Timelines

The time travel issue has come up again. See combox for Hero Meets Villain. As the first of two stages in addressing this -

If someone remembers having lived in a timeline where there was a Holocaust but experiences living in a timeline where there was no Holocaust, then we can designate these timelines as 1 and 2, respectively, without as yet committing ourselves to any theory either about the existence of either of these timelines or about the relationship between them.

Two Theories

(I) A Single Discontinuous Timeline

Only timeline 2 exists. Timeline 1 does not exist and never has existed in any dimension of time. Indeed, timeline 2 itself (now misnamed) is the only temporal dimension. The quantum nature of the universe is such that sometimes a time traveller randomly appears/arrives from nowhen with spurious memories of a timeline that does not exist and has never existed. This explanation is offered in Poul Anderson's Time Patrol series.

Problem:

Sometimes a Time Patroller says that he might travel into the past and delete the timeline that he is now in. If a deleted timeline has no existence and if the Patroller does carry through with deleting this timeline, then it follows that this timeline that he is now in - he is conscious of it and talking about it - does not exist. This is a contradiction.

Second stage later.