In John Crowley's Great Work of Time is found material that should convince most prospective time travelers to have second thoughts if they think they can improve the present by going back and modifying the past. Although the best minds in the story attempt to apply a science of orthogonal thinking to the problem of time travel-- it doesn't seem to work. If, as some theorize, reality, or our universe, breaks instant by instant into many, or an infinite number of parallel universes, therein lies the rub. It might prove relatively easy to return back to the past along a single "reality line" that you are already a part of-- but once you turn around and attempt to travel the other way to the future-- well, the possibilities become endless; meaning, you are lucky even to return to a future in which you have had a previous existence(true if you go back farther than the time you were born). Also, for every instant you are in the past, you would be generating all sorts of variant universes that did not happen, would not have happened, if you had not visited. That is more to the point of ethics of the tale.
Bottom line: though the story's mathematicians attempt to get "orthogonally close" in their returns to the future, unfortunately for the British, even the best of possible new realities are not close enough at all.
At least there are cigars.
All this in a tale that makes no reference to how the travel is actually accomplished! Well, Einstein did not need actual clocks either.
One nice thing about the story is that the reader is above and beyond the constraints that confine the participants in the tale. If something exists beyond our universe that we can never know because our existence is locked into a holographic replay, then this type of fiction is the only way we can get out.
That leads me to a curious point about myth, narrative, and science. We made the myths and narratives initially to stand in for our very limited knowledge. Then came more knowledge, better methods, science. But eventually we will hit (or some of us are already there?), the wall of "not-knowing" because our science cannot proceed outside our "local system." So, really nothing has changed. Only narrative can take us beyond. I like the new talk about conservation of information, because it suggests that the universe itself exists at least in part, as a story-- not just the atoms, the worlds upon worlds-- but the sum of the narratives it contains.
And of course we realize that although humans love their beginnings and endings-- it's just a species thing, and not necessarily physics.