This commentator format is quite unfamiliar to me, and somewhat uncomfortable. I don't know whether I'm supposed to flatter the speakers, criticize them, grade them, or merely parrot them. Or should I go off on my own? This latter is tempting. If unleashed I could provide you with true answers to all the questions before us, philosophical, historical, physical, mathematical, physical-mathematical, and so on. But I'll bite my tongue and try to stick to the commentator role. First, a few words on the topic of the opening session this afternoon - why are philosophers interested in quantum field theory? Quantum mechanics undoubtedly abounds in genuine, deep and still unresolved philosophical questions. These are usually posed, at least in popular accounts, in the context of finite systems of nonrelativistic point particles. In preparation for the conference, I asked myself: does relativistic QFT introduce any really distinctive philosophical problems? There are several possibilities, which I can only express in low-brow form. For one thing, a field is really a collection of infinitely many degrees of freedom, one for each point in space. I can well suppose that infinity raises interesting questions for philosophers. Certainly for physicists, especially in the field theory context, it has been a great preoccupation. As we'll hear later from Jackiw, infinity has its useful aspects. Next, for systems of relativistic particles in interaction, it is no longer so easily possible to speak of measurements of position and momentum of individual particles, except perhaps in asymptotic regions.
This commentator format is quite unfamiliar to me, and somewhat uncomfortable. I don't know whether I'm supposed to flatter the speakers, criticize them, grade them, or merely parrot them. Or should I go off on my own? This latter is tempting. If unleashed I could provide you with true answers to all the questions before us, philosophical, historical, physical, mathematical, physical-mathematical, and so on. But I'll bite my tongue and try to stick to the commentator role. First, a few words on the topic of the opening session this afternoon - why are philosophers interested in quantum field theory? Quantum mechanics undoubtedly abounds in genuine, deep and still unresolved philosophical questions. These are usually posed, at least in popular accounts, in the context of finite systems of nonrelativistic point particles. In preparation for the conference, I asked myself: does relativistic QFT introduce any really distinctive philosophical problems? There are several possibilities, which I can only express in low-brow form. For one thing, a field is really a collection of infinitely many degrees of freedom, one for each point in space. I can well suppose that infinity raises interesting questions for philosophers. Certainly for physicists, especially in the field theory context, it has been a great preoccupation. As we'll hear later from Jackiw, infinity has its useful aspects. Next, for systems of relativistic particles in interaction, it is no longer so easily possible to speak of measurements of position and momentum of individual particles, except perhaps in asymptotic regions.
This two-tier conference signals a new phase of philosophers' interest in quantum field theory, which has been growing noticeably in the last few years. However, some prominent physicists have shown their deep suspicions against ignorant philosophers' intrusion into their profession, and have expressed their hostility quite openly. In the philosophy community, some prominent philosophers of physics have also expressed their suspicions against the rationale of moving away from the profound foundational problems raised by Einstein and Bohr, Bohm and Bell, such as those concerning the nature of space-time and measurement, possibility and implications of hidden variables and nonlocality, and stepping into the technical complexity of quantum field theory, which is only an application of quantum mechanics in general without intrinsically distinct philosophical questions to be explored. In order to dispel these suspicions, it is desirable to highlight certain aspects of quantum field theory which require philosophical reflections and deserve further investigations. This discussion intends to suggest that philosophers can learn many important lessons from quantum field theory, and may be of some help in clarifying its conceptual foundations. At this stage of crisis that quantum field theory is experiencing now, the clarification may contribute to the radical transformation of our basic concepts in theoretical physics, which is necessary for a happy resolution of the crisis and the emergence of a new promising fundamental physical theory. Generally speaking, philosophers are interested in the metaphysical assumptions adopted by science and the world picture suggested by science.
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.
Philosophical introduction The following seemingly trivial story raises important questions which lead to the philosophical issues essential for our discussion. My cat is alive and well. I can describe her by size, color, behavior, etc. I can watch her, touch her, play with her, and feed her. I know this animal is really there. But my biologist friend came to visit and informed me that my cat is really nothing but a very complicated collection of different kinds of cells in mutual interaction, and he can prove it to me by having me look through his microscope, and, if I would only let him, by dissecting my cat. But the biochemist next door has a quite different opinion: he claims that my cat is really just a very complex assemblage of organic compounds, proteins, nucleic acids, etc., etc., all in mutual interaction. He, too, can prove his claim. Of course, physicists know better: a cat, like all matter living or dead, is in last analysis really nothing but atoms bonded together to form the complicated molecules my biochemist friend is talking about. And they can prove that too. But, finally, one cannot ignore the elementary particle people who tell us that atoms are just composed of quarks, gluons, and electrons, so that a cat is really, really just a very complicated assembly of those few types of elementary particles in mutual interaction.
