Loop the Loop

July 09, 2008

Those of us who were hardcore fans of The X-Files TV series during its nine-season run are waiting with bated breath for the premiere of the new film, The X-Files: I Want to Believe, later this month. Mulder and Scully! Together again! What could be better than that? To tide me over in the interim, I've been combing through my DVDs of the series and revisiting my favorite episodes.

One of those is "Monday," from Season 6 (1999), in which Mulder and Scully are caught in a time loop: the same day repeats itself in an endless cycle. (Yes, just like Bill Murray in Groundhog Day.) There are many different permutations within the time loop, but it's always the same outcome: a bank robbery goes horribly wrong because the robber turns out to have a bomb strapped to his chest. The bank blows up, and everyone dies -- including Mulder and Scully -- until finally there's a permutation in the unfolding chain of events that results in a better outcome. And the time loop is undone.

Time loops are a common trope in science fiction, and they're based on a quirky feature of Einstein's theory of general relativity: a hypothetical permutation of warped spacetime called a closed timelike curve. Under general relativity, it is mathematically possible, at least, to travel in the same direction, always moving forward, and yet still end up right where you began. Time doesn't run backwards; it runs in circles.

Einstein's key insight with general relativity is that acceleration is equivalent to gravity, much like mass and energy are equivalent. So spacetime is curved, not flat. The amount of mass or energy determines the degree of curvature, and the more it curves, the stronger the gravitational pull. Since space and time are one, this means that time can flow at different rates for different observes even if they aren't moving relative to one another (per special relativity). Their respective gravitational fields just need to have different strengths. 

Theoretically, it is possible that if enough mass or energy is present, the fabric of spacetime can curve so much that it literally folds back on itself. The cosmologist Igor Novikov has famously compared time to a river, flowing from the past into the future. General relativity says that this temporal river can speed up or slow down as it "flows" through the universe, thanks to the warping of spacetime.

More rarely, a sort of whirlpool or eddy may form, essentially separating one small piece of time's river from the main flow of events: a closed timelike curve. And a time loop is one specific form a closed timelike curve can take. (*Killjoy mode on*) The catch: it would take an enormous amount of energy to create a closed timelike curve: like, all the energy in the Milky Way galaxy combined, and possibly more besides. That's why these permutations are theoretical. (*Killjoy mode off*)

If Mulder and Scully checked their watches in the middle of their time loop, they would find that time always runs forward, even though they keep ending up right back where (and when) they started. How is this possible? Shouldn't time run backwards -- i.e., rewind -- at some point? Not in this instance. Think of it this way. We perceive the planets in our solar system as moving in elliptical orbits. In fact, they are moving in straight lines, and those lines follow the curvature of spacetime. It's just tough to see that curvature when you're right in the middle of it. In the case of a time loop, spacetime is so dramatically warped that one point in the "future" literally bends backward and touches a specific point in the "past."

Mulder and Scully's predicament is similar to how  computer program will keep looping in on itself until a certain set of predetermined conditions is met. In "Monday," there are many different ways the chain of events can play out, but they always end up back in the same place. Only one variable -- the robber's girlfriend, Pam -- can change the outcome.

Pam is unique, in that she is the only person caught in the loop who is aware of what's going on. (Mulder gradually gets a vague sense of deja vu, but he doesn't actually remember the prior loops.) That's another feature of fictional time loops: in order for the plot to progress and resolve, at least one person has to be aware of the looping events before he or she can change the outcome.

And that's where science fiction departs radically from theoretical physics. In a true closed timelike curve, we could only continually relive the same sequence of events, over and over, without being aware of it. We could not alter the past and/or change the future, because this would violate causality.We can't see light arrive on Earth before the stars emit that light. And we can't learn from an experience that has yet to occur.

In a true closed timelike curve, Mulder and Scully would be trapped permanently in an endless looping cycle where nothing ever changed, and they wouldn't even know it. Sometimes letter-perfect physics makes for rotten television. Thank goodness for artistic license.

Photos: (top) Still from The X-Files: I Want to Believe. Source: IGN. (bottom) Artist's rendition of Earth warping spacetime. Source: Marshall Space Flight Center.

Comments

[Sean Carroll]

I think there are really two different ways to be stuck in a closed timelike curve. One would be if your own worldline were truly closed -- you literally exactly repeated the same events over and over. That is closest to the X-Files/Groundhog Day model, except as you say there are no sneaking suspicions that something funny is happening, and -- more dramatically -- you must always have been on that loop, forever. You don't have any past that preceded your life on the loop; the loop is all there is for you.

The other possibility is to travel on a nearly-closed curve. Then you could enter the loopy region from a well-defined prior existence, and loop around as many times as you like, accumulating time and experience as you go. The trick is that you would see every past copy of yourself pass by -- as well as every future copy! Don't know any movies that use that trick, although there are a couple of famous Heinlein stories.