Except Primer-style time travel, where you can actually change the future of the universe by going back in time, is not very well-defined. Leaving aside the difficulty of reconciling such time travel with relativity, it is unclear to me what the rules are that govern returning to a particular time slice. What aspects of the past state are allowed to change, and what must remain the same? Are there any constraints at all?
The sort of time travel we see in the Harry Potter books (SPOILER jura uneel naq tnat geniry onpx va gvzr gb fnir Fvevhf Oynpx) is a much better example of well-defined time travel. There's no "changing the future" involved. Every causal loop is subject to strong consistency constraints.
Well, every story that has people traveling or communicating faster than light basically has not-well-defined time travel in it. Which includes most scifi ever written, I'd guess.
EDIT: New discussion thread here.
This is a new thread to discuss Eliezer Yudkowsky's Harry Potter and the Methods of Rationality and anything related to it. With two chapters recently the previous thread has very quickly reached 500 comments. The latest chapter as of 17th March 2012 is Ch. 79.
There is now a site dedicated to the story at hpmor.com, which is now the place to go to find the authors notes and all sorts of other goodies. AdeleneDawner has kept an archive of Author's Notes. (This goes up to the notes for chapter 76, and is now not updating. The authors notes from chapter 77 onwards are on hpmor.com.)
The first 5 discussion threads are on the main page under the harry_potter tag. Threads 6 and on (including this one) are in the discussion section using its separate tag system. Also: one, two, three, four, five, six, seven, eight, nine, ten.
As a reminder, it's often useful to start your comment by indicating which chapter you are commenting on.
Spoiler Warning: this thread is full of spoilers. With few exceptions, spoilers for MOR and canon are fair game to post, without warning or rot13. More specifically: