Folks who’ve been with me a long while know one of my happy Christmastime traditions is watching the Aardman Animation film Arthur Christmas. The film also gave me a great mathematical-physics question. You should watch the movie, but you might also consider the questions it raises.
First: Could `Arthur Christmas’ Happen In Real Life? There’s a spot in the movie when Arthur and Grand-Santa are stranded on a Caribbean island while the reindeer and sleigh, without them, go flying off in a straight line. What does a straight line on the surface of the Earth mean?
Second: Returning To Arthur Christmas. From here spoilers creep in and I have to discuss, among other things, what kind of straight line the reindeer might move in. There is no one “right” answer.
Third: Arthur Christmas And The Least Common Multiple. If we suppose the reindeer move in a straight line the way satellites move in a straight line, we can calculate how long Arthur and Grand-Santa would need to wait before the reindeer and sled are back if they’re lucky enough to be waiting on the equator.
Fourth: Six Minutes Off. Waiting for the reindeer to get back becomes much harder if Arthur and Grand-Santa are not on the equator. This has potential dangers for saving the day.
Fifth and last: Arthur Christmas and the End of Time. We get to the thing that every mathematical physics blogger really really wants to get into. This is the paradox that conservation of energy and the fact of entropy seem to force us into some weird conclusions, if the universe can get old enough. Maybe; there’s some extra considerations, though, that can change the conclusion.