Sadly, I’m not here to announce that applications are now being accepted for students who would like to participate in this year’s Undergraduate Theory Institute. That’s because there is no such thing as the Undergraduate Theory Institute, at least as far as I know. (Google doesn’t know of one either.) But I think it would be a great idea — maybe if I post it here on the blog someone will start it.
It’s increasingly common for physics students to particpate in some kind of research during their undergraduate years. The NSF has a very successful Research Experience for Undergraduates program, for example, that funds students to do summer research, typically at an institution other than their own. Getting involved in research as early as possible is a great idea for students, for a number of reasons. Most importantly, the flavor of doing real research, where the answers aren’t in the back of the book, is utterly different from almost any classroom experience or even self-study, where you are trying to learn material that someone else has already mastered. The move from following a course of study to striking out into the unknown is one of the hardest transitions to make during graduate school, and getting a head start is an enormous help. On a more prosaic level, it’s useful to work closely with an advisor who can end up writing letters of recommendation. And let’s not forget that it can be a lot of fun!
Unfortunately, the prospects are very different for students who want to do theory vs. experiment. It’s often true that, on an experimental project, a student with just a hand on the basics of introductory physics can come in and learn something about the particular experiment being undertaken, and after a brief learning period can soon be contributing seriously to the work. On the theoretical side, the learning curve is much less steep, and a lot more background knowledge is required before a student can do something interesting. In my field, until you’ve at least taken courses in quantum field theory and general relativity, it’s hard to do original work.
Nevertheless, like many other theoretical physicists, I get a lot of requests from undergrads who would like to do research. I very much enjoy doing research and having students, but to be honest it’s often very difficult to find things for them to do, since the background just isn’t there. I’ve done it, quite a few times — I’ve supervised four Bachelor’s theses, and three summer research students. Sometimes everything falls into place, and it ends up with an interesting publishable paper. More often it’s an excuse to let the students learn a bit GR or QFT, and maybe get started on the very basics of a problem, before they grow up and graduate.
There’s a perfectly good response to this situation, which is: even if you eventually want to become a theorist, it’s a great idea to do experimental research as an undergrad. Maybe you won’t be immersed in the kind of work you ultimately want to pursue, but (1) understanding something about how experiments work is an unambiguously good thing, and (2) the important lesson is not in the details of the particular field, but in what it’s like to do research, which is almost independent of the type of research you’re doing. That’s what I did, when at Villanova I did work on photometry of eclipsing variable stars; I got a nice paper out of that. (And my favorite star, Epsilon Aurigae, will be going into eclipse again in another couple of years, at which point I expect our model to be spectacularly confirmed, and fame and fortune to follow.)
And I tell this to people all the time, but still the students want to do theory! Impatient little buggers. But I can hardly blame them — we lure them into the field with elaborate tales of black holes and supersymmetry and dark energy, and it only eventually becomes clear that they won’t really learn about that stuff until they’re well into grad school, if then.
So I had the idea for an undergraduate theory institute. The amount of theoretical background you need to do useful work is quite substantial, much larger than one could squeeze into one summer, it’s true. On the other hand, six weeks of fairly intensive study between the junior and senior year could serve to introduce enthusiastic students to many of the basic ideas they will eventually be encountering as theorists. If nothing else, they could become familiar with a bunch of buzzwords they’ll be hearing for years. That sounds superficial, but could potentially be of great use — it means that they can immediately start going to seminars and chatting with professors when they get to grad school, and have a much better grasp on the kinds of ideas that are being thrown around.
So, a six-week summer course for undergrads. Much self-study, but regular lectures by faculty and perhaps postdocs. A couple of seminars on sexy stuff of current research interest, as a reward, but mostly focusing on the basic tools of theoretical research in field theory and gravitation. (Since that what I know about — other specialties are welcome to chime in!) Here’s what I imagine the syllabus to basically be like:
- Special relativity, index notation, vectors, tensors.
- Lagrangian and Hamiltonian mechanics.
- Classical scalar field theory.
- Gauge theories and electromagnetism.
- Basics of Lie groups, SU(n).
- Non-abelian symmetries.
- Spontaneous symmetry breakdown, the Higgs mechanism.
- Topological defects.
- Spacetime curvature and Einstein’s equation.
- Schwarzschild and Robertson-Walker spacetimes.
- Basics of field quantization and Feynman diagrams.
