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there is a difference between branching timelines and parallel timelines.
if you go back in time, and branching timelines is true, then your presence in the past creates a new future that branches out from the past, which your trip has not affected.
if you go back in time and parallel timelines is true, you enter a completely separate timeline, one that was, like the one you came from, premade with all past and future events (including your arrival) already in place.
The first comes from the idea that the future is created by the past, the second holds that a timeline is complete from it's point of iteration, and that time travel simply moves people from one to the other, where their trips through time have already been factored in among the many infinite number of timelines that exist wholly separate from one another.
the only thing thee two models have in common, is that they agree that time travel into the past is allowed for, and that events in the past are identical up to the point where the traveler arrives.
but in one there is one timeline with a single past splitting into many futures.
While in the other, there are many timelines, that span the distance from the beginning of the universe to it's end, and it is merely that some of these have identical pasts until a point where the rest of one timeline is different from another.
if drawn, imagine one side of the page is the beginning of the universe, and the other side it's end.
a branching timeline starts as one line drawn from the beginning towards the end, which then splits into two, and each of these split in two as well, and so on, until there is a branching tree.
a model of the parallel timelines is a bunch of straight lines going directly from the beginning of the universe to the end, never touching or intersecting.
there's another significant difference to these models, one grants a great deal of agency and importance to the time traveller, who literally serves as the catalyst for the creation of a new future.
but in parallel timelines, it may seem the same from the time traveler's perspective, but in fact, he had not served as a catalyst for the creation of anything, he merely moved from one complete timeline to another, and his trip was not even unexpected, as he was essentially fated to leave one timeline at his point of departure, and appear in the other timeline at his point of arrival, he can't even arrive off schedule (though from his perspective, he is a completely free actor).