Thursday, August 16, 2012

Sealing Up Time

"But I thoughtwhat about changing your own past?  What about the paradoxes?"

Dr. Vanner pursed her lips.  "Yes, I wondered about that too."

"So what happens if I shoot my grandfather?  Not that I would, but I could."

"Well, Jason, it turns out that's a bit of an interesting question, whether you could or not.  But grandfathers are very large, complicated things.  People are always trying to figure out how time travel could possibly work with grandfathers, and bullets, and messy macroscopic objects like that.  It's easier just to deal with simple particles first.  You figure out the particles, the grandfathers take care of themselves."


"Well, grandfathers are made out of particles, aren't they?"

"I guess that's one way to think of them."

"You know, I had a grandfather too."  Dr. Vanner smiled warmly.  "Anyway, I think the best way to answer your question is by way of example.  Say you're a particle.  An electron.  You didn't come from nowhere, you started out as a muon.  But muons don't live very long; they decay in a few microseconds to yield a couple of neutrinos, and you."  She sketched on the board as she spoke.

"Meoh right, I'm an electron."

"That's right.  Now you, as an electron, can live essentially forever.  You step into the time machine (or a smaller version of it), and you go back in time.  Just a little bit: say, a microsecond."

"Ahh, I think I see where you're going.  I'm going to bump the muon just enough so that it decays somewhere else, and even if it decays into me, I'm nowhere near the time machine to go back in time.  Paradox."

"Exactly.  So what's the resolution?  The resolution is that particles aren't billiard balls.  As an electron, you don't really bump into the muon.  You 'interact' with it."

"What difference does that make?"

"The difference is that the interaction has a random element.  If I hit a cue ball into another billiard ball in the same exact way, over and over again, both balls will go off in the same directions, over and over again.  It's predictable, deterministic.  That's why you can have expert billiard players.  But subatomic particles aren't the same way.  They can hit in exactly the same way, as far as we can tell, but the results may be completely different from one time to the next.  There are no expert electron players.

"And that's the key.  There's going to be one way or another that you could end up hitting that muon that will end up with it decaying into you at the right place at the right time.  Maybe you give it an extra nudge, and it goes a bit faster in the same direction, but it decays sooner than it would have.  Maybe it goes off in a different direction, but when it decays into you, you still end up heading toward the time machine."

"But if there's so many different ways it can happen, which one actually does happen?"

"That's a complicated question.  The simplest way I can think of to understand it is to imagine the universe as a kind of simulation.  If we conduct an ordinary quantum-mechanical experiment, there's a certain probability that the experiment will end up one way, and the rest of the time, it ends up another way.  It can do that because the experiment is anchored on only one end: the start.

"But in the time travel case, it's actually anchored on both ends.  When you the electron exist at a particular time and place, there's an anchor at that point.  The universe is in a more or less definitive state at that point.  Normally, that's the only anchor.  But in this case, when you travel back in time, there's a second anchor, in that we know you have to end up back (or should I say 'forward'?) in the time machine.  In between, nearly anything can happen—subject to the laws of physics.

"So imagine that the universe runs a simulation.  How many different ways can you start at the first anchor point, and end up at the second anchor point?  Which ones are most likely, when you adhere to the laws of physics?  We don't even know which ones are most likely beforehand, except in the very simplest of cases."

"So as an electron, I end up taking the most likely path back to the time machine?"

"No, not quite.  If the chances of you taking that path are three in five, then three times out of five, that's the path you'll take.  Or you could end up taking a once-in-a-million path (like bouncing off of three other particles before entering the time machine); it's just that you only have a one-in-a-million chance of doing that."

"But I always end up back in the time machine."

"That's right."

"But then it sounds like I can't ever change anything.  If the universe is anchored on both ends, what point is there in going back in time?"

"Very good question!  The point is that the second anchor point is not a 'complete' anchor point.  The first point is.  It covers the whole universe.  But the second anchor point only consists of you.  The only thing that's required is that youthe original you, remember, not the one that goes back in timeyou have to end up in the time machine.  Everything else can change."

