Learning Relativity in the Subway

On the subway home from yesterday, there was a boy and his parents. I'm not a very good judge of age, but I'd put him around 2 years old; he was talking, but not the most steady on his feet. Generally, my reaction to toddlers on the subway quickly falls into one of two possibilities: "aww, cute" or more frequently "please stop screaming."

This child was well-behaved enough, and I saw a very interesting thing happen. He was sitting on his mother's lap, on the right-hand side of the train. Thus, to his right was the direction of travel. His father, sitting across from him, was asking if he knew how many stops they had before they got off the train. The child, thinking hard, decided instead to point out that everything outside the train windows was moving "that way," to his left.

The father said, no, the train was moving "that way," pointing to the child's right and the direction of travel. Having none of it, the boy insisted, no, that way--left and against the direction of travel. They went on like this for a while, before the father gave up, and the mother distracted the boy with a small box of goldfish.

Mmmm, goldfish.

I found it strangely fascinating, watching the two argue about what exactly was moving, and in which direction. The boy, knowing full well that he was sitting down, and clearly watching the stations and lights whiz by from right to left, correctly stated his observations from the center of his at-rest coordinate system. The father, aware of his position in the larger coordinate system consisting of the whole city, correctly stated his observations from a moving point within that larger system. Both were right, but both continued to try and convince the other to change coordinate systems.

The source of their confusion is that the boy is still thinking concretely, unable to change his frame of reference to the world outside the train. Adults, though able to think abstractly and change their frame of reference, often refuse to change once they've chosen one. Most adults would never say, "get on the 1 train, and wait for the third stop to arrive." But both father and child sat there, staring at each other across the subway car, teetering on the edge of one of the first principles of Relativity.

Sometimes we need to remember, when talking to each other, to define our frame of reference.