Notes on the board
Times are in seconds and distances in light-seconds (ls), so light moves 1 ls per second and every light ray in the diagram climbs at 45°. Speeds are fractions of the speed of light, c. Every position, time and clock reading comes from the Lorentz transformation between the platform and the frame you ride with.
The top strip is everything at one moment of your time: the rails and platform clocks belong to the platform; each train carries its own clocks, synchronised in its own frame. Below, the spacetime diagram shows the whole history, distance across and your time up; the dashed orange line is now, the moment shown in the strip.
Seen from another frame, a moving train’s clocks run slow by γ and are out of step along its length: the front clock lags the back one by v L₀. A moving train is shorter by γ, because measuring a length means marking both ends at the same moment, and “the same moment” differs between frames; the dashed coloured lines are each train’s own “now”.
The interval s² = Δt² − Δx² between two events is the same in every frame. The dotted curves t² − x² = constant do not move when you change frames; everything else slides along them.
Click a train, traveller, tunnel or event to select it; drag events in the diagram, drag trains and tunnels along the track, and drag a train’s round handle in the diagram to change its speed. Drag empty diagram to pan. Space pause · F next frame · Delete removes · 1–7 plates.
Drawn for clarity: train heights, clock faces and the speed of play. Trains are rigid and move in straight lines (the traveller’s turn is instant); what is shown is what each frame measures, not what a camera would see, since light takes time to reach an eye.
Further reading: Taylor & Wheeler, Spacetime Physics · Feynman Lectures, Volume I, chapter 15
Theoria · Special relativity 0.5 · Drawing board