Today a symposium is being held in Aspen to celebrate the twentieth anniversary of the “First Superstring Revolution”. The canonical story of this “Revolution” is that twenty years ago this month, on a dark and stormy night at a workshop in Aspen, Michael Green and John Schwarz completed a calculation showing that gauge anomalies canceled in a specific superstring theory, thus changing physics forever. The more complete story of what happened at that time goes more or less as follows:

By 1984 Witten had been taking some interest in superstring theory for a while, giving a talk on the subject in April 1983 at a conference on Grand Unified Theories, but not publishing anything about it himself. In 1983 at the Shelter Island conference he had shown that the popular unification idea of the time, using supergravity on higher-dimensional spaces and the Kaluza-Klein mechanism, could not give the kind of asymmetry between left and right handed particles that occurs in the standard model (this has had a revival in M-theory, which these days invokes singular compactification spaces to get around Witten’s no-go theorem). The failure of supergravity ideas had gotten him interested in superstring theory, but he was concerned about the issue of gauge and gravitational anomalies in the theory, anomalies that he worried would render the theory inconsistent. In his 1983 paper about gravitational anomalies with Luis Alvarez-Gaume, they noted at the end that these anomalies canceled in the supergravity theory in ten dimensions that is the low energy limit of the type II superstring. This theory didn’t allow for low-energy gauge theories so wasn’t useful for unification. Witten suspected that the type I superstring (which could be used for unification) would have insurmountable problems with anomalies, but the Green-Schwarz calculation showed that these anomalies could be canceled for a specific choice of gauge group.

Evidently Green and Schwarz talked to others about their new result at the 1984 Aspen workshop, but I would suspect that no one was very impressed (if anyone who was there knows differerently, I’d be interested to hear about it), since superstring theory was generally considered pretty much a far-out, highly unlikely idea. Green and Schwarz were well aware that their only real hope for getting attention was to get Witten interested, so on September 10th they sent him a copy of their paper via Fed Ex (this was before e-mail) at the same time they sent it off to Physics Letters B. Witten immediately went to work full time on superstring theory, with his first paper on the subject arriving at Physics Letters B on September 28th. I think this is really the point at which one should date the First Superstring Revolution.

Witten was at the height of his influence, and the news that he was now working on superstring theory spread very quickly through the particle theory community. I had just finished my graduate work at Princeton and was starting a post-doc at the Institute for Theoretical Physics at Stony Brook when I heard the news. Over the next six months to a year I remember hearing from a couple colleagues who had gone down to Princeton to talk about their work with Witten, only to hear from him that, while what they were doing was all well and good, the future was in superstring theory, so they should drop what they were doing and start working on that.

My own attitude was that it didn’t look like a very promising idea. It was a complicated theory and didn’t really explain anything at all about the standard model. I figured that there would be a lot of smart people working on it for a while and within a year or two either they would get somewhere with the idea and it would be clear I had been wrong, or they wouldn’t, and everyone would lose interest. Neither I nor anyone else could conceivably have guessed that 20 years later superstring theory would still not explain anything about the standard model, but would completely dominate particle theory.

One reason for this is the string theory hype machine continues in high gear. The University of Chicago has issued a press release telling us that “growing numbers of physicists see superstring theory as their best chance” to formulate a theory of everything. Jeff Harvey is quoted as saying that “It’s an intellectual enterprise that’s extremely exciting and vigorous and full of ideas”, which is very different than what I hear string theorists telling me in private.

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JC,

I think that you’ve grasped my essential point. This is not to say that there should be

nobookwork, it is just that the majority of the marks should be for the problem, which it should not be possible to answer unless one has actuallyunderstoodthe material. Call them silly if you like, but the examples you give are exactly the kind of thing I had in mind.Chris,

If you were the professor making up some of these particle theory or gravity exam papers for the tripos III, what sort of trick problems would you put on it that would require some ingenuity and/or lateral thinking (which are not of the “$500 parrot” or “regurgitation” variety)?

