The last course report covered the first six classes of the relativity unit. This week, we had the final two relativity lectures, and today was the start of quantum mechanics.
Class 7: This lecture was about how you can use special relativity to show that a magnetic field in a stationary frame is an electric field in a moving frame. The basic idea is that when you move to a frame that is moving in the same direction as the (canonical) current, you see the spacing between the negative charges decrease due to length contraction, meaning that the wire no longer appears neutral. This leads to an attractive force on a stationary charge in that frame, that turns out to be equal to the magnetic force experienced by the charge in the lab frame.
I saw this as an undergrad taking E&M out of Purcell, and it’s one of the few things I remember clearly from that class (the professor was approximately eight hundred years old, and his handwriting was so bad he made every Greek letter look like a “q” (or a “Q”)). The textbook I’m using contains a brief and equation-free discussion of the topic; I fleshed it out with equations from another source, and it makes a good way to tie up all the special relativity topics we covered.
Class 8: I had meant to use this class as a math background class, doing the Swashbuckling Physicist’s Introduction to Complex Exponentials, because the math department doesn’t teach them in the classes that are pre-requisites for my class. In the comments to the last report, though, dr. dave asked “No mention of General Relativity?” I realized that that was a serious omission, and the math topic isn’t really essential for the next week or so of classes, so I decided to put that off, and do one lecture on General Relativity.
The class was essentially identical to what I told the dog. Only, you know, without the dog. I talked about the equivalence principle and how that leads to the conclusion that light must follow a curved path in a gravitational field. And if you put that together with the fact that light always follows the shortest path between two point, that means that gravity must cause space-time to curve. I ended by talking a little about the Eddington eclipse observation (and the epic failures that preceded it), gravitational lensing, and LIGO, which wrapped things up nicely, because we started relativity with Michelson-Morley.
Thursday, I gave an exam during the lab period. The test was designed to fit in our 65-minute lecture periods, but as usual, the average time to completion was more like an hour and twenty minutes. Which is why I give the tests in the lab period.
I haven’t graded them yet, and won’t talk about the grades here, anyway.
Class 9: Today’s class was the beginning of quantum mechanics, dealing with black-body radiation. I did a quick review of Young’s double slit experiment, which shows that light is a wave, and then talked about the observed properties of thermal radiation (Wien displacement law, Stefan-Boltzmann law, Planck formula for the spectrum). To illustrate the problem Planck faced while trying to derive his formula, I went through the Rayleigh-Jeans approach, leading to the Ultraviolet Catastrophe (which I realize is slightly ahistorical, but it gets the point across), and then explained how Planck’s quantum postulate fixes the problem.
I didn’t go through the math of how to get the formula from that assumption, because it’s not critical to the class. I did go through showing how the Planck formula recovers the Rayleigh-Jeans result in the long wavelength limit, and how you can get the Wien displacement law from the Planck formula. The Stefan-Boltzmann law is part of the homework assignment.
It was a pretty good class, especially considering that I spent the morning distracted by worrying about Sick Baby. I ran about two minutes over, which is good for me, and got through everything I wanted to cover.
Monday is the photoelectric effect, then the Compton effect. Which are also the two labs we’ll be doing in the next few weeks, so that’s good…