What about comic book time travel? Creating alternate timelines instead of actually changing anything.
Well, that's not restricted to comic books. It's one concept of how changing the past might go. And it's the messiest of all, in my opinion. Consider this:
- You go back in time to change something
- A new timeline is created
Now where do you go when you go forward in time again? If you return to your original timeline, you're in one where you never changed anything, so what was the point? If you go forward to the same time in the new timeline, you disappear forever from the original timeline. Your family and friends, they'll never see you again. And in the new timeline it's almost certain there are now two of you.
None of these are easy to resolve in a satisfying way, except possibly the two yous: merge them into one person with the memories of both. But even that...imagine their lives diverged enough that they have conflicting memories of the same events? The alternative is you replace the other you (not cool, man! They were a person and you just erased them.)
What alternate universe stories usually do is ignore all of this as best they can. That also to me makes them the laziest and least satisfying. The most satisfying are stories like Primer, and the two versions of 12 Monkeys (the film is a closed loop, the TV series has a singular timeline that is repeatedly changed in unexpected ways). Or Back To The Future, where you're not supposed to take any of it at all seriously.
On the subject of "is it safe?" No. The original timeline is safe because it cannot be changed. The actions you take in the past never happened there. The new timeline? You'll only know the effects of your actions when you get back to the present. And whatever they are, you can't change them without creating yet another timeline, and you'll leave behind the timeline you messed up.