Update 03/01: Having wrapped your head around the grandfather paradox, let me melt your brain with another time travel paradox in this last post of the time travel trilogy!
My girlfriend and I recently watched the 1980s classic Somewhere in Time. It’s a wonderfully old-fashioned romance with an enchanting score by John Barry, starring the late Christopher Reeve (you know, the guy from Superman). Although we found the movie a bit too sentimental, clichéd and corny at times, I really enjoyed watching it, and I must confess the story has haunted me ever since . . .
The story begins in May 1972. Richard Coller (played by Christopher Reeve) is a young Chicago playwright. On the opening première of his first play, he’s approached by an old and mysterious woman. She presses a beautiful pocket watch in his hand, and begs him to “come back to me”! Mystified, Richard sets out on an investigation and discovers that the old lady, Elise McKenna, used to be a famous actress in the early 1900s. Upon seeing a portrait of Elise as a young woman (played by the gorgeous Jane Seymour), Richard falls in love. His obsession for her quickly grows, and Richard finally seeks the help of an old philosophy teacher, who tells him how to travel back in time to meet the young Elise.
The time travel method (although scientifically highly implausible) is pretty straight-forward and relies on a special kind of self-hypnosis. All Richard needs to do, is to isolate himself in a room, and remove all the modern-day objects around him that would otherwise remind him of the present. He dresses up in period costume, lies on his bed, and starts chanting that he is in the year 1912, until — as if by sheer magic — Richard is transported to that particular moment, right into the life of the young and radiant Elise McKenna.
One hour of romantic scenes later (I spare you the details), Richard and Elise are happily together in their bedroom. Elise, wondering what time it is, takes Richard’s pocket watch from the floor and checks. Meanwhile, Richard has grabbed his jacket, and feels something in his inner pocket. It turns out to be a coin from 1972 . . . He has made a mistake! A second later, Richard is abruptly returned to 1972, and wakes up in the same bed that originally transported him to the past, leaving the young Elise in terror behind. Music up, credits roll.
The story is perfectly self-consistent. There are no grandfather paradoxes since Richard doesn’t try to alter the past, but merely fulfills it by meeting Elise in the past and by giving her the pocket watch. But here’s the question that has haunted me ever since: where did the pocket watch come from?!
If you would consider the clock’s worldline (the path it traces in both space and time, making up its history) it would form a closed loop, much like a hula hoop, where Elise “first” got the watch from Richard in 1912, and then returned it to Richard in 1972, such that he could give it back to her in 1912. Such mysterious worldlines are called closed timelike curves or CTCs for short. But this implies that the watch exists without ever having been created!
Ascending and Descending
Perhaps the following analogy will help. The pocket watch can be likened to the monks in Escher’s famous litograph Ascending and Descending. As Escher commented: “It may be part of [the monks’] daily ritual duty to ascend the stairway in a clockwise direction during certain hours. When they are tired, they can change direction and descend for a while. But both motions, though not without an abstruse meaning, are equally useless.”
For each monk, locally, it is clear who is ahead of him and who is behind. But globally, since the monks are walking on a never-ending circular staircase, it’s absolutely impossible to tell which monk came “first” and which one came “last.” The same problem would occur if you were to travel along a closed timelike curve. Locally, the future would always be “ahead” of you, and the past “behind” you, but globally, every event would be in both the past and the future of every other event; there would no longer be a “first” or “last” event.
This lack of a “first” and “last” event is something we’re not familiar with. Just like stairs have a clear beginning and end, clocks normally have worldlines that are nearly vertical, with a clear beginning in the past (the point where they were first manufactered in the factory) and a clear end in the future (the point where they fell on the ground and shattered into bits and pieces). In Richard and Elise’s case, in contrast, the pocket watch is traveling along a CTC and therefore lacks any beginning or end; it thus seems to have appeared out of the blue, creatio ex nihilo.
The Quantum Mechanics of Creatio ex Nihilo
You might wonder at this point whether objects really can emerge out of the blue. Can one get something from nothing? After all, there’s no such thing as a free lunch, they say. Yet the laws of quantum mechanics do allow a particle (and its corresponding antiparticle) to be created out of nothing (what we, scientists, call the vacuum). Creating an electron (and its antiparticle, the positron) for example is pretty simple in this way. But creating an entire pocket watch would be extremely unlikely, making it highly improbable that we will ever encounter a pocket watch like the one in Somewhere in Time in our own universe.
The Jinn of the Time Machine
In October 1992, the Russian time travel pioneer, Igor Novikov (whom we already met in my previous post) and his colleague Andrei Lossev, published an important paper in the journal Classical and Quantum Gravity. The purpose of their paper was to discuss the paradoxical nature of objects along CTCs (like the watch from Somewhere in Time). They decided to name such objects jinn (also spelled djinn) from the Arabic word for a spirit or genie. After all, much like Aladdin’s genie, who was unleashed by rubbing a magical oil lamp, the pocket watch too, seems to have been created by pure magic (or should I say love?).
Here’s the problem Novikov and Lossev considered. Let's say the watch somehow got into self-existence. Now, recall that Elise received the watch in 1912, and only returned it to Richard in 1972. Surely, in the intervening 60 years, the watch must have accumulated quite a lot of wear-and-tear: a scratch here and there, perhaps a crack in the glass or a dent in the golden frame. But how then is Richard ever going to give back the original watch to Elise? In 1912, the watch was still in mint condition, but here he is in 1972 with an old and broken pocket watch! Clearly then, while Richard travels back to 1912 — thus closing the timelike loop — the watch must somehow get repaired in order to return to its original state.