Something like that, anyway. It seems like a tremendous amount to cover, but it would all be fairly brisk, and there are benefits to be gained by seeing it all at once in the same place, surrounded by a group of other bright students studying the same material. Wouldn’t you have loved to have such an introduction as an undergrad? If we put together some nice lecture notes, I’m sure it wouldn’t be too hard to get them published as a cheap reference book.
All I need now is a substantial (and reliable) source of funding, someone to write the lectures and deliver them, a host institution, and an organizational wizard to take care of logistics. I will look over the whole operation as a benevolent, if somewhat disconnected, father figure, whose main role will be to shoot the breeze with the students at the late-night coffee and whisky hours. Any takers?
One shouldn’t neglect the “easy” research road for undergrad theorists: computational projects. It’s a lot easier to solve many equations numerically on a computer than it is to derive nice analytical solutions on paper. I’ve seen undergraduate research students doing useful work using condensed matter Monte Carlo and molecular dynamics simulations, gravitational wave signal detection routines, and in your own field, mucking around with CMBfast code. Giving the ever-increasing prevalence of numerics in physics, this isn’t even something that is relegated to students and other peons — it’s the bread and butter of many theorists’ day jobs.
Of course, the advanced theory and mathematics is necessary to fully understand what’s going on, but that’s true for experimentalists as well. Not having it, though, doesn’t have to be an obstacle to budding theorists any more than it is to their experimentalist counterparts. Running, tinkering with, and analyzing the output of existing computer codes is probably nowadays the theoretical equivalent to soldering and gluing in a lab.
P.S. I presume you meant to say that the theoretical learning curve is much more steep, not much less steep.
I’d be happy to do at least a few lectures! But it sounds like a bit much; a few years ago I was the TA/grader for an undergraduate cosmology course which covered maybe three or four at most of the topics you listed, spread out over a quarter (10 weeks)… and it seemed like some students were barely keeping up.
1. Thanks to string theory, it is no longer true that a student has to know QFT and GR to do original research. All they need to know is a little algebraic geometry.
2. The traditional way for students to get involved with theoretical research is through computer programming.
Therefore, the solution is to give your undergrads a computer and set them loose to explore the landscape. Within months they will have accomplished some Stanford quality theoretical research.
Oh man! I would’ve loved to have something like that as an undergrad.
It may also be a good idea to make it a two-summer program. Spend one summer preparing the students and have them come back to try to do some real work.
As a student, I think I agree with BG in that the first summer might be a bit too intensive. Perhaps it could work out to attempt less topics and have the student learn some of them in the year in between the two summers. Of course, this may involve a bit more commitment on the part of the advisor.
Dream-land sounds like a good place to start looking for the realization of this dreamy idea.
Isn’t the scope you outlined nothing more than all the material mandatorily covered in graduate school? And how many years of actual studying and experimenting with the concepts does it actually take an average physics graduate student to grasp them? And how many years of post-graduate work does it take to become actually comfortable and confident, if at all? Too ambitious and too overwhelming.
Having been one of the statistics you mentioned, I would go ahead and defend the excuse for learning some GR and/or QFT one on one with an advisor outside of the usual course-work setting. Putting it lightly, it’s just more fun. No deadlines to meet being one of the reasons. Having all the time in the world to derive and re-derive what not until you finally scope the result to make some sense. And head-on start at learning it in the class-room later. Because the truth is that no genius out there, understood Feynman’s diagrams, or the significance of the metric from the first attempt. It took many classes, many problems, many questions, and many discussions. True, surrounded by bright kids is an adventage in the process of understanding(as is in the process of mis-understanding)(in fact, all I learned I sponged off from my peers and one-on-one advisors; classes were over-rated).
Just for completeness. I spent one summer on an experimental project which was utterly boring, and only taught me the discipline to write proper C code. Then I spent two glorious summers enjoying GR, QFT, rollerblading and softball.
Further, writing a paper on what has been learned, no matter how insignificant, and delivering a brief speech, is a good excercise no matter what the future direction is. (Understandably, I didn’t share this view back in the day, clearly express in endlessed complaints). In a class-room setting, this can be achieved, but not nearly as successfully.
Little steps each day will take you to greater understanding, than one giant leap at one time. What is the rush! Relax and enjoy the ride, and maybe it will be a long one.
Even when I wish I knew everything, I sit back, and relax in my sea of ignorance, enjoying the process of learning. There is no learning destination. Maybe at death. But that is too grim.
Cheers and Happy New Year.
For the coffee and whiskey? Yes.
Now I’m confused about “learning curve.” What is it supposed to be a plot of? Wouldn’t it take longer to climb a shallow curve than a steep one?
