Time Travel

I’ve been reading this biography of Benjamin Franklin, which has gotten me thinking: The crux of most time travel stories is that somebody has to go back in time to assist or protect some pivotal figure. The Terminator and Back to the Future movies, right off the bat. There’s always a huge split - the future without that person is bleak and miserable. What if you went back in time to protect someone, and encountered several other time travelers who were there to protect different people? In each of your futures, none of the other people had survived, and yet, you came out okay. Any one of them would have filled some critical role, or possibly, none of them were really critical - they just got credit for what was really a popular movement. Or maybe you encounter someone from further into your future who had come back to eliminate the person you were assisting - the events they made possible had unforeseen, long-term consequences. Has anyone done a story like this?