Spacetime versus Spacespace
This Demonstration shows a spacetime and a spacespace configuration of light cones. Two space stations, at distance 10 from each other, begin emitting regular transmissions at . At , a meeting is arranged halfway between the two space stations, so that representatives from many inertial reference frames can watch the first signals arrive together. Such a momentous event leads to a decision to make this the origin of all their reference frames: .
This Demonstration models acceleration only at . This is the only time at which the origins coincide. Only at the setting can you change rapidity without changing position in the top graph. (It is still really fun to watch with a slow time rate going forward and a fast rapidity going back-and-forth.)