Time Travel: Donnie Darko and Looper

"Different temporal parts of the same occurrent can overlap. If we hear a concert delayed in time and the concert itself we accept them as equally real. We notice naturally that there is a difference between the entanglement of meeting a younger ego and the experience of hearing simultaneously a concert and its former replica, only delayed in time. If a wave is sufficiently coherent it can annihilate itself in a region of space or time by interference. We can delay occurrents in time but cannot delay continuants in time. To record the moving image of a person means to access information about a temporal part of him and this record is less real than the continuant itself because it is ontologically dependent on it: an object in time can be delayed in time only as image and by this process the original reality of the object is lost. We cannot accept that two different temporal parts of an object could stand in almost the same space and have the same degree of reality. One of them have to be less real. It is clear that a time journey is itself an occurrent, as it has temporal parts, it is a process and it has phases.A clear four-dimensionalist tendency affects the scientific description of time travel".

- Extracts from "Time Travel and theories of Time" (2000),
written by Ioan Lucian Muntean.

The Terminator: The main timeline is set, and traveling back in time cannot change anything. Indeed, traveling back in time to change the present will sometimes cause the very thing you're trying to avoid, as happens in The Terminator (for obvious dramatic reasons). This is among the more plausible time travel theories, as it avoids those messy paradoxes.Back to the Future: There are, I suppose, many ways to interpret time travel in this movie, but in this theory, there is still only one timeline, but you can change the past (and thus the present). In this theory, it's possible to go back in time and kill your father (before he had you), and in such a case you will "disappear." This is also a common theory, but the presence of paradox makes it less plausible.
The End of Eternity: In Isaac Asimov's novel, a group of people known as Eternals develop time travel and decided to improve upon history by introducing carefully calculated changes in the timeline. There is more to it than that, but the concept of a society using time travel to manipulate history is an important concept that is relevant to DD.Lightning: In Dean Koontz's novel, time travel is only allowed in one direction: to the future. This takes care of the "kill your father" paradox rather neatly. You can, however, change the future. There is a catch though, which is probably more for dramatic effect, but which bears importance in the Donnie Darko discussion - essentially, fate doesn't like it when you attempt to change something in the future: "Destiny struggles to reassert the pattern that was meant to be." Donnie Darko (Jake Gyllenhaal) wakes up disoriented at the edge of Carpathian Ridge' cliff.

Donnie Darko sort of contains elements of all four, and since it includes the Back to the Future theory, it also sort of includes a paradox".
Source: kaedrin.com

“Looper is set in a present-day world in which a group of hitmen are sent their victims from the future,” although Johnson assured fans that there was much more to the film than that.My full /Filmcast interview with him (where we discuss symbolism in Bloom, as well as that film’s ending) will be going up on the site shortly, but in the meantime, hit the jump for some details about the next script he’s working on, a sci-fi film called Looper.

It should be noted that Johnson is still working on the second draft of the script and thus, any and all of these details may be different by the time the film goes into production. Among the elements of the film that Johnson revealed:

The film will be set roughly thirty years in the future.

The film will depict a dystopian society that has gone to “hell”.

A disruptive element will have traveled back in time from even further in the future. The time travel element is part of the setup, much like in The Terminator, but not an active ongoing part of the story".
Rian Johnson with Rachel Weisz at "The Brothers Bloom" TIFF Press Conference on 9th November 2008.

Looper will be “very dark, very violent. It’s the exact opposite of Bloom.”
Rian Johnson on the set of "The Brothers Bloom" in Prague.

Source: www.slashfilm.com