No scientific theory has caused more puzzlement and confusion than quantum theory. Beginning in 1900, the theory developed in fits and starts and found a consistent mathematical framing only when John von Neumann published his Mathematische Grundlagen der Quantenmechanik in 1932 [12]. But even today, we struggle to understand the world as pictured by quantum theory. Physics is supposed to help us to understand the world, and yet quantum theory makes it seem a very strange place. One might be tempted to push aside our puzzlement as the result of our clinging to a primitive worldview. But our puzzlement is not merely a psychological obstacle; it is also an obstacle to the development of physics itself. This obstacle is encountered primarily in our attempts to unify quantum theory and the general theory of relativity. As argued persuasively by Chris Isham (who is represented in this volume), Lee Smolin [10], and others, the primary obstacle between us and future physics is our own failure to understand the conceptual foundations of current physical theories. How, then, are we to make conceptual progress? What is the process by which we find a new perspective, a perspective in which previously puzzling phenomena find a place in an intelligible—and perhaps beautiful—structure? I do not wish to make prescriptions or to claim that conceptual progress can be achieved in only one way. But this book begins with the Ansatz that conceptual progress might be achieved through free creations of the human intellect.
No scientific theory has caused more puzzlement and confusion than quantum theory. Beginning in 1900, the theory developed in fits and starts and found a consistent mathematical framing only when John von Neumann published his Mathematische Grundlagen der Quantenmechanik in 1932 [12]. But even today, we struggle to understand the world as pictured by quantum theory. Physics is supposed to help us to understand the world, and yet quantum theory makes it seem a very strange place. One might be tempted to push aside our puzzlement as the result of our clinging to a primitive worldview. But our puzzlement is not merely a psychological obstacle; it is also an obstacle to the development of physics itself. This obstacle is encountered primarily in our attempts to unify quantum theory and the general theory of relativity. As argued persuasively by Chris Isham (who is represented in this volume), Lee Smolin [10], and others, the primary obstacle between us and future physics is our own failure to understand the conceptual foundations of current physical theories. How, then, are we to make conceptual progress? What is the process by which we find a new perspective, a perspective in which previously puzzling phenomena find a place in an intelligible—and perhaps beautiful—structure? I do not wish to make prescriptions or to claim that conceptual progress can be achieved in only one way. But this book begins with the Ansatz that conceptual progress might be achieved through free creations of the human intellect.
Abstract The development of quantum theory was driven by a consistently repeated failure of classical physics to accommodate the results of ever more sophisticated experiments on the microphysical world of radiation, elementary particles, atoms, and molecules. Each break-through in the development of the theory’s conceptual structure was followed (sometimes very rapidly) by new experimental data that just did not fit, pointing to the need for yet further refinements. As is typical in such a radical change in the approach to acquiring scientific understanding, old and often unsuitable concepts were forced into service to meet the needs of the new description. Confusion reigned. The major figures in the theory’s early development took up radically different positions on the theory’s interpretation, and, as we will see, the debate became polarized in ways that remain relevant today.
No scientific theory has caused more puzzlement and confusion than quantum theory. Physics is supposed to help us to understand the world, but quantum theory makes it seem a very strange place. This book is about how mathematical innovation can help us gain deeper insight into the structure of the physical world. Chapters by top researchers in the mathematical foundations of physics explore new ideas, especially novel mathematical concepts at the cutting edge of future physics. These creative developments in mathematics may catalyze the advances that enable us to understand our current physical theories, especially quantum theory. The authors bring diverse perspectives, unified only by the attempt to introduce fresh concepts that will open up new vistas in our understanding of future physics.