If I didn’t know any better, the only “trick” questions I can think of offhand would be mostly hypothetical “what if” types of problems. Perhaps silly ones like:

– “Imagine if the gluon is not a gauge field in qcd, but is really a scalar field with an SU(2) symmetry in the scalar fields. (a) Write down a possible renormalizable “scalar qcd” Lagrangian and the Feynman rules from it. (b) Calculate various tree level quark-antiquark scattering amplitudes. etc … etc …”

– “Imagine if parity is really conserved in the weak interactions. (a) How would this change the V-A interaction picture? etc … etc …”

– “Imagine if in the Standard Model, the up, down, strange & charm quarks all had the same identical non-zero mass, while the top & bottom quarks have the same identical mass but heavier than the masses of all the other quarks. (a) Are there any new symmetries, which are not present in the regular Standard Model? (b) Write down the tree level electron + positron –> quark + anti-quark scattering amplitude. (Electron mass can be taken as “small” relative to quark masses). etc … etc …”

– “Imagine if QCD had a gauge group of SU(7) and 23 vertical particle families, instead of the normal QCD SU(3) gauge group and 3 generations of vertical particle familes in the Standard Model. (a) Write down the Feynman rules. (b) What is the new beta function, and how does it compare to the normal QCD Standard Model case? etc … etc …”

– “Imagine if the electroweak gauge group is really U(1)xSU(3) instead of U(1)xSU(2). (a) Is there a Higgs breaking pattern which produces a massless photon? (b) If there is a massless photon in part a, what are the other gauge bosons? If there is no massless photon, what are the gauge bosons anyways after Higgs breaking? etc … etc …”

I just made these up out of thin air. Not really all that brilliant or even that insightful, when all I did was just do things like change the group structure and/or properties of various particles.

Anybody else have a better criteria for particle physics and/or gravity problems which require some ingenuity and/or lateral thinking, besides just copying problems out of some old long forgotten research papers from many years ago?

Recent princeton math quals are here: http://www.math.princeton.edu/graduate/generals/

A click on a name gives a summary of that session. Some are quite fun to read actually: “Can you give a heuristic proof of Fermat’s Last Theorem? — this last one was asked by Aizenman, the physicist!! Wiles and Faltings seemed only slightly amused.” ðŸ˜‰

Reading the begining of David Nadler’s one, it looks like the level did go down a bit as compared to some decades ago…

Harvard is here: http://www.math.harvard.edu/graduate/quals/

I couldn’t find the physics ones.

Hello JC,

If you do mathematics research (including mathematical branches of theoretical physics) at Cambridge then getting a “distinction” in their part 3 exam is more or less a requirement. In my year there were about 56 of us taking part 3 with “applied” options and about the same number taking the “pure” options. Of the “applied” group, about 13 got distinctions, although not all of them stayed to do PhDs in Cambridge. The more informal structure you discuss with assignments, etc. was not possible because of the competition involved. Having said that, a small part of the course was an “essay” (mine was on SU(5)), but most of the marks were based on 15 hours in the exam room. Outside of Cambridge, part 3 is largely ignored. The first year of a graduate course achieves the same purpose elsewhere and arguably more efficiently as without the need to photographically memorise lecture notes one can concentrate on understanding rather than rote learning. I remember being at interview at Sussex University and Tony Leggett telling me that Cambridge expected the rest of the nation to await the results of the part 3 exams before awarding research places, but their time scales were such that they were unable and unwilling to do this.

One advantage of a parrot test is that it is easier for the examiners. If you pose a question that can only be correctly answered if the student has understood the material, as opposed to having just memorised his/her lecture notes, then fifty students will give fifty widely different answers and a lot of time will be spent by the examiner chasing blind alleys in the responses, just to make sure that they

really wereblind alleys.The other problem is that the more advanced the course, the smaller the gap between examiner and student, and therefore the smaller the right of the examiner to judge.

Cambridge is cynical about this: the message is just this – doing well in our memory test is a necessary hurdle and if you don’t like it, then just go elsewhere.

