Five Under-Appreciated Ideas in Undergrad Physics

13Sep08

This is an old post that I never got around to fleshing out and finishing. I figured it was worth posting before letting my blog freeze-out (yeah, that was a Boltzmann equation reference).

More than half a decade ago I was sitting in the same course and had a very inspirational TA and now I’ve been toying with the idea of TA’ing the “honors” freshman physics sequence at my new university.

Along those lines, I’ve been thinking about a few ideas that I don’t think are emphasized enough in the typical undergraduate curriculum. These ideas, I think, are important in developing a healthy ‘physics intuition.’

  1. Symmetry. The use of symmetry to solve problems, group theory as the language of symmetry. E.g. how to we `intuitively’ use symmetry to reduce higher-dimensional problems to lower-dimensional problems (e.g. polar/spherical coordinates). Mention symmetry as a `deep physical principle’ in gauge theories, for example.
  2. Geometry. Emphasize the geometric foundation of physics, even in elementary physics. E.g. thinking of cross products as areas with an application to Kepler’s laws and angular momentum. This is a recurring theme that I think needs to be made explicit much more at every level. Lagrangian mechanics courses ought to draw more on the structures of differential geometry.
  3. Dimensional Analysis. Every freshman should understand the power of dimensional analysis and scaling. (I believe there’s a very nice textbook by Barenblatt.) More advanced students should see how dimensional analysis is still a very powerful tool, e.g. Stevenson’s excellent “Dimensional Analysis in Field Theory” review (http://dx.doi.org/10.1016/0003-4916(81)90072-5).
  4. “Duality”. E.g. Electromagnetic duality. More loosely, being able to interpret one problem in terms of another problem. e.g. hydrodynamics as E&M.
  5. Back of the Envelope. Learning to make good order of magnitude calculations.


3 Responses to “Five Under-Appreciated Ideas in Undergrad Physics”

  1. I, for one, implore you not to stop your blog, even if your new entries, understandably, appear with a slow trickle. (Of course, I am of the opinion that well-mannered blogs such as yours will not be held against the author, as they simply can not, so long as the author develops a career that can only nullify arguments as the blog as a “distraction.” However reasonable I hold this position to be, you may feel otherwise.)

  2. Hey Steg — thank you for the very kind words, but unfortunately I just simply don’t have enough time to write in any semi-regular manner. I’ve found my queue of partially-written posts have just gotten so long that the older drafts have simply become irrelevant with time.

    Give my regards to Chris B.!

  3. 3 Weldon MacDonald

    I’ll agree with you and then some.
    Not just dimensional analysis, students come through a ugrad degree, without ever really understanding the nature of measurement and it’s huge place in experimental physics.
    Try a course in solid state without understanding solid geometry, let alone symmetry. Students are simply not prepared to extend their vision in this way.
    Duality is supposed to be a high school topic, after a fashion, it is a least addressed in the standards. In a ugrad degree so little time is spent on circuits that it’s difficult to get into the specifics, it’s usually left to the engineers, or optional courses.
    What I find missing on your list is math. The math requirements for a physics ugrad simply don’t address the needs of a physicist. Where’s he linear algebra, numerical analysis, differential geometry, etc…
    When I mentioned this to the chair of my department, his answer was We can only ask so much in a BSc, 45 credits simply isn’t enough, it’s up to the student to take electives to cover the stuff we can’t fit in. He has a point. Physic majors should be taking a second major in applied math, which is surprisingly easy. They should also be doing ugrad research, if they plan on graduate school.



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