From Eternity to Here (19 page)

Figure 25:
The gate into yesterday, showing one possible world line. A traveler walks through the front of the gate from the right (a) and appears out the back one day in the past (a‘). The person spends half a day walking around the side of the gate to enter from the front again (b) and reappears one day earlier (b’). Then the person waits a day and enters the back side of the gate (c), emerging from the front one day in the future (c‘).

It sounds magical and wondrous, but all we’ve done is describe a particular sort of unusual spacetime; we’ve identified a set of points in space at unequal times. Nobody is disappearing in any puffs of smoke; from the point of view of any particular observer, their own world line marches uninterruptedly into the future, one second per second. When you look through the gate from the front, you don’t see inky blackness, or swirling psychedelic colors; you see the field on the other side, just as you would if you looked through any other door. The only difference is, you see what it looked like
yesterday
. If you peer around the side of the gate, you see the field today, while peering through the gate gives you a view of one day before. Likewise, if you move around the other side and peer through the gate from the back, you see just the other side of the field, but you see what it will look like tomorrow. There is nothing to stop you from walking through the gate and immediately back again, any number of times you like, or for that matter from standing with one foot on either side of the threshold. You wouldn’t feel any strange tingling sensations if you did so; everything would seem completely normal, except that an accurate fixed clock on one side of you would read one day later than a fixed clock on the other side.

The gate-into-yesterday spacetime clearly contains closed timelike curves. All you have to do is walk through the front side of the gate to go back in time by one day, then walk around the side of the gate back to the front, and wait there patiently. After one day has passed, you will find yourself at the same place and time in spacetime as you were one day earlier (by your personal reckoning)—and of course, you should see your previous self there. If you like, you can exchange pleasantries with your former self, chatting about what the last day was like. That’s a closed timelike curve.

This is where the paradoxes come in. For whatever reason, physicists love to make their thought experiments as violent and deadly as possible; think of Schrödinger and his poor cat.
⁸¹
When it comes to time travel, the standard scenario is to imagine going back into the past and killing your grandfather before he met your grandmother, ultimately preventing your own birth. The paradox itself is then obvious: If your grandparents never met, how did you come into existence in order to go back and kill one of them?
⁸²

We don’t need to be so dramatic. Here’s a simpler and friendlier version of the paradox. You walk up to the gate into yesterday, and as you approach you see a version of yourself waiting for you there, looking about one day older than you presently are. Since you know about the closed timelike curves, you are not too surprised; obviously you lingered around after passing through the gate, looking forward to the opportunity to shake hands with a previous version of yourself. So the two versions of you exchange pleasantries, and then you leave your other self behind as you walk through the front of the gate into yesterday. But after passing through, out of sheer perverseness, you decide not to go along with the program. Rather than hanging around to meet up with your younger self, you wander off, catching a taxi to the airport and hopping on a flight to the Bahamas. You never do meet up with the version of yourself that went through the gate in the first place. But that version of yourself did meet with a future version of itself—indeed, you still carry the memory of the meeting. What is going on?

ONE SIMPLE RULE

There is a simple rule that resolves all possible time travel paradoxes.
⁸³
Here it is:

• Paradoxes do not happen.

It doesn’t get much simpler than that.

At the moment, scientists don’t really know enough about the laws of physics to say whether they permit the existence of macroscopic closed timelike curves. If they don’t, there’s obviously no need to worry about paradoxes. The more interesting question is, do closed timelike curves
necessarily
lead to paradoxes? If they do, then they can’t exist, simple as that.

But maybe they don’t. We all agree that logical contradictions cannot occur. More specifically, in the classical (as opposed to quantum mechanical
⁸⁴
) setup we are now considering, there is only one correct answer to the question “What happened at the vicinity of this particular event in spacetime?” In every part of spacetime, something happens—you walk through a gate, you are all by yourself, you meet someone else, you somehow never showed up, whatever it may be. And that something is whatever it is, and was whatever it was, and will be whatever it will be, now and forever. If, at a certain event, your grandfather and grandmother were getting it on, that’s what happened at that event. There is nothing you can do to change it, because it happened. You can no more change events in your past in a spacetime with closed timelike curves than you can change events that already happened in an ordinary, no-closed-timelike-curves spacetime.
⁸⁵

It should be clear that consistent stories are
possible
, even in spacetimes with closed timelike curves. Figure 25 depicts the world line of one intrepid adventurer who jumps back in time twice, then gets bored and jumps forward once, before walking away. There’s nothing paradoxical about that. And we can certainly imagine a non-paradoxical version of the scenario from the end of the previous section. You approach the gate, where you see an older version of yourself waiting for you there; you exchange pleasantries, and then you leave your other self behind as you walk through the front of the gate into yesterday. But instead of obstinately wandering off, you wait around a day to meet up with the younger version of yourself, with whom you exchange pleasantries before going on your way. Everyone’s version of every event would be completely consistent.