BTW: I am not sure I agree with the point about there being a limited number of bite-size questions one can ask in a graduate exam. It may just be that more ingenuity/lateral thinking is required.

Peter,

How recent and widespread has it been for math departments to move away from the comprehensive/preliminary exams tradition, to just students passing a certain number of courses? Are there any particular strong reasons for this change?

Over the years, I remember overhearing several older physics professors talking about how even the Princeton and Harvard comprehensive/preliminary exams for PhD students, have been getting “watered down” and “easier” or “less demanding” over the years. Has this sort of thing been happening too over the years in math PhD programs?

I remember several professors I knew who did their math PhDs at Harvard in the 60’s and early 70’s. They all mentioned that the math comprehensive/preliminary exams at the time were really demanding and “killer”. (Whether they were exaggerating things deliberately, I don’t know). They said that it was common for many students to quit grad school by the time they completely passed all of their exams, largely due to reasons like burnout and/or a subsequent loss of interest in math grad school. They thought that it was the math department’s way of weeding out as many students as soon as possible, and that the folks who didn’t flunk out or quit were the “cream of the crop”.

Chris,

Was there any purpose and/or advantage in doing the tripos III exams? Did the doctorate program at Cambridge or other British universities require it as a prerequisite? Was there a thesis and defense required for the tripos III?

On the surface, for stuff like quantum field theory, particle theory, general relativity, etc … it seems like it would be more practical if the course material was done as assignments and perhaps a final take-home exam and/or an oral exam. Except for the more “trivial” quantum field theory and particle theory problems, there doesn’t seem to be many “insightful” problems that are doable in a timed 3 or 4 hour examination setting (ie. problems that are more insightful than the “regurgitation” or “$500 parrot” variety).

I remember in one graduate course I took which covered things like scattering theory, second quantization of the Maxwell field, Dirac equation, etc … (the sort of stuff covered in Sakurai’s “advanced quantum mechanics” book), we were given a take-home exam which had one really long nasty calculation to do. It turned out it took most of us around 40-50 pages to do this calculation from start to finish, for which we were given a week to finish it. The professor didn’t think a timed 3 or 4 hour exam format was practical for this particular course. All other courses I took afterwards like quantum field theory, particle theory, supersymmetry, Lie group theory, etc … were mostly just assignments and sometimes an oral exam or presentation. In fact many of the course assignments were just “optional” and the professor frequently didn’t even care whether anybody handed them in or even did any of them. A few courses didn’t even have any assignments or exams. At that level the professors just assumed the students had enough self-motivation to figure things out on their own, and didn’t feel that it was worth their time to make up assignments for the students.

Part 3 was the closest to an “arts” exam in a science subject that I have ever experienced.

I.e. mostly short questions, which required long answers which were entirely bookwork.

E.g. Q. 2 of “Advanced Quantum Field Theory”, 1981

“Explain how the Higgs mechanism works in the Salam-Weinberg model, including a brief discussion of the physical motivation for the structure of the symmetry in the model.”

You can give a “perfect” answer to this just by memorising your lecture notes, and that is what I think they wanted you to do. A $500 parrot (see below) would be able to do this.

I chose to actually digest the information and produce an answer which may or may not have corresponded to my lecture notes. Maybe that is why I did not do especially well.

I came across Cambridge’s web site that has old copies of the mathematics tripos III exams.

http://www.maths.cam.ac.uk/ppa/PartIIIyy.html

http://www.maths.cam.ac.uk/ppa/

The quantum field theory and particle physics exam papers look like they’re just generic problems almost straight out of field theory books like Peskin & Schroeder or Ryder, and particle physics books like Griffiths or Halzen & Martin. The general relativity and comology exams look like they’re just generic problems out of various books like Weinberg, Wald, etc … and other GR and cosmology textbooks.

To top it off, there’s even exam papers for supersymmetry and string theory! It looks like they aren’t much more than the sort of problems and calculations straight out of the Polchinski and Wess & Bagger textbooks.

