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Could it be something to do with ' how do you get back ?'...unless you can travel with your time machine how can you activate it in the past (before it was invented) to bring you back ?
Lee, what you descrobe is what I referred to as parallel universes. There is EITHER paradoxes OR sets (probably infinite sets) of parallel universes. A traveller who changes something in the past can only return to a universe where that change was made (by him) and not to the universe from which he started. This is logically correct but, although attractive from a Schrodinger cat point of view, I believe is not sustainable in many (if any) of the Quantum Theories that study such matters more deeply - I think there is a problem with the total energy. It would also be a pain if you trod on a blade of grass that somehow changed the world to something unrecognisable when you return to the future. This concept has been explored by many SciFi books.
I'm a great believer in the simplest explanation being the most likely. The simplest explanation in this case being what I said. It takes but 1 premise - that if you travel back from time B to time A, then from time B's perspective A->B happened the way it did & cannot be altered. Bifurcation & conservation of energy are irrelevant.
But he did exist at time A because he went back to it. He just hadn't been born yet.