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?
First: The term “learning curve” originally referred to a plot showing skill at a task versus level of experience with that task. Those two quantities could be measured in many different ways, but the point of the curve was to measure how much practice or training improved a person’s (or, just as frequently in research situations, an animal’s) facility in doing something.
A “learning curve” in the original sense was something that one could draw on a piece of graph paper, and it had a definite mathematical meaning. Moreover, it did not measure in any way the difficulty over time of a course of study. However, the term has been reinterpreted in popular use, and to say something has a “steep learning curve” is an idiom meaning that the material gets difficult relatively quickly. However, different people still use the term to mean slightly different things. Since the idiomatic usage is not based on any real mathematics, if one tried to work backwards and figure out exactly what the term ought to mean, one can quickly get muddled.
On the actual subject of the post: I think this would be a nice idea. However, Sean’s proposed course of study is probably just too broad. I have always advocated that undergraduate physics students who are really interested in theory should take, alongside their physics classes, a heavy complement of mathematics classes. Courses in complex analysis, group theory, and probability are indispensable and can easily be fit into the first two or three years of undergraduate study. Analysis and partial differential equations also come in handy, but they are harder and less universal in their applicability. Understanding this material well can make the related topics in physics much easier when they finally appear.
Back on the subject of the proposed curriculum for Sean’s program, I would suggest striking out classical field theory, topological defects, and anything involving the Einstein’s equations in their general form. I have never, as a practicing field theorist, found a need for any classical field theory more advanced than that taught in sophomore-level linear mechanics classes. In fact, I would claim that any topic in quantum field theory that makes nontrivial reference to the real field character of the theory is a fairly advanced topic. Topological defects, interesting as they are, are strictly a special topic. Many theorists will never need to deal with them at all; and to treat them in any kind of general fashion requires a mathematical facility that many professors of theoretical physics lack. With the Einstein equations, the problem is that the equations and the general structure of geometrodynamics is so complicated that it’s almost impossible for a beginning student to digest what’s going on with them without immediately restricting oneself to very special cases. However, since almost all the interesting physics involves such special cases or small perturbations around them, it’s better just to zip through the generalities and get to something simpler, like the Friedmann equation or the linearized Einstein equations.
I would go!!!!
I think what you are proposing is essentially a summer semester of undergraduate study… with a pretty heavy courseload.
But, if this scheme might help, we have an REU program here at WSU where we usually have about one theory student per year (out of total 10, sometimes more, sometimes less). What we do is that we have a one-credit REU-preparation course for our students in the winter semester PRECEEDING the summer program. We lecture on the basics of particle and nuclear physics, computing, and basic experimental techniques. This ensures that the summer program is not just another semester of learkning, but truly is a research experience. Theory student(s) usually sit with the rest of the students, but brush up additionally on what they would be doing in the summer.
I had students doing projects on heavy quarkonium, as there is nice connection to nonrelativistic quantum mechanics. And the results are publishable… and the students do all the problems on their own…
Currently, I’m a grad student in GR. In my undergrad research, I developed cosmic ray detectors. It was — as you point out — a useful introduction to independent research. However, I might have become an experimentalist if that was all I had seen.
One summer in undergrad, a couple friends and I got together and convinced Bob Wald to help us go through his General Relativity. We’d meet with him to ask him to clarify certain issues; he’d answer our questions and assign us problems from the book. We would then spend a couple nights reading what we needed to answer the problems, and work through them. Wald was adamant about not preparing lectures, so we were forced to think for ourselves, and dig on our own.
I think we not only made great progress in understanding GR for ourselves, but also got a taste for something closer to theoretical research. It wasn’t new to the world, but it was new to us.
You can cover the topics you list in a summer (maybe not with every undergrad, but with many), you will spark interest in pursuing theory as a career, and you will give those future theorists a much-needed leg up.
Maybe you don’t need a big, formal program to help out. Plus, it might not take as much work from you old folks as you think.
A summer institute like this for future theorists sounds like a wonderful idea, and would make me a bit jealous. When my brother was an undergraduate in physics, many years ago, he was able to spend summers doing interesting research projects. As an undergraduate in math, I had no interesting opportunities of any kind. At that time, there wasn’t even a concept of undergraduate research, except perhaps for the senior honors thesis. And I always thought it peculiar, because back then there were more summer activities for high school students! I spent two summers, one at Notre Dame and another at Berkeley, in NSF sponsored math programs when I was in high school. I agree with Sean that the summer between Junior and Senior years is ideal for some accelerated look-ahead learning.
Dude, if you really want to push this, I’ll work with you on it. It could be an excellent “summer school” proposal.
All of that being said… before a certain age, many people don’t realize that they aren’t theorists. Like, say, me for example. I’ve anecdotally observed that the fraction of incoming Physics grad students who think that they want to do theory is much larger than the fraction who graduate that way. This may be changing as undergraduate research becomes more ubiquitous; when you’ve spent most/all of your time on classes, it’s easier to visualize theory (even if incorrectly) than it is experiment. (Esp. since lab classes tend to be lame more often than classroom classes do.) We really should be encouraging undergrads to get experimental research experience.
