"He pushed down a crawling horror that he felt now and then. What if we destroyed the world by being here? We could have. They could have all gone out like a match in the wind as soon as we changed something back here - all dead or not even that, all of them never existing, a might-have-been. The Arnsteins thought that the Event would produce a branching, two trunks on the tree of time, but nobody could know for sure. Come to that, nobody knew anything about the Event except what it had done." (p. 39)
The Event is a premise. We have to accept that it is unexplained - although it could be explained later. We do know some things for sure. People who were prevented from existing would not be like a match extinguished by the wind but like a match that had never been made. If an event in 1250 BC has a consequence in the late twentieth century, then that consequence does not occur "as soon as" the event in 1250 BC.
I argue that, if the twentieth century remembered by the Nantucketers existed, then it remains true that it existed. It does not make sense to say that an event occurred, then was prevented from having occurred. To say that it occurred in one timeline and not in another is not to say that it occurred, then did not occur. However, suppose that an event that is remembered as having occurred did not in fact occur, i.e., suppose that the memory is false?
3. A Discontinuous TimelineIf causality is violated, then the prevented cause, e.g. the time traveller’s departure, simply does not occur, although it is ‘remembered’ by the appearing time traveller, and the effect, i.e. his appearance, is uncaused, therefore not really an effect. Events are discontinuous, as in quantum mechanics. This seems to be logically possible but is extremely paradoxical in the sense of apparently contradictory:
a traveller appearing now could be from the past, from the future or from no time;
anyone leaving the present to kidnap Hitler will still fail because Hitler was not kidnapped but travellers from possible futures could prevent those futures;
some past events could have been caused by arbitrarily appearing time travellers that we do not know about;
a traveller arriving in what he regards as the past does not know whether he remembers a real future or a prevented one;
in fact, before leaving the present, a traveller knows that his memories are valid but, on arriving in the past, he does not know this!
Time travellers in this discontinuous timeline would almost certainly think in terms of divergent or multiple timelines even if time travel theory denied them.
The causal principle can be partly salvaged with the following diagram:
-copied from here.