Penultimate lecture today in the graduate electromagnetism class. These last four lectures are a lightning tour through some important concepts – showing how many of the things we’ve been doing all semester fit with Special Relativity. (For example, amusingly, showing that the Lorenz gauge condition is in fact Lorentz invariant…) It is fun to show a powerful example of how an important guiding principle (such as writing equations in a Lorentz-covariant way) can end up making several features of the theory seem much more natural, while also leading to new physics. This is fun to do, although it does mean that I end up writing whole new notes for this since I am not a fan of the way some of these electromagnetism books (Jackson included) decide to treat time in an odd way, such as treating it as imaginary (which must be so confusing to some students) just so as to write Lorentz transformations like a rotation, or using mostly negative signatures for spacetime, and so forth. And, inexplicably, using different units of measurement from the choices made in the rest of the book… Anyway, so the last two lecture-writing sessions have mostly been one of fiddling with minus signs and factors of c, 4 Pi, minus one, and so forth. Joy. Well, the group seems excited since they’re beginning to see things that they’d seen in other classes and it is all making some sort of sense now (Klein-Gordon equation, duality, etc., etc…) I think the last class will show how many of these things flow from variational principles. Maybe I’ll find a little time to do the Born-Infeld model? I’m excited too, although I’ll be sad to end the class and stop working with this fun group of students.
Today I managed to grab a few sketches on the train. This afternoon coming home on the Expo line these two snoozing gentlemen were kind enough to sit still for a few minutes each for me to get down a few impressions of their features. This was all helped a bit by the train sitting still for a while as we waited for a truck to get off the line. Apparently it was parked or stuck there.
Perhaps not helpful was this young guy who watched me drawing and then decided Continue reading ‘Covariant’