But, yes, also letting them have the opportunity for theory research experience is great, particularly if we can make sure that it doesn’t suck all of the student market away from the experimentalists.
I haven’t read the other 30 comments, just your article, but there is a whole big category missing from your topics : computational physics. A LOT of theory is simulation/computer based, but students are coming into graduate school much more computer illiterate than they did 10-20 years ago. This may sound surprising, since by and large they are more comfortable with comptuers, and have been using them longer. However, 10-20 years ago, being computer literate meant understanding filesystems and knowing how to program. Now, being computer literate means knowing the web and knowing instant messenger. Some rare students know how to use a spreadsheet or Mathematica. Very, very, very few know any real programming, and it’s a HUGE barrier for theorists and experimentalists alike.
-Rob
Rob,
I’m surprised to hear that most entering physics grad students don’t know how to program. I’m an undergrad at Chicago and most undergrads here participate in experimental research, which almost inevitably involves some form of programming (especially in particle physics and astrophysics), so most people learn programming one way or another (there’s also a computational physics course for undergrads). And I’m astonished that there are people who don’t know how to use spreadsheets. Doesn’t everyone use spreadsheets to store and analyze data in lab courses?
Almost all of the physics undergrads I knew at the ol’ trade school had some amount of practical programming experience. We skipped out on the programming classes taught by the CS department, so most of us couldn’t program a Scheme interpreter in Scheme, but everybody seemed to have a pretty good handle on MATLAB, maybe Perl and/or Python, and possibly C/C++. I learned microcontroller assembly language while working on a rather elaborate hat (to be worn at the Ig Nobel Prize ceremonies), but soon forgot it after that.
We picked up these skills mostly during experimental work, either in our “Undergraduate Research Opportunities Programs” (UROPs) or in Junior Lab. (One of my biggest gripes about my undergrad education is that the Physics Department filled sophomore year with marshmallow fluff while making junior year almost impossibly hard, and not even hard in a useful way. The rationale I’ve heard professors give is that junior year — where you hit the real stuff in quantum mechanics along with a lab class that takes twenty hours per week, bare minimum — is supposed to separate the “sheep from the wolves”. Having survived it, I can agree with that idea, more easily than I could while I was going through it. Still, it seems wrong-headed: much of Junior Lab’s difficulty comes from having to learn so many disparate things at once. Not only do you have to learn the physics involved, but at the same time you have to learn how experimental errors and data-analysis statistics work, pick up MATLAB and LaTeX skills, learn how to write a paper, learn how to give a presentation. . . . Why not work these ancillary skills into a more moderate lab class sophomore year, integrated with the waves/optics class, so the students can learn the practical skills they need and spend more time the following year being frustrated by the actual physics. Oh, and bring Lagrangian and Hamiltonian mechanics back into the sophomore classes! Yes, you can get a physics degree from MIT without having integrated an action, save for a couple homework problems in 8.033 and the cramming everyone does before the GRE. Rant concluded.)
I’d also love to work on course material for this. Keep us all posted, please!
Sean,
Your idea is great, but it’s limited by the traditional concept of “institute.” How about an online “theory institute” that wouldn’t be limited to a spatial or temporal location? First, judging from the sample input of these comments, you would have many, many more resources to draw upon. Second, given this same sample of responses, you would have many, many more participants willing and able to take advantage of the offering.
With a little help from your friends, you could hold live online video sessions (at very little cost) where you could play the coveted role of “father figure,” and “shoot the breeze with the students at the late-night coffee and whisky hours.” In fact, these could be held with local participants, with real coffee and whiskey, while virtual lurkers listened in the background, offering the occasional observation or even driving the conversation betimes, by asking questions.
If you pulled this off, you would be breaking new ground in education and probably be featured in the NYT, for instituting important social innovation. Finally, and maybe most importantly, I, for one, would be willing to pay a reasonable fee to join such a pioneering effort, even if I had to do it more than once to master the material.
Sean,
I did research as an undergrad starting in my freshman year, spent a summer with an experimental group at Fermilab, got my name on a published atomic/nuclear theory paper junior year, and went into theory. So I believe that ug theory work is possible and desirable.
That having been said, your proposal doesn’t seem to me to be the most effective means of getting undergrads to make worthwhile contributions to theory. The main obstacle to undergrad to contribution is not the lack of easily accessible textbook knowledge of the sort you intend to dispense. It is the obscure lore, the nowhere-defined-but-everywhere-used terms, the unspoken connections that are assume to be obvious but aren’t.
When I was an undergrad, I often dreamed of something like 1-800-Ask-A-Physicist (no Internet to speak of during my ug years) to help me out during my desperate struggles to master issues at 2:00 am.
