I think we need to put mathematical labels on things in order to make sense of this. I'm going to propose the following scenario:
Jack on the platform thinks that he is globally at rest. We will call his frame ##Q##.
Ashley is on the train, and she doesn't care to look outside of it. From...
I would like to think that I understand how 4-velocity is defined in special relativity. It makes sense to me that one takes a differential segment of the world line ##(dt, d\vec x)## and translates it into a frame in which its spatial component disappears, leaving only ##(d\tau, 0) =...