The Good Old Time Travel Paradoxes III

3. A Discontinuous Timeline

If 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:

A

C

(B)

ABC is the usual causal order but here B is the time traveller’s departure and C is his arrival which prevents B. A is an earlier event, like the invention of a time machine, which would have caused B. Thus, A occurs and would have caused B which would have caused C which, however, occurs and prevents B. Thus, indirectly, A causes C. C would not have occurred without A although, to a casual observer, AC looks like a causality violation.
-copied from here.