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Does anyone have any suggestions as to what is a good topic for a short talk on theoretical physics to a bunch of Math and Physics undergrads that might make them "embrace" theoretical physics? Thanks. (Brain storm: String theory, quantum tunneling, etc...?) Also it would be great if someone could suggest some resources.

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This is a topic for chat. – mbq Aug 18 '11 at 15:50
@mbq: what a pity, I had a nice answer prepared :( I wonder what's the problem with this question (if it's made CW). There have been dozens of request for talks about math at MO and they were always welcomed. – Marek Aug 18 '11 at 15:53
This is--of course--a topic of great interest to the whole community, but people hold conferences on outreach so it is not a matter that can be treated well in the Q&A format. – dmckee Aug 18 '11 at 16:12
Right now user hasn't the rep to participate in chat, the cure for that is to answer a few questions. – dmckee Aug 18 '11 at 16:12
I upvoted because I would have liked to listen to such a talk when I was an undergrad. – yayu Aug 18 '11 at 16:54
up vote 8 down vote accepted

Well, I can tell you what got me into physics. Already at high school I have been fascinated by quantum theory, general relativity and string theory (mostly thanks to Hawking's popular books) and this hasn't gone away. One might argue that these three huge areas is already all there is to theoretical physics but only at the university did I discover fascinating subject of statistical physics and condensed matter theory which should certainly also been mentioned (of course, there are great many other areas; by not mentioning them I certainly do not imply they are not important or interesting). Now, so much for general talk, let's look at some concrete stuff.

  • Nature of the space-time and gravity explained in completely geometrical terms (already geodesics on curved spaces are very entertaining).
  • Anything about black holes. What happens near them, the fact that you can gain energy from rotating hole using Penrose's construction, what happens when you cross the ring singularity, etc. Also, black hole thermodynamics and evaporation could be mentioned (and if one feels up to it they can also mention the holographic principle and all the recent advances in AdS/CFT that connect this area with nuclear physics).
  • Particle physics. Some Feynman diagrams, the most important particles, the way forces work through particle interaction and some important results such as confinement, explanation of radioactive decay through exchange of massive bosons, etc. The possibilities are endless and I know people love this because it is both very fundamental and also understandable since you can explain most of it by just drawing few wavy lines :)
  • Phase transitions. Explaining them from the microscopic point of view, talking about spontaneous symmetry breaking, etc. There is already lots of interesting stuff going on with quite ordinary stuff (see this video) but one can also discuss the phase diagram of QCD. Statistical physics permeats all physics since it's what you need to get from fundamental laws to observable phenomena in any area.
  • Some condensed matter systems. Electronic properties of matter, band gaps, phonons, etc.
  • Lasers. They are just cool :)
  • Plasma (either EM or nuclear). Discussion of basic properties, instabilities, reasons Tokamaks are complicated.

Now, all of the above topics are great but as whole lecture that I personally would find most intriguing (at the undergraduate level), I would welcome the historical account of force unifications: E+M -> EM, weak force, strong force, electroweak, GUT, supersymmetry, string theory interleaved with introduction of SR, GR and quantum theory as they came along in the above succession. This might be bit too much for a single talk though :)

As for the string theory, I am not so sure. It will surely have to stay strictly at popular level since the audience will have (I presume) no grasp of GR or QFT. One can mention Calabi-Yaus and the way they relate to the string spectrum. Dualities are a huge topic but again it might not be easy to explain what is dual to what. I guess you can look for inspiration into the Brian Greene's Elegant Universe.

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As someone who started in math as an undergrad and then ended up in physics I can say that I wasn't clear on the distinction between the two subjects. I treated physics as if it were one big math problem and not as an experimental science. Theoretical physics and math are no doubt related but when presented together it often ends up being the case that one is smashed into the other in such a way that it looses its essential character. It makes me think of string theory lectures I've been to that looked like straight up math given in a theorem proof format and relativity classes where the instructors talked up a storm on tensors but they just pushed indexes around and nothing about multi-linear algebra was really called on. The end result was it took a long time to realize this and recognize how the two are complimentary and to not just blindly smash math stuff into the physics shaped hole and vice versa.

