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Credit: Rex Ziak
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Interview of David Griffiths by David Zierler on June 1, 2021,
Niels Bohr Library & Archives, American Institute of Physics,
College Park, MD USA,
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Interview with David Griffiths, Professor Emeritus of Physics at Reed College. Griffiths discusses his current projects on Sidney Coleman’s lecture series and a completing a fifth edition of his textbook on electrodynamics. He surveys the current interplay between experiment in theory in today’s world of particle physics, and he reflects on his career rooted in small teaching colleges, as opposed to pursuing an alternate path at large research universities. Griffiths recounts his childhood in Berkeley and then in Madison in support of his father’s academic career, and he describes finishing out high school in Vermont before attending Harvard. He laments the poor physics education Harvard offered when he was an undergraduate, and he explains his decision to remain at Harvard for graduate school, where Sidney Coleman and Carl Bender advised his thesis work on massless field theory. Griffiths discusses his postdoctoral appoints at the University of Utah and then the University of Massachusetts, and he explains how the November revolution at SLAC resonated with him. After brief teaching appointments at Mount Holyoke and Trinity Colleges, Griffiths explains his decision to join the faculty at Reed and how he learned to strike the right balance between teaching and research. He describes the origins and his motivations in writing textbooks for physics students and how he has integrated pedagogy into his mentorship of students. Griffiths discusses the influence of Kuhn in his more recent survey of physics in the twentieth century, and at the end of the interview, he explains why including students in his own research is both personally and academically meaningful.
Okay, this is David Zierler, Oral Historian for the American Institute of Physics. It is June 1st, 2021. I am delighted to be here with Professor David J. Griffiths. David, it's great to see you. Thank you for joining me today.
Alright, David. To start, would you please tell me your title and institutional affiliation?
Reed College. I'm Professor Emeritus of Physics.
When did you go emeritus?
In what ways have you remained affiliated with Reed, active with what's going on at Reed in physics?
Well, as you can see, I still have an office here. This last year, I haven't been down here very much, but we live very close to the campus, so I've been coming down maybe once every two or three weeks. But ordinarily, I would be here four days a week. My wife forbids me to come the fifth day of the week, so Thursday is my day to stay home, ordinarily. Let's see, what's my connection with Reed? I've taught several times since I became emeritus, when the department needs somebody to teach. For instance, I'm ordinarily the only one on the faculty who would teach elementary particles, although actually in the last three or four years, we've had a particle physicist on the faculty, so he's taken over that. Otherwise, I've stepped in from time to time. A colleague of mine fell off a ladder and broke his wrist, and I took over his course. So, I play the role of sort of a utility in-fielder. I've taught most of the courses in the department in the past, and if there's a need, I will do that. I've also taken occasional senior thesis students, and I lecture sometimes. If somebody is going away for some reason, I take over their lecture.
David, just a snapshot in time, circa June 2021. What have you been working on yourself of late, and more generally, what's been compelling to you more broadly in physics?
Okay. Two book projects. I've been working on typing and editing the lecture notes of my PhD advisor, Sidney Coleman, on relativity. This is based on my lecture notes which I retained from when I took the course in the '60s, a good friend of mine, David Levin, who also took the course, and David Politzer, who took it a couple of years later. So, I have those three sets of notes, and combining them and refining them and what not. I have just actually finished sending off to Cambridge University Press what will be called Sidney Coleman's Lectures on Relativity. So, that's one book project. I'm starting to do a 5th edition of my electrodynamics book, which is revisions. Obviously, new problems and things like that. But perhaps you were asking more about research activities, I don't know. My current project is a modest one, but it's turning out to be actually quite amazing. Believe it or not, the motion of a charged particle in the field of an infinite wire carrying a uniform current, so the magnetic field of an infinite steady current goes like 1/r, and circles around the wire. There have been surprisingly few studies of the motion of a charged particle in this sort of cylindrical symmetry field. A former colleague of mine, Nelia Mann, who's now at Union College, had done some computer studies and found, to her surprise, that the motion tends to be what I've come to call a double helix. It's basically helical motion around the wire, but superimposed on that, a smaller helical motion around the major helix. So, the typical motion of this system is -- how should I describe it -- one helix wrapping around another helix, which was sort of surprising. And if you add an electric field, give the wire some charge, then you can change the drift velocity and actually collapse the helix to a single donut-shape trajectory, a confined trajectory. I don't know if this is of any interest to anybody except me and my two coauthors, but I was fascinated, first of all, that the motion was basically soluble, and secondly, that it has this, to me, kind of surprising pattern. And I guess, thirdly, that so few people have ever looked at it. There are just a few who have done special cases. So, that's one project. Another project that I'm working on, but I don't know that this will issue in any kind of publication, is, a friend of mine at Harvard, Jacob Barandes -- you might possibly have run into him -- has constructed an electromagnetic theory, classical electromagnetism of intrinsic electromagnetic dipoles. You start with a particle with intrinsic spin, and a number of people from time to time have investigated whether there's such a thing as a classical, purely classical theory of intrinsic spin. Particles that carry spin that's not associated with any motion, but simply is, like the spin of an electron in quantum mechanics. Ordinarily, in a classical context, if you're talking about spin, you have in mind something like the rotation of the Earth on its axis, daily rotation. Well, that is actually orbital motion of all the rocks and dirt clods that make up the Earth. So, in that sense, classically, spin is really just a composite object that's rotating, perhaps in a limit as the size gets very small. But the question is, could you construct a classical theory of intrinsic spin, the way that the spin of the electron is intrinsic. It's a true point particle in quantum theory. We know you can do it quantum mechanically. Can you do it classically? And Barandes has come up with a theory that I'm not 100% convinced is totally internally consistent, but seems to be exactly this, a theory of intrinsic electromagnetic dipoles associated with this intrinsic spin. The reason that this is intriguing to me is that in my electrodynamics book, I make a point of the fact that magnetic forces can do no work. That follows directly from the Lorentz force law. It's an open and shut case in classical electrodynamics. I'm sorry, it's as clear as can be. But everybody has their example of a magnet lifting a paperclip, or a magnetic crane lifting a junk car, or something like that, in which it sure looks as though magnetic forces are doing work. So, I have had over the years more complaints than any other comments on my E and M book. How can you claim that magnetic fields do no work when obviously they do? Well, I've always assumed that was essentially a quantum mechanical thing that simply had no explanation in true classical electrodynamics. But if Barandes is right, there does exist a classical theory -- it's beyond electrodynamics. It's not classical electrodynamics, because in classical electrodynamics, magnetism has to be associated with the motion of electric charges, and there are no intrinsic dipole moments in true classical electrodynamics. But if you keep Maxwell's equations, and simply add one extra term to the Lorentz force law, apparently, you can get a coherent consistent theory that's a little bit beyond -- a slight generalization of classical electrodynamics that does allow for intrinsic magnetic dipoles, and magnetic forces can do work on those intrinsic magnetic dipoles. So, there's a hell of a long-winded explanation of what I've been working on. So, very exciting to me because it would satisfy all of these people that I've told magnetic forces -- I still insist, in classical electrodynamics, magnetic forces cannot do work. Simple as that. Open and shut case. Follows straight from the Lorentz force law. But if you're prepared to extend the Lorentz force law, and you can prove that that does not lead to internal inconsistencies, as I suspected when I first saw this, then you could have a quasi-classical theory that does allow for magnetic forces to do work.
David, to go back to the book project on Sidney Coleman. Of course, his lecture skills are legendary, and I wonder if you can explain a little bit about how maybe some of the science from that era needs to be updated, but perhaps, the timelessness of his abilities as a lecturer are something that so many people understand, and that's a motivator for this project.
Yes. Let me back up a little bit and say that actually this is the second project in a sequence of three that are done by the same editors -- myself, David Derbes in Chicago, and Richard Sohn in Massachusetts. The first one that we did was Coleman's lectures on quantum field theory, and that now actually exists. I have a copy of it somewhere. I would wave it in front of you, but I don't see it now. Oh, there it is. This is the quantum field theory book, and as I say, after we were done with that, we thought, how about -- Coleman taught quantum field theory for about 15 years or so. It became a very famous course. In fact, in retrospect, I now realize that virtually all modern graduate textbooks on quantum field theory are the children or grandchildren of Coleman's approach to the subject. He sort of set the agenda for the modern quantum field theory course. I never took the course, ironically, because when I was a graduate student, even though he was my PhD advisor, Julian Schwinger was on the faculty, and Schwinger insisted that only he could teach quantum field theory. So, it was not until Schwinger left Harvard that Coleman was able to teach this now-famous course. Anyhow, that was the first book, and the second one is a much smaller project. That thing is a thousand pages long, but -- where was I going with that? Coleman is unique. Not only was he a brilliant lecturer, but he also had a way of zeroing in on subtleties in important fundamental principles in a theory in a way that I think most, even professional physicists, didn't really have as clean and sharp vision of the fundamental principles. The relativity book is, as the course was, 50% special relativity and 50% general relativity. Offhand, you would say, special relativity for graduate students? What is that? We all know special relativity -- not much to be said about it. But this is special relativity for people who already know special relativity cold and are ready to hear Sidney Coleman tell them -- treat the subject in a much more deep and profound way. So, the first half is a very sophisticated, advanced treatment of special relativity. The second half is a very elementary treatment of general relativity. It has to be elementary because it was only half a semester on general relativity. Coming back to the question that provoked this. You wanted to know --?
About the timelessness of Coleman's approach to lecturing in physics.
That's right, and that's what started me thinking about the quantum field theory book first. Some aspects of that book, between you and me, are rather dated. Especially toward the end, he has a long section on elementary particle physics. This is elementary particle physics as of 1968 or so. A lot of it is wildly out of date now. We had, as editors, a choice. Do we try to make this a modern book departing from what Coleman actually said, or do we want to think of this more as a historical document, and something that somebody can look at and know what was going on in quantum field theory in the 1960s? And we chose to go for the latter. So, it's a faithful, historical treatment, but a lot of it, quite out of date. Similarly, the relativity -- although, in some respects, I think it's not so critical in that case. In general relativity, all kinds of stuff has happened since the '60s that simply is not mentioned in Coleman's treatment, but as I said, the part on general relativity is fairly elementary anyway. I mean, he treats no solutions except the Schwarzschild solution, interior and exterior Schwarzschild solutions. So, there are now lots more exact solutions that are known. Probably there were a few even at the time, but he didn't treat them. So, is it out of date? The quantum field theory book certainly is in some respects out of date. And I think for that reason, probably not terribly useful as a textbook on the subject, but the sort of thing that will be a fantastic reference for people teaching the subject to see how a real master treated the fundamentals. I hope something the same will be true of the relativity book.
David, a purely speculative answer by necessity, but it's been fun asking people in the field their instant reactions to the g-2 muon anomaly experiment at Fermilab, and the possibility that maybe finally this is physics beyond the standard model. What's your sense of things as they stand now?
Well, my ignorance is almost total. So, you're asking not for an informed opinion, but for my hunch.
More along the sense of, you've been around the block a few times, and you perhaps recognize potential hype when you see it. Along those lines.
I don't think it's hype, but what I do think is that the theory is extremely difficult and complicated. The electron's anomalous magnetic moment is fairly clean because the electron is so light that virtual processes are not that relevant, and quantum electrodynamics is straightforward. We know exactly how to do that. But the muon is so heavy, 200 times heavier than the electron, that—I'm sorry. All kinds of strong interactions come into the calculation for the muon. An electron can produce an electron and a photon, and a photon can produce an electron-positron pair, but that's about the end of the line. In the case of the muon, the Feynman diagrams that go to represent the anomalous magnetic moment of the muon, involve pions and quarks and baryons as strongly interacting particles, as well as contributions from the electron, of course, and the tau. It's a much more complicated calculation. And you know, when the anomaly was first discovered when the experiment was running at Brookhaven, shortly after the anomaly -- in other words, a theory not agreeing with the experiment (there's an anomaly piled on top of an anomaly here because the magnetic moments of the muon and electron are anomalous to begin with, simply because of higher order corrections to the old Dirac theory, which gave a very simple answer, but the anomaly that we're talking about now is the fact that the theory doesn't agree with -- the experiment doesn't agree with the theoretical predictions). Shortly after that second anomaly was first announced, the people who did the theoretical calculations realized that they had made a sign error somewhere in the calculation. This didn't completely correct the problem, but it made it less severe. There was a lesson in that. I don't fault them at all for making an error. For god's sake, it's an enormously complicated calculation. But my gut instinct now is to say the remaining one is probably not a fundamental problem with the standard model, but more likely is some subtlety in the calculation. That's my guess, but it's a complete guess.
Of course. More broadly, David, as somebody who has been sensitive to the interplay between experimentation and theory, what's your overall sense of the field right now, in terms of where the experimentalists are providing guidance and where the theorists are providing guidance the experimentalists?
