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.

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