Spacetime diagram

A spacetime diagram represents events using spatial and time coordinates, often with horizontal $x$ and vertical $ct$. A particle's world line records successive events on its trajectory; lines describing the propagation of light define the light cone.

The axis convention matters when reading a slope. With $ct$ vertical, a constant-velocity trajectory has $dx/d(ct)=v/c$, so the drawn vertical-to-horizontal slope is $c/v$. Light rays then lie at $45^{\circ }$ when the two axes use equal length scales. A stationary object has a vertical world line.

Such a diagram makes special relativity geometric: changing an inertial frame changes how events are assigned spatial positions and times, while causal relations remain constrained by light propagation. A diagram showing only one spatial coordinate suppresses other motion rather than proving it absent.