Anyway — I think people would be surprised at how much could be covered in six weeks over the summer. Much more than in a one-semester course, for the simple reason that you can be remarkably superficial! If I’m teaching a GR course, I want to derive the expressions for the Riemann tensor and connection coefficients, prove that they behave properly under coordinate transformations, etc. Here, they’d just get the formulas and move on to calculating. I covered all of GR in a few hours at the SLAC Summer Institute a while back, starting in the morning and finished in time for lunch.
Also, I’m assuming that the students come in with some prior exposure to Lagrangians and special relativity (not to mention quantum mechanics and E&M), so those are really just touch-up reviews.
As an undergrad I worked in experiment, and I would really strongly encourage anyone interested in doing theory to do so. Plenty of theorists, even those doing relatively phenomenological things, seem to have a very skewed notion of what experimentalists do and what a given experiment is or is not capable of.
Also, from what I’ve seen, undergrads who are capable of doing theory research will be taking graduate courses anyway, at least if they’re attending schools with decent graduate programs. I know plenty of people who took QFT as undergraduates. I really think one of the best things schools can do for theory-minded undergrads is to make it easier for them to do things like this. I had no problem skipping some prerequisites, but I did have my coursework slowed down by well-meaning advice and official guidelines. Also, in my senior year I was told by the undergraduate program chair that I had failed to complete the official course requirements because I had taken graduate courses in place of some of the expected undergraduate courses. I was told that they would allow me to do this, so long as I didn’t tell any other students that they could “get away with” this! It was all rather odd.
You know, I never really thought about it, but I think you’re right on the whole learning curve thing. It really ought to be a shallow learning curve after all, even though no one uses it that way. (They probably imagine it takes a long time to climb a steep hill, so a learning curve that takes a long time to climb must be steep.)
As for your course suggestion, I would have loved to have had such a summer course. I agree that you can get up to speed on learning subjects at a “calculation” level much faster than at a “grad course” level. I’m still not sure whether it would be enough to get an undergrad up to speed on doing theory research. Even grad students take a while before they start becoming useful in a lot of theory areas. A six-week concentration on just a few of those topics would probably be sufficient to jump-start a project focused on those topics, though. But perhaps I am being overly pessimistic since I have never participated in a summer school boot camp myself.
A steep learning curve is one where it is difficult to make much forward progress until one has mastered something difficult. A shallow learning curve has many easily digested concepts that slowly build up. One feels that one is making progress. A steep learning curve has some very challenging concepts at the beginning and one does feel like one is making progress until challenging concepts are mastered. Theoretical physics is the paradigm of a steep learning curve.
It looks like David Griffiths’ “Introduction to Elementary Particles” textbook covers half of the topics in that list, in a relatively painless manner for undergrads.
I can’t think of any particular books and/or papers which cover the remaining topics in a relatively painless manner. Maybe Ryder and/or Zee’s books on quantum field theory could cover basic field quantization and perturbation theory in a “cartoon-like” manner? Offhand I can’t think of any really elementary presentations of general relativity, that would be relatively painless or “cartoonish”.
Sean,
I know I am no expert yet, but if something were to come of this I would help write/give lectures in the future. I love doing that, I do it for the theory group here at BYU. I hosted a semester long weekly seminar on Nakahara’s book at BYU and lectured about a lot of advanced things. I love doing this kind of stuff.
I would personally finance going to such an institute in the future to lecture. Of course, it may be a couple years before I can convince the appropriate people to trust me. But they will eventually, so I will pledge my help in advance.
Again, just want to pledge my support if anything comes of this.
I always interpreted the “learning curve” as a plot of difficulty vs. time (or “knowledge”, or some proxy for it). So a field with a steep learning curve is one that gets difficult very quickly, whereas a shallow learning curve means one can learn quite a lot before encountering too much difficulty.
Anyway, I guess the aim of the summer course is to give undergrads some tools so they can get started? How much theory work requires only a superficial understanding? I once developed an intense one-week introduction to cosmology for gifted high school students, and I found that often I would -try- to give some “superficial” understanding to get them started calculating, but I kept realizing they were missing some key detail and repeatedly had to back up and fill in a lot of background. I realized that many things in cosmology weren’t so “superficial” to begin with.