It's almost entirely the latter right at the moment. It has been, I think to a dangerous extent, for the last 40 years. The experiments are so difficult, so time consuming, so expensive nowadays, the relevant experiments, that basically theory has gotten way out ahead of experiment. This is a dangerous, dangerous situation, and it has meant, I think, a generation of floundering among theorists, frankly, with highly speculative theories that would be lovely if one of them turned out to be true. But the guidance from experiment has been -- we're talking in elementary particle physics here -- the guidance from experiment has been almost nonexistent. Let's start in the '90s. They discovered the top quark, and we now know the mass of the top quark. Very nice, but it would have been infinitely more interesting if the top quark had not been discovered. It was just a question of what the mass of the thing is. Nobody doubted that the top quark existed, so when it was finally discovered, people's reaction was, good. That's just what I thought it was going to be. No, they thought it would be a whole lot lighter, and they got forced to higher and higher masses as time went on and experiments kept not discovering it. But it wasn't a surprise. The only surprise was, what is its mass? That is significant, but not huge. I would say, although I would get spanked for this, that the discovery of the Higgs was pretty much in the same category. It would have been much more interesting if the Higgs had not been discovered. Of course, everybody's reaction would have been then, oh well, unfortunately it's a little too heavy for the LHC to discover it. But again, it was so anticipated for so long that it was totally unlike the discovery of the Psi/J meson in 1972, or whenever it was, where an experimental discovery comes out of the blue, completely unexpected, and totally revolutionizes the whole discipline. The Higgs and the top quark -- well, you're going to say neutrino masses. Yes, fantastic, but in retrospect, we should have expected it. I don't think many people did expect it, but there's no good reason why the neutrino should be massless. The photon has got to be massless. The graviton, if it exists, has got to be massless. The gluons have got to be massless, or else everything goes crazy in the theory. So, we have good reasons for why they should be massless. There is no good reason for why neutrinos should be massless. Actually, the very best reason is that it makes some calculation a little bit easier. So, if I'm teaching elementary particle physics, I stipulate in the beginning, even now, in this course the neutrino is massless, because it saves me a lot of time and energy in doing the calculations, and you're not very far off. So, neutrinos have mass, yes. That is a significant discovery. Significant experimental result, neutrino oscillations. But again, it was not something that just changes everything radically. It makes some calculations a little bit more cumbersome.
David, I'd like to front load a broadly retrospective question about your career at this point, because I think it will punctuate our subsequent discussion. That is, I'd like to ask you to reflect on the fact that your career has been spent largely at small teaching schools. So, I wonder if you've ever thought about the other road you could have taken, being a student of Sidney Coleman, going to Harvard, and perhaps ending up at a large research university. Obviously, there's no way to know what could have happened, but I wonder if you could describe broadly what you have been able to achieve in your career teaching at small schools, and what you've been prevented from achieving teaching at small schools.
Boy, that's a long question. Have I thought about the distinction? You better believe it. I had two postdoctoral positions, University of Utah, and then at University of Massachusetts. And at the end of that time, I applied both to research universities and to liberal arts colleges because I was uncertain. Both of my postdoctoral positions had been, what was rare at the time, part-time teaching positions. I think one of them was one third time teaching, and one of them was half-time teaching. Partly because this was attractive to me. I had been a teaching assistant as an undergraduate and as a graduate student, and I liked teaching. But I was uncertain about which direction to go, and at that point, I took a job at Mount Holyoke College, which is a liberal arts college, and found that I really liked teaching a lot. The teaching that I had done at Utah and at the University of Massachusetts (Amherst), I really, really enjoyed it. You asked if I had thought about this. I thought very, very deeply about it, or at least a lot about it. I realized that I loved research when it was going well, but theoretical physics -- I don't know if this is true for everybody, but for me, it was very much a rollercoaster. Something would be working, and I'd love it. I would be up all-night doing calculations and everything, and it was almost like -- I say, I loved it. It was almost obsessive, I think, when it was working. But then, I would hit a brick wall, and nothing would work. Everything I'd touch, no, that doesn't work. This doesn't work. Try to find a different research project. No, can't think of anything that's going to -- so, research was fantastic, but frustrating and unreliable. The teaching was steady, and I remember how I was feeling with teaching. If research wasn't going well, I would say to myself, you know, I'm going to spend this afternoon working out the best damn lecture on X, whatever was the next thing in line, and just give a stunning lecture tomorrow. And I would do it, and I would come out feeling that I had accomplished something, and it was very satisfying and pleasing to me to be able to put together the best possible explanation. Of course, as soon as I'd given a lecture, I would think of ten things I should have done differently and can't wait until next year when I get to teach this again, and next time I'll do right. Anyhow, after two postdoctoral positions, I applied to both. Took the job at Mount Holyoke, which was full-time teaching, of course. I did a little bit of research there, but not a whole lot, and then went to Trinity College in Hartford, which was my first tenure-track position. Again, a little bit of research, but not very much. Reed College has been, for me, the perfect combination because we have a senior thesis program. Every senior writes a senior thesis, and this doesn't actually have to be original research, but it's best if it's original research. Well, do you call it research? I would say, looking back on it, of my thesis students, about a third of them, I would say, yes, it was a real piece of research, and something very minor but new was achieved in the process. Two thirds of them, either the project really didn't work out well, or the student for some reason stumbled or something. It was okay. Met the requirements, but it was not what I would call genuine research. But most of my research, almost all of my research since coming to Reed has been in connection with senior thesis projects. A Reed faculty member is required to do research not because there's some dean breathing down your neck, as is true at most places, including liberals arts colleges, but because you have to be working with senior thesis students.
And you have to be current in the literature yourself, is the idea.
Yes. You have to be actively engaged in stuff. I'm hesitating because this is not quite true. In the math department, most senior theses are, take a chapter from a graduate level textbook on something or other, and write it up in your own words. It doesn’t pretend to be original. It's what, in physics, we would call a library thesis. You didn't do anything new, but --
You synthesized the material.
Yeah, and that's perfectly legitimate at Reed. But it's not my ideal, not most faculty members' ideal. In the physics department at Reed, at least, we like to think of the senior thesis project as a research project in which the student is 100% in charge. This is a myth, but it's a good myth. The student is involved in choosing the question, figuring out how to attack it, doing the actual calculations, and then writing it up, all aspects of it, just as it would be for an actual research project. Again, in other disciplines, they have a different model. Our biology department, for instance, the typical thesis is not something that a student came up with, but a student came into a professor's office and said, “I'd like to work with you.” And they said, “Fine, the next project in my research curriculum is X. Here's your table, and here are your reagents. Go to work, tickling this frog.” Or whatever they're going to do. But in physics, we like to pretend that the student has input and ownership of all aspects of it. This, as I say, is a bit of a myth, and although I'm probably the most dogmatic in insisting on this model as the ideal, there have been many cases since I've been at Reed where there was a research problem that I just desperately wanted to work on, and the perfect student walked in my door, and I said, “Let's do this.” I'm sorry, I kind of dictated the thesis project and how to approach it. But I try to be coy about it, at least at the beginning until they get desperate and say, “I can't come up with anything. Please give me a topic.” Let's see, where were we? The role of research at Reed. We try to be, unlike at a university, very broad in our research interests so that practically any student who comes up with a project that they want to work on, there would be somebody in the department who knows a little about it or would at least be willing to supervise it. So, that has meant that I, for instance, have done most of my research work on electrodynamics and quantum mechanics, and occasionally elementary particle physics, which is what I was trained as -- my graduate work was in elementary particle physics. I've had a number of theses in elementary particle theory, but it is tough, frankly, to come up with a serious research project for an undergraduate in elementary particle physics. It's easy to do data analysis or something, and it's often possible to get your hands on data from a big lab or something. But I personally don't like that so much. I would like the student to have some notion of what the theory is and what we're trying to accomplish here. Not simply analyze a whole bunch of data on a computer.
David, how do you understand your remarkable contributions in the field of textbook writing, being a professor at teaching schools?
Well, that would never have happened if I had been at a research university.
Okay, that's what I wondered, but I was curious if you saw it in such binary terms.
But even at Reed, my first sabbatical, I proposed to go to Stanford, to SLAC, and write a textbook on elementary particle physics, which at the time barely existed at the undergraduate level. So, I put in an application to Reed. We have to justify a sabbatical project, and I remember one of my colleagues, a dear friend of mine, who was on the committee judging these things, said, “That doesn't sound like a worthy project to me, writing a textbook. If I wanted to write a textbook, I would gather up my lecture notes and send it off to a publisher.” That’s not what I had in mind for a textbook, but it is what the mythology about textbooks is, and what nine out of ten textbooks are. But as I say, that's not my vision of a textbook. I thought of a textbook as, you know, if I teach a course in electrodynamics, and I do a wonderful job, that's great for 21 students who happen to be in that class at Reed College. But if I wanted to reach a larger audience, textbooks seem to me the way to do that. But the truth is that I never intended to write textbooks. What happened was that I would teach a course for five or six times, electrodynamics in the first instance, and quantum mechanics, and then elementary particles. I would teach it a number of times and was not entirely satisfied with the textbooks that are available. They didn't do it really the way I wanted it done, or the explanations weren't clear in my opinion, or whatever. So, I would find myself handing out lecture notes, and more and more freed myself from textbooks altogether. At that point, the very first one was complete accident. I was at Mount Holyoke, and I was teaching electrodynamics for -- I guess, that was the fourth or fifth time that I had taught it, because I had taught it as a postdoc also. And some publisher's representative showed up. In those days, they used to do this much more than they do now. They would send around representatives to try to promote their introductory physics textbook, because that's where they make the money. They would come and advertise their book and give you a free copy and tell you how wonderful you were and everything. One of these guys, from Prentice-Hall, I remember vividly; I was trying to get him out of my office because I wasn't teaching the intro course and it wasn't relevant anyhow, and there was something else I was trying to do. Anyhow, he said at one point, “You're not working on any writing yourself?” And I saw my opportunity and gave him a stack of the lecture notes, and said, “Yes, I'm working on electrodynamics.” He took it away, and I thought nothing of it, and about two months later I got a phone call from them saying they wanted to publish it. So, that's how I got into the publishing business.
Well, David, we're going to take all of these ideas and develop them more broadly in the course of our discussion, but for now, let's go all the way back to the beginning. Let's start first with your parents. Tell me a little bit about them.
Both of them were university professors, starting in Berkeley and winding up at University of Washington. My father, a historian, and my mother, a zoologist. So, what can I tell you about them?
Did you see your mom in pathbreaking terms as being an accomplished scientist in her generation as a woman?
Yes and no. She was an ardent feminist, but surprisingly, I would say, docile. When they went to the University of Washington, he had a position in the history department, a regular faculty position. They had an anti-nepotism rule at the time, that two, husband and wife, could not both be regular professors at the institution. So, she was not employable as a professor. However, she was employable on a temporary basis as some kind of instructor or so in the zoology department. So, she should have fought this, but she didn't. It wasn't until much later that women colleagues and graduate students persuaded her to fight it. So, relatively late in life, she actually became a tenured professor also (they got rid of the anti-nepotism rule). So, where was I? The question was, was it unusual for her to be -- yes, it was, but she was not on an equal footing with my father because of this anti-nepotism thing, and she simply tolerated it for a long, long time. They would never tell her until late in the spring whether she was employed for the next year. She didn't know. Then, at the beginning of the summer, they would tell her, “Yes, you can teach so-and-so, such-and-such subject next fall.? So, in the summer she would be scrambling to prepare to teach what was sometimes a completely new course for her. But she loved teaching. She was very good at it.
Did your parents involve you in their careers? In other words, even when you were a little kid, did you have a rough understanding of what a life in academia looked like?
I guess so. What I remember most vividly as far as that goes is that dinnertime conversations were always -- not always, I'm sure, but were dominated by how terrible the students are this year. Every year, I remember being puzzled by this. “The students, they're so lazy, and not as good as they were five years ago,” or whatever. And then I read once a quote from -- I think it was Socrates or Aristotle or somebody -- saying exactly the same thing, that the students -- you know, it simply can't be the case that for 2000 years students have gotten worse and worse every single year. But I think I understand it now. It's a sort of weird psychological phenomenon. You remember the wonderful students, and you blissfully forget the not so wonderful students. So, your memory is always a rosier past than the present.
And where did you grow up, David?
Well, that's complicated. Berkeley, until the 8th grade. Then, Wisconsin. My parents were at UC Berkeley. My father was on the faculty in the history department there. He did not get tenure, and then we moved to Wisconsin, to Lawrence College, now Lawrence University, in Appleton. Then, after about three or four years, they moved to Seattle. And for my last two years of high school, I went to a boarding school in Vermont, the Putney School, on a farm.
When did you get interested in science?
