In the very peculiar Doctor Who episode "Joy to the World," the character of Joy Almondo is being controlled by a device inside a briefcase that -- if activated -- will release as much energy as a supernova, destroying the Earth (and the rest of the Solar System). But just at the nick of time, a future version of the Doctor (from exactly one year later) arrives and gives the current Doctor the override code, saving the day.
The question comes up, though, of how the future Doctor knew what the code was. The current Doctor, after all, hadn't known it until he was told. He reasons that during that year, he must have learned the code from somewhere or someone -- but the year passes without anyone contacting him about the briefcase and its contents. Right before the year ends (at which point he has to jump back to complete the loop) he realizes that his surmise wasn't true. Because, of course, he already knew the code. He'd learned it from his other self. So armed with that knowledge, he jumps back and saves the day.
Well, he saves the moment, at least. As it turns out, their troubles are just beginning, but that's a discussion for another time.
A similar trope occurred in the 1980 movie Somewhere in Time, but with an actual physical object rather than just a piece of information. Playwright Richard Collier (played by Christopher Reeve) is at a party celebrating the debut of his most recent play, and is approached by an elderly woman who hands him an ornate pocket watch and says, in a desperate voice, "Come back to me." Collier soon goes back in time by six decades, finds her as a young woman, and they fall desperately in love -- and he gives her the pocket watch. Ultimately, he's pulled back into the present, and his girlfriend grows old without him, but right before she dies she finds him and gives him back the watch, closing the loop.
All of this makes for a fun twist; such temporal paradoxes are common fare in fiction, after all. And the whole thing seems to make sense until you ask the question of, respectively (1) where did the override code originally come from? and (2) who made the pocket watch?
Because when you think about it -- and don't think too hard, because these kinds of things are a little boggling -- neither one has any origin. They're self-creating and self-destroying, looped like the famous Ouroboros of ancient myth, the snake swallowing its own tail.
The pocket watch is especially mystifying, because after all, it's an actual object. If Collier brought it back with him into the past, then it didn't exist prior to the moment he arrived in 1920, nor after the moment he left in 1980 -- which seems to violate the Law of Conservation of Matter and Energy.
Physicists Andrei Lossev and Igor Novikov called such originless entities "djinn particles," because (like the djinn, or "genies," of Arabian mythology) they seem to appear out of nowhere. Lossev and Novikov realized that although "closed timelike curves" are, theoretically at least, allowed by the Theory of General Relativity, they all too easily engender paradoxes. So they proposed something they call the self-consistency principle -- that time travel into the past is possible if and only if it does not generate a paradox.
So let's say you wanted to do something to change history. Say, for example, that you wanted to go back in time and give Arthur Tudor, Prince of Wales some medication to save his life from the fever that otherwise killed him at age fifteen. This would have made him king of England seven years later instead of his younger brother, who would have become the infamous King Henry VIII, thus dramatically changing the course of history. In the process, of course, it also generates a paradox; because if Henry VIII never became king, you would have no motivation to go back into the past and prevent him from becoming king, right? Your own memories would be consistent with the timeline of history that led to your present moment. Thus, you wouldn't go back in time and save Arthur's life. But this would mean Arthur would die at fifteen, Henry VIII becomes king instead, and... well, you see the difficulty.
Lossev and Novikov's self-consistency principle fixes this problem. It tells us that your attempt to save Prince Arthur must have failed -- because we know that didn't happen. If you did go back in time, you were simply incorporated into whatever actually did happen.
Timeline of history saved. Nothing changed. Ergo, no paradox.
You'd think that physicists would kind of go "whew, dodged that bullet," but interestingly, most of them look at the self-consistency principle as a bandaid, an unwarranted and artificial constraint that doesn't arise from the models themselves. Joseph Polchinski came up with another paradoxical situation -- a billiard ball fired into a wormhole at exactly the right angle that when it comes out of the other end, it runs into (and deflects) itself, preventing it from entering the wormhole in the first place -- and analysis by Nobel Prize-winning physicist Kip Thorne found there's nothing inherent in the models that prevents this sort of thing.
Some have argued that the ease with which time travel into the past engenders paradox is an indication that it's simply an impossibility; eventually, they say, we'll find that there's something in the models that rules out reversing the clock entirely. In fact, in 2009, Stephen Hawking famously hosted a time-travelers' party at Cambridge University, complete with fancy food, champagne, and balloons -- but only sent out invitations the following day. He waited several hours, and no one showed up.
That, he said, was that. Because what time traveler could resist a party?
But there's still a lingering issue, because it seems like if it really is impossible, there should be some way to prove it rigorously, and thus far, that hasn't happened. Last week we looked at the recent paper by Gavassino et al. that implied a partial loophole from the Second Law of Thermodynamics -- if you could travel into the past, entropy would run backwards during part of the loop and erase your memory of what had happened -- but it still leaves the question of djinn particles and self-deflecting billiard balls unsolved.
Seems like we're stuck with closed timelike curves, paradoxes notwithstanding.
Me, I think my mind is blown sufficiently for one day. Time to go play with my puppy, who only worries about paradoxes like "when is breakfast?" and the baffling question of why he is not currently getting a belly rub. All in all, probably a less stressful approach to life.
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