Quantum theory is our deepest theory of the nature of matter. It is a theory that, notoriously, produces results which challenge the laws of classical logic and suggests that the physical world is illogical. This book gives a critical review of work on the foundations of quantum mechanics at a level accessible to non-experts. Assuming his readers have some background in mathematics and physics, Peter Gibbins focuses on the questions of whether the results of quantum theory require us to abandon classical logic and whether quantum logic can resolve the paradoxes produced by quantum mechanics. He argues that quantum logic does not dispose of the problems faced by classical logic, that no reasonable interpretation of quantum mechanics in terms of 'hidden variables' can be found, and that after all these years quantum mechanics remains a mystery to us. Particles and Paradoxes provides a much-needed and valuable introduction to the philosophy of quantum mechanics and, at the same time, an example of just what it is to do the philosophy of physics.
Quantum theory is our deepest theory of the nature of matter. It is a theory that, notoriously, produces results which challenge the laws of classical logic and suggests that the physical world is illogical. This book gives a critical review of work on the foundations of quantum mechanics at a level accessible to non-experts. Assuming his readers have some background in mathematics and physics, Peter Gibbins focuses on the questions of whether the results of quantum theory require us to abandon classical logic and whether quantum logic can resolve the paradoxes produced by quantum mechanics. He argues that quantum logic does not dispose of the problems faced by classical logic, that no reasonable interpretation of quantum mechanics in terms of 'hidden variables' can be found, and that after all these years quantum mechanics remains a mystery to us. Particles and Paradoxes provides a much-needed and valuable introduction to the philosophy of quantum mechanics and, at the same time, an example of just what it is to do the philosophy of physics.
This book is a quantum mechanics text, written on the assumption that the purpose of learning quantum mechanics is to be able to understand the results of fundamental research into the constitution of the physical world. The text essentially concerns itself with three themes, these being a logical exposition of quantum mechanics, a full discussion of the difficulties in the interpretation of quantum mechanics, and an outline of the current state of understanding of theoretical particle physics, The reader is assumed to have some mathematical skill, but no prior knowledge of physics is assumed. The book will be used for final-year undergraduate courses in mathematics and physics, and of interest to professionals in philosophy and pure mathematics.
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.
What do we expect of a quantum logical interpretation of quantum mechanics worthy of the name? In what sense should it resolve the paradoxes? What scope should it have? Should quantum logic, if it is successful in the micro world, replace classical logic in the macro world and in mathematics? We distinguish between two kinds of quantum logical interpretations of quantum mechanics. An example of the first kind, the activist kind, will do much more than simply rewrite the assertions that quantum mechanics makes about the quantum world in an unfamiliar notation - in the elementary language of quantum mechanics. It will offer a solution to the major puzzles of quantum mechanics. It will show that the paradoxes of quantum mechanics can be resolved if we do away with classical logic and replace it with quantum logic, at least in our descriptions of quantum phenomena. It may defend a form of quantum-mechanical realism, a sort of quantum logical particle view of quantum systems, protecting it from the paradoxes that classical logic would impose on it. The second kind of quantum logical interpretation, the passive or quietist kind, is less ambitious. A quietist interpretation offers a solution to the paradoxes only in the following sense. It will assert that quantum mechanics, when it describes quantum phenomena in the elementary language, need not generate paradox, that the so-called paradoxes are not even formulable in quantum logic.