It still might work, but you’d need someone far more brilliant than me to develop the curriculum 🙂
The problem I see with a theory summer school is that it isn’t research: it’s completely a “classroom experience”. The students will spend their most productive undergrad summer (from the perspective of grad school apps) taking a class. While this will serve future theorists well and give them a jump-start into grad research, I don’t think this was the aim of the proposal. It won’t give them the understanding of what a research physicist does day-to-day, which is really the point of undergrad research, more than learning physics (not to denigrate learning physics or anything, this is also said in the original post). Moreover, if good work can be done with only a “calculating level” of the material, then I’d think that ancillary skills like programming would figure heavily into what the student would need for that particular project, and research experience is what really gives students these ancillary skills. My experience is that you need one of two things to do, say, HE theory as a beginning student: QFT or FORTRAN, and QFT at the calculating level won’t eliminate the need for FORTRAN.
Also, six weeks really leaves only 4 or 5 weeks remaining in the summer, too little time to return to your institution to work with an advisor there.
I did experimental work as an undergrad, hated it, and now I’m a theory grad and like it much more. But since experiment is the norm in physics, I can’t say I regret trying it. At the very least I’m not in the shoes of one fellow grad who asked “What’s that thing on your desk?” to an experimentalist. (“It’s a soldering iron.” “So what’s the coil thing it sits in?” “It’s so the hot tip won’t burn anything.”)
I did a project in Quantum Computers, all you need is LinAlg and QM and you’re ready to go.
I think it’s in the topics, really…. probably experimental research groups will have better theoretical topics to pursue as well.
Or interdisciplinary. Statistical physics models for evolution was another (non research) project I had.
Sean,
Wouldn’t a summer school of this sort be more appropriate between sophomore and junior year, or for that matter, freshman and sophomore year? Or maybe even for really highly motivated high school kids?
When I was first in college, I tried to study basic quantum mechanics on my own and managed to get as far as doing time dependent perturbation theory calculations and some basic quantum field theory (ie. tree level Feynman diagram calculations). Though at the time, I don’t think I really understood it completely. If there was such a summer school of this sort in those days, I probably would have applied.
As an undergrad who is currently doing a senior thesis in theory, this topic is of direct relevance to me. Although it would be great if undergraduates could be exposed to such exciting topics as those mentioned, I’m not sure if it would help the aspiring theorist too much. I was able to undertake a thesis with a much less extensive background than would be acquired in such a program: I had taken Sean’s undergrad GR class, knew the basics of QFT, and that’s about it (although my mathematics background is probably quite a bit more extensive than the average physics undergrad). I found that once you convince the professor that you’re serious about working on a problem and understand the basics, you can pretty much pick up what you need as you go along. I feel I’ve learned more over the past four months than I have in any class.
In short, I just wanted to point out that doing theoretical work as an undergraduate is not as far-fetched as most people say it is. I think it takes a basic knowledge in a few subjects and an intense desire to learn as much as you can on your own. A summer program would probably help, but I don’t think it would be too valuable.
In the UK we have two kinds of undergraduate physics degrees, the bachelors (BSc) and the MPhys. The M stands for (where have we heard that before?) ‘Masters’ but this is not actually a masters degree but an extended undergrad degree. Anyway… it includes – at least the way we cover it at my university (Surrey) – a full research year. This our students spend at an international research facility in the Europe of North America such as at Yale, Berkeley, Florida State, MSU etc. This they do during a calender year in between the Autumn and Spring semesters of their final year, so they have pretty much covered a lot of the basics (qm, special rel, electromag, condensed matter). Sometimes the students choose a theory research project and we try to place them accordingly. For instance I fixed up a student work in the theory group at TRIUMF Lab in Vancouver on modelling nuclear reactions in astrophysics. All good stuff and our students really get a lot out of their year. they often get their names on papers including PRLs and get to present their work at international conferences. They come back for their final semester very keen to sign up for PhD having had a decent taste of life as a grad student at the cutting edge.
As an undergrad who has two years left and will be taking graduate classes next fall, I have to say that I would apply if this was available. I’m currently working through Gravitation, and I think that the goal wouldn’t necessarily need to be cover all of a subject, or even all of the derivations. If your applying to the program, I would think one could probably pick up a book and understand most of it (not necessarily easily). There are definitely subjects that are non-intuitive where a good lecture would have saved significant hassle (forms, for example) and enable someone to pick up the rest on their own much easier. I think that would be a much better use then concentrating on calculations. Picking up a book and figuring out how to do calculations is (relatively) easy compared to trying to pick up a book and understand the deeper concepts. I’ll also add I’ve noticed studying on your own is significantly easier if you have even 30 minutes of time to talk to someone / get a few questions straightened out once or twice a week, so there would be a definite positive effect from being around other undergrads. I’d even venture that you could cover a bit more (or in more depth) if you had people read a bit of background material before coming (specifically the special relativity and mechanics). Even if it was still reviewed, it would be easier then having people come in blind. I don’t think it would be problematic to cover that in 6 weeks, especially if you didn’t have to try to do it while taking your other undergraduate classes.
