 Each worldline has a “length” as measured by the metric \(g\); this length is the elapsed time along the worldline. Take two events on a manifold \(M\) which can be connected by a worldline. The elapsed time between the events might be large along one worldline and small along another. Intuitively, if a worldline is such that it stays close to the boundaries of the cone structures (i.e. if the trajectory stays “close to the speed of light”), then the elapsed time is relatively small. (See Figure 2.1.2.) In fact, it turns out that if two events can be connected by a worldline, then for any number \(t&gt;0\), there is a worldline connecting the events with an elapsed time less than \(t\)! 