World coordinates

World coordinates are a set of coordinates that measure the path a body takes when moving through the world. If $\mathcal{P}$ is a point particle, its world coordinates at time $t$ are written as $\mathcal{X}(t;\mathcal{P})$, where the addition of $\mathcal{P}$ as an argument allows us to distinguish the paths taken by different particles. The world coordinates of a body are what an observer standing at the origin sees, expressed in a chosen coordinate system. This observer is called the world observer.