A.5.13 (HL)—Space-time diagrams

Read the axes

A space–time diagram plots position horizontally and $ct$ vertically; the time axis is labelled $ct$, so both axes have distance units. An event is a point $(x,ct)$. A world line joins the events of one object through time.

Interpret a world line

A vertical world line represents an object at rest in that frame. A straight tilted line represents constant velocity. A light ray has $v=c$ and lies on the 45° light line when the axes use equal scales; no physical world line may be steeper toward the x-axis than the light line.

Read simultaneity and coordinates

To find an event’s time, project horizontally to the $ct$ axis; to find position, project vertically to the $x$ axis. Lines parallel to an observer’s $x′$ axis represent equal $t′$, while lines parallel to $ct′$ represent equal $x′$.

Common trap

Do not treat the slope as an ordinary $x/t$ graph slope without accounting for the $ct$ axis and the diagram’s scale. Always identify which frame’s axes are being used.