Loopers is your basic cowboy science fiction time travel story with a twist. If you like Bruce Willis without Cybill Shepherd, then you’ll love this movie, though Willis is only in about a quarter of the movie. The premise of the movie is that some mobster has taken control of the mobs, unifies them, and is now a shadow government within the US and has planet wide reach. In short, the whole story line is a self-fulfilling prophecy redux. And when I say redux, remember, I’m talking about time travel so there is a lot of looping. (If you haven’t read Movies Part 2a, click here.)
The mob uses time travel to execute people in the past. They send people into the past and an assassin, called a looper, kills them when they blink into existence (in the past). (I will use a capital ‘L’ for the movie Loopers and a small ‘l’ for the assassins called loopers.) However, the mob is also paranoid. And when a new boss, the Rainmaker, takes control, he closes all the loops. (Presumably so that no one will turn stool pigeon but perhaps because he wants to protect his creation and he already knows that a looper goes back in time to kill him because it already happened to him, the Rainmaker, as a child. You begin to see the potential problems and paradoxes. Let’s push on.)
The movie starts off with loopers closing their loops. This means that the past self of a looper executes the future self of a looper. When this happens, the looper gets payment in gold rather than in silver and he or, I presume, she throws a party. Loop closed. So far, no paradoxes. There’s no reason a past self could not kill a future self in the past and still continue. This would produce a closed timelike curve, a closed loop, if you would. General Relativity allows for closed timelike curves. This is the basis for much of the movie and all of its plot. However, I don’t think they reviewed the mathematics. Let’s do a little of that now.
The math for this gets a little hairy. I will try to explain it without too many symbols and equations. A closed timelike curve, as opposed to a spacelike curve, is a worldline in a Lorentzian manifold. A worldline is like the science fiction concept of a world’s timeline, that is, the path an object takes in space-time. A worldline plots the course of events in a Lorentzian manifold. Let me repeat that for clarity. A closed timelike loop is a worldline in a Lorentz manifold, or a particle in space-time, that returns to its starting point. Thus, time travel in the backwards direction might just be possible.
A Lorentzian manifold is a pseudo-Riemannian manifold. In a pseudo-Riemannian manifold the metric tensor need not be positive-definite, as is the case with Riemannian manifolds. The Lorentzian manifold has as its metric signature (1,n-1) or (n-1,1). A pseudo-Riemannian manifold, with a signature of (p,1) or (1,q) allows tangent vectors to be classified into timelike, null or spacelike. (Just to be clear, a metric tensor on a manifold is a function that takes a pair of tangent vectors and produces a scalar.)
Hold on to your hats because even though this next section won’t involve math, the concepts I am about to pour into your brain are a bit thick and tricky to understand. Even though the math would make them more clear, there are still questions that need to be answered before a final conclusion can be made, specifically, will we invent a theory that will subsume General Relativity? For example, a theory of quantum gravity could replace GR and then we would not have solutions that would allow closed timelike curves for anything bigger than a particle. This is Hawking’s chronology protection conjecture. I should note that particles, such as the electron, moving backwards in time do not have anything to do with macroscopic terms such as “cause” and “effect. Feynman proposed that a positron is an electron moving backwards in time. The electron in question may be the same electron as the positron in question except moving backwards in time. It is this possible property of particles that the movie uses on a macro level to justify time travel.
Another idea that disallows paradoxes in a closed timelike curve is chronological censorship. If chronological censorship is correct, then every closed timelike curve would pass through an event horizon which might prevent an observer from noticing the causal violation. Thus, since no one notices any causal violation, there is no causal violation. As David Hume discussed, when examining two events, the one that happened first is, by definition, the cause and the one that happens next, the effect. Therefore, there is no retrocausality. As with relativity, one would have to compare clocks with an observer outside of the frame. Since, given the event horizon, there is no observer outside the frame, there is no violation. (To be clear, in general relativity, an event horizon is a boundary in spacetime beyond which events cannot affect an outside observer. Event horizons are the point of no return when approaching a blackhole. Things get very tricky beyond the event horizon of a blackhole.)
