HL only: A.5 Galilean and special relativity. Read a space-time diagram by locating an event from its position and time coordinates, then interpreting the gradient or angle of its world line to determine its motion. A steeper world line usually represents a lower speed when time is on the vertical axis.
The Reasoning
A space-time diagram represents one spatial dimension on the horizontal axis and time on the vertical axis. The vertical axis is often labelled (ct), rather than , so both axes have units of distance.
An event is a single point representing something occurring at a particular position and time. A sequence of events for one object forms its world line.
| Feature | Interpretation |
|---|---|
| Vertical world line | Object is stationary because its position is constant. |
| Straight, tilted world line | Object moves at constant velocity. |
| Curved world line | Object accelerates. |
| Horizontal separation | Difference in position between events. |
| Vertical separation | Time interval, or times the time interval on a (ct)-axis. |
| Light ray at | Light moves at , provided the and (ct) axes use equal scales. |
For a world line making angle with the time axis,
Therefore, a world line closer to the light line represents a faster object. A massive object must have , so its world line lies inside the region bounded by the light paths.
Events on the same horizontal line are simultaneous in the reference frame represented by those axes. In another inertial reference frame, the axes are different, so the same events may not be simultaneous.
A common misconception is that a steeper line means greater speed. With time vertical, the opposite is true: a vertical line has , while increasing tilt indicates increasing speed.
Exam Technique
For a Sketch question, label both axes, events, world lines, and light paths clearly. Before calculating a velocity, check whether the vertical axis is or (ct), identify the angle’s reference axis, and use the diagram’s stated scale.