Well, this comes back to my parents a little bit. My father knew nothing about physics or mathematics, but he was a very modern historian, and he believed that all aspects of human life should be subject to historical discussions. So, he would study religion or science, and he was a Marxist. Communist, actually. Both of them were for a while, but my father for a long time, a Communist. He had this notion that science, and physics in particular, was the perfect human intellectual endeavor, and that everything else should be imitating physics. So, he had this exaggerated admiration for physics, which he did not understand. My mother was a math major, and then later a zoologist. She was an authentic scientist, and she did understand it. But the influence on me, ironically, was more my father, because I think it was he who sort of instilled in me the notion that the perfect thing was to be a physicist. A scientist, and a physicist in particular. So, from junior high school on, I always knew I was going to be a physicist. I didn't have the slightest idea what a physicist was, but I was going to be a physicist. Actually, by the time I went to college, I remember thinking I might be a physicist, or I might be a historian. What happened was -- it was interesting -- in physics, if I got the right answer, and my reasoning was not unreasonable, I was rewarded for that, I guess, in the form of grades or whatever. But I took a couple of history courses, and if I couldn't quote five dead white men on some subject, then it was not considered legitimate. I remember, once, writing a paper on John of Salisbury -- I don't remember a thing about John of Salisbury, but we had to write a paper in this history course, and I wrote it on John of Salisbury. He was the most convoluted, obscure writer you can imagine, but I discovered by picking bits and pieces from here and joining them to a little piece of something that he had said somewhere completely different, that I could arrange it all into a fairly coherent and rational argument. I was pleased with this, and wrote this up as my paper, and the teacher in the course, who was a graduate student, called me in and said of my paper -- I told her exactly what I had done. She said, "That makes me so angry, I could spit," an expression I had only heard from my southern grandmother. She considered it absolutely intellectually irresponsible that I had taken John of Salisbury -- did I take it out of context? I don't think I made up anything, but I did repackage it, and I was pleased with that. But the different way I was treated in history -- if you can't quote all the authorities, then keep your mouth shut -- and in physics, where if you found a clever way to do something, more power to you, I found it very liberating, and history very stifling. So, that, I think, is what confirmed me in physics.
Tell me about the decision to go to the Putney School for the last part of your high school.
Do you know Putney School at all?
Well, it’s complicated. It has to do with my parents' politics, I think. When we left Berkeley, my brother was ready for high school, and we were going to Appleton, Wisconsin, which is where Lawrence College is. It was Joe McCarthy's hometown, and Joe McCarthy was still alive. In fact, his funeral procession a couple of years later passed right by our house. I had the day off from school. So, my parents were terrified of putting my brother into the local high school in Joe McCarthy's hometown, because my brother couldn't keep his mouth shut, and he had written a paper in Berkeley about McCarthy, and they thought that he was going to be in trouble. From old leftist circles, they had known the founder of Putney years earlier. So, they knew about Putney, and they decided that it would be a good idea for him to get out of town. So, they sent him to Putney. He loved it, and as a result, when I got to be appropriate age, they couldn't very well say no to me. I wanted to go, so for my last two years, I went to Putney, and it was wonderful. I did love it. There was also -- but this was almost accidental -- a fantastic physics and math teacher there. To this day, the way I think about physics problems, or calculus problems, traces right back to my high school physics course with Ed Shore. It doesn't trace to anything that I learned in college. I mean, I learned a lot of information in college, but the way of thinking about the subject.
What kinds of schools did you apply to for undergraduate? Were you at the top of your class? Was Harvard seemingly within reach?
No idea if I was in the top of the class or not, but at the time, I applied to two places: Reed College and Harvard, both of which were common destinations for students from Putney. A lot of my good friends went to Reed, but at the time, I remember -- Putney, you know, is a tiny little school. There were, I think, 200 students there when I was a student there. Everybody knew everybody. It was a boarding school, so I remember thinking I want to go to a place that's huge and anonymous. I had this vision that I want to go to a place where, if I disappear for a month, nobody's going to know and nobody's going to care. I don't know why I had this vision. Putney was -- I loved it. It was a small, intense community, but I thought if I go to Reed College, that's going to be a little more of the same, whereas Harvard I was pretty sure would be more anonymous. So, it was on that basis that I chose Harvard. After about a month, I got over it, and regretted ever since that I had not come to Reed, which I would have loved.
And the plan was physics from the beginning at Harvard.
Did you declare the major right away?
I think probably we did. I do remember this, that physics was, at the time, I think, the most common intended major for incoming Harvard students. I don't know when you technically declared a major, but somehow in your application or something, you had said what your intentions were. And physics was the most common intended destination when I first came in. When I left, it was one of the least common majors, and psychology had become the most common -- and a lot of them were the same people. There was sort of a progression out of physics and into something perceived as a little simpler.
What were your initial impressions on the department of physics at Harvard? Who were some of the luminary professors who may have made an instant impact on you?
None made an instant impact on me. I didn't encounter good professors at Harvard until my junior year, possibly. My first two years at Harvard were a wasteland in physics, as far as quality of teaching is concerned. I had a lot of teachers there who frankly would not have lasted a semester at Reed, but they were fine at Harvard because they were, or had been, significant researchers or whatever.
I wonder if that left an impression on you, the lack of emphasis on pedagogy at Harvard.
You better believe it. My son went to Harvard, against my advice. But he had a much better time, and I think Harvard was genuinely -- is now genuinely more concerned about teaching. When I was there, teaching was a distraction for the faculty, and they made no secret of it whatsoever. There were some spectacularly good teachers. Sidney Coleman, absolutely. Norman Ramsey, Ed Purcell, fantastic teachers. But they were almost accidentally fantastic teachers. Certainly, Harvard didn't reward them or promote them on their teaching. They did it just because it was in their blood or something. Partly, as I say, I think Harvard has improved a lot, and partly, my son was a whole lot more tolerant than I was. He took a course in the philosophy department, a course in ethics, with 900 students in it. It was in Sanders Theater, and he was sitting way back in the balcony. He loved it. He would tell me about the lectures. My notion of a philosophy class is 12 students and a wise guy sitting under a tree and talking about philosophy. The idea that a philosophy course would be 900 people and you're way back in the back and can barely see the guy who's lecturing, I didn't like that. My son, as I say, was a lot more tolerant and had a better time. But where were we? You were saying memorable teachers.
David, what about even as an undergraduate, did you sense at Harvard a hierarchy between theory and experimentation?
Oh, good question. I'm not sure that I was sensitive to that as an undergraduate.
In other words, maybe the superstars were the theorists, and the experimentalists, not so much. Or not.
That simply was not my experience. That's a new question to me, and I'm thinking about it right now. Coleman, brilliant teacher and theorist, of course. Norman Ramsey, not a brilliant teacher, but a good teacher. Ed Purcell, a brilliant, brilliant teacher. But Ramsey and Purcell were both experimentalists. So, I would not have had that takeaway, I think. But another confounding issue is I think the theorists did not teach undergraduates very much. I didn't have Coleman until I was a graduate student. Of course, I guess he hadn't arrived until I was a graduate student, maybe. I'm not sure. No, he came before '64, I think. Anyhow, I guess, the simple answer is no. I was not that sensitive to --
Were you open to theory or experimentation, or did a particular professor or class set you on a particular path?
I was, to the extent that I was aware of the distinction. I was open-minded about it until my first year as a graduate student. My first year as a graduate student, I had a research assistantship in Norman Ramsey's molecular beams lab. That was experimental, obviously. I became a pretty skillful machinist that year. I did a lot of work on Bridgeports (milling machines), and lathes, and so on. And I loved working in the machine shop, but in the laboratory, I remember sitting around with other graduate students, and sometimes Ramsey would come into the lab, and they would be talking about, you know, what kind of metal should we use for such-and-such a purpose? It's got to be a little bit flexible and can't be too heat sensitive. Somebody'd say, oh, you need molybdenum, or something, you know? And the people who were really good at this just had an incredible memory for facts about materials and stuff, and how different molecules would behave and so on. And I realized I don't have the mind for that sort of thing. My memory is not terribly good, and I'm not really terribly interested. They were fascinated by the different behaviors of different molecules in metals and whatnot. So, I remember at least having the sensation after that year in Ramsey's lab that this was not for me. I was not going to be very good at it. Meanwhile, I did have a course with Coleman, and that was my model.
How parochial was your appreciation of physics, or not, beyond Harvard? In other words, in the early 1960s, was somebody like Murray Gell-Mann on your radar, or was your world of physics strictly a Harvard world of physics?
No, certainly not strictly Harvard. In fact, I didn't have much notion of what was going on at Harvard. We were never encouraged to find out what was happening in the labs, or among the theorists. Even as graduate students, hardly at all. There were seminars, and I used to go. As an advanced undergraduate, at least, I went to seminars. I understood not a word of them, but I think by osmosis you pick up some sense of what's going on. But almost never were they actually Harvard people that were giving the seminar. They brought in people from outside. So, was I aware? No, I was not particularly aware, and as I say, even as a graduate student, not particularly aware. It is astonishing to me, and actually kind of scandalous, when I think back on it, that I took a couple of reading courses from Shelly Glashow while I was a graduate student, exactly -- looking back on it, exactly when he was involved in the work for which he got the Nobel Prize. But did he suggest that I read about that stuff? No. He considered it wildly speculative at the time and he had me reading papers by Weinberg. Weinberg's second sum rule, about pion scattering or something. I remember not a word of it. It was opaque and deathly dull. And yet, at that very moment, he was doing Nobel Prize winning stuff. And here's a graduate student, walks into his office asking for what to read as a prospective particle theorist, and he didn't give me a clue what he was thinking about. That's partly Glashow, I think. He is an amazing guy with an idea every minute. Most of them garbage, but every once in a while, one that's fantastic. He and Coleman made a perfect combination, because Coleman was the opposite. He could demolish any idea. You'd tell him some new idea, and he would immediately see ten flaws in it. So, Coleman and Glashow were good. Glashow would tell Coleman what his latest cockeyed scheme was, and Coleman would tell him why it wouldn't work, and Glashow would go back and come up with another one. But every once in a while, as I say, he came up with something that passed Coleman's test, and then they probably knew it was good.
As an undergraduate, do you have a specific memory of thinking to yourself, I'm going to do this in graduate school. I'm going to pursue a life in physics.
No. Sort of like what I told you before, I knew I was going to be a scientist and a physicist from a very early age for no terribly good reason. I like physics, but I must say, the instruction at Harvard was so terrible, especially in the first two years, but actually even in the third year. I remember courses that were really awful. I did then encounter Ramsey, and he was great, and my senior year, Purcell. But learning physics was not a happy experience at that point for me. I liked the subject itself once I understood it, but I remember going to lecture after lecture and not understanding a word that this turkey was talking about. Now I can look back on it and say, that was just lousy instruction. It was not my fault. But at the time, I assumed it was my fault. But I do remember having this repeated experience that about a month later, like when an exam was rolling around or something, and I looked back at my old lecture notes, now I understood the subject. I'd done a bunch of problems on it, and I talked to my friends and whatnot, and now I did understand it, and it made perfect sense. At that point, it was very satisfying and pleasant for me. But the process of learning with lousy instructors is grossly inefficient and unpalatable. I sometimes think that I learned the subject better at Harvard than most of the students at Reed learn the subject, either because I taught myself or I learned it from hashing things out with fellow students, or whatever. It was not because the teaching was good, but precisely because I had to fight for it, I think I learned it ultimately better. That's a horrible thing to concede for someone who's devoted his life to teaching, but I think somehow, if it works, the sort of bad teaching method probably is effective and beneficial.
David, this all suggests that you would have hightailed it out of Harvard as soon as you could have for graduate school, but I wonder if intrinsically you appreciated that the role of pedagogy was much different as a graduate student, and that's where Harvard's true value lay for you.
No. I didn't have that sense. I was dumb. Frankly, I will not name him, but the absolute rock bottom instructor at Harvard… I took two courses from this man. Why did I ever take the second course? Well, because it was the subject that seemed most sensible in the sequence of classes. The fact that he was a lousy teacher, I don't think it even dawned on me at the time. To think in those terms, I thought, as I said, that there was something wrong with me, that I was just kind of slow learning this stuff. Looking back on it, the guy was an abysmal teacher, and I was just plain dumb to take another course from him. For graduate school, if I were doing it over, I would not -- well, I've already told you, if I were doing it over, I would have come to Reed as an undergraduate, and I would have gone to Cornell as a graduate student. But I went to Harvard for both. I shouldn't trash Harvard. As I said, I think I got a fantastic education there, but sort of in spite of the institution.
Was it inertia, David? Were you just already there, and was there a culture at Harvard where, you're already at Harvard; why would you go anywhere else? To what extent were those parts of the equation?
