[ollysb]

It may not be possible to have a stable timeline that involves time travel i.e. if time travel exists, someone always ends up travelling back and messing up the timeline so that time travel isn't discovered. If timelines which include time travel are inherently unstable then the timeline(assuming there's only) would stabilise when time travel isn't used at any point. This does leave the door open for time travel tourism though, where you just go back and observe but without changing history in any way. The method of time travel would actually have to prevent changing the past though otherwise the potential for abuse would lead you back to the unstable timeline issue.