In this magisterial work, Roland Omnès takes us from the academies of ancient Greece to the laboratories of modern science as he seeks to do no less than rebuild the foundations of the philosophy of knowledge. One of the world's leading quantum physicists, Omnès reviews the history and recent development of mathematics, logic, and the physical sciences to show that current work in quantum theory offers new answers to questions that have puzzled philosophers for centuries: Is the world ultimately intelligible? Are all events caused? Do objects have definitive locations? Omnès addresses these profound questions with vigorous arguments and clear, colorful writing, aiming not just to advance scholarship but to enlighten readers with no background in science or philosophy. The book opens with an insightful and sweeping account of the main developments in science and the philosophy of knowledge from the pre-Socratic era to the nineteenth century. Omnès then traces the emergence in modern thought of a fracture between our intuitive, commonsense views of the world and the abstract and--for most people--incomprehensible world portrayed by advanced physics, math, and logic. He argues that the fracture appeared because the insights of Einstein and Bohr, the logical advances of Frege, Russell, and Gödel, and the necessary mathematics of infinity of Cantor and Hilbert cannot be fully expressed by words or images only. Quantum mechanics played an important role in this development, as it seemed to undermine intuitive notions of intelligibility, locality, and causality. However, Omnès argues that common sense and quantum mechanics are not as incompatible as many have thought. In fact, he makes the provocative argument that the "consistent-histories" approach to quantum mechanics, developed over the past fifteen years, places common sense (slightly reappraised and circumscribed) on a firm scientific and philosophical footing for the first time. In doing so, it provides what philosophers have sought through the ages: a sure foundation for human knowledge. Quantum Philosophy is a profound work of contemporary science and philosophy and an eloquent history of the long struggle to understand the nature of the world and of knowledge itself.
Quantum paradoxes The next few chapters are devoted to resolving a number of quantum paradoxes in the sense of giving a reasonable explanation of a seemingly paradoxical result in terms of the principles of quantum theory discussed earlier in this book. None of these paradoxes indicates a defect in quantum theory. Instead, when they have been properly understood, they show us that the quantum world is rather different from the world of our everyday experience and of classical physics, in a way somewhat analogous to that in which relativity theory has shown us that the laws appropriate for describing the behavior of objects moving at high speed differ in significant ways from those of pre-relativistic physics. An inadequate theory of quantum measurements is at the root of several quantum paradoxes. In particular, the notion that wave function collapse is a physical effect produced by a measurement, rather than a method of calculation, see Sec. 18.2, has given rise to a certain amount of confusion. Smuggling rules for classical reasoning into the quantum domain where they do not belong and where they give rise to logical inconsistencies is another common source of confusion. In particular, many paradoxes involve mixing the results from incompatible quantum frameworks. Certain quantum paradoxes have given rise to the idea that the quantum world is permeated by mysterious influences that propagate faster than the speed of light, in conflict with the theory of relativity. They are mysterious in that they cannot be used to transmit signals, which means that they are, at least in any direct sense, experimentally unobservable.
Beginning in 1900 with 1-iax Planck's hypothesis of quanta, physics has been embarked on a course which has raised serious questions about the true nature of physical reality, about the foundational assumptions and structures of science, and about the relationships between physical reality and physical theory. In particular, attempts to give a physical interpretation to quantum theory seem to result in "pictures" of nature which are paradoxical. A subatomic entity is described by the theory as exhibiting the properties and behavior of both particle-like phenomena and wavelike phenomena. Since it seems unreasonable that a single entity could be both a point-like mass and a wave spread out through a region of space, quantum theory would seem to be less than satisfactory or less than complete at the interpretational level. The purpose of this dissertation is to investigate the underlying causes of this paradox. The dissertation proceeds by reviewing the development of quantum theory and the emergence of the paradox. Next, the problem of physical interpretation is examined and several of the more significant existing interpretations are discussed and analyzed. Finally, the foundations of science and the general structure of scientific theory are examined in a search for the origins of the paradox. As a result of these investigations and analyses, it is concluded that the paradoxical nature of the physical interpretation of quantum theory is the consequence of certain paradigms and preconceptualizations about physical reality which have been incorporated into the theory at the foundational level. These fundamental assU14ptions produce, within quantum theory, a forced marriage of the plenum and atomic views of physical reality. They also produce an ambiguity with respect to the nature of causality which is charaeteristic of the theory. These problems are reflected in the mathematical formalisms and physical concepts of the theory as well as in its metaphysical foundations. Lastly, methods of resoling the paradox are discussed. It is argued that a successful solution is possible, but that it would involve the creation of a new metaphor-an extension of the present language--which would lead science to a deeper, subquantum level in terms of which the present paradox would vanish.