You know, the idea of Harvard as sort of the pinnacle, I don't think I was ever infected by that. In fact, when other people treated it that way, I kind of despised it. But I was a good little boy, and I did what I was told. Actually, ironically, they claimed at the time that they almost never accept their undergraduates as graduate students. Turned out to be, at least then, a complete lie, because five of us from that graduating class were admitted to the Harvard physics department as graduate students. I think that was an unusually large number, but they certainly were not prejudiced against their own undergraduates. But I remember thinking if I go to a different institution I'm probably going to have to retake the courses because it won't be a perfect match, so if I stay at Harvard -- I had already taken several graduate level courses at that point. I was already partway into my graduate studies. I thought that a big part of graduate school was coursework. In the event, after two years, I was done with all of the courses that were available. I think I maybe took one more course after the first two years, but that was not the hurdle at all as a graduate student. I would have liked to have taken some more courses later on. I should have spread it out a bit, but as I said, I was dumb. I was trying to get the coursework out of the way so that I could concentrate on research.
Was working with Sidney a foregone conclusion, or did you only develop that relationship as a graduate student?
No, it was not a foregone conclusion. I don't believe that I had ever heard of the guy as an undergraduate. And I don't think it was until my second year as a graduate student that I took a course from him. I took two courses from him, a group theory course and this relativity course. No, I mean, at some point obviously I did know who he was and took these courses from him, but I guess I really admired him because, first of all, he was a spectacular teacher, and secondly, he had this uncanny knack for explaining things in a crystal-clear way. I've already told you; I had this experience as an undergraduate of going to class after class, in which, lecture after lecture, frankly, I didn't understand what the person was talking about. Luckily, I did manage to put it together after the fact, but with Coleman I never had that impression. Coleman, or Purcell, or Ramsey, these were people who every single lecture, pretty much every single word was crystal clear right from the beginning. Then, I started to realize that there are people who can do this and a lot of people who can't. It was only then that I started to realize, looking back on it, that the quality of instruction had been pretty poor that I had been getting, and it was not entirely my fault. Where were we? How did I come to be working with Coleman?
I wanted to work with Coleman. By then, I knew I wanted to be a theoretical particle physicist, and Coleman was just such a -- the most brilliant physicist I'd ever known. But I didn't have any kind of real rapport with him at all. I was a very proud student. I never went to office hours. Once or twice as an undergraduate, and never again as a graduate student. Coleman told me after I got my PhD -- he said, "We call you the Silent Man," because I guess unlike the other graduate students, I was not constantly going and asking him questions and stuff. I always had this feeling, if there's something that I don't understand, I should think about it very carefully before I go and talk to the professor. Then, usually, after I'd thought about it carefully, I'd figure out what the answer was, so there was no occasion to go and ask the question anymore. But Coleman, coming back to how I got signed up with Coleman, I knew I wanted to work with him, but I also had heard forbidding rumors from other people. I think Tony Zee -- if I remember right, Tony Zee had gone to Coleman and said, “I would like to work with you. What would you suggest as a research problem?” And Coleman said, “If I had a research problem, I would work on it myself,” and sent him away. So, I was intimidated by that. And meanwhile, I had been working a lot with Carl Bender, who was a fellow graduate student with me, on a project that he had started actually from Schwinger's field theory course. We were both in the field theory course together, and after every lecture we would get to either his apartment or mine, and rewrite our lecture notes from Schwinger's lectures, because they were brilliant. They were also very difficult, and we wanted to have perfect lecture notes for this course. Anyhow, Carl and I were working on this project, and I thought, I'll write up a hunk of this project I'm working on with Carl Bender, and present it to Coleman, and see if he'll -- it was my way of establishing my competence. If he was sufficiently impressed, he would say, “Yes, I'll take you on as a thesis student.” So, I did it. Took a writeup of some stuff that Carl and I had done together to Coleman and presented it to him. And Coleman said, “Okay, I’ll look it over; come back in a week.” I came back in a week, “I didn't have a chance to look it over yet. Come back in two weeks.” I'd come back. This went on for about a month and a half, and finally I went back, hoping that he would say, “Okay, you can work with me on your PhD thesis,” but he said -- I remember this verbatim. “Your thesis is fine. Type it up.” That was the extent of my mentor experience with Sidney Coleman. It was not entirely unique, by the way. Carl Bender also was technically a student of Coleman's, but in fact, he worked with T.T. Wu at MIT, and Coleman was only the pro forma advisor. I think Tony Zee also worked with somebody at MIT, and Coleman was his pro forma advisor. I worked with Carl Bender, who was a fellow graduate, and Coleman was my pro forma advisor. There were a few exceptions. Jeff Mandula worked very closely with Coleman, and I think there were, even in those early days, a couple of other cases. David Politzer certainly worked part of the time closely with Coleman. But I never had the experience of working with a graduate mentor, really. I did as Coleman said. I typed it up, and that was my thesis. Pretty good thesis, by the way, if I do say so myself. But if anybody was my thesis advisor, it was Carl Bender.
David, on the social side of things, being a graduate student at Harvard in the late 1960s, early 1970s, particularly in light of your parents' politics, were you involved at all? Were you political at all? Were you doing anything with regard to the antiwar movement?
Yes. I went on all the demonstrations. I went down to Washington and marched on the Pentagon, and all that sort of stuff, but I was never in a leadership role at all. I hate telling other people what to do, and leadership in politics involves exactly trying to persuade other people to do something that they're not inclined to do otherwise. I just, temperamentally, find that extremely difficult to this day. I campaigned for Obama. I do my duty in that sense, but I hate it. I went to Mississippi in 1964 for the summer voter registration there, and some people found that exhilarating. I found it depressing and I could force myself to do it, but I don't like it.
Did you recognize in real time, when you were doing your graduate research, what a formative and foundational moment this was for particle physics?
No. I was quite completely unaware. Again, I don't think I was unique in this. I've already told you that I don't think Glashow was aware of the importance of what he was doing. You know, it's ironic in retrospect, but Glashow's early papers were not that widely read. So, looking back on it, I could say, yes, the '60s were a time -- really from let's say about 1963 to about 1972 -- were a time of fantastic developments in elementary particle physics. When I entered graduate school, elementary particle physics was kind of a quagmire. There was incredible amounts of stuff and information, all of these dozens and dozens of different particles, but no rhyme or reason. And then finally, the eightfold way came along, and that at least started to package the elementary particles into some kind of shape. But still, there was no dynamical theory to speak of. I guess that it was finally clear that there was a hierarchy of interactions. You know, strong interactions, electromagnetic, weak, and gravitational. I think I could have told you that by the time I was a starting graduate student. But beyond that -- I'll tell you a story. For our qualifying exam for the PhD at Harvard -- I don't know if this is still true, but at that time, you didn't take a written exam in which you solve problems. Rather, you presented some topic from current research literature to a group of two or three faculty members and gave essentially a sort of seminar on some topic of your choosing. I remember, I went to Coleman and said that I was thinking of doing my qualifying exam on Yang-Mills theory, which was the original -- well, not the original, there was one from the 1920s, but the original of the new generation of local gauge theories. It was intended in the '50s to be a description of the strong interactions, for which it was kind of misguided. But it works for the weak interactions, and works beautifully for electrodynamics. It doesn't do anything except reproduce QED in that case but puts it into a very nice framework. But are you familiar at all with Yang-Mills theory?
Sure, of course.
Oh, okay. Well, so, I told Coleman that I wanted to do my qualifying exam on Yang-Mills theory, and he said, “Oh, no. Don't do that. It's a lovely idea, but it goes nowhere. It's a dead-end.” This was, I'm talking about 1965, I suppose. And that was Coleman, the most brilliant physicist there was. But as I said, it was sort of in his nature that he could see the defects in anything, and it wasn't working for the strong interaction, so he said, “Don't touch it.” He suggested that I do it on Cabibbo theory, which was a theory of weak interactions that had just come out. So, that's what I did. I calculated the lifetime of every conceivable meson and baryon that could decay by leptonic weak interactions, and calculated to an absurd number of significant digits, and everything. Then, about two weeks before I was scheduled to give the exam, it was going to be Coleman and Glashow -- maybe just Coleman and Glashow as my examining committee. But I saw an announcement on a bulletin board that Cabibbo himself was coming to Harvard to give a series of lectures on his theory. His lectures were going to come after my oral exam, but I realized that he was going to be physically at Harvard when I gave the exam. We were allowed to invite outsiders to come to the qualifying exam, although almost nobody ever did, but this put me in a horrible quandary because it would be kind of natural to invite Cabibbo to come, but I was terrified because here was the author of this brand-new theory, and was I dead sure that I had completely understood it? But I finally got up the courage and invited him to come, so it was Coleman and Glashow and Cabibbo. So, I gave this seminar on Cabibbo theory. It turned out to be a brilliant move, because Coleman and Glashow had an incentive to make their student look good in front of this visiting dignitary, and Cabibbo wanted his theory to look good in front of these Harvard professors. So, all three of them were incredibly kind and generous to me, and basically, I just talked. They didn't interrogate me at all, and I showed them -- I had put up on the blackboard my calculations of all of the lifetimes and everything, and it went beautifully. How did I get off on that?
No, that's fine. In all of your graduate research, what was going on experimentally, in experimental particle physics that may have been relevant for your research? If the answer is nothing, that's telling in and of itself.
You know, this is embarrassing, but nothing that I can remember at all. The Cambridge Electron Accelerator was a fairly new instrument just up the block from the physics department, and that was doing experiments on QED at the time. In fact, I do remember that there were some preliminary results that came out of that that were inconsistent with predictions of quantum electrodynamics. That happened to be the case while I was taking quantum field theory from Julian Schwinger, who had done all the calculations. I remember one day in class, somebody said, “What do you make out of the latest results out of the Cambridge Electron Accelerator?” And Schwinger, who was always irritated when somebody asked a question, sort of looked at his watch and said, “Well, I think they have problems with their calibration.” And three or four months later, when they had polished up their results, and the disagreement with the theory had gone away, they conceded that it was a problem with the calibration. How Schwinger knew that, I don't know, but that's the only experimental result that I remember being aware of, because of that incident.
Anything memorable from your oral defense? Any questions that knocked you for a loop?
The defense of my thesis?
Because that's not the qualifying exam, but a later experience with almost the same cast of characters. So, it was Coleman and Glashow and Arthur Jaffe. No. First of all, when I asked Jaffe if he would be on the committee, he said, “Yes, but I won't have time to read your thesis.” So, I don't believe he had read the thesis. Coleman had certainly read the thesis. Glashow, who knows? They didn't ask many questions. They let me talk for a while, and then we all went out and had a beer. So, no. And it was an absolute -- I shouldn't say a letdown, but no, it was pleasant and uneventful.
What did you see as your contributions at that stage in your career?
You mean, what was I planning to contribute?
No, I mean, even with your thesis. In what ways was your thesis responsive to some of the broader questions in elementary particle theory at the time?
Ah, well, not very. But if you had asked me at the time, I would have probably given you a slightly different answer to that. It was on massless field theory, so massless particles of higher spin, especially. You know that a particle of spin s has 2s+1 degrees of freedom, the different orientations for the spin, is one way to think about it. So, there are 2s+1 degrees of freedom for a massive particle with spin s, but for a massless particle of spin s, there are only 2 degrees of freedom. The maximum, and the absolute minimum, minus that. So, for spin one, for instance, the photon, there are two possible orientations. Classically, we would think of this as two transverse polarizations. There's no longitudinal polarization for a photon. So, the massless limit is a very tricky limit in general. Not for spin zero, because then there's just one degree of freedom period. For spin 1/2, there are two degrees of freedom, and that's the same whether you do it as 2s+1, or just the maximum/minimum. But for spin one, already there are three degrees of freedom for a massive particle and two degrees of freedom for a massless particle. So, that's already a little bit tricky, and it gets to be more and more so as you get to higher spin. So, for massless particles of higher spin, first of all, it was known -- Carl Bender had discovered this -- that there is no tensorial, second rank, symmetric stress tensor for a massless particle of spin 3/2. You can't do it. Schwinger -- when Carl told Schwinger this, Schwinger didn't believe it, but he went home and did the calculation, and the next day he came back and said, “You're right. There is no tensorial stress tensor for massless spin 3/2,” and it just gets worse and worse for higher spin. So, there's no stress tensor, and moreover, in working out the implications of that, Carl and I realized that there's a problem with the representation of massless particles. You know, for a massive particle of spin one, it's represented by a four-vector. For spin one half, it's represented by a spinner. Spin zero, it's represented by a scalar, and so on. But these integer, or half integer spin representations of the Lorentz group, they work for massive particles, but they're not true, not correct for massless particles. Spin one, QED works for -- it's just on the edge of working. There does exist a stress tensor for massless spin one. That's the well-known stress tensor for electrodynamics. But if you go above that, there is no stress tensor, and particles do not naturally belong to the irreducible representations of the Lorentz group. They belong to what are known as indecomposable representations of the Lorentz group. I don't know how much I should get into this, but --
So, my thesis was on, first of all, constructing the stress tensor for massless particles of higher spin, correctly represented. And then, the other half of it was, what is the appropriate representation under the Lorentz group for massless particles of higher spin? Now, that's just a preamble to the answer to your question. Did I think this was going to be important? It might have been important. As it turns out, there are no massless particles of higher spin. There's the graviton, if it exists, but that's a different kettle of fish, because it's not simply a massless particle with spin two. It's all tangled up with general relativity. So, that's a separate case. But for massless particles, at the time, there was the neutrino, which was considered massless, for, as I've already said, no good reason, but we thought the neutrino was massless. But that's okay, because there's no problem with the representation of spin 1/2 particles. Spin one, the photon is a massless particle. Yes, there is problem with its representation, but QED manages to, in a sense, sweep that under the rug. Just by the skin of its teeth, spin one massless particles, the theory works. Already, if there had been a massless particle with spin three halves, or spin two, or spin 17, God knows, then my thesis might have played an important, I do believe. But there aren't any. So, it's sort of ho-hum. But I didn't know that at the time. Nobody knew that at the time. Since the neutrinos seemed to be massless, and the photon was certainly massless, it seemed reasonable to imagine that there might be massless particles of higher spin. But as it turns out, as far as we know now, there simply aren't any.
