Both science and philosophy have been characterized as seeking to understand the nature of reality. They are sometimes even pitted against each other, suggesting that the success of science undermines the relevance of philosophy. But attending to the sort of understanding or explanation being sought offers a different picture: contemporary physics as practiced sometimes fails to provide a clear physical account of the world. This lies at the root of the dissatisfaction with standard quantum theory expressed by Einstein, Schrodinger, and John Bell. As an example, close consideration of Schrodinger’s famous cat example suggests that physicists often have missed his point. What a philosophical disposition can contribute is not alternative physics, but rather the sort of careful attention to argument needed to extract a physical picture from a mathematical formalism.
Both science and philosophy have been characterized as seeking to understand the nature of reality. They are sometimes even pitted against each other, suggesting that the success of science undermines the relevance of philosophy. But attending to the sort of understanding or explanation being sought offers a different picture: contemporary physics as practiced sometimes fails to provide a clear physical account of the world. This lies at the root of the dissatisfaction with standard quantum theory expressed by Einstein, Schrodinger, and John Bell. As an example, close consideration of Schrodinger’s famous cat example suggests that physicists often have missed his point. What a philosophical disposition can contribute is not alternative physics, but rather the sort of careful attention to argument needed to extract a physical picture from a mathematical formalism.
Both science and philosophy have been characterized as seeking to understand the nature of reality. They are sometimes even pitted against each other, suggesting that the success of science undermines the relevance of philosophy. But attending to the sort of understanding or explanation being sought offers a different picture: contemporary physics as practiced sometimes fails to provide a clear physical account of the world. This lies at the root of the dissatisfaction with standard quantum theory expressed by Einstein, Schrödinger, and John Bell. As an example, close consideration of Schrödinger's famous cat example suggests that physicists often have missed his point. What a philosophical disposition can contribute is not alternative physics, but rather the sort of careful attention to argument needed to extract a physical picture from a mathematical formalism.
Quantum mechanics is our most successful physical theory. It underlies our very detailed understanding of atomic physics, chemistry, and nuclear physics, and the many technologies to which physical systems in these regimes give rise. Additionally, relativistic quantum mechanics is the basis for the standard model of elementary particles, which very successfully gives a partial unification of the forces operating at the atomic, nuclear, and subnuclear levels. However, from its inception the probabilistic nature of quantum mechanics, and the fact that “quantum measurements” in the orthodox formulation appear to require the intervention of non-quantum mechanical “classical systems,” have led to speculations by many physicists, mathematicians, and philosophers of science that quantum mechanics may be incomplete. Among the Founding Fathers of quantum theory, Einstein and Schrödinger were both of the opinion that quantum mechanics is in some way unsatisfactory, and this view has been amplified in more recent profound work of John Bell, among others. In an opposing camp, many others in the physics, mathematics, and philosophy communities have attempted to provide an interpretational foundation in which quantum mechanics remains a complete and self-contained system. Among the Founding Fathers, Bohr, Born, and Heisenberg maintained that quantum mechanics is a complete system, and a number of recent proposals have been made to improve upon or to provide alternatives to their “Copenhagen Interpretation.” The debate continues, and has spawned an enormous literature.
The difficulties of the old quantum theory were largely dispelled by the development of quantum mechanics in the 1920s. First Heisenberg (1925) developed the rather abstract matrix mechanics and soon after Schro¨dinger (1926; see also Eckart, 1926) developed the physically more appealing wave mechanics. Subsequently he showed them to be mathematically equivalent. The physicists were greatly relieved; now they had once again a mathematical formalism that enabled the results of experiments to be calculated. It was possible to move forward. It is certainly a very elegant and indeed beautiful formalism, and does enable the results of many physical measurements to be calculated with great accuracy. It is used daily by atomic and nuclear physicists; there is no other way to make calculations. From the earliest days there has been intense debate about the interpretation of quantum mechanics, and it shows no signs of being settled; if anything it is becoming more intense over the years. As Penrose has remarked, no one understands quantum mechanics. Feynman (1967; see also Sykes, 1994) also admitted that ‘nobody understands quantum mechanics’, and Einstein once remarked: ‘I have thought a hundred times as much about the quantum problems as I have about general relativity theory’ (Pais, 1994, p. 57). It should therefore be evident that the most that can be done here is to try to show where the real difficulties lie, and how the failure to recognize that quantum mechanics is an essentially statistical theory has led to a series of confusing quantum paradoxes. It is just these paradoxes that have often been used to support theological speculations. It is useful to ask what ‘understanding quantum mechanics’ actually means. Certainly it means being able to calculate the results of many measurements. The same applies to Newton’s theory of gravitation, which we understand in the sense that we can use it as a basis of calculation, although we do not really understand the gravitational force itself. Very often, especially in modern physics, the mathematical formalism does not give us the sort of intuitive physical feeling for what is going on that we often obtain from classical mechanics. Perhaps we can never achieve more than this for quantum mechanics. In classical mechanics we can assume that a property that is measured objectively exists prior to the interaction of the measuring apparatus with the observed system. Quantum mechanics, however, ‘is incompatible with the proposition that measurement discovers some unknown but pre-existing property’ (Peres, 1997, p. 14). There is an important distinction between mysteries and absurdities. We may be forced to live with mysteries, but there is no reason why we should put up with absurdities such as the wave-particle duality, tunnelling through potential barriers, acausal events and the collapse of the wave function. These are the quantum paradoxes that will be discussed later on. They arise within the Copenhagen interpretation of quantum mechanics and are solved by other interpretations. These alternative interpretations enable us to make conjectures about what is going on, even though we cannot understand it in detail. This is acceptable and a stimulus to further research. It is certainly difficult enough to understand quantum mechanics, but there is no need to try to visualize logical absurdities in the effort to do so. Quantum mechanics is a mathematical formalism that makes it possible to calculate the results of some experiments. Anything more than this, such as questions about the interpretation of what is measured and whether it tells us what is actually going on in the system being studied, belongs to philosophy. Thus we are concerned here with what is essentially a philosophical debate; if it were just a matter of physics the debate would have been settled long ago. One of the difficulties is that it invokes the results of experiments and uses the language of quantum mechanics. Inevitably this language uses philosophical terms and then it is easy to give the impression that the philosophical propositions are in some way entailed by the physical results. These in turn can influence theological thinking. In order to be quite clear which arguments are justified and which are not, it is essential to separate the three levels of discourse: physical, philosophical and theological. Our task is to relate these together, and this immediately raises the traditional problems of the philosophy of science, including the relation of experiment to theory, and of theory to explanation. We begin by discussing experiments, distinguishing between those that are real and those that are imaginary.
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.
Those defile the purity of mathematical and philosophical truthy who confound real quantities with their relations and sensible measures. —ISAAC NEWTON, Principia Before we say anything about quantum mechanics, let us take a quick look at the Newtonian (or ‘classical’) view of the physical universe. According to that view, nature consists of an enormous number of particles. When Newtonian physics is combined with the theory of the electromagnetic field, it becomes convenient to think of these particles as dimensionless (even if there is a kind of conceptual strain involved in trying to think of something as having a mass but not any size ), and as possessing electrical properties – negative charge, or positive charge, or neutrality. This leads to the well-known ‘solar system’ view of the atom – with the electrons whirling around the nucleons (neutrons and protons) just as the planets whirl around the sun. Out of atoms are built molecules; out of molecules, macroscopic objects, scaling from dust motes to whole planets and stars. These latter also fall into larger groupings – solar systems and galaxies – but these larger structures differ from the ones previously mentioned in being held together exclusively by gravitational forces. At every level, however, one has trajectories (ultimately that means the possibility of continuously tracing the movements of the elementary particles) and one has causality (ultimately that means the possibility of extrapolating from the history of the universe up to a given time to its whole sequence of future states).