I would whole-heartedly support this intensive, accelerated summer course. This is in part because I find myself trying to make time to independently study some of the topics listed in Sean’s “curriculum” since my undergraduate curriculum doesn’t leave a lot of room to take specialized coursework (I am cramming nuclear/particle physics, graduate quantum theory, graduate stat mech, a special topics math course on math methods in QM, and an intro to string theory course into my last semester as an undergrad, largely because this is the first time I’ve had any room in my schedule to take such classes, and I am utterly excited to finally have some flexibility in my curriculum.). I am applying to several of the top-ranked universities for grad school, and having excelled at a state school (in my home state) with a rather average reputation has left me wondering what sort of preparation the bulk of students going into these programs will be. As such, I have enthusiastically, but perhaps a little nervously, been pursuing opportunities to expand my knowledge as far beyond the undergraduate curriculum as I can, and you can say that is partly because I naively believe that the undergrads coming out of Caltech, Harvard, MIT, etc, will have been exposed, by the virtue of their exalted institutions, to more graduate-level concepts by the time they graduate with their 4-year degree.
Sean, you and any other well-wishing theorists should have brought this up years ago…and I only say that because I have wished for something similar myself in the past and would have leapt at the opportunity. If anything, it would have been nice to have a structured introduction to these higher-level theoretical topics to help ease the transition into self-guided independent study.
Sign me up, Sean! I’d take that course in a heartbeat. And Jim Al-Khalili, I love that you mentioned MSU in that list of international research destinations. Woo Go State! 🙂
I agree with Paul. Even I, who am clearly leaning into experimental physics, would’ve liked to have such a summer experience.
Sean, we need you to make this Undergraduate Theory Institute. If you have some time left, build a time machine, ’cause I want to go back in time to my junior year and enroll.
This sounds like a wonderful idea. When I was an undergrad I did three REUs. For my first one I thought I’d be doing some kind of experiment and enjoy it, since I loved the physics labs. But when I got there, I got paired up with a theorist. I had to go through one chapter of Jackson in the first few weeks of the summer to be able to understand all the equations that were involved in the project. It was hard work, but it was so rewarding that at that point I decided I’d be a theorist. In my second REU I did observational work (data analysis of red giants’ spectra), and liked it but didn’t love it. In the third REU I did experimentation, but I was mostly writing code for analysis of the data from the experiment — though I did get to play with circuit boxes and soldering irons, which was rather interesting and boring at the same time. In any case, even though the REUs were great experiences where I learned about research and explored areas that I would have never thought about, an intensive summer institute on some field of theoretical physics or astrophysics would have been incredibly useful.
I did get to participate in one eventually, but not as a student. UT Brownsville has a summer school thing in gravitational waves. Most of the students are undergrads, with one or two first-year grads thrown into the mix. I was an upcoming fourth-year astro grad then, working on black hole mergers and structure formation, so my advisor (who lectured in the summer school sometimes) asked me to be his TA that summer. The students learned so much. Everything from GR to astrophysical sources to numerical relativity was discussed there. It was even a nice refresher course for me to remember those subjects. Those students walked away from the summer school knowing so much. And they enjoyed learning because many of them did not have the opportunity to learn about these things in their undergrad programs, but were interested in working on something gravitational in grad school.
Anyhoo — yes, a summer institute in theoretical physics sounds like a great idea. Additional and/or complementary summer institutes in other fields of physics/astrophysics would also be great.
I would have loved to have attended such a thing. As an undergrad more interested in theory than experiment, I nevertheless got involved in experimental research instead, for the same reasons that Sean stated. And I am rather grateful to my past self for having made that decision, because I find it inconceivable now that anyone can do science of any sort without knowing how the experimental process works in real life, and not as given by some abstract philosopher of science. However, I do find it rather frustrating that after being lured into physics by promises of the deep mathematical beauty and whatnot that lies beneath it, I don’t get to taste any of it as an undergrad. Well, almost none anyway — a mathematical physics course taught by a theorist this quarter is making up for some of that lack, but only after two years of mind-numbing courses that were no more than drills in how to do calculations.