Though if I was writing any of these relativity and/or particle theory related tripos III exams today, I think it would be a matter of me being able to write out the solutions as fast as I can in 3 or 4 hours. Whether or not I (or anybody else) actually learned anything, is another question.

I’ve always noticed over the years that folks doing very well on physics and/or math exams, has very little correlation to their understading of the subject in general. I knew one guy that did very well in all his undergrad and masters level math and physics courses, but it turned out he was good at memorizing many solutions and guessing at answers, but not really understanding what he was doing. When he started doing research, he literally slammed into a wall and didn’t know what to do, like a “deer in the headlights”. He ended up dropping out of grad school without even starting on any research projects.

I don’t know much about what is going on in physics departments these days, but the math department here has moved somewhat away from this kind of system towards one where the students just have a pass a certain number of grad courses.

When you look at exams of this kind, you realize that most physics problems are either basically trivial and can be solved in a couple lines, or quite difficult and would require several days of work to solve correctly. There’s only a limited number of non-trivial problems that can be solved in a half-hour or so, these end up being used over and over again, often creatively dressed up to look different.

Peter,

Sounds like the same sort of comprehensive exams I remember having to write in graduate school.

Years later I came across several books that were a compilation of problems from exams of this sort: one from was University of Chicago, another was from Princeton, and two additional books looked like they were from Stony Brook. There was a further series of books that looked like they were compiled in China, from many graduate level comprehensive/preliminary exams from many American physics PhD programs.

Over the years I saw many other physics comprehensive/preliminary exams of this sort from many other universities. It seems like many of these exams (even recent ones from Princeton), were recycling many of these problems every 15-20 years. Not too many really “original” looking problems that stood out over the years.

I always wondered what the origins of these sorts of exams are, and whether they are still just a “custom” that is done to this very day. Several physics PhD programs don’t even have these exams anymore! Only other reason I can think of for them still being done today, is as an easy way of weeding out the weaker and/or lazy students.

I wonder if these sorts of exams are also commonly done in physics graduate programs overseas, say in Britain, Japan, and continental europe. One case I can think offhand would be the notorious series of Landau exams which Laudau used as a prerequisite for entry into his research group. Another set of exams that looked similar on the surface to the american preliminary/comprehensive exams, would perhaps be the “tripos” series of exams at Cambridge. Anybody know more about these Cambridge “tripos” exams, and how they compare to the comprehensive/preliminary exams done in American universities?

Actually a book has been published containing many of the problems from these exams, on Amazon you can even see the table of contents. It is called “Princeton Problems in Physics”

From what I remember, the topics covered on the prelims were mechanics, EM, quantum mechanics and stat. mech., at the level of a standard first year graduate course. The generals covered solid-state physics, special and general relativity, nuclear physics, particle physics and atomic physics. No QFT. These were exams everyone had to take, both experimentalists and theorists, so they weren’t heavily theoretical.

Peter,

What exactly was covered in those preliminary and general exams that physics grad student had to pass in their first and second years at Princeton? Would it be stuff at the level (or slightly higher) of Jackson (E&M), Goldstein (classical mechanics), Merzbacher and/or Sakurai (quantum mechanics), etc …? Was anything like quantum field theory covered (ie. at the level of Peskin & Schroeder, Ramond, and/or Weinberg’s books)?

I don’t know how much physics Witten took as an undergrad at Brandeis, but he majored in history and minored in linguistics. His father, Louis Witten is also a physicist, does general relativity, so he probably learned some physics early on. After Brandeis he seems to have spent a little time as a grad student in economics at Wisconsin, and worked on McGovern’s 1972 presidential campaign. He enrolled at Princeton in the applied math program, which allows you to work in many different departments, then ended up shifting over to physics.

Princeton has a very serious set of preliminary and general exams that grad students have to pass in their first and second year. I certainly learned a lot of physics studying to pass those exams, and I’ll bet Witten did too.

