Randomness

Since we're about to finish up relativity, I've been thinking a lot about what I think is the 'correct' way to cover mechanics, E&M, and relativity. In doing some reading, I ran across this quote, which made me think even more that our usual approach is severely lacking:

"The influence of the crucial Michelson-Morley experiment on my own efforts has been rather indirect. I learned of it through H.A. Lorentz's decisive investigations of the electrodynamics of moving bodies (1895) with which I was acquainted before developing the special theory of relativity . . . What led me more or less directly to the special theory of relativity was the conviction that the electromotive force acting on a body moving in a magnetic field was nothing else than an electric field. - Albert Einstein

Just something I find interesting: despite what you might hear in intro courses or popular accounts, E&M played a big role in inspiring relativity, it was not merely the speed of light and the aether.

Problem is, the history is in a way conceptually out of order, and harder to teach (IMHO). My evidence being how relativity is often presented in intro-physics sequences: as a total non sequitur, just sort of shoved in there. Moreover, in spite of the preserved historical ordering of topics, the motivation given usually starts out with the Michelson-Morley experiment and the aether, and quietly ignores EM forces in different reference frames. Thus, we keep the historical ordering, but throw out crucial parts of the original (and exceedingly insightful) motivation!

I prefer to follow the Mechanics -> Relativity -> Electromagnetism ordering, which I guess I've made obvious now. Relativity is hard conceptually, but I find students have a harder time with electromagnetism at first, particularly magnetism. Having relativity under your belt at least makes the magnetic field seem less arbitrary, which is reassuring I think. Introducing relativity after mechanics and E&M, while historically accurate, sometimes makes it seem like an ugly hack, which it wasn't at all. If you are going to do relativity after E&M anyway, why not cover the E&M aspect too? Purcell's book does a wonderful job.

On the other hand, doing relativity after mechanics is harder to motivate sometimes, and one has to resort to strange little thought experiments to find anything wrong with Newtonian physics. Thinking about relativity right after a mechanics course, though, has your brain in the right mode and the kinematics fresh in your mind.

Of course, I suppose it is just difficult either way, reality is a harsh mistress. And Poincare probably deserves more credit than he gets.