mathematics than found in many discussions of the subject, making for a fascinating course in how mathematics and physics interact.
Mathematicians really understand what mathematics is. Theoretical physicists really understand what physics is. No matter how fruitful the interplay between the two subjects, the deep intersection of these two understandings seems to me to be quite modest. Of course, many theoretical physicists know a lot of mathematics. And many mathematicians know a fair amount of theoretical physics. This is very different from a deep understanding of the other subject. There is great advantage in the prospect of each camp increasing its appreciation of the other's goals, desires, methodology, and profound insights. I do not know how to really go about this in either case. However, the book in hand is a good first step for the mathematicians. The method of the text is to explain the meaning of a large number of ideas in theoretical physics via the splendid medium of mathematical communication. This means that there are descriptions of objects in terms of the precise definitions of mathematics. There are clearly defined statements about these objects, expressed as mathematical theorems. Finally, there are logical step-by-step proofs of these statements based on earlier results or precise references. The mathematically sympathetic reader at the graduate level can study this work with pleasure and come away with comprehensible information about many concepts from theoretical physics … quantization, particle, path integral … After closing the book, one has not arrived at the kind of understanding of physics referred to above; but then, maybe, armed with the information provided so elegantly by the authors, the process of infusion, assimilation, and deeper insight based on further rumination and study can begin.
Quantum mechanics is one of the most challenging subjects to learn. It is challenging because quantum phenomenon is counterintuitive, and the mathematics used to explain such a phenomenon is very abstract, and difficult to grasp. This textbook is an attempt to overcome these challenges. Every chapter presents quantum ideas step- by- step in a structured way with a comparison between quantum and classical concepts. It provides a clear distinction between classical and quantum logic. Conceptual questions are provided after every important section so that the reader can test their understanding at every step. Such an approach aids in preventing misconceptions. Problem solving is not restricted to solving differential equations and integration. But it requires to systematically and creatively analyze a problem, to apply the new and powerful concepts for finding a solution and to understand the physical meaning of the solution. The tutorials on special topics are an effort to teach problem solving by actively engaging the reader in a thinking process, to apply the concepts and to understand the physical meaning of the solution. The simulations are provided for some of the topics. The simulations aid in the visualization of the quantum phenomenon, and for meaningful understanding of the mathematics. This approach may lead to development of "quantum mechanical intuition "as well as learning mathematical techniques for problem solving. Most importantly, the book is not flooded with numerous topics that makes the reader confused and distracted, rather the most important topics are discussed at a deeper level. The understanding of quantum mechanics is incomplete without understanding the early ideas and experiments that lead to the development of the quantum theory. Thus, the first two chapters of the book are dedicated to such topics. The key features of this book are: A simplified, structured, and step-by-step introduction to quantum mechanics. The simplification is attained through use of two-level system, step- by- step discussion of important topics in a simplified language at a deeper level, analogies, and visualization using illustrations and simulations A systematic arrangement of topics, and numerous worked- out examples. The presentation of the structure in the mathematical formalism of quantum mechanics provides clarity in understanding complicated and abstract mathematics. It also helps to understand the distinction between the quantum mechanical and classical approaches Conceptual questions at the end of every important section. The conceptual questions can be used in a classroom as a point of discussion between an instructor and students Tutorials on special topics. Simulations on special topics aid in the visualization of the physical phenomenon, and demonstration of the application of mathematics An in-depth discussion of the wave-particle duality, measurement problem, and their philosophical implications in Chapter 2 provides an understanding of the broader meaning of quantum mechanics
All men by nature desire to know, states Aristotle in the famous first sentence of his Metaphysics. Knowledge about fundamental particles and interactions, that is, knowledge about the deepest aspects of matter, is certainly high if not top on the priority list, not only for physicists and philosophers. The goal of the present book is to contribute to this knowledge by going beyond the usual presentations of quantum field theory in physics textbooks, both in mathematical approach and by critical reflections inspired by epistemology, that is, by the branch of philosophy also referred to as the theory of knowledge. Hopefully, the present book motivates physicists to appreciate philosophical ideas. Epistemology and the philosophy of the evolution of science often seem to lag behind science and to describe the developments a posteriori. As philosophy here has a profound influence on the actual shaping of an image of fundamental particles and their interactions, our development should stimulate the curiosity and imagination of physicists. This book can be used as a textbook on quantum field theory for students of physics or as a monograph for philosophers and physicists interested in the epistemological foundations of particle physics. The benefits of an approach resting on philosophical foundations is twofold: the reader is stimulated to critical thinking and the entire story flows very naturally, thus removing all the mysteries from quantum field theory.