Despite scholarly consensus on the empirical facts, ever since its inception in the 1920s there has been deep disagreement about how to interpret quantum theory. “To interpret a physical theory is to say what the world would be like, if the theory were true.” All scientific theories require interpretation, since strictly speaking what they describe are our experiences of the world rather than the world itself. Thus, whether we are trying to explain or merely describe the world, we are always engaged in inference. To make inferences we need a context for interpretation. For any given claim this context is provided locally by related theories, more broadly by disciplinary paradigms, and ultimately by worldview claims about the nature of reality. The challenge in interpreting scientific theories is to integrate them into this hierarchy of knowledge. Usually this is not too difficult. New theories often require adjustments to nearby theories, but in doing so we can rely on paradigms to make them cohere. More rarely paradigmatic assumptions are themselves challenged, but in that case scientists can fall back on their worldview to make sense of the needed changes. By implication, the most difficult interpretive problems arise when our worldview is called into question, which leaves us without any frame of reference on which to fall back. Quantum theory poses a worldview problem. Prior to the quantum revolution the classical worldview could not be tested scientifically and so it was essentially metaphysical. Even though it corresponded to our experience of material objects, we lacked proof that it adequately represented the deep structure of reality. By giving us access to that deep structure for the first time, quantum mechanics made it possible to do such a test, or “experimental metaphysics.” Unfortunately, the results seemed to contradict classical assumptions, at least on the sub-atomic level.
Introduction Chapter 1 dealt with one of the deepest mysteries in modern science: how to explain consciousness. This Part deals with another mystery: how to make sense of quantum mechanics. Both involve a problem of reconciliation with the classical worldview, which is one hint that the two mysteries might be related. A second is that, unlike classical physics, which makes no reference to or allowance for consciousness, quantum theory raises the issue of consciousness and its relationship to the physical world in a very direct way. These hints do not necessarily mean there is a connection between the two mysteries, but by the end of this Part I hope to have shown why it would be natural to look for one. My more immediate aim here is to give the social scientific reader an introductory understanding of the experimental findings of quantum theory, its key concepts, and the debates about its interpretation. The discussion assumes no prior knowledge of quantum physics and makes no use of mathematics. Quantum theory without equations might seem like an oxymoron, and certainly reading this Part will not enable anyone to use quantum theory. But to a perhaps surprising degree it is possible to understand quantum theory without being able to use it. Its findings can be communicated in ordinary language, and the same goes for its main concepts and interpretive debates. One consequence of this has been the emergence of a virtual cottage industry of books on quantum theory for a lay audience. Most are written by physicists, and many are quite good. However, it is not just popular treatments that do without equations: much of the professional philosophical literature does as well. (I draw on both kinds of literature below.) Philosophers of physics are trained to understand the math, of course, which is necessary for a full appreciation of the issues.
We still lack any consensus about what one is actually talking about as one uses quantum mechanics. There is a gap between the abstract terms in which the theory is couched and the phenomena the theory enables each of us to account for so well. Because it has no practical consequences for how we each use quantum mechanics to deal with physical problems, this cognitive dissonance has managed to coexist with the quantum theory from the very beginning. The absence of conceptual clarity for almost a century suggests that the problem might lie in some implicit misconceptions about the nature of scientific explanation that are deeply held by virtually all physicists, but are rarely explicitly acknowledged. I describe here such unvoiced but widely shared assumptions. Rejecting them clarifies and unifies a range of obscure remarks about quantum mechanics made almost from the beginning by some of the giants of physics, many of whom are held to be in deep disagreement. This new view of physics requires physicists to think about science in an unfamiliar way. My primary purpose is to explain the new perspective and urge that it be taken seriously. My secondary aims are to explain why this perspective differs significantly from what Bohr, Heisenberg, and Pauli had been saying from the very beginning, and why it is not solipsism, as some have maintained. To emphasize that this is a general view of science, and not just of quantum mechanics, I apply it to a long-standing puzzle in classical physics: the apparent inability of physics to give any meaning to 'Now'-the present moment.
Quantum theory as a scientific revolution profoundly influenced human thought about the universe and governed forces of nature. Perhaps the historical development of quantum mechanics mimics the history of human scientific struggles from their beginning. This book, which brought together an international community of invited authors, represents a rich account of foundation, scientific history of quantum mechanics, relativistic quantum mechanics and field theory, and different methods to solve the Schrodinger equation. We wish for this collected volume to become an important reference for students and researchers.