I've done time travel before. Admittedly it's been a long time, but alas...
Generally speaking, you don't edit previous posts, you keep moving forward, then after a certain amount of "time" has passed, you trigger an event that allows players to go back in time to resolve something. Maybe one of their compatriots died, so they go back in time when able to stop the death from happening, but in doing so create a new timeline with the old instances of themselves still existing, but as new people.
For example: Maybe PC's A, B, and C were in a love triangle. B and C like A, A likes B and C but can't decide which one it wants. C dies, causing A and B to grow close. They go back in time to save C, as C was their friend.
The timeline then changes as a result. In this new timeline, A and C ended up together, and B is left to the wayside. The two instances of the characters--the "old" versions that were changed instantly, slowly start to affect their "newer" versions and vice versa, until they become identical people, and hit crisis point, merging into one. You could then have instances where, say, C is terrified of the unknown consequences of being brought closer with his dead "other", and decides to go back in time again and again, making more versions of the future to prevent the ultimate cataclysm of losing itself to crisis point, or potentially losing A to B again on top of losing itself.
Eventually, you would have so many timelines, that you could justify anything, and this is where the fun truly begins, as timelines finally start to collapse in on one another. You could end up with a merged timeline in which dinosaurs never became extinct, but humanity did end up managing to reach its modern incarnation, so now you have a T-Rex rampaging through New York, and that alternate version of Earth now needs to recoil from the changes to the environment that occurred, humanity would have to change, its cultures quickly adapting or dying off to these sudden schisms in reality. People would suddenly find themselves involved with other people they don't even know, or find people they once knew as having ceased to exist. Enemies become friends, friends become enemies, and nothing is ever quite left with the feeling of wholeness again.
-Then-, in that one, singular moment, you have achieved the apex of creativity: The ability to justify the creation of anything, in any situation, with characters you've established.
-That- is the power of time travel.
It often gets flubbed though. It's really hard to write convincingly without tearing plot holes the size of the big bang into it... But when you -can- manage to achieve it...