What we are really discussing, then, is the flow of information. In Newtonian physics, the state of any point is affected by the state at all other points at the same time. That is, information, signals, travels instantly. Special Relativity, on the other hand, puts a speed limit on the how fast information can travel. This gets very interesting in the case of time travel and also at singularities. (Click here to read Emily Redelmeier’s paper Cosmic Censorship.)
Given that the observers notice the causal violations in the movie Loopers, continuously and flagrantly, we can assume that no censorship is protecting the timeline (worldline), and since closed timelike curves and time travel are allowed in the movie, there is no Chronology Protection Agency either. Even though, in the movie, there are laws forbidding time travel, which the mob violates, there is no automatic protection except for the mobs own self-censure. In other words, these laws are the presumed reason the loops are being closed.
Everything from here on out is a spoiler of some sort.
One of the loopers, Seth, played by Paul Dano, fails to kill his target, the old Seth, played by Frank Brennan. Seth runs to Joe, his best friend and our hero, played by Joseph Gordon-Levitt, and begs for help. Joe hides him but eventually Joe turns Seth in to protect his silver from the mob, which threatens to penalize Joe by taking it. This is where the fun with time begins. (Old Joe is played by Bruce Willis. Oh yes, there is going to be a lot of looping time travel. There isn’t a lot of branching as there is in Primer.)
Now that the mobsters have Seth, they can do whatever they want. They can’t kill Seth because he needs to be alive to satisfied the time loop. Thus, the movie gives a nod to time loop paradoxes. They avoid killing Seth as self censorship. The mobsters do not want to create a paradox, either from fear that the timeline will collapse, that is change the future, or from fear of the law and its agencies. But as we will see, paradoxes are unavoidable.
The mobsters carve a message into young Seth’s skin and cut off the fingers of that hand. There’s no blood and the skin is scarred over as if it were an old loss. When old Seth does not show up at the appointed place at the appointed time, they cut off his other fingers. Old Seth now is desperate and runs to the address. His nose disappears, then a leg and another leg and he crawls to the door of the address scarred into his arm and bangs on it. The door opens and he is shot by one of the enforcers who are after him. In the meantime, his younger self is on life support on an operating table. We hear the sound of a ventilator. Young Seth is presumably carved up but alive.
In Seth’s case, this would mean that the old Seth that travels back into time is causally connected to the young Seth. Time travel did not break the causal connection. Thus, there is no event horizon or chronological protections of any kind. This results in information traveling backwards in time. This is a causal violation but it is a weak one since the antecedent of all this still happens in the past before the consequence but only weakly so since old Seth is in the past. However, there is another stronger violation or paradox and it is related to the Grandfather Paradox.
The Grandfather Paradox is where you go back in time and kill your grandfather. Well, if you killed your grandfather, then your father would not have been born and therefore you would not have been born. If you had not been born, then you could have have gone back in time to kill your grandfather.
So, if the mobsters or their doctor carved up young Seth, when they send a carved up old Seth back in time to before young Seth gets carved up, there is no way that carved up old Seth can run away from young Seth and therefore the looped worldline unravels. Even if young Seth realizes that old Seth is himself, what could he do? Let the carved up old Seth live and take care of him? No. In the end, young Seth would kill old Seth out of either fear or compassion and once again the timeline unravels. If he didn’t kill old Seth, he’d have to look after old Seth. Since young Seth doesn’t get carved up, would old Seth be restored? And if so, would this mean that old Seth could once again escape? If this happened, the new world timeline would still unravel. Or lets say that young Seth puts old carved up Seth away in an old folks home in France under an assumed name. Well, then, when the mob catches young Seth, what happens to old Seth if they carve up young Seth? Would old Seth be restored and then carved up, carved up more, or nothing since he’s already carved up? Or if they carved up young Seth in a different fashion, and by different I mean one millimeter different from how young Seth was carved up to begin with, would the timeline unravel? What if they don’t send carved up old Seth but kill him rather than send him back? Timeline unravels because young Seth would no longer be running for his life and wanted by the mob and its enforcers. In all cases, after they carve up young Seth, the timeline would unravel. Thus, young Seth would not be carved up and old Seth would still be healthy and could run away from young Seth causing young Seth to be carved up… You get the idea.