That said, here is my suggestion: Find a result like this one on 1-dimensional magnetic systems and their possible relationship to a 248-dimensional Lie algebra and pre-chew it for the undergrads. Highlight the interplay between the two subjects and how their distinct (and essential) techniques pulled the whole story together to give an explanation of reality.

I LOVE to see the two subjects come together in a result like this. This is the kind of work that drives both subjects and shows the best of what both worlds offer. That's what I wish I'd have had driven home when I was a junior just starting to see things for myself.

Full disclosure: I actually posted on this paper on my blog a while back but I think it's a good example of how physics and math work together.

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+1 for the physics shaped hole :) Also, that chain is a great example, it is one of my personal favorites too. – Marek Aug 19 '11 at 6:46

The physics of the early universe? Not my field but a version of theoretical astrophysics/cosmology... Inflation, multi-universe type stuff?

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I think style is more important than topic. A talk with different viewpoints (math - physics - experiment - connections between topics) and different levels of abstraction and complexity can be really great. I find nobody is offended if you spend some time on the big picture as long as you don't dumb down the entire talk. People will forgive you if they become confused when you spend some time trying to be clear about a really complex issue. People tend not to be offended if they are bored or confused by some fraction of the talk (as long as its not the whole thing). And people tend to like things that have big connections or give glimpses to complicated stuff that they would like to learn more about. People like it if you take the time to explain some tricky stuff (even if they forget it two seconds later). And the glimpse to the future or to big (and important) unsolved problems can be a hook for your audience.

Another style issue is to consider your talk as a `story'. People like certain types of stories, ..e.g., I tried this but it failed, I was misled by this idea but then understood why and then I tried this and it worked! (Obstacles overcome by protagonist). If you set up a paradox and then explain it. If you present something as hopelessly complex and then outline a route to breaking it down to understandable pieces. If you suggest a simple experiment and then describe why it gave wrong and misleading results.... I try to remember that as a lecturer I am essentially an entertainer. I am not naturally a joker so the story line is key. I would recommend you choose a topic you really care about (and let that come through in your story) rather than suggest a topic.

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In my opinion the most amazing thing about theoretical physics is that it works at all, ever. Mathematics is created, typically constrained only by pure reason and aesthetic decisions. On the other hand (as has been mentioned in other answers) physics is first and foremost an experimental science. So our ability to dream up models and solve them with well(or ill!)-defined mathematical structures, and at the end of the day make quantitative predictions about nature that tell us whether or not our insight is total crap, well that's an amazing thing -- and the fact that we understand a little bit of why that is is therefore $\mbox{amazing}^{(\mbox{amazing})}$.

Which is all to say that scaling and universality are the things that pushed me into theoretical physics, at least. ("Well, you see, by noting a subtle symmetry of critical hamiltonians, we can easily explain why all of this properly scaled real, measured data falls on exactly the same curve!")

(and a postscript: string theory is a topic that is deeply embedded in the "popular-science" consciousness [not necessarily a bad thing] but honestly, my cruddy, misinformed undergrad idea that all successful theoretical physicists must be string theorists almost kept me away from theory entirely. The kids who already get excited about string theory don't seem to require any extra nudge from the experts.)

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I find it appalling that of all the topics touted hear as ways to inspire undergraduates, by and large none of them are really understandable by a general undergraduate physics audience. This is what is wrong with physics today: a lot of people talking about things they pretend to understand but really don't. What about the many topics that are already in the undergraduate curriculum? The problem is that they are taught fomulaically. I would have liked to see almost any physics topic treated with really good physical insight; one sore point I can recall in particular was Lagrangian mechanics.

In short, I don't see anything uninspiring about learning physics. Give me billiard ball collisions, give me coupled pendulums, give me Carnot cycles, whatever: just teach it as though it's more than a formula to memorize for the exam.

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