David, how was the market for postdocs after you defended? What opportunities were available?
Well, you know, I got my PhD in, whatever it was, May or June of 1970, but I've already told you that I had gone to Coleman to try to butter him up to see if he would be my thesis advisor. That was in February or March of the same year. So, I had no idea that I was going to be getting my PhD that spring until sometime late in March, by which time all of the postdoctoral positions had already been taken for the following year. But it turned out that the University of Utah had just gotten a grant from the National Science Foundation, a so-called Department Development Grant. NSF was trying to beef up physics, and maybe science in general, I don't know, at departments in the hinterlands. Places that were not prominent, prestigious institutions, and pump them up and get them going. So, Utah got a grant. Most of the places, I discovered later, that had gotten these Department Development Grants, would invest it in one or two big names that they would offer a sort of pro forma position. They would show up for two or three weeks a year, and then they could list this person as a member of their faculty. University of Utah had a very different attitude, that was actually very clever I thought. They hired from all over the world a whole bunch of postdocs, who then did a lot of the teaching, so it was nice for the faculty that were already there, and also brought a very vibrant research culture to the university of Utah that they hadn't really had before that. So, I was one of this cohort. They got the grant just in March, so they were way too late for attracting great postdoctoral students, at least from this country. But fortunately for me, I hadn't known to apply for a postdoctoral position until just when theirs opened up. Roy Glauber actually ran into me in the hallway one day and said, “I hear you're going to get your PhD this spring.” And I said, “Yes, big surprise.” And he said, “Well, are you looking for a postdoctoral position? Because I just heard from the University of Utah that they're hiring a whole bunch of postdocs.” So, they did. I applied for it and got it.
Did you recognize at that point that teaching would become a much more important part of your overall career than some of the people that you learned from at Harvard?
I think I had a pretty good notion, but I'm not dead sure of that. I certainly was interested in pursuing a postdoc, and I guess if you had asked me at that point, I would have said, no. Chances are I'm going to go to a research university and I'll do some teaching on the side, and that will be fun but that won't be my career.
What were your impressions when you got to Utah? Coming from Harvard, did it feel like a backwater, or was it a vibrant place?
I remember driving the road, when you come down through the mountains, and finally there's Salt Lake City in front of you, thinking, my god, what have I got myself into, that I was going to this absolute desert. I mean, it is kind of a desert in the summertime. In the winter, it's a gorgeous city, but not so much in the summer. Anyhow, yes, I thought that I was going to purgatory. But it turned out to be a wonderful place because there were these postdocs from all over the world. So, it was a very lively place. Very cosmopolitan. It was fun. I would not have liked to have spent my whole career there, but for two years, it was wonderful.
Did you take it as an opportunity with your research to expand on your thesis, or did you want to pursue new research projects?
I wanted to pursue new research projects. In point of fact, I spent the better part of the first year tidying up loose ends from my thesis. So, Carl and I wrote one more paper. We had already published two papers on the subject, and a third one that frankly was largely my work, I wrote at the University of Utah. I think I was intending to do a little bit more on that subject. I did write another paper, but Carl thought it was not as interesting as the other three, so we never did publish the third one. And then, I was actually assigned -- my supervisor there was Jim Ball. Looking back on it, what I should have done was said, okay, I'm done with fleshing out my PhD research. Now, I'm open and looking for some new subject. What could you suggest? And maybe I would have worked very closely with him. As it turned out, there was another postdoc who came at the same time, Steve Pinsky, and Pinsky worked very closely with Jim Ball, but I did not. I was sort of the -- would have been the odd man out. I should have been more aggressive. I certainly should have been, as a graduate student, more aggressive in going to Coleman earlier and pursuing Glashow and Weinberg and the others. But again, I tended to be kind of on the timid side, and Jim Ball never came to me, saying, “Why don't you do X?” So, I guess then I didn't go to him.
On the teaching side, what classes did you teach at Utah?
I taught junior level E and M. That was the first time I taught the subject, but I then taught it a second year at Utah. Also, I think I taught a section of the intro course. But junior level E and M was a memorable course I taught there, two years running. And then I went to U Mass, and I guess I did not teach it at UMass, but I taught E and M again at Mount Holyoke three times, and at the end of that time, that's when it became the book.
Was a faculty position at Utah in the cards? Did you explore that opportunity at all?
I didn't. I think that it was pretty explicitly not in the cards. I don't believe that any of that cohort of postdocs -- I think there were about 25 of us -- I don’t believe any of them actually stayed there after the two years. And it's quite possible that was explicit right from the start. I don't know.
When did you start looking for your next opportunity, based on that?
Well, in my second year at Utah, I applied for postdoctoral positions and got the one at UMass. I couldn't tell you where else I applied at that point. I don't know why UMass came up, particularly, but -- I'm sorry, I draw a blank on that. I must have seen an ad somewhere.
More broadly, were you aware of what was happening in real time with things like asymptotic freedom and grand unification? Was this sort of like headline news in your world, or not yet?
No, it was not headline news in my world. This is going to be very embarrassing, but I remember Jim Ball and Steve Pinsky talking a lot, and we had some seminars at the University of Utah about the results of the deep inelastic scattering experiments at CERN and at SLAC, and thinking, well, that doesn't sound terribly interesting, smashing electrons off protons, or neutrinos off protons. I didn't realize that this was the first serious evidence for the real existence of quarks. How I was so dense that I didn't pick up on that, I really -- in retrospect, it's kind of amazing to me. Because later on, when I was teaching elementary particle physics, that was sort of a crucial series of experiments, and actually, a very simple interpretation that it was basically the Rutherford experiment done over again, but on the proton, showing that there were three, in fact, pieces inside the proton. It set up the quark model as serious business. There really were three quarks in there. But at that time, even though I know that I was aware of the experiments going on, I didn't understand their significance at all. You know, that reminds me of another thing I worked on at the University of Utah. And it may be that Jim Ball actually proposed this to me. There was a theory paper that came out from a Swiss guy, Weiler, on the fine structure constant. He claimed to have derived the fine structure constant from first principles. You know, fine structure constant, 1 over 137, which combines Planck's constant, the speed of light, and the charge of the electron into a dimensionless package and sets the scale for all of atomic physics. So, a magic number, and everybody, every particle theorist at least, dreams of finding a formula for what is after all this pure number of fundamental significance. Weiler claimed to have done that, but the paper was written in French, and I was the only one around who could read French. So, I got a copy of the paper, and they wanted me to translate it, which I did. I wrote up a translation of Weiler's paper, which was largely unintelligible. The guy is a mathematician, and he pretty clearly didn't understand physics, but that didn't become so obvious for about six months, when he came up with a second paper. This time, calculating the mass ratio between the electron and the proton. And that is something that nobody believes is a fundamental number. The fine structure constant is fundamental, absolutely. The mass ratio for the proton and the electron, there's nothing fundamental about that. So, that sort of tipped his hand that this guy didn't really understand what he was talking about. But meanwhile, I had devoted a couple of months to the fine structure constant. It was an interesting subject because subsequently, when people started to realize that this was nonsense, a lot of people started coming up with their own numerological formulas for the fine structure constant. It turns out to be very easy. There's a ritual. You find some product of simple numbers that comes pretty close to 137, and then you tweak it by finding another number that is very close to 1, a little bit smaller or a little bit larger, and then you just multiply the original number by various different powers of your tweaking constant, and you can correct, therefore, the number that wasn't quite right, and come up with a perfect formula for the fine structure constant. It's easy to do it, and they're now on the books, literally dozens of formulas for the fine structure constant, all of them numerological --
Was UMass a good experience for you?
Yes and no. I had a pretty good time there. The teaching was very good. I taught a graduate math methods course, which was very useful to me. I had taken a graduate math methods course when I was a graduate student, but you know, it's a huge subject, and when I was teaching it, it gave me a chance to revisit the subject and investigate areas of the subject that I hadn't gone into before. So, that I remember as being very satisfying. On the other hand, I published, I think, exactly nothing at the University of Massachusetts. That was embarrassing to me, and also no doubt contributed to the fact that I then took a job at Mount Holyoke College. So, I wasn't entirely honest when I said before that research, I loved it when it was working. The other part of it is that when it wasn't working, nothing was being published either, so I realized that I didn't want to be dependent on a job that was going to require that I either publish lots of garbage, or that I was going to be constantly in trouble for not publishing when I should have been.
Now, Mount Holyoke was a tenure track position?
No, it was not. It was a temporary position. Two and a half years, awkwardly. The half year somehow combined with a half-time position at Hampshire College, which is also right nearby there.
Did the November Revolution register in real time for you?
Yes, hugely, because I think -- let's see, 1972.
November '74 is the J/Psi.
Yes, but I'm trying to think. I think that I was at Mount Holyoke by then, but if so, just barely. Anyhow, I gave a talk on the subject within a couple of weeks. So, either late November, or possibly it was early December of '74, UMass wanted somebody to -- everybody had heard about this particle, but to summarize what was going on. It was not known then what exactly this particle was, and I reviewed possible different candidates in a seminar there. So, I was very aware of it, and I guess because I probably had been talking to people about it, they had me give this seminar. But I sort of vaguely remember driving up from Mount Holyoke for that, so I think I was already at Mount Holyoke.
Were you able to do any research during your Mount Holyoke years?
Yes. Actually, one of the papers that I'm most pleased with to this day was done with a senior thesis student at Mount Holyoke, Ellen Szeto. It was -- you know, I'm always nervous with the word research. I'll tell you what this paper was, and then you can tell me whether it counts as research or not. I don't know if you've looked into the radiation reaction in classical electrodynamics, but it has its problems. The Abraham-Lorentz-Dirac formula leads to runaway solutions and acausal pre-acceleration. It's not a happy aspect of classical electrodynamics. But there are two different ways of getting your hands on the Abraham-Lorentz formula for the radiation reaction. One is, this is essentially the recoil for a charged particle that's radiating. Because it's radiating, it's losing energy, so the same particle, if it were neutral, would accelerate a certain amount, but because it's charged, it accelerates somewhat less, typically, because it's losing energy in the form of radiation. It's a sort of recoil effect. In fact, some people call it radiative recoil. There are two ways of getting at this. One is conservation of energy. That's how Abraham first did it. And then there's Lorentz's way of doing it. He tracked it down to the self-force on a charged particle. He used a model of a spherical cell, a uniformly charged spherical shell. The fact is, in classical electrodynamics, Newton's third law of motion does not hold. It cannot hold: the force of charge A on charge B is not the same as the force of charge B on charge A. It is, of course, in the case of static charges: the Coulomb force is the product of the charges over the distance squared. So, for a static charge, Newton's third law does hold. But for accelerating charges, it does not hold. So, what Lorentz did was take a spherical shell and chop it up into all of its constituent little pieces of charge. Piece of charge here acting on a piece of charge over here. The force of one on the other is not the same as the force of the other on the one. Add those up over the entire sphere, and you get a net self-force of the charge on itself, like picking yourself up in a basket by pulling up on the handles. In Lorentz's telling of the story, it's a result of the breakdown of Newton's third law within the structure of an extended object, and it yields exactly the same Abraham Lorentz formula. But it is a very cumbersome calculation, both in Lorentz's version and in any polished-up version that's come since. We have better ways of doing it than Lorentz did, one of which is in Jackson's classical electrodynamics, a slightly polished up version, but it is still a complicated calculation. But that's because we're doing it for spherical geometry. And it occurred to me, working with this student Ellen Szeto, that exactly the same mechanism would work if instead of regarding the charged particle as the limiting case of a spherical shell, where size goes to zero, divide the charge into two pieces, what we called a dumbbell model. Just two pieces, and try accelerating that with the force of one end on the other not the same as the force of the other on the end, so the total dumbbell has a net self-force on it. It's much easier to calculate. You can do it without all the complexities that come really from the spherical geometry. Of course, it's not a likely model for an elementary particle. An elementary particle is not, after all, two separated charges like that. But nevertheless, if you're just trying to illustrate the mechanism, it's a beautiful pedagogical device. That's why I say I didn't know whether you'd count it as research or not, because it's essentially of only pedagogical interest. But it is, to my mind, very significant pedagogical interest, because it does make this otherwise very difficult graduate level argument accessible to undergraduates. It illuminates the basic mechanism, and you can do it for a dumbbell that's moving longitudinally, or transversely, and it works out beautifully for both geometries. So, that paper I published with Ellen Szeto; I guess you said, did I do any research at Mount Holyoke? I did publish something. Was it research? Yeah, I counted it as research.