We can have much more dramatic stories that are nevertheless consistent. Imagine that we have been appointed Guardian of the Gate, and our job is to keep vigilant watch over who passes through. One day, as we are standing off to the side, we see a stranger emerge from the rear side of the gate. That’s no surprise; it just means that the stranger will enter (“has entered”?—our language doesn’t have the tenses to deal with time travel) the front side of the gate tomorrow. But as you keep vigilant watch, you see that the stranger who emerged simply loiters around for one day, and when precisely twenty-four hours have passed, walks calmly through the front of the gate. Nobody ever approached from elsewhere—the entering and exiting strangers formed a closed loop, and that twenty-four hours constituted the stranger’s entire life span. That may strike you as weird or unlikely, but there is nothing paradoxical or logically inconsistent about it.
⁸⁶

The real question is, what happens if we try to cause trouble? That is, what if we choose not to go along with the plan? In the story where you meet a slightly older version of yourself just before you cross through the front of the gate and jump backward in time, the crucial point is that you seem to have a
choice
once you pass through. You can obediently fulfill your apparent destiny, or you can cause trouble by wandering off. If that’s the choice you make, what is to stop you? That is where the paradoxes seem to get serious.

We know what the answer is: That can’t happen. If you met up with an older version of yourself, we know with absolute metaphysical certainty that once you age into that older self, you will be there to meet with your younger self. Imagine that we remove messy human beings from the problem by just considering simple inanimate objects, like series of billiard balls passing through the gate. There may be more than one consistent set of things that could happen at the various events in spacetime—but one and only one set of things will actually occur.
⁸⁷
Consistent stories happen; inconsistent ones do not.

ENTROPY AND TIME MACHINES

The issue that troubles us, when we get right down to it, isn’t anything about the laws of physics; it’s about free will. We have a strong feeling that we can’t be predestined to do something we choose not to do; that becomes a difficult feeling to sustain, if we’ve already seen ourselves doing it.

There are times when our free will must be subjugated to the laws of physics. If we get thrown out of a window on the top floor of a skyscraper, we expect to hurtle to the ground, no matter how much we would rather fly away and land safely elsewhere. That kind of predestination we’re willing to accept. But the much more detailed kind implied by closed timelike curves, where it seems that the working out of a consistent history through spacetime simply forbids us from making free choices that would otherwise be possible, is bothersome. Sure, we could be committed determinists and imagine that all of the atoms in our bodies and in the external world, following the unbending dictates of Newton’s laws of motion, will conspire to force us to behave in precisely the required way in order to avoid paradoxes, but it seems somewhat at variance with the way we think about ourselves.
⁸⁸

The nub of the problem is that you can’t have a consistent arrow of time in the presence of closed timelike curves. In general relativity, the statement “We remember the past and not the future” becomes “We remember what happened within our past light cone, but not within our future light cone.” But on a closed timelike curve, there are spacetime events that are both in our past light cone and in our future light cone, since those overlap. So do we remember such events or not? We might be able to guarantee that events along a closed timelike curve are consistent with the microscopic laws of physics, but in general they cannot be compatible with an uninterrupted increase of entropy along the curve.

To emphasize this point, think about the hypothetical stranger who emerges from the gate, only to enter it from the other side one day later, so that their entire life story is a one-day loop repeated ad infinitum. Take a moment to contemplate the exquisite level of precision required to pull this off, if we were to think about the loop as “starting” at one point. The stranger would have to ensure that, one day later, every single atom in his body was in precisely the right place to join up smoothly with his past self. He would have to make sure, for example, that his clothes didn’t accumulate a single extra speck of dust that wasn’t there one day earlier in his life, that the contents of his digestive tract was precisely the same, and that his hair and toenails were precisely the same length. This seems incompatible with our experience of how entropy increases—to put it mildly—even if it’s not strictly a violation of the Second Law (since the stranger is not a closed system). If we merely shook hands with our former selves, rather than joining up with them, the required precision doesn’t seem quite so dramatic; but in either case the insistence that we be in the right place at the right time puts a very stringent constraint on our possible future actions.

Our concept of free will is intimately related to the idea that the past may be set in stone, but the future is up for grabs. Even if we believe that the laws of physics in principle determine the future evolution of some particular state of the universe with perfect fidelity, we don’t know what that state is, and in the real world the increase of entropy is consistent with any number of possible futures. The kind of predestination seemingly implied by consistent evolution in the presence of closed timelike curves is precisely the same we would get into if there really were a low-entropy future boundary condition in the universe, just on a more local scale.

In other words: If closed timelike curves were to exist, consistent evolution in their presence would seem just as strange and unnatural to us as a movie played backward, or any other example of evolution that decreases entropy. It’s not impossible; it’s just highly unlikely. So either closed timelike curves can’t exist, or big macroscopic things can’t travel on truly closed paths through spacetime—or everything we think we know about thermodynamics is wrong.

PREDICTIONS AND WHIMSY

Life on a closed timelike curve seems depressingly predestined: If a system moves on a closed loop along such a curve, it is required to come back to precisely the state in which it started. But from the point of view of an observer standing outside, closed timelike curves also raise what is seemingly the opposite problem: What happens along such a curve cannot be uniquely predicted from the prior state of the universe. That is, we have the very strong constraint that evolution along a closed timelike curve must be consistent, but there can be a large number of consistent evolutions that are possible, and the laws of physics seem powerless to predict which one will actually come to pass.
⁸⁹