Djinn and paradox

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. 

[Image is in the Public Domain]

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.

****************************************

Reversing the arrow

In my short story "Retrograde," the main character, Eli, meets a woman who makes the bizarre claim that she experiences time running backwards.

She's not like Benjamin Button, who ages in reverse; she experiences everything in reverse.  But from our perspective, nothing seems amiss.  From hers, though... she remembers future events and not past ones:

Hannah gave him a long, steady look.  "All I can say is that we see the same things.  For me, the film runs backwards, that’s all.  Other than that, there’s no difference.  There’s nothing I can do to change the way things unfold, same as with you."

"That’s why you were crying when I came in.  Because of something that for you, had already happened?  What was it?"

She shook her head.  "I shouldn’t answer that, Eli."

"It’s me, isn’t it?  For me, I was just meeting you for the first time.  For you, it was the last time you’d ever see me."  I winced, and rubbed my eyes with the heel of my hand.  "Jesus, I’m starting to believe you.  But that’s it, right?"

Hannah didn’t answer for a moment.  "The thing is—you know, you start looking at things as inevitable.  Like you’re in some sort of film.  The actors seem to have freedom.  They seem to have will, but in reality the whole thing is scrolling by and what’s going to happen is only what’s already written in the script.  You could, if you wanted to, start at the end and run the film backwards.  Same stuff, different direction.  No real difference except for the arrow of time."

Einstein's General Theory of Relativity shows that space and time are inextricably linked -- spacetime -- but doesn't answer the perplexing question of why we can move in any direction through space, but only one direction through time.  You can alter the rate of time's passage, at least relative to some other reference frame, by changing your velocity; but unlike what the characters in "Retrograde" experience, the arrow always points the same way.  

This becomes odder still when you consider that in just about all physical processes, there is no inherent arrow of time.  Look at a video clip of a pool ball bouncing off the side bumper, then run it backwards -- it'd be damn hard to tell which was the actual, forward-running clip.

Hard -- but not impossible.  The one physical law that has an inherent arrow of time is the Second Law of Thermodynamics.  If the clip was long enough, or your measurement devices sensitive enough, you could tell which was the forward clip because in that one, the pool ball would be slowing down from dissipation of its kinetic energy in the form of friction with the table surface.  Likewise, water doesn't unspill, glasses unbreak, snowbanks un-avalanche, reassembling in pristine smoothness on the mountainside.  But why this impels a universal forward-moving arrow of time -- and more personally, why it makes us remember the past and not the future -- is still an unanswered question.

"The arrow of time is only an illusion," Einstein quipped, "but it is a remarkably persistent one."

Two recent papers have shed some light on this strange conundrum.  In the first, a team led by Andrea Rocco of Surrey University looked how the equations of the Second Law work on the quantum level, and found something intriguing; introducing the Second Law into the quantum model generated two arrows of time, one pointing into the past and one pointing into the future.  But no matter which time path is taken, entropy still increases as you go down it.

"You’d still see the milk spilling on the table, but your clock would go the other way around," Rocco said.  "In this way, entropy still increases, but it increases toward the past instead of the future.  The milk doesn’t flow back into the glass, which the Second Law of Thermodynamics forbids, but it flows out of the glass in the direction of the past.  Regardless of whether time’s arrow shoots toward the future or past from a given moment, entropy will still dissipate in that given direction."

In the second, from Lorenzo Gavassino of Vanderbilt University et al., the researchers were investigating the mathematics of "closed time-like loops" -- i.e., time travel into the past, followed by a return to your starting point.  And what they found was that once again, the Second Law gets in the way of anything wibbly-wobbly.

Gavassino's model shows that on a closed time-like loop, entropy must peak somewhere along the loop -- so along some part of the loop, entropy has to decrease to return it to where it was when the voyage began.  The equations then imply that one of two things must be true.  Either:

1. Time travel into the past is fundamentally impossible, because it would require entropy to backpedal; or
2. If overall entropy can decrease somewhere along the path, it would undo everything that had happened along the entropy-increasing part of the loop, including your own memories.  So you could time travel, but you wouldn't remember anything about it (including that it had ever happened).

"Any memory that is collected along the closed time-like curve," Gavassino said, "will be erased before the end of the loop."

So that's no fun at all.  Lieutenant Commander Geordi LaForge would like to have a word with you, Dr. Gavassino.

Anyhow, that's today's excursion into one of the weirdest parts of physics.  Looks like the Second Law of Thermodynamics is still strictly enforced in all jurisdictions.  Time might be able to run backwards, but you'd never know because (1) entropy will still increase in that direction, and (2) any loop you might take will result in your remembering nothing about the trip.  So I guess we're still stuck with clocks running forwards -- and having to wait to find out what's going to happen in the future at a rate of one minute per minute.

****************************************