Did you expect to stay at Trinity for longer than you actually did?
Yes, that was my first tenure track position, and we bought a house in West Hartford. My daughter went to a school that she loved there. My wife was very happy there. But I was not that pleased with Trinity. I'll tell you a story. I already mentioned that I applied to Reed as an undergraduate.
Right. I figured there must have been some poetry to this narrative.
Well, I had always regretted that I had not gone to Reed as an undergraduate. So, when I got my PhD, I applied for a postdoctoral position -- I think I applied only to the University of Utah, but I also wrote to Reed College that year, and every year after that for the next seven years, I wrote to Reed College asking whether there was a chance of a position at Reed. And each year, I got back a little postcard, I think verbatim the same postcard year after year from the chairman of the department -- no, not verbatim because the chairman of the department changed every two years -- but I got this little postcard saying, “Unfortunately, we have no opening, but we'll keep your letter on file in case there's an opening in the future.” I knew what that meant. They tossed it in the wastebasket. But the last year, when I got my job at Trinity College, was the first year I did not write to Reed College, because this was a tenure track position, and I assumed that was going to be my career at Trinity College. But that year, the secretary of the department -- not the department itself, but the secretary of the department -- wrote me a little letter saying that she had noticed my forlorn letters over the years asking whether there was an opening in the physics department, and she wanted me to know that this year there was an opening.
David, why this mythic connection with Reed, of all places? You're at Putney. Obviously, you're going to apply to Harvard. Of all the small schools out there, why Reed as an undergraduate, and why this retaining interest to somehow be a part of the Reed community, even as a professional?
And by the way, it was not incorrect. Reed was the perfect place for me, partly because of the combination of research and teaching, but mostly because of the quality of the students. When I was at Trinity -- I don't mean to trash Trinity -- I had a pretty good time there for one year, but Trinity was everybody's third choice. The students were constantly telling you that they should have gone to Amherst, or Bowdoin, or Williams, but somebody stabbed them in the back and gave them a lousy letter of recommendation or something, so they had to come to Trinity. And the faculty were all telling you that they were supposed to have a faculty position at Yale, but for some reason, somebody screwed them, so there they were at Trinity. Nobody really wanted to be there, was my feeling about it. And then I got to Reed, and the faculty were all telling you what fantastic students they had, and that this was the greatest place, that the students were brilliant. The students were no more brilliant than the best students that I'd had at the University of Utah, but what they are is unbelievably dedicated. All liberal arts colleges claim that their students are very studious and academically committed and all that, but Reed is the only place, including Harvard, where I've found this to be actually true. I remember one of my first experiences at Reed was down in the locker room, in the gym. I'm a swimmer, so I was down there to go swimming, and realized that the student conversation in the locker room was all about their Hegel lecture that morning. At Trinity, it was considered absolutely rude to talk about your classwork outside of class. In the lunch hall, you're supposed to talk about fraternities and the progress of the football team, you know? But at Reed, everybody's focus and attention were their academics. It's a little bit overly precious sometimes, but it's so much more refreshing, especially for a teacher, than the opposite.
What were your expectations? When you talk about the perfect blend between teaching and research, what was your course load, and how was it communicated to you how much original research you should be doing at any given time?
The answer to the latter is easiest. Almost never. Nowadays, much more. If somebody is a candidate for tenure at Reed for instance, they're going to pay a whole lot of attention to publications. I think it's sad, frankly, for two reasons. First of all, I think, in general, the world would be a better place if about 75% of all publications had never been published, because there's this, to me, childish emphasis on publication -- publish or perish, you know? People feel compelled to publish garbage, and they do. Most publications in physics, we would be better off if they had not been published. You say, well, everybody's making an incremental change and improvement, or something like that. Well, that's not true. What they're doing is clouding the works, by and large. So, having said that, I like to publish. I flatter myself that I publish when I think I've got something useful to say that would actually benefit somebody else. I've never felt, at Reed, obliged to publish because that's part of my job or something. Nowadays, as I say, more so -- when I first came to Reed, there was a guy in the department who never published a word. Nicholas Wheeler, who's, second to Coleman, the most brilliant physicist I've ever known. He does not publish and will not publish. He writes these incredible monographs. In the old days, he would literally calligraph them himself. Beautiful -- he's a genius at taking some subject in the literature, writing it up in his own words, so that what had been this convoluted, complicated, murky subject, and it comes out as this beautiful, crystal-clear thing in his hands. Nowadays he types them all, and they're actually available on the web. But he will not publish anything. Is it original? No, in a certain sense, it's not. He's taking something that's in the literature, and as I say, cleaning it up. Polishing it. I think it's not research. It's not, at least, original research, but it is a contribution of the highest order. But it wouldn't satisfy a modern dean -- he wouldn't have survived a year at a research university because he refuses to publish this stuff. But at Reed, that was perfectly acceptable. What the college has always required is outstanding teaching and scholarly productivity. But that doesn't have to issue in publications, and if it does issue in publications, well… I guess I'll leave it at that. It doesn't have to issue in publication as far as Reed is concerned. At least, traditionally. Probably not true anymore.
David, rather than engage you chronologically on each of the major textbooks -- Introduction to Elementary Particles; Introduction to Quantum Mechanics; Introduction to Electrodynamics -- I'd like to instead ask you to compare and contrast your various motivations in terms of writing the textbook. You already discussed how you fell into the textbook business accidentally, even by happenstance, but that doesn't explain how you motivated yourself to see each of these projects to fruition. So, first, let's talk generally about gaps in the literature and gaps in the pedagogy that you saw with each of these projects. We'll just take your answer generally from there.
Super question. I'll start with elementary particles, gaps in the literature. I wrote that in 1984, when I was on sabbatical at SLAC. I had been teaching elementary particle physics to undergraduates at Reed a number of times, and I was convinced that it actually works at the undergraduate level. I had grown up in the '60s with the notion that elementary particle physics is simply not a mature enough subject theoretically to be accessible at the undergraduate level. There were very sophisticated pieces of theory, and then there were oodles and oodles of lore that you had to learn if you were going to be a professional, but that didn't belong in the undergraduate curriculum. I think that was true until about -- you mentioned 1974. Let's say, 1974 was a good turning point. By then, there was enough coherent theory on the books that it really started to make sense to teach it to undergraduates. Also, I had gone to an Aspen conference run by Max Dresden, who among other things, taught basic Feynman calculus, Feynman diagrams, in the context of a very simple model that he called the ABC theory, that was a steppingstone to evaluating realistic Feynman diagrams, that made it possible for undergraduates to actually evaluate simple Feynman diagrams, calculate cross sections and lifetimes. In other words, to do serious calculations in elementary particle physics. The package of, first of all, a maturing of the subject, and secondly, my encounter with a way of presenting serious calculations in particle physics, from Max Dresden, made me realize that this is a subject that is really teachable to undergraduates, and ought to be part of the standard undergraduate physics curriculum. By 1984, I was convinced of that from having taught it several times, but there was no book on the subject. There were books on elementary particle physics -- usually combined with nuclear physics -- that would tell you bits and pieces, and by then would tell you there are up and down quarks, and maybe strange quarks, and maybe would teach you a little bit about the eightfold way, and classification schemes for baryons and mesons and leptons. But there was one book that came out a little bit before mine, Halzen and Martin, that was the first step toward a serious elementary particles book. I think they considered it was for beginning graduate students, but it could almost be used for undergraduates. A little bit too sophisticated for undergraduates, but that was it. So, talk about a gap. I wanted to convince the physics community that serious elementary particle physics, not qualitative stuff, but serious elementary particle theory was teachable to undergraduates, and all I needed was a textbook on the subject. So, that's why I wrote the textbook on the subject. It was partly for my own courses, and certainly based on my own courses, but that was my motivation. I was proselytizing. I did a study at the time to find out what undergraduate institutions taught elementary particles, and there was one such institution. Haverford had such a course, and Reed College had such a course, and then universities would have it at the graduate level, but nothing but a qualitative course at the undergraduate level. I was, I must say, completely unsuccessful in persuading -- I mean, to this day, most places will not teach elementary particle physics to undergraduates. They consider that it's somewhat irresponsible to even try. But I'm sorry, they're just wrong. It can be done, and now there are several other books that do the same thing in one way or the other. But at the time, I thought the whole problem was there's no book. Now I realize that most physicists are actually kind of scared of elementary particle physics. I mean, they've heard about pions, and it seems awfully complicated, and they just don't want to get into it. If they realized that there were books out there that make it accessible, they might change their tune, but it hasn't happened yet. By the way, we were talking earlier about developments in elementary particle physics, and whether the last 40 years or so has been actually a kind of dry time for the field. I think that it has been a dry time for the field, and one of the ways that I measure this is the fact that my elementary particles book has been in print ever since. The second edition only came out two or three years ago, but up until then, why on earth was a book that was published in the mid '80s still in print, or even vaguely relevant? The answer is that not a whole hell of a lot had changed at that level. There's no mention of the mass of the top quark, because it wasn't discovered yet. There's no mention of masses of neutrinos because they didn't know about that yet. But apart from that, it was pretty much unchanged. The second edition was some changes, of course, but there hasn't been a comparable period, really, since 1900, which an elementary particles book would still be relevant 30 years later. So, complicated story, the particles book. E and M, I didn't plan to write a book. It was just more and more refined lecture notes. Why did I start to do lecture notes? Because I was dissatisfied with the textbooks. E and M -- there's no particular controversy about how you teach E and M to undergraduates. What the subject matter has got to be, even the order in which you present the arguments is not particularly controversial. What's the difference between my approach and other people's? I would like to believe that my arguments, my explanations are a little bit clearer than some. I hope so. It's more informal in style, but apart from that, E and M books frankly are interchangeable, a dime a dozen.
You would even include Purcell in that.
Purcell is the greatest ever, but that's at a more elementary level. I wouldn't use Purcell for juniors. For sophomores, or conceivably for freshmen, that's what Purcell was written for. And pedagogically, it doesn't work except for -- I was his chief TA, by the way. He had been getting complaints from people. They said, “That's a beautiful book. Maybe you can use it for honors students at Harvard, but you can't use it for most students.” And Purcell always said, “That's nonsense. This book was written for every physics student.” And one year, he put his money where his mouth was and undertook to teach at Harvard the non-honors version of the freshman E and M course. And I was his chief teaching assistant that year. I went to every single one of his lectures, which were spellbinding. They were brilliant lectures, and his demonstrations were fantastic. But by the end of the semester, he said, “They're right. You can't use this book, even at Harvard, for the non—” It's not that it's so sophisticated. Mathematically, it's not very sophisticated, but physically, it's very sophisticated. It's very demanding of a student. The kind of student who wants to solve the problems by paging back and finding the relevant-looking formula, but not actually reading the chapter, it's a hopeless book for them. You have to read some chapters two or even three times. Once, to get a sort of sense of what he's trying to do, and then once to understand in detail what he's doing, and maybe a third time to sort of polish it up. I don't know. It just requires a very sophisticated and dedicated student, and most students are not up to that. But Purcell's is the greatest textbook -- maybe the greatest textbook ever written on any subject in physics. But mine is much more standard, junior level. Maybe a little bit clearer, maybe a little bit more user friendly, but basically, I've been astonished at how successful that book has been. I don't understand it, frankly.
Now, did you see the quantum mechanics book as, to some degree, stepping out of your comfort zone, and did you relish that?
