Looper's Time Travel Paradoxes
Time travel stories are tricky; there always seem to be loose ends left dangling, and/or connections that don't quite add up. Looper, unfortunately, suffers this problem as well.
The biggest issue, as always, is the multiverse factor: if a guy from the future comes to the past and starts mucking with history, it either A) creates a separate timeline that runs parallel to the original one (allowing for two versions of history), or B) The actions in the past forever alter the flow of a single timeline, allowing for just one version of events. Looper plays fast and loose with this time travel mechanic, at times relying on both single timeline and multiverse timeline approaches to push the story forward.
For example: Old Joe still existing after he meets and affects Young Joe shows that multiple timelines are possible - but tricks like Young Joe carving messages in his arm that show up on Old Joe as scars would have us assume that there is one timeline wherein the fate of one Joe is directly tied to the other. Johnson gets by the issue via vague expositional throwaways such as Old Joe's memory - is it being revised by his actions in the past? Or is he open to remember several versions of history? (Sorry, no clear answers - it's too cloudy to say for sure!)
However, a few minutes of thought reveal a lot of paradoxical problems woven into this plot:
Old Joe & The Rainmaker
The biggest thing to address is the paradox involving Old Joe's mission to stop the Rainmaker (Cid). Looper shows us a montage of Joe's life in which Young Joe in fact unwittingly kills Old Joe out in the cornfields, and goes on to live what he thinks will be his happy, post-looper life - only to become the drug addict gun-for-hire (and eventual lover) that is Old Joe. Old Joe then jumps back to the past to change this course of events, and the movie we witness is therefore the alternate timeline where Old Joe escapes his execution.
...However, the movie hints (in the diner scene with young and old Joe) that Old Joe's heinous actions in the past are what push young Cid to become the fearsome "Rainmaker." As we see in the climax of the film, Old Joe's crazed mission forces Young Joe to kill himself to save Cid - but this is a paradox.
If The Rainmaker exists in Old Joe's future timeline, it suggests that Old Joe's baby-killing mission in the past was predetermined to happen. So then how could there ever be a version of events where Old Joe was executed by Young Joe, and Young Joe goes on to become Old Joe?
Even if Old Joe had fulfilled his destiny (killing Sara, disfiguring Cid), Young Joe would have been aware of his older self's actions and been changed by them - he wouldn't become the Old Joe we saw in the montage, because the exact thing that would've made Cid the Rainmaker would also change Young Joe forever (the presence of Old Joe).
Bottom line: Old Joe's timeline where both he and the Rainmaker co-exist is a paradox. A version of history wherein Old Joe kills Sara and creates the Rainmaker is also a paradox. Old Joe cannot be the origin of the Rainmaker as we are told he is.
In a climactic moment, Young Joe (via voiceover) describes seeing an unending cycle of time travel violence that creates monsters like the Rainmaker and Old Joe - and the only way to break it is suicide. A noble speech, noble idea, good plot twist and intriguing thematic arc... but it doesn't hide the fact that there is a big gaping paradox at the center of the movie.
Young & Old Seth
This tangential subplot to the film actually raises quite a few paradoxal issues. Similar to Young Joe, Young Seth (Paul Dano) fails to kill his older self. Old Seth goes on the run until Kid Blue (Noah Segan) and the gatmen capture Young Seth and surgically amputate him as a means of incapacitating Old Seth.
Here again, we get a muddled version of timeline mechanics: If history is one timeline, then Old Seth should have instantly seen the amputated changes to his body the moment he escaped from Young Seth; the fact that limbs disappeared one at a time suggests multiverse possibility (Young Seth loses one finger, but there's still alternate possibilities wherein he keeps the other nine, etc.). But if we're talking multiverse theory, the Old Seth we see shouldn't be affected by the amputations - it should be some alternate Old Seth of an alternate timeline who suffers that fate.
That's not to mention the sheer number of future events that would have been altered when Young Seth is left incapacitated; start thinking about the Butterfly Effect and your head is liable to explode.
The Two Joes
Like the Seths, the paradoxal nature of Looper's time travel story is seen in the two Joes. Simply put: it's impossible for these two Joe's to both exist and have a connection whereby Young Joe can leave scar messages in Old Joe's skin, or Old Joe is clouded with Young Joe's memories. Again, the movie shows us that Old Joe comes from a particular timeline, and that the Young Joe we meet is living in a now alternate timeline, where Old Joe's actions steer him down a very different path.
In single timeline theory, Old Joe should've suffered a Back to the Future vanishing act the moment that Young Joe turns any one of the emotional corners he does in that second act of the film on the farm (bonding with Cid, falling for Sara, realizing he could one day become a baby-killer, etc.). Young Joe had already started down a path of emotional growth and change, meaning he could never become the Old Joe we meet - yet when Young Joe kills himself, poof! Old Joe is gone as if they are directly tied to one another. Either Old Joe should've reflected the emotional changes in Young Joe (which would've prevented him from baby killing ) - OR, Young Joe's suicidal act shouldn't have affected Old Joe, since Old Joe would've been from an alternate timeline.
We could go on and on like this, but we would inevitably find ourselves arriving back at the same conumdrum: time travel theory: you just can't have it both ways. Looper crafts a very good story out of a wild sci-fi premise, and while it dodges a lot of its own potholes scene-to-scene, when viewed from a distance its clear that Rian Johnson has not yet cracked the time travel movie conundrum.
For an in-depth discussion of the film by the Screen Rant team check out the Looper episode of the SR Underground podcast.
Looper is now playing in theaters.