"Wait a minute.  So forget about me being an electron and everything.  I'm me, Jason Sawyer.  I enter the time machine, and I go back a day or so.  I could see anything.  I could see methe original me.  And anything might happen, but in a day or so, that original me has to end up getting into that same time machine.  But everything else could change.  I might forget to do yardwork that I actually did earlier today.  When Ithe time-traveller mecatches back up to this present, I would know that the yardwork didn't get done.  But if you were watching, you'd all of a sudden see the leaves suddenly strewn across the yard, instead of put away in the yard trash?"

"Not quite.  Remember, when you rake the leaves, it affects more than just the leaves.  If I were watching and the leaves never got done, I'd never have any memory of the leaves being in the trash, would I?  So in fact, yes, the leaves would still be on the ground, but it wouldn't look to me like they suddenly appeared on the lawn.  In my brain, there would be lost any impression that the leaves were ever raked in the first place.  At least, I assume that's the most probable outcome.  There are all sorts of other outlandish possibilities that are more drastic but which I probably wouldn't have to worry about."

"All right, forget about the trash.  What about if I went back, really far back, far back enough to...well, let's not say I shot my grandfather, but I somehow set him up with someone other than my grandmother.  How can I possibly end up in the time machine then?"

"Hmm, let's think..."  Dr. Vanner considered this.  "OK, well, how well did you know your grandfather?"

"Huh?  Uhh, kind of?  Ihe died when I was eight.  How does that matter?"

"It matters because it's not sufficient that you end up in the time machine.  You also have to end up going into the time machine in a state that's sufficiently 'consistent' (in a technical sense) with the way you ended up going into it 'the first time.'  And that state includes your brain: everything you remember and know about yourself and your experiences.

"So what happens?  You obviously have to go into the time machine.  So somehow, some collection of particles comes together to form you.  The way it actually happened is just one possibility: Your parents conceive you, and you start out as a small number of particles.  Over time, you take on some particles, and lose some other particles, and eventually, grow up to be who you are today.

"Now one other possibility is that somewhere, near here, just a few moments ago, a collection of particles just randomly happened to show up to make...well, you, but including all the memories you currently have (which would, in that case, be completely fictional).  In a classical world, that's impossible.  In a quantum-mechanical world, it's merely improbablealthough we're talking really, really improbable.  Like you could run the universe a googol times and it wouldn't even come close to happening.  Still, it's possible.  And because by setting your grandfather up with someone other than your grandmother, you've already eliminated a bunch of probable outcomes that end up with you in the time machine, all the improbable options get a boost, so to speak.  As Sherlock Holmes said, 'When you have eliminated the impossible, whatever remains, however improbable, must be the truth.'  In this case, by setting up your grandfather on a date, you've made certain options impossible, and they're eliminated.  More than one path remainsall of them improbable a priori, perhapsbut one of them has to happen, in order for you to get back in that time machine.  The option of just a bunch of particles coming together to make a fully-formed you is always available.  If nothing is left besides that, then that's what'll happen.  In this case, though, I bet something else is more likely than that."

"Like what?"

"Like...suppose that after you set up your grandfather with someone else, you go off to visit the world.  You're not going to hang out with him forever, do you?  So after you leave him, suppose he breaks it off with the other person, and gets back with your grandmother.  And everything else happens more or less the same, so far as producing you is concerned.  His life history would be a bit different, but not in ways that are really all that critical.  That's why I asked you how well you knew him.  Do you know who he was with before he met your grandmother?"

"Hmm...not really."

"Exactly.  Remember, what happens to everyone else can change, but you have to stay more or less the same.  So my guess is that the most probable outcome is that his life would change in ways that you never knew about in the first place, so that when you go into the time machine 'the second time,' whatever you knew about your grandfather the first time remains true."