No. It was similar in that I taught the course at Reed probably five or six times. Here, we have a full year of quantum mechanics, full year of E an M, too. So, actually, one thing that's a little usual about my E and M book is that it's written really with a full year course in mind, and most people only teach one semester. So, it's got more advanced material in it on radiation theory and relativity than some of the other books do. But quantum mechanics, again, we teach a full year of it, and the book is designed for a full year course. But as I say, I had been teaching the course many times. There are a lot of textbooks on quantum mechanics for undergraduates, but quantum mechanics is a little bit different situation. As I say, E and M, there's no dispute about what the book should be. I mean, we're talking about the details only. In the case of quantum mechanics, there are radically different ways of presenting the subject, and mine is one take on how to present quantum mechanics, the one that I happen to feel pedagogically most comfortable with. But as I say, there are radically different ways of presenting the subject that I enormously admire. John Townsend's book, out of Harvey Mudd, or David McIntyre’s from Oregon State University, take a very different approach to the subject. Mine is based on position space quantum mechanics, wave functions, starting with the Schrödinger equation. I was determined that the Schrödinger equation would appear on the first page of my book, and it does. But the wave function, psi, lives in Hilbert space. It is mathematically a subtle and tricky kind of object, which you sort of sweep under the rug, but eventually it's going to come up and bite you. The radically different approach that Townsend and McIntyre take is to start with a two-level system, essentially a spin 1/2 system, where the mathematics is much, much simpler. You're dealing with two component vectors, basically, and all of the observables, instead of being self-adjoint operators in Hilbert space, they're Hermitian matrices in a two-dimensional vector space. It's much, much cleaner mathematically, and you can teach all of the fundamental principles of quantum mechanics without the mathematical complexities that are involved in Hilbert space, even if you sort of try to conceal them as much as possible. Of course, both approaches have to be confronted eventually, so in Townsend's book you do eventually get to the Schrödinger equation for wave functions, and in my book, you will eventually get to the two-level system, the spin 1/2 system, but it's taught in the context of angular momentum, and spin angular momentum. You can ask the question, if the two-level system is so much cleaner mathematically, why don't you teach it that way? And actually, if I were going to teach it again, I think that I would probably use McIntyre's book and teach it that way, just because I'm curious how it goes. I've never dared to teach it that way myself because the motivational problem strikes me as being very, very tricky. How do I go into class on the first day and say, imagine a system in which there are only two possible states, or linear combinations of those two states, and having students look at me as though I was the man on the moon, or something? When you're coming out of classical mechanics, unless you go to something like classical optics and talk about polarization -- that's a system that has two different linear polarizations, and you can have linear combinations of those -- but what's the connection between that and mechanics? It's awkward. I just don't know how to motivate my very first lecture if I was trying to start that way. John claims -- and I think I've heard this from David also -- that you can do it. You simply say, imagine that there are two levels, and we're going to represent this by a two-element object that we're going to call a spinner, and then we're going to make linear combinations of that, and then we have operators acting on it. Apparently you can get away with it, but the motivational problem is what's always held me up on that.
How do you deal with the fundamental mysteriousness of quantum mechanics, and conveying these concepts to undergraduates? I mean, before, you were talking about the concern with even elementary particle physics at the undergraduate level. There's so much in quantum mechanics that even celebrated physicists don't understand. How do you deal with these things in conveying these concepts in a textbook for undergraduates?
My strategy is to bring them out as much as I can into the light of day. Not to conceal them -- mathematical difficulties, I do tend to postpone as long as I can, but the conceptual problems of quantum mechanics, the measurement problem, I believe in confronting them head on. Head on, when they're approachable. You touched on a very tricky point. Structurally, what I do is introduce the Schrödinger equation and the wave function, and then I say, what does this wave function actually tell us? Well, it tells us the possible outcomes of a measurement. And then I ask the question, suppose that I make a measurement, and I find the particle at position A. Where was it immediately before I made that measurement? And then I talk about different schools of thought about that. And then I sort of drop the subject for a while, and then at the very end, I come back to that and hit it again with Bell's theorem and Schrödinger's cat and decoherence and talk about the conceptual difficulties. But at that point, it's after they've already, hopefully, mastered the nuts and bolt of the subject. I can't stand popularizations of quantum mechanics that love to say, well, a particle is neither a wave nor a particle. The electron behaves sometimes like one and sometimes like the other, and there's no coherent way to picture it. I don't like that because if somebody has not studied quantum mechanics, I think that it's mumbo jumbo. Whereas, if you've got through to the spin 1/2 particle, you can really tell a story in a way that makes a whole lot more sense. Suppose I've got a particle, and its z-component of angular momentum is plus a half h-bar; that's one of its possible eigenstates. Very good. Now, I ask the question, what is the x-component of its angular momentum? Well, I'm sorry, I can't tell you. It's a linear combination of two different eigenstates. So, what does that mean as far as a measurement is concerned? Well, if you measure it, there's a 50/50 chance that you'll get plus a half h-bar, and a 50/50 chance that you get minus a half h-bar. Does that mean that it doesn't have an x-component of spin? Yes, in a certain sense, it does. Does that mean that you don't know what its state is? No, I know exactly what its state is. Its state is spin up along the z direction. There's no ambiguity about what its state is, but that state simply doesn't contain the information what the outcome of the x-measurement is going to be. I think in the case of the spin 1/2 system, you can tell that story in a way that's persuasive -- that the listener has a finite chance of understanding what you're talking about. Whereas if you say it to a layman who doesn't know anything about spin 1/2 particles, I'm sorry, it just doesn't mean anything, and you're actually doing a disservice to even pretend. So, that's a complicated series of answers to your question. Yes, I believe in confronting the conceptual issues head on, but not necessarily right at the beginning. Some of them are best left to the very end of the subject.
David, to go back to your father and his recognition that history could be put in such beautiful service to science, I wonder what opportunities you've seen in writing these textbooks to insert a historical perspective, an appreciation that all of these discoveries exist in a historical narrative, and they build on each other over time.
You know, I have several responses to that. I believe in what you might call a folk history of the subject, which is not necessarily the true history of the subject, especially in something like particle physics. In particle physics, historically, there were a thousand horrible dead ends that didn't lead anywhere, and we just forget about -- well, don't talk about those. The folk history is a series of triumphs, one after another, making a sort of logical sequence. So, in my elementary particles book, the first two chapters are essentially a folk history of the subject, but I don't pretend that it's an accurate history of the subject. There are lots of things that I leave out because they're best left out, but it's not an honest history. But it does help you to understand the subject to learn about how the different particles came to be. How the positron came into the subject via Dirac and Anderson’s experiments, and then the muon came into the subject as Yukawa's meson, but turned out not to have anything to with Yukawa's meson. I don't know, it's an interesting story, and it helps you to keep track of what's otherwise a complex cast of characters. Quantum mechanics, I was taught the subject, the first month or so was completely historical. We spent two or three weeks on Planck's black body formula, because the professors seemed to think at the time that they had to persuade us kicking and screaming that classical mechanics was incorrect. We had been hearing about quantum mechanics since we were in grammar school, for god's sake. We wanted to get on with the subject, and I'm sorry, Planck's black body spectrum, after Planck, an established physicist, had studied this problem for many years, he had a right to say there's something fundamentally wrong with classical physics. We need something new here. Planck had a right to say that. David Griffiths, after three weeks in a sophomore physics course talking about Planck's black body spectrum, it seemed to me there were a thousand different ways to wiggle out of this that didn't really require a revolution. Planck had a right to that conclusion; I didn't have a right to that conclusion. So, it was really just diverting, and not very helpful, to start the subject with the black body spectrum. Yes, it belongs somewhere in the course, but not right at the beginning. And also, damn it, it's very misleading because the origins of quantum mechanics all involve the photon, if you think about it. There's Planck's black body spectrum, and there's Einstein's theory of the photoelectric effect. Both of them involve the photon, and a photon is a massless particle, and if there was ever something relativistic, a massless particle is it: it belongs to quantum electrodynamics, not to non-relativistic quantum mechanics. So, if you're teaching non-relativistic quantum mechanics, the word photon should not ever appear. It does appear a couple of times in my book, in the context of, it's radiation theory, but I sort of apologize for it. It's almost impossible to talk about radiation theory without using the language of photons, but it doesn't belong in a non-relativistic quantum mechanics book. So, there, that's my second comment on the historical approach. I don't like the historical approach to quantum mechanics, because I think it's diverting, and I think it's in some fundamental sense misleading.
What was it like to win the Millikan Award?
Oh, I don't know. I don't believe in these things very much, but I was touched by it, especially because a dear friend of mine and colleague had nominated me for it. So, it was a little ironic because I gave a talk at an AAPT meeting. When they give you the award, you're supposed to make a speech that then gets printed in the American Journal of Physics. And my talk was interpreted by a lot of the physics education research people as an attack on physics education research. It was not my intention at all. I think physics education research is a mixed bag. Some of it, like the stuff at University of Washington, has opened my eyes to ways of explaining things in physics. But on the other hand, a lot of it is very dogmatic. You've got to do things our way, because we've done research, and we proved that the only way students can learn is X, Y, and Z. That part I don't believe at all. I do agree that there are lousy ways of teaching. I have already confessed that I experienced a good deal of that. I have theories about what makes for lousy teaching. I don't know what makes for great teaching. I've seen lots of different great teachers, and I would hate to have to give you a prescription for what makes good teaching of physics. I was in some respects ambivalent. For instance, I talked a little bit about the Hestenes test, the Force Concept Inventory, which was one of the sort of founding inspirations for physics education research. But I think that people used to -- I don't know that they do anymore -- put too much emphasis on the fact that students, even after they've taken a first-year course in physics, are still confused by intuitions that they picked up in grammar school. I don't think that's quite as wicked as the physics education research people would have us believe. It doesn't prove that they've learned nothing. It just proves that those intuitions are sometimes persistent.
And it sounds like your definition of successful physics education is at once simpler, and more broadly conceived. In other words, success can mean simply turning on a lightbulb in a student's eyes into understanding how the world works. It can mean getting a good grade and really understanding the material. It can mean going onto graduate school, and even beyond. There's no simple way of defining success.
I guess that I would define it, not some of the things that you said, but understanding of basic phenomena or principles of physics. That's what I'm trying to convey. You know, my parents, as I told you, were both professors, and they had this notion that I think is fairly common. They always claimed that what I'm teaching is not subject matter. I'm teaching students how to think. I learned very quickly in my teaching career that a lot of my students could think a whole lot better than I could, or at least a whole lot faster than I could. What I was doing is, I knew something, understood something about the physical world that they didn't, and that they wanted to know. So, my business as a teacher was not to teach them how to think, although in some vague, indirect sense, maybe that's true, but I was going to explain things so that they would come to understand basic principles of physics. I have a very un-exalted notion of what my role as a teacher is: to explain things in as efficient and as appetizing a way as I possibly can. So, my parents, again, subscribed a little bit to the notion that a teacher is sort of like a drill sergeant or a gymnastics instructor. Your business is to make these students jump through a bunch of flaming hoops or something. I don't know; that sort of rubs me the wrong way. I'm trying to liberate students from perhaps incorrect intuitions, or simply from ignorance.
And you're also, it sounds, ambivalent on where they take that knowledge and understanding. Some of them might go into medicine, and some of them might successfully image a black hole for the first time.
Absolutely, yes. I actually believe that physics is outstanding training for human life. It's liberating. Maybe all science is that way. Maybe all education is that way, but I'm not quite so certain of that. If you're talking about poetry, or French philosophy or something, being crystal clear in explaining something is probably not a virtue, because part of the fun of poetry or French philosophy is trying to figure out what on Earth that turkey is trying to say in this convoluted way. Usually, if you actually untangle it all, the actual message turns out to be fairly trivial. But physics is different. It's fundamentally important, and it's very non-trivial. There's no reason not to be as clear and as accessible as you possibly can. So, I've always, in teaching, favored the simplest possible way of explaining something. When kids right out a graduate school come and they want to teach classical mechanics, they always want to start with the Lagrangian, or maybe even with the Hamiltonian or something. My reaction is, you know, that's the third floor of abstraction. Let's start out with Newtonian mechanics, which is very concrete and non-abstract, and then ascend to the higher levels of abstraction later in the subject, not at the beginning. Every graduate student wants to teach what they most recently learned. But it's not, in my opinion, good teaching of physics.
I neglected to ask at the very beginning, when we talked about your titles, when you were named to the Howard Vollum Professor chair, who is or was Vollum?
Howard Vollum was a Reed alumnus from the physics department. His senior thesis in the '30s involved building a very primitive oscilloscope. He invented -- I believe it's the case that he invented the triggering mechanism that is really the essence of an oscilloscope. You know, to wait to a particular point on a signal, and then trigger the sweep, and then wait for that same thing to roll around again, to trigger so that you get a pattern that's not just a jumble. I think oscilloscopes had existed before Howard Vollum, but they didn't know how to trigger properly. As a result, unless you had a very simple signal, it was just garbage. But then he founded Tektronix, which is the premier maker of good oscilloscopes, which is, I was going to say, a Portland firm. It was actually outside of Portland. And he gave a bundle of money to Reed College, including this endowed chair, I guess.