If you have a restless intellect, it is very likely that you have played at some point with the idea of investigating the meaning and conceptual foundations of quantum mechanics. It is also probable (albeit not certain) that your intentions have been stopped on their tracks by an encounter with some version of the "Shut up and calculate" command. You may have heard that everything is already understood. That understanding is not your job. Or, if it is, it is either impossible or very difficult. Maybe somebody explained to you that physics is concerned with "hows" and not with "whys"; that whys are the business of "philosophy" ---you know, that dirty word. That what you call "understanding" is just being Newtonian; which of course you cannot ask quantum mechanics to be. Perhaps they also added some norms: The important thing a theory must do is predict; a theory must only talk about measurable quantities. It may also be the case that you almost asked "OK, and why is that?", but you finally bit your tongue. If you persisted in your intentions and the debate got a little heated up, it is even possible that it was suggested that you suffered of some type of moral or epistemic weakness that tend to disappear as you grow up. Maybe you received some job advice such as "Don't work in that if you ever want to own a house". I have certainly met all these objections in my short career, and I think that they are all just wrong. In this somewhat personal document, I try to defend that making sense of quantum mechanics is an exciting, challenging, important and open scientific endeavor. I do this by compulsively quoting Feynman (and others), and I provide some arguments that you might want to use the next time you confront the mentioned "opinions". By analogy with the anti-rationalistic Copenhagen command, all the arguments are subsumed in a standard answer to it: "Shut up and let me think"
reprinted in the British trade journal Physics World in 1990, three separate and 5 lengthy replies from establishment physicists were printed in subsequent issues. For outsiders, especially scientists who rely on physicist's theories in their own fields, this situation is disquieting. Moreover, many recall their introduction to quantum mechanics as a startling, if not shocking, experience. A molecular biologist related how he had started in theoretical physics but, after hearing the ideology of quantum mechanics, marched straight to the Reg istrar's office and switched fields. A colleague recalled how her undergraduate chemistry professor religiously entertained queries from the class - until one day he began with the words: "No questions will be permitted on today's lecture." The topic, of course, was quantum mechanics. My father, an organic chemist at a Midwestern university, also had to give that dreaded annual lecture. Around age 16, I picked up a little book he used to prepare and was perplexed by the author's tone, which seemed apologetic to the point of pleading. It was my first brush with the quantum theory. 6 Eventually, I went to graduate school in physics. By then I had acquired an historical bent, which developed out of an episode in my freshman year in college. To relieve the tedium of the introductory physics course, I set out to understand Einstein's theory of relativity (the so-called Special Theory of 1905, not the later and more difficult General Theory of 1915). This went badly at first.
Surely, after 62 years, we should have an exact formulation of some serious part of quantum mechanics? By ‘exact’ I do not of course mean ‘exactly true’. I mean only that the theory should be fully formulated in mathematical terms, with nothing left to the discretion of the theoretical physicist … until workable approximations are needed in applications. By ‘serious’ I mean that some substantial fragment of physics should be covered. Non-relativistic ‘particle’ quantum mechanics, perhaps with the inclusion of the electromagnetic field and a cut-off interaction, is serious enough. For it covers ‘a large part of physics and the whole of chemistry’. I mean too, by ‘serious’, that ‘apparatus’ should not be separated off from the rest of the world into black boxes, as if it were not made of atoms and not ruled by quantum mechanics. The question, ‘… should we not have an exact formulation …?’, is often answered by one or both of two others. I will try to reply to them: Why bother? Why not look it up in a good book ? Why bother? Perhaps the most distinguished of ‘why bother?’ers has been Dirac. He divided the difficulties of quantum mechanics into two classes, those of the first class and those of the second. The second-class difficulties were essentially the infinities of relativistic quantum field theory. Dirac was very disturbed by these, and was not impressed by the ‘renormalisation’ procedures by which they are circumvented. Dirac tried hard to eliminate these second-class difficulties, and urged others to do likewise.