If time travel is possible, then it has already been invented. We would already know about it because "they" would have come back to tell us about it. We would already be doing it. In fact, this would be true not only of time travel itself but of all technology. No more stone age tools, if all it takes is one person from the future going back to introduce the most advanced possible technology. Time travel is the negation of time itself. We cannot say "at some point in the future we will learn this," because there is no future anymore. There is not such thing as a "not yet." There is no past either, needless to say.

If time travel exists in its stupid science fiction modality, then other times are other places that exist right now as we speak, somewhere else. The third century B.C. is like a place one can go visit. But then again, every year in this century, every month of this year, every day--down to the most minute subdivisions of time--are places to which one could "travel." But in a sense, then, we are already there, in each place, and each time/place exists right now. If I go to 1964 then I would be myself in 1964. That's who I am in that temporal context. Otherwise, if I go back to a time where I actually existed, but am still myself now doing that, then there are two selves looking at each other. Or there could be infinite selves, since time travel posits that every moment of time exists simultaneously to every other moment--displaced along some spacial dimension.

To travel to a place where I did not or will not exist as myself, on the other hand, is still to posit an intolerable duplication of reality at the molecular level.

The problem with SF is that it doesn't take its ideas seriously enough.