I shall have to think about this bifurcations for a while; presumably it requires a multiverse.

In the meantime here are some more thoughts inspired by the fact that serious scientists can make the kind of statement in my OP.

Gott’s story, perhaps conveniently, makes no mention of what happens to the older “self” after the meeting. There seem to be two possibilities: In the first of these he returns to the point in time from which he went back, (let us call this point “X”). In which case, presumably, he continues to age, and eventually dies. At first glance, this may seem to answer the question as to whether the original self can progress beyond point X, once the time loop has been formed. However, we must remember that point X, like every other point in spacetime, is a unique and immutable event; so when the younger self reaches point X, he must, again meet his older self, (because point X cannot occur with and without the older self) thus raising the question as to whether the original self has progressed beyond this point, or not, bearing in mind that this is not a repeat visit to point X, it is the one and only time that point X will occur. If we were right in thinking that the formation of the initial loop set a succession of loops into action it is difficult to see how we can avoid a scenario in which progressively more “selfs” meet at point X and progress together, presumably, all to die at the same time, only to “reappear” at point X to meet the next self as he reaches the time travel event. At first glance, it may seem as though we have a contradiction here, in that I talk of the older self as having progressed from point X; yet I have the younger self meeting the older self again at point X when he arrives there, surely the older self would have moved on by then. What we have to keep in mind, though, is that, as we saw above, point X is a unique spacetime event. It cannot occur with and without the older self, or any other character who is ever at that event. Obviously, this must mean that if the build up of multiple “selfs” at point X does occur, then all those selfs must always have been at point X. In fact, because there seems to be no end to the number of selfs who will eventually arrive at point X, it might be argued that this gathering of selfs could be limitless, some might say “infinite”. It begins to look as though, if this scenario ever became a reality, the Universe would be stuck, “eternally”, in a time loop beyond which it could never progress. Can such a cosmic misfortune be brought about by the action of one person who succeeds in travelling back through time and meeting her or his younger self? One more point that has to be considered is that if point X is to play host to an unlimited number of selfs, then all these selfs must have been there when the original self took his trip back in time. Bearing in mind the fact that, at this juncture, the time loop had not been formed, where did all these other selfs come from and who decided how many there should be? There is still another complication. Not only must the original self meet all the other selfs at point X before going on the journey through time, all these selfs approached point X from the past, along a “continuous succession” of unique spacetime events, none of which can have occurred with and without a single one of the multitude of selfs.

The second possibility is the bifurcation one, which needs some thought.