 One can see how the definition corresponds to the story above. Bob travels along the half-curve \(\gamma\) and records an infinite elapsed time. Moreover, at any event on Bob’s worldline, Bob can send a signal to the event \(q\) where Alice finds the result of the computation; this follows from the fact that \(\gamma\) is contained in \(OP(q)\). Note that Alice’s worldline and the starting point \(p\) mentioned in the story did not make it to the definition; they simply weren’t needed. The half curve \(\gamma\) must start at some event – this event is our starting point \(p\). Since \(p\) is in \(OP(q)\), there is a worldline from \(p\) to \(q\). Take this to be Alice’s worldline. One can show that this worldline must have a finite elapsed time.