No, not this philosophy of time travel.
It is my opinion that time travel, in which one has a real chance to change events after going backwards in time, is impossible. If time is a moving now then going backwards in time would mean changing the entire universe. If time exists all at once then changes are impossible. And if the multiple worlds interpretation of quantum physics is correct then the best you can do is simply end up in a different branch, since everything that can happen does happen, with or without time travel. And, in addition, there are worries about how an event in the future could even be said to cause some event in the past (the appearance of the time traveler).
But it is not my place to speculate about physics. Let us assume that meaningful time travel is possible, that we can go back into the past and make choices that change the future. Let us also assume that paradox isn’t an issue. But, even with the practical questions concerning time travel out of our way, there are still ethical considerations. We know that any change in the past, no matter how small, can have widespread effects in the future. And this means that instead of a world populated by people we know the world would be full of different people, no matter what changes we made (assuming we went far enough back in time). So is making any change immoral then, since doing so would erase a large number of people from time?
Although I do think time travel has ethical implications, I do not think that worries about erasing people from time are among them. Although killing someone is usually a bad thing, that is not what the time traveler is doing, he or she is preventing them from existing in the first place. And by making their changes they are granting a completely different set of people existence. Why should the original group of people be considered more worthy of existence than the new group? In any case our everyday decisions have this kind of impact already. Let us say that we are doing some activity, and plan on doing it for some time. As things stand there will be some group of people ten thousand years in the future. But if we decide to stop before we planned to then there will be a different future, and a different group of people will exist ten thousand years in the future. Even so we don’t consider the fact that one group of people will exist, and the other won’t, as a result of our decision to have any ethical relevance to what we decide to do. I have argued previously that the ethical choice is the one that results in the best outcome (by some standard of best), and this holds true not only for everyday decisions, but for those of time travelers as well. If the time traveler knowingly makes changes that result in the world being worse then they have acted unethically, and if they make changes that result in a better world then they have acted ethically.
What makes time travelers different than the rest of us, ethically, is the knowledge they can have about the results of their choices. A time traveler could visit the future, return, make a change, and then check the future again, thus giving them perfect knowledge about the results of their choices. And not only would they know the results of their choices with perfect accuracy they could also know the effects of their choices thousands and thousands of years into the future. As I mentioned previously a choice, made differently, will result in a vastly different future, as long as that future is sufficiently far away. But knowing what that difference will be is impossible, and so it usually doesn’t factor into our decisions. Ethically we aim for the best result, but we can only make reliable predications as to what that result would be over a relatively short time scale (at the most tens of years). But the time traveler is in a different position. They can know the long term effects of their choice to eat waffles for breakfast instead of pancakes. And thus because they can find out they have a responsibility to (just as we have a responsibility to be aware of the results of our actions). Additionally, the time traveler must make more difficult ethical choices than we do: does he or she favor a moderately well off civilization or one with a period of great suffering followed by a period of great prosperity? In light of these considerations I have to say that time travel is a technology that I am glad I don’t have access to. Sure it would be fun, but the ethical responsibility would be crushing.