Up until the whole string theory thing, it’s really clear why Witten was so respected. His papers are marvels of clarity compared to most people’s, and many of them contain remarkable insights into the still mysterious problems of how to understand QFT non-perturbatively. There’s no mystery at all about why many physicists and mathematicians think so highly of him, his intellectual accomplishments are just huge, even if they are not to everyone’s taste. His impact on mathematics has also been huge, he richly deserves the Fields medal he got.

One sad thing about the dominance of string theory is that it has so overshadowed his best work. Within string theory he has done quite a lot, but you could argue that others have done more important work there than him (Green, Schwarz, Polchinski, Maldacena).

A typical reaction to my research work between 1984 and 1987 was the following: “You are wanting to abandon a theory that has been verified to eleven places of decimals. The burden of proof is therefore on you. You must at least deliver results to the same degree of precision before you can expect anyone to sponsor you.”

Whether the anomalous magnetic moment, etc. can be calculated to the required accuracy in my approach is still an open question. No-one has been working on it. On the other hand the approach works in obtaining basic scattering amplitudes and is content to reside in 3+1 dimensions.

In regard to Superstrings, there is

certainlyno guarantee that the standard model or even, it seems, general relativity will be reproduced (despite the fact that producing a quantum theory of gravity was part of the original motivation), and yet it seems to get pretty much all the sponsorship.I call this inconsistent, and I call it stupid.

I was a bit more pig-headed than average, but I wonder how many other young people (as I was then, anyway) have had good ideas quoshed because Ed Witten or whoever else who happened to decide the direction of research did not think it was cool.

Chris,

Seems a lot of the sociology behind physics research is along the lines of “monkey see, monkey do” or a “pied piper” luring away kids. Arguably one can see that in many other activities in the world, as in the “copycat” syndrome when something very popular and/or profitable comes up.

At times I wonder how much of the string and particle community is exactly that of “monkey see Witten’s work, monkey tries to do Witten’s work”.

The Ed Witten phenomenon reminds me of a joke:

A man goes into a pet shop to buy a parrot.

“How much is that one?” he asks.

“Five hundred dollars,” says the sales assistant.

“

Five hundred dollars!?for aparrot?”“Ah yes, but she can touch type, and take dictation.”

“And what about this one?”

“Seven hundred dollars.”

“

Seven hundred?That’s ridiculous!”“I know that sounds a lot, but this parrot is fluent in three languages and knows how use Word and Excel.”

“And this one?”

“A thousand dollars.”

“A

thousand. What does he do, then? Write operas?”“Actually we don’t know what he does. But the other two call him ‘Sir’.”

When I was a graduate student (1980-1984) it was no exaggeration to say that Ed Witten was the single most influential mathematical physicist. Although I am not sufficiently

au faitwith his work to say whether this was justified, I would venture the observation that the emphasis was, and remainsmathematical, i.e. pretty mathematical constructs appeared to excite him more than having the theories make contact with reality. It was the – in my view – excessively theoretical nature of his work that put me off joining the bandwagon.Peter,

I remember hearing stories about Witten majoring in something like history or political science when he was an undergrad. Did he take any physics courses at the time? If not, was he literally a “self taught” guy who taught himself everything he needed to know about undergraduate and graduate level physics, by cranking out zillions of problems and reading some papers on his own?

Witten was very clearly the leading figure in particle theory before string theory, during the period 1980-84. It’s because of this that the string theory idea took off so fast. By 1984 everybody was looking very carefully at anything Witten was doing and often immediately going to work on it themselves. It’s very hard to over-estimate his influence at that time.

He got his Ph.D. in 1976, and very much impressed the faculty when he was a student. I first met him

when he was a post-doc at Harvard in 1978, and was just starting to make his reputation. By 1980 he was already a young star and Princeton offered him a tenured professorship even though he was only a post-doc.

Peter,

How popular was Witten in the particle theory community before string theory got popular? I knew someone who knew Witten personally in the 1970’s before he was a superstar. In those days he thought Witten was definitely above average, but he didn’t think was a superstar or Einstein-like genius at the time. If nothing else, he thought that Witten could have at least gotten an assistant professor job at a place like Princeton or Harvard in those days.