There is a way out of the Grandfather Paradox and that is when the time traveler steps out of the closed timelike curve (or loop), another world line is created that is not casually connected to the old world line. (Click here to read an article in Scientific American about this topic.) But if that were the case, then old Seth would not be carved up magically because young Seth would not be casually connected to old Seth. So, this doesn’t work and there is no easy out for this movie. Physics does not work in the universe of Loopers.
The whole movie was based on either the Grandfather Paradox or the anti-Grandfather Paradox, that is the inverse of the grandfather paradox. The inverse of the Grandfather Paradox is where your future self is in the past changing the future, another type of paradox, a combination of bootstrap and retrocausality, and you stop him by killing yourself. I dub this the anti-Grandfather because rather than your present self going back in time to kill your grandfather, your present self kills your future self by killing himself. (Yes, I coined the term anti-Grandfather Paradox.)
The anti-Grandfather Paradox is used at the end of the movie. The young Joe realizes that the old Seth is the cause of creating the Rainmaker. Old Seth has traveled back in time to keep the Rainmaker from killing his wife by killing the Rainmaker as a child. This is a form of the Grandfather paradox because if Joe’s future wife is not killed, then Joe would not have a reason to go back because the Rainmaker’s thugs would not kill Joe’s future wife and would not force all the looper loops to be closed. (Whew!) Thus, the timeline unravels and Joe would not have a reason to go back in time. Even if his loop is later closed anyway, for whatever reason, old Joe would not have a reason to kill the Rainmaker as a child because the cause of his loop closing would not be the Rainmaker.
But old Joe never kills the Rainmaker as a child because the young Joe realizes that the attentions of the Old Joe is what makes the child the Rainmaker. That is, a nasty, hateful thug. Young Joe thinks, if only old Joe would just leave the kid and his mother alone, the mother might be able to make the child a nice person and a protector of humanity rather than its scourge. So he kills himself and old Joe disappears. The movie is neatly wrapped in a bow. Or maybe not.
If the child never becomes the Rainmaker because his mother is alive and she turns him into a good, loving man by loving him and attending him because she is not killed by old Joe, then once again, there would be no reason for old Joe to travel back in time, nor would his loop be closed, etc. and we would have a paradox and the timeline unravels once anyway. No matter how you slice it, the plot in the movie would unravel because it sets up paradox layered on paradox and any resolution of any of the time loops would cause havoc in the worldline.
Personally, Willis’s unshaved head caused a lot of havoc in the timeline. He allowed the sides to grow in and it is not a good look for him.
So, in conclusion, this movie not only ignores multiple time travel paradoxes, the plot line is completely impossible. Thus the movie could not have ever been written and this worldline would unravel and my post unwrite itself.
Now what was I just saying….? Ah, I was talking about my math studies. Yes, I may not be posting on my blog as much in the future because I am reviewing mathematics. I always felt that I did not get a great grounding in higher mathematics or even in basic mathematics even though I was always in advanced math programs such as Math-X etc. I also want to review logic, reread Church’s thesis, and learn Linear Logic. Thus, I have decided to start from the beginning and relearn math in a more pleasant, less stressful way. I started with basic algebra and have progressed rapidly in the last few weeks. I’ve also been studying general topology and measures. I am interested in metric spaces, manifolds and signed measures. I feel I need to reground myself for my science fiction and fantasy writing. It also makes reading physics articles much easier to read. Plus, it’s a lot of fun. As a friend of mine said to me, it’s certainly not the worst way I could spend my recreational time.