"Whoa.  Wait.  That means that I have...I can't really change too much about the people that I know really well.  Like Mom, Dad, my sister, and even you a little bit.  But, everything else and everyone else could change drastically?  Maybe I'd go back, and as a result of my getting my grandfather to go out on even one date with someone different, I still come back with the rest of my family, butoh, let's just sayno World War II, ever?"

"Well, that's possible, but still unlikely, even after you eliminate the impossible.  Remember that World War II wasn't started by just one thing.  There were triggers, but there were broad forces too that were behind it.  The second anchor, and the fact that what happens is likely the most probable thing, means that the whole 'butterfly effect' thing is not as chaotic as one might think.  Just setting up your grandfather on one date is unlikely to reset all of world history.  In order to change that, you'd probably have to go back quite a bit further in time.

"Also, by the way, keep in mind that your time-traveled self is still aging.  If you go back far enough to set up your grandfather on a date, by the time you get back here to 2027, you'll probably be about as old as your grandfather would have been today.  That's assuming you make it all the way back.  There's no guarantee of that."

"Wait, I thought I had to get back.  To get into the time machine."

"No, remember, that's the original you who has to do that, not the time-traveled you."

Jason hesitated for a second.  "Right," he said finally.  "It's very confusing.  And it's weird to think that the results of going back in time are so intimately connected with me.  I can change really distant things a lot, but everything I know well is savedat least to the degree that I know them.  How is that possible?  I mean, this machine doesn't know a thing about me."

"It doesn't know it in the usual sense, Jason, but when you enter it and go back in time, it knows everything about your current state, at the moment you go back.  It fixes it.  That's the second anchor.  The thing that makes all the other changes possible is that it is only you who is anchored in time and space.  Everything else is floating partly freeand the less you know about them, the freer they are.  Even me, to a point.  Although I still have to be able to invent the machine.  So I feel pretty safe, especially if I know the person well who's traveling in it."

"Why don't you get into it?"

Dr. Vanner looked for a moment as though she were going to answer that.  "II can't explain that to you yet," she said finally.  "You'll have to take my word for it that there's a good reason for me not to get into it."

"Hmm, OK."  Jason looked thoughtful again.  "All right, one more question.  Suppose I do something really drastic.  I shoot myself before I get into the machine.  Or I do something really memorable to myself, something that didn't happen the first time.  How can Ithe original meend up back in this time machine in a...what did you call it?"

"A consistent state."

"Yeah, that."

"Well, there's a limit to how reliable our senses are.  How do you know you didn't already go back in time and make a big noise in front of yourself?  Because you don't remember it.  But what makes you so sure that it didn't happen?  Is your memory that reliable?  There must have been some things that have happened that you don't remember.  Normally, it's because those things happened so far in the past that the memory has faded.  We have the notion that the memory is still there, locked inside us somewhere, that we just can't find it.  But what if the memory really went away?  My guessalthough I really don't know, I haven't tested itis that you'd just lose all memory that it happened."

"Weird.  But what if I shot myself?"

"That depends.  Maybe the shot misses, even though you think you hit yourself?  Maybe you miraculously heal in seconds?  Those sound ridiculously improbable, but you've already eliminated as impossible all the normal paths, so the truth must be something outlandish.  Even if you stay to watch yourself die, at some point, your body, reasonably healthy, must make its way into the time machine.  In that case, you might very well see your dead body vanish in front of your eyes, just in time to make it into the time machine at the right moment.  Again, impossible in the classical world, but possible in the quantum-mechanical world, andif you've already eliminated everything elseeven, in a sense, inevitable in that world."

"So the original me is immortal."

"The original you, yes," agreed Dr. Vanner.  "But only up to the point you get in that machine.  From that point on, that you vanishes, and the time-traveled you reappears at some point further back in time.  And that you is vulnerable.  Anything at all could happen to that you."

Excerpt from "Time Binder" copyright (c) 2012 Brian Tung

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