Spacetime Diagrams
A spacetime diagram plots one dimension of space sideways and time upward, so an object's whole history becomes a single line — its worldline. Because the speed of light is the same for everyone, light always travels at 45°, forming a light cone that divides the future and past you can reach from the events you can't.[1]
Events A and B happen at the same time in the rest frame (same height). Boost to a moving frame and its axes tilt toward the 45° light line; "now" is no longer horizontal but the x′ direction. Read each event's time along those tilted lines and they no longer match: in this frame ct′A = 1.31 and ct′B = 0.22 — B happens first. Nothing about the events changed — only who counts as "simultaneous." Note the light line never tilts: its speed is the same for everyone.
The striking payoff is the relativity of simultaneity. Switching to a frame moving at speed tilts both of its axes toward the light line: the time axis ct′ (the traveller's own worldline) and, crucially, the space axis x′ — the set of events that frame calls "at the same time." Since that line of "now" is tilted, two events that are simultaneous for one observer occur at different times for another.[2] There is no universal present slicing across all of spacetime; each observer carries their own.
This is the same cross-term that appears in the Lorentz transformation — here made visible as the slope of the moving observer's "now." It's also the key to untangling the apparent contradiction of the twin paradox.