Feynman diagrams have fascinated physicists and philosophers since they were introduced to the world about 70 years ago. Clearly, they help in calculation; they have allowed nearly impossible problems to be solved with relative ease. This is agreed by all, but that is probably where the consensus ends. Are they pictures of physical processes? Are they just devices for keeping track of mathematical formulae, that do the real work? Are they some sort of mix of both?They are almost as famous as representations of the Bohr atom, even though most people could not give even a sketchy account of what they do. In spite of this they have taken on a role as a cultural icon. Feynman used them to decorate his own van (Fig. 1). The van was even used in an episode of the popular TV series The Big Bang Theory. They have been used as art work in everything from posters, to coffee mugs, to wallpaper. But none of this is particularly helpful in understanding how they work.If we ask working physicists who use Feynman diagrams what it is they are doing, we get a variety of responses. One is puzzlement; a shrug of indifference. Even those very skilled at using Feynman diagrams might be hard pressed to explain (to a philosopher’s satisfaction) what’s happening. After all, most of us can ride a bike but would be similarly hard pressed to explain in any detail what we’re doing. A more common response might go like this: The diagram, or series of diagrams, is a schematic picture of some physical process, say, two electrons interacting, which we then link to mathematical terms. After writing out the mathematical terms in the form of a series, we calculate and get the probability of an interaction happening. This sounds good initially, but runs into trouble when we ask what a “picture of a physical process” could mean? This is, after all, the quantum world where things do not move continuously through space and time. It seems doubtful the diagrams could be diagrams of things in the physical realm. They are connected to physical reality and they are connected to wonderfully accurate predictions. And yet, mystery remains.The following articles on Feynman diagrams address several timely issues, both historical and contemporary. These are metaphysical and epistemological questions related to models and how we represent the world. The papers are united by these themes, but otherwise are independent of one another. They are arranged alphabetically and can be read in any order.James Robert Brown, “How Do Feynman Diagrams Work?” takes the view that they are not representations or models of the world at all. Like others, he stresses that they cannot be pictures of reality, since, thanks to the Heisenberg relations, there can be no such thing as a trajectory. Rather than seek some other more abstract type of representation, he introduces a distinction between descriptive and prescriptive flow charts. The latter could be a representation of physical reality, but not the former. A prescriptive flow chart is more like a recipe to bake a cake. He takes Feynman diagrams to be this sort of thing.Mauro Dorato and Emanuele Rossanese, “The Nature of Representation in Feynman Diagrams,” also reject the idea that Feynman diagrams can be considered to be pictures or depictions of actual physical processes. But unlike Brown, they do not abandon the thought that they can be models in some sense. They appeal to a famous account by RIG Hughes, known as the Denotation, Deduction, and Interpretation theory of models, where “models” are to be interpreted as merely inferential, non-representational devices constructed in given social contexts by the community of physicists.Letitia Meynell, “Picturing Feynman Diagrams and the Epistemology of Understanding,” assumes that Feynman diagrams are pictorial representations but agrees with Brown and Dorato and Rossanese that they do not represent actual physical processes. She then takes up the following puzzle: If Feynman diagrams represent states of affairs, but do not do so truthfully, what can their epistemic value be? She argues that Feynman diagrams have been epistemically powerful (at least in part) because, as pictorial representations, they facilitate an understanding of QED, and particle physics more generally. Appealing to Feynman’s own remarks, she draws out what it might mean to have an understanding of something that is not factive. Although her approach allows for a thin sense of substantively non-factive epistemic success, it is continuous with a factive sense of understanding that is more familiar in the sciences.Michael Stöltzner, “Feynman Diagrams: Modeling between Physics and Mathematics,” analyzes Feynman diagrams within the context of recent debates about models in science and against the backdrop of other diagrammatic methods in mathematical physics when dealing with infinite or asymptotic series. This allows one to avoid the dichotomy of whether Feynman diagrams represent mathematical or physical objects, or a mere tool mediating between them. Along those lines one does not, however, obtain a universal answer to the question as to what Feynman diagrams represent. A single Feynman diagram, in actual scientific practice, can stand for a single mathematical expression or for a physical phenomenon depending on whether the diagram stands for a single term in an infinite series or for a subseries that is given a physical interpretation. Stöltzner’s reading of the representation problem also derives support from the historical fact that Feynman was initially motivated by the Breit-Schrödinger model of a quivering electron and from interpreting this model within the context of stochastic processes.Adrian Wüthrich, “The Exigencies of War and the Stink of a Theoretical Problem,” approaches these topics from an historian’s point of view, shedding light on the issues by focussing on debates in this historical context. As he put it in his subtitle, Wüthrich’s aim is to understand the genesis of Feynman’s electrodynamics as mechanistic modelling at different levels. Feynman’s idiosyncratic method of dealing with quantum electrodynamic phenomena has been cast as an instance of a non-rigorous, modular and rule-based style of theorizing. Given such a characterization, it seems natural that significant changes in Feynman’s style were triggered by work he was assigned during World War II, where quick fixes may have counted more than derivations from first principles. Indeed, Feynman’s theoretical proposals of an improved electrodynamics do bear traces of Feynman’s war-related work, which immediately preceded it. However, Wüthrich explains, the attempt to apply the vocabulary of the “new mechanistic philosophy” to lesser known pieces of archival evidence brings to the fore a new kind of shift in Feynman’s style. Feynman’s disposition for such a shift may also have been fostered during the war, but it was forced upon him by a specific theoretical difficulty, which was largely unrelated to his war-time research.These articles contain some technicalities, but they should all be sufficiently accessible to general readers who would like to know more about Feynman diagrams and how they relate to theories, models, mathematics, and the world. The best philosophy of science is intimately linked to and draws upon current science and its history. It pays close attention to details: the details of theorizing, the details of models and how they function, the details of experimentation and measurement, and so on. We hope this collection of five articles on Feynman diagrams, by focussing closely on detail, will contribute to a better understanding of these strange but highly productive ciphers and symbols.