On Wednesday I made a snap decision on my feet in class and went with it. I’d done this several years ago at the same point… Let me explain.
At some point in teaching Relativity I come to do some thought experiments that follow through the consequences of Einstein’s postulates about the speed of light being constant for all observers and that all inertial observers are equivalent… You rapidly discover things like time dilation and length contraction this way. The length contraction discussion usually involves someone riding an object of a given length (from their perspective) at velocity v, and how someone on the ground watching them go by sees the length as shorter… This is Lorentz-Fitzgerald contraction…
Well the point is that you need to do some careful accounting and so it is good to label the measurements made by each person carefully, and the times on their clocks, and so on and so forth. Back in the middle 90s I used to teach this at Kentucky using a rocket, with observer riding on the rocket, with observer on the ground. Times measured by each were denoted and , of course.
Then one day in 2001 when teaching it in Durham (I’d moved to England) I realized that it would be worthwhile updating it a bit, so in view of the buzz about the books and the film of that year, I changed it to a broom, with Harry riding on it during a game of Quidditch, with Hermione looking on. This made also for nice notation, with times measured by each being and . This state of affairs persisted in my notes for some years.
Then yesterday just before starting that thought experiment I decided that it was a bit tired, and the last of the films was last year, and this crop of students probably think of the whole Harry thing as all so last decade anyway.
So I thought for a while, stopping mid-sentece. The students looked at me as though I was nuts (understandably) and I tried to decide what to change it to. Back to a rocket? No…
Then I had it. Let’s get out in front of the upcoming big two films and set up the notation now! So I decided to swop the broom for a dragon called Smaug, and Bilbo is riding him (yeah, I know that’s a departure from the text). I added insult to injury by putting Gandalf in the village for the observer on the ground, although now I think I should have used Balin, or Bard (the latter an excellent suggestion from one of the students when he saw where I was going with this). That way I’d have and .
Yeah, crazy. I know…
Some Related Asymptotia Posts (not exhaustive):