How much opportunity have you had in terms of recruitment, or even evangelism, in getting out the word that for students who could get into places like Caltech or Princeton, that they should come to Reed, that they should have it on their radar because of the emphasis in teaching, because of the emphasis for all of the ideas that you represent?
My own feeling about that is I haven't done any self-conscious proselytizing at all. I hope that reputation eventually develops, and I think that has happened to some extent with Reed. Not as much as I would like, but it's interesting because several outstanding students that we've had are actually transfers from Caltech. Richard Crandall transferred from Caltech after a year, and later was on the faculty at Reed. He died recently but was a brilliant fellow. And Morris Copeland went to Radcliffe, as it was at the time, and transferred to Reed after one year. Oh, and Tyler Abbott, one of my thesis students, didn't transfer here -- he came straight to Reed, although he had been admitted at Harvard and Princeton and all over. Another brilliant student, but he visited Reed and saw a spark here that he liked the look of. So, the word is out, but in very limited circles, I would say. I wish Reed was better known, but I think this sort of thing has to happen by word of mouth. I feel the same way about my textbooks, by the way. Publishers always want to put advertising blurbs on the back, and advertise in journals, or something like that. And I told them, I don't want any of that stuff. I would like the books to sell themselves if they're going to or die if they're not going to. But I don't want anybody buying one of my books because Murray Gell-Mann said this is a good electrodynamics book, or something like that.
After you retired, and you got to work on Revolutions in Twentieth-Century Physics, I wonder how explicitly referential you meant to be to Kuhn's Structure of Scientific Revolutions.
Oh, yes, I think so. Although, I didn't self -- well, let's see. Yeah, the word revolutions, I think -- yes, of course. It wasn't as though I was taking Kuhn and trying to see how I can doctor up that title and put it on my book. But by the way, that book has been totally unsuccessful. It has found a market of zero, essentially. And that's alright. I guess that I was afraid of that in a way, but on the other hand, I had taught the course several times to non-science students, and I don't like popularizations of physics. Things like Hawking's [A] Brief History of Time, that talk about physics but don't actually teach you to do it, and I think very often give you a very misleading -- you know, because they want to use intriguing terms, and precisely want you to be amazed by the physics rather than understand the physics. That kind of rubs me the wrong way. So, I wanted to write a book that would be for non-science people, but teach them actually, with a little bit of nuts and bolts, about what's going on in the subject. Not the speculative supersymmetry, but real, established physics. But because I don't believe you can understand that stuff without doing occasional problems, I sprinkled through the book problems, and I was told right at the beginning, you put problems in there with numbers and equations, nobody's going to read it. But I wanted it to be an honest introduction to the subject. My sister, for instance, who always claims to be very interested in what I'm doing, I sent her a copy and said, “This will explain what I've been doing with my career. I want you to do the problems, and I'll help you with them.” She read, I think, through three or four pages, and did the first problem, which was something about converting units or something like that. Something very trivial but essential to understanding and being able to do any problems that come later. She bailed out at that point and read no further. She was honest about it. “You know, numbers, they confuse me.” Well, okay. If you're not willing to do the problems, I'm not willing to give you fancy words that you don't understand.
Do you see Kuhn's notion of paradigm shifts as lending itself particularly well to progress in physics over the course of the 20th century?
Yes and no. You know, I haven't thought a whole lot about this, but I think -- I've always believed that in some sense there's an overarching paradigm of science, or particularly, of physics, that has not changed. So, paradigm shifts on a smaller scale, yes. A more reduced scale, yes. I think it is a very illuminating way to think about things, and I could identify you four or five paradigm shifts that have come to elementary particle physics in my lifetime as a physicist. But I still think there is sort of an overall strategy that has not changed and probably will never change for science. Maybe that's a cop-out. So, revolutions is a little bit too strong a term, to my mind, because it doesn't really totally replace anything. It builds on what was there before and -- I don't know.
You mentioned how books like A Brief History of Time can rub you the wrong way in the sense that they popularize physics in perhaps a misleading way. I can't help but ask, in your rich tenure as a communicator of science, at all of your invited talks that you give not just to other physicists, but to the broader audience, how have you seen opportunities to correct some of the problems in the way that physics is popularized?
Well, I haven't really that often talked to a completely lay audience, I would say. Although, I have occasionally. I don't know. I guess, with a careful choice of what you talk about, or what you don't talk about. For instance, I've given talks sometimes to high school classes about special relativity. Special relativity, you know, is founded on Einstein's two postulates. The first one is the principle of relativity. A little bit awkward to explain that the principle of relativity is one half of the theory of relativity, but you can get over that and tell them that Galileo knew all about the principle of relativity, that the laws of physics are the same in a moving reference frame. The only thing that Einstein brought to that is maybe that he would say it applies to everything, and not just mechanics. But if you're limited to mechanics, Galileo would have said the same thing. Nothing new there. But the really revolutionary postulate is the universal speed of light. The fact that the speed of light is the same for all observers. And then, I go straight to the question of, what does this mean exactly? Well, suppose that you're on a train, and it's going at 60 miles an hour down the track, and you walk at two miles an hour down the aisle of the train. How fast are you going relative to the ground? Well, high school students all can tell you, 62 mph. How did you get that? Well, I added the 60 to the 2. I see, so there's a formula there. Velocity of A with respect to C is the velocity A with respect to B plus the velocity of B with respect to C. Okay, that seems to be our agreed upon formula, and everybody accepts that. But wait a minute. What if I shine a flashlight down the aisle? How fast is the wave front of the beam of light going relative to the ground? Well, 60 plus the speed of light. No, Einstein's postulate says it's got to be the speed of light relative to all observers. That's what the universal speed of light says. Ah, that's what it means. Then obviously it's incorrect. Well, Einstein wasn't stupid. He realized this objection, and he tracked it down to the formula you just told me about velocity of A with respect to C being velocity of A with respect to B plus the velocity of B with respect to C. And he said, actually, that's incorrect. There's a denominator in there which is what -- and then, fiddling with the algebra of that denominator, go back to exactly the same problem and show that actually, if you believe that formula instead, then the velocity of anything that goes at the speed of light is the same on the train as it was on the ground. Magic. But then, how could that formula that we all believe possibly be wrong? Well, Einstein realized that that means that the measuring apparatus on the train is not functioning the same as the measuring apparatus on the ground. Time and space themselves are different as measured on the train and as measured on the ground. So, what you were trying to do was add measurements based on the train's equipment to measurements based on the ground's equipment, and those pieces of equipment are just not functioning the same. It's a question of space and time. But personally, if I'm introducing special relativity to an audience like that, I have to confront the velocity addition formula, because otherwise, there's just this perfectly obvious objection to special relativity and the reader immediately bails out when they think of that. So, confront it head on, and the students actually learn something from that, I think. That is teachable. You know, I haven't used any calculus or any fancy machinery, or anything else. But I have said something that's hopefully illuminating to a non-physicist. Somebody who's not that advanced in mathematics.
David, we've worked right up to the present in the sense that we covered your recent activities right at the beginning of our talk. So, I'd like to ask for my last question, one that is both broadly retrospective and will ask you think about where things are headed in the future. So, I'll just note editorially, it's really quite touching and even beautiful how you proudly list in your publications your co-authorship with so many undergraduates. It's a unique thing. You don't see that so often. I wonder if you could talk a little bit about some of the pleasures or satisfactions in doing research with undergraduates, research that has both a pedagogical value for them, but even research where you are engaged with the physics yourself.
Well, I'll start by denying that, partially, and then I'll come back and correct it. When I first came to Reed I was skeptical about the required senior thesis for all students. You know, at Harvard, physics was the one discipline in which you were not permitted to write a senior thesis. Most places have a senior thesis as an honors experience, but not as a requirement for everybody. I took to heart the physics department at Harvard's notion that, what could an undergraduate do that would be of the slightest significance? So, when I came to Reed, I was skeptical about the required universal senior thesis program, but I was cured of that after five or six years. Now I firmly believe in it, because I can't predict which student is going to flower in this experience, and which student is going to stumble. The most pleasant experiences I've had with senior theses involve the student who is kind of mediocre in the classroom but given a project of their own to work on, suddenly discovers that they have the makings of a real scientist. I've had the opposite experience too, by the way, of students who were excellent at solving problems that were canned and very carefully formulated and based on a chapter of material that you knew exactly where to go for the source. Students who were wonderful at solving problems like that but were hopeless when given a sort of open-ended experience where they had to formulate a problem or figure out how to approach it, where the problem was not that well-defined to begin with. So, it cuts both ways. But the experiences that I've liked the most, I guess, working with students, have been similar to research in general -- discovering some kind of new thing that surprised me, or a new way of thinking about something. I don't know. Let me give you an example from fairly early at Reed. I had a student by the name of Nicholas Tuffilaro. He's now in oceanography at Oregon State, but he was very nervous about starting his senior thesis and he came to me with a project. He said that he wanted to do what he came to call a swinging Atwood's machine. You know what an Atwood's machine is. You have two masses hanging from a pulley, and if they're both the same mass, then they balance each other. But he wanted to study the case where you let one of them swing back and forth, and then by a kind of centrifugal effect, a lighter mass can balance a heavier mass, at least in the sense that on the average, they will not be going up or down. They may be moving around and bouncing up and down, but the heavier mass doesn't take off completely and just pull the other one over the top. Actually, you can get a nice dynamical balancing between a lighter mass and a heavier mass. I remember, when he told me about this, my reaction was “That's probably a nice problem, but really there's not a senior thesis there. This is too trivial. You could explain this to your grandmother.” But Nicky's reaction was, “That's great, I can explain this to my grandmother, but I think there's more to this problem.” And he persuaded me that it was okay, at least for a starting point for a thesis. This was in the early days of computation, when we had only fairly primitive computers on campus, but he was interested in computation, and this thesis turned out to be an absolutely beautiful project because he could master the problem, a very minor problem, but he became the world's authority on this trivial little problem that you could explain to your grandmother. He hit it from every possible perspective. He built the machine and tested it in a laboratory. He analyzed it theoretically, which is more complicated than it sounds, and he studied it computationally, discovering that there were periodic solutions, and there were also chaotic solutions. This was when chaos was just coming in as a subject of study. And Nicky's thesis was actually one of the first detailed studies of a chaotic system. This, he wrote up as a thesis. It was one of the most exciting theses that I've had. It established his career. He went on to graduate school and wrote a bunch of papers on more and more sophisticated treatments of the same problem. But even for his thesis, he had studied complicated structures that we get, like heart shapes where one of the swinging mass executes a heart shaped motion, meanwhile being balanced by this heavier mass on the other end. It was a trivial system in the sense that anybody can understand what it is, but the motions that it produces are fantastically complicated and incredibly elegant, and a certain amount can be done theoretically on it, and a whole lot computationally. Nowadays, it's a more or less trivial computational problem that you can do on a laptop. But at the time, it was much more difficult. How did I get off on that? You asked about theses projects --
The pedagogical and scientific pleasures of just working with undergraduate students.
Yes, well, there was one where the student taught me that there's a whole lot of physics in this otherwise very mundane problem. Here's another one. Tyler Abbott did a thesis entitled Acceleration Without Radiation. As you probably know, an accelerating charged particle radiates, gives off electromagnetic radiation. But that's for a single particle. If it's accelerating, it radiates. You can have composite structures such as, for instance, we were talking about before, where the charge is uniformly distributed over a spherical shell. You could have this spherical shell breathe in and out. Every particle on it is accelerating in and out. And yet, the structure as a whole does not radiate. There's no radiation from a breathing spherical shell. In fact, the electromagnetic fields exterior to the shell are identical to what they would be if it were all concentrated at the center. Not true for points inside, but fields outside are simply the fields of a point charge at the center. So, a composite structure, all parts of it are radiating, and yet, the object as a whole does not give off any radiation. How can that possibly be? Well, in a certain sense, it's total perfect destructive interference in all directions. You can think of the object as a whole conglomeration of point charges, all of them radiating, but what is the net radiation? It's the electromagnetic fields out at large distances from the object. Those electric field are actually canceling each other by destructive interference, so there's no net radiation, even though each piece is, in a certain sense, radiating individually. Well, this tells you a whole lot about the nature of radiation that you maybe didn't anticipate. So, Tyler's thesis was on the general subject of accelerating objects, necessarily composite objects, that don't radiate. And we found, actually, there are a large collection of these systems, sometimes very surprising, that don't radiate even though every part of it is radiating. So, his thesis was Acceleration Without Radiation, and I learned an incredible amount from working on that thesis with Tyler. To this day, I think I understand radiation better than most people who studied the subject only casually do, and it all derives from that experience.
I can't think of a more fulsome corrective to your own undergraduate experience back at Harvard.
David, this has been a great pleasure spending this time with you. I'm so glad we were able to do this, and I want to express my appreciation. So, thank you so much.
Oh, well, you're very welcome.