Among physicists, the word “symmetry” means “sameness across differ- ence”. The prefixes “sym” and “syn” mean “same”, so “symphony” means “many musicians making the same sound” and “synchrony” means “same time”. “Metry” comes from the Greek word for “measure” (as in “metric”) and here means “size” or “shape”. Thus a face has a symmetry when it has the same shape on different sides, but the charm of a human face often lies in its slight asymmetries.
One of the most outrageous aspects of Einstein’s theories is their unexpected symmetries. Suppose that two identical spaceships, A and B, are approaching each other and will pass each other in empty space, and each is moving inertially at a steady speed along a straight line. Spaceship A will find that that spaceship B’s lengths are contracted and hours are dilated. Everything in stubby spaceship B happens in slow motion.
But, Einstein said, spaceship B is also moving inertially and it can also make measurements. According to its rulers and clocks, spaceship A is contracted and slowed. There is a perfect democracy among sets of rulers and clocks. That is, according to Einstein, spaceship A is shorter than spaceship B and spaceship B is shorter than spaceship A. Hours on spaceship A are longer than those on spaceship B and hours on spaceship B are longer than those on spaceship A. Time dilation and length contraction are symmetric. The different measurements show the same effects.
This prediction seemed to be complete nonsense to many physicists when they first learned of Einstein’s theories: it seemed to be a blatant contradiction. But Einstein was able to explain that it did make sense, and was not at all contradictory. Understanding this will help us learn to envisage the new nature of space and time discovered by Einstein.