Violating the Second Law of Thermodynamics
But this scenario goes against the infamous Second Law of Thermodynamics which (roughly) says that everything deteriorates and breaks down, and that eventually everything must die. More scientifically, it states that the entropy of an isolated system — which is a measure for the “disorder” or “randomness” of a system — will always increase over time. As time unfolds, our Universe gets more chaotic, not more orderly. In mathematical notation:
Here’s a simple example: pour some milk in your cup of coffee, and then try to un-mingle them by swirling the liquid with your spoon. It won’t work! You can’t undo the original mixing. In a similar sense, eggs fall and shatter like Humpty Dumpty, but the reverse will never happen. We are all born young and healthy and grow old and wrinkled, never the other way around (except for Benjamin Button).
OK, I hope you got the idea! But now consider the jinni watch again, which behaves exactly like Benjamin Button. It’s as if the watch can reverse the arrow of time, and “grow young” again. The only sensible way in which this is possible, is if the watch had access to some external source of energy to make the necessary repairs.
It’s really no different with my office desk. At the end of the semester, my desk always looks messy and cluttered, because its entropy spontaneously increases over time! (At least, that’s the excuse I always use.) Now, since desks don’t naturally return to their ordered state (as this would violate the Second Law), I have to invest energy in the cleanup of my desk.
But whereas such entropy-lowering processes are theoretically possible, they are highly unlikely to occur spontaneously. The more energy that is required, the more improbable they become. Bringing a 1972 watch back to its original state of 1912 — and by this I mean, identical atom by atom to the original — would require a gargantuan amount of energy.
It thus seems extremely unlikely that we'll ever encounter a jinni watch in our Universe, both because of the quantum mechanics of particle-antiparticle creation (see above) and because of the Second Law of Thermodynamics. A jinni electron or a jinni positron, on the other hand, might well pop-up in our Universe from time to time.
The Unproven Theorem Paradox
But a jinni doesn’t always have to be a material object. Novikov and Lossev distinguished between two kinds of jinn: the (material) pocket watch from Somewhere in Time is a jinni of the first kind. A jinni of the second kind, in contrast, would consist of pure information.
Consider the following scenario: On one of your weekly visits to the library, you borrow Einstein’s book The Meaning of Relativity. Spellbound by its content, you jump in your time machine and flash back to the year 1900, where you meet Einstein in his favourite coffee house. Excited, you tell him what a great scientist he will become, but Einstein looks rather puzzled.
Luckily you took the book with you to show him. Intrigued, Einstein slowly thumbs through the pages, and gets inspired. As you return with the book to your present, Einstein eagerly starts working and ultimately writes The Meaning of Relativity which had inspired him in the first place.
But then, who came up with the special theory of relativity? The truth is, it emerged from nowhere! This is the unproven theorem paradox (or information paradox because the information concerning Einstein's theory doesn't have a discernible origin).
The original version of the paradox goes something like this: let’s say you wanted to impress your girlfriend or boyfriend this year by proving a truly horribly complicated theorem. Now, given your limited skills at math, and the fact that Valentine’s Day is rapidly approaching, chances are slim you'll come up with a clever solution in time. So instead, you build a time machine and flash forward to the future. You get to the nearest library, google your name, and to your big surprise, retrieve a paper in which you proved the theorem. You bring it back to 2015, wrap it in some Valentine gift paper, and voila, there's your proof! Having successfully impressed your girlfriend/boyfriend, you submit the paper to the journal in which you originally found the paper, and your job is done. But who proved the theorem? The answer, once again, is no one!
As for my last example, let's do the nasty in the pasty (with thanks to Sandra, Greg and Karen for a literally mind f*cking discussion in Café Noir). I'll assume for this example that you're of the male sex. Let's say you traveled to the not-too-distant-past and met a really cute girl, with whom you eventually end up in bed. Of course, the girl will later turn out to be your own mother! [I know, it's already bad enough to contemplate your parent's love life, let alone to imagine yourself as a participant, but bear with me for a few more lines.] Nine months later, a little boy is born, who turns out to be — you already guessed it — yourself! Awkward! You've accidentally become your own father!!
This (admittedly rather twisted) scenario is only possible if 50% of your DNA is coming from your mother, and the other 50% is jinni DNA that magically came into self-existence and that is continuously traveling back and forth between the past and the future in a closed timelike loop (see my amateurish sketch above). Of course, the real moral of the story is to always wear a condom! Especially when you're time traveling!
Challenge: Can you think of a possible way to resolve the unproven theorem paradox? I’m looking backward to your comments!
Toomey, D. The New Time Travelers. New York: W. W. Norton & Company, 2007.
Everett, A. and Roman, T. Time Travel and Warp Drives: A Scientific Guide to Shortcuts through Time and Space. Chicago: The University of Chicago Press, 2012.
Gott III, J. R. Time Travel in Einstein's Universe: The Physical Possibilities of Travel Through Time. London: Weidenfeld & Nicolson, 2001.
Novikov, I. D. and Lossev, A. "The Jinn of the Time Machine: Nontrivial Self-Consistent Solutions." Classical and Quantum Gravity 9, no. 10 (1992): 2309-2321.