Five Under-Appreciated Ideas in Undergrad Physics
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.’
- 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.
- 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.
- 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).
- “Duality”. E.g. Electromagnetic duality. More loosely, being able to interpret one problem in terms of another problem. e.g. hydrodynamics as E&M.
- Back of the Envelope. Learning to make good order of magnitude calculations.
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