I think that http://www.ask-the-theoretical-physicist.org, accessible only to undergrad registrants, would be more useful. The FAQ compiled from such a site would, I believe, be far more valuable than the textbook knowledge that you propose to dish out.
While I’m not enthusiastic about an online “institute” because its hard to deal with equations efficiently, I think, in general trying to do something “bigger” then a physical program is a bad idea. There are right now plenty of sites where physics students congregate, be it chat rooms or forums, but they all are too big to keep track of most of the discussions without spending all of your time on them. Worse, the quality of posts varies enough that you can’t even be sure that the information is half-accurate. While others may have differing opinions, I don’t want to watch an impersonal video online or read some chat; that, for the most part, is doable now for many subjects. Its inevitable that any online system will accumulate enough users that it won’t be worth it to use for anything more then video lectures or socialization. There is a reason that collaboration is most efficient in person, and moving online seems like a disastrously bad idea. Technology does not always make ideas better.
I agree with G. There is no substitute for direct interpersonal contact with instructors and peers. The professions of physics or math is, despite the impressions of some, are very much a social activity, and the earlier students are involved the better. It helps build confidence and helps the student answer this question before they apply for and get into grad school: is this where I want to be?
There are always pros and cons to every approach, whether it’s research or education. However, the key to success is always to minimize the cons and maximize the pros in any given effort. One of the biggest cons to an online “institute” used to be the lack of adequate technology and the associated expense of dealing with that challenge. That’s no longer a problem, but its inverse is: the technology is so ubiquitous and the expense so negligible that too many unqualified participants can easily swamp the system.
However, the pros of the online “institute” are plainly manifest, since it enables many to benefit who couldn’t otherwise. I think the challenge is to properly characterize and manage the desired participation. Clearly, haphazard participation in large, unstructured, chat rooms or online forums, is not the way to characterize the online participation at the proposed tute.
What is wanted is a careful, deliberate, response to the prepared lectures. Such response could be managed in different ways, both to minimize the effort of instructors, and to maximize the learning process. I have some ideas along that line that might be helpful at some point.
Of course, the ideal participation, is, and always will be, an active, personal presence, but since one doesn’t have to preclude the other, I think the combination of both is the best of all possible worlds. The reality shows of television, as much as I loathe them, provide an excellent example of the access that technology can provide. Uncontrolled online access to the persons present would clearly not be desirable, but periodic access, after the fact and at appropriate times, would be immensely helpful to so many, as Belizean points out:
The main obstacle to undergrad to contribution is not the lack of easily accessible textbook knowledge of the sort you intend to dispense. It is the obscure lore, the nowhere-defined-but-everywhere-used terms, the unspoken connections that are assume to be obvious but aren’t.
But it’s the discussion of the textbook knowledge that brings these things out. As Belizean wrote:
When I was an undergrad, I often dreamed of something like 1-800-Ask-A-Physicist (no Internet to speak of during my ug years) to help me out during my desperate struggles to master issues at 2:00 am.
If I recall correctly, there’s an instance in the Feynman Lectures, where he explains something about differentiating and then adds, “I don’t know why they don’t teach this in school, but they don’t.” What a wonderful reality show his lecture series and associated confabs with students would have made.
This sounds like a great idea!
I had the oportunity to participate in two summer programs in famous national labs. Having read books like Kaku’s Hyperspace and Greene’s The elegant universe, I was (and still am) in love with all the “fancy” ideas like superstring theory. Of course, my research experience in these labs served to discover more things, things that I did not thought about.
When I found myself building an apparatus for single-molecule microscopy, I learned that not everything is written in index notation ;-). I really did not cared much about that project, but my mentor was able to present her field of study as alive and attractive. It was a physicist, working with chemists, biologists and one psychiatrist. It was more like a science thing than a just plain physics thing. I liked this about my first summer, most of the good stuff came as simple things like sitting down in real, formal discussions in the lab and even meeting a person who attended the Feynman lectures. (Not to mentioned the embarrassment of being asked hard questions by a Nobel Laureate during my final presentation). I did not had much “theory”, but overall I was happy that I got to see another side of things (I do not want to say another side of physics…).
During the second summer, the physics content was better in the sense that I was able to build samples and present real results. I got the experience of one full day at the beamline (with lack of lunch included…). Still, all of this was far from strings and fields. I agree with Sean, students that are interested in theoretical topics should still try these research experiences. They serve to learn about new, different things and meet all kind of people (I met my current girlfriend in one…).
When I applied to graduate school, I guess both my research experinced made belive the committee thought I was going to follow experimental physics and I believe they were surprised to learn of my interest in string theory. I am currently working my way through my first year and so far so good. So Sean, if you need some henchmens, tell me and I would gladly help with gruntwork, like note-typing, etc.
Why not just require the students to read “The Road to Reality” as a prerequisite (including doing all the exercises of at least medium difficulty)? That would at least get them familiar with the basic terminology and concepts of GR and QFT, and leave more time for the kind of material that can’t be readily absorbed through self-study.