People all have their own ideas of what a time machine would look like. If you are a fan of the 1960 movie version of H. G. Wells’s classic novel, it would be a steampunk sled with a red velvet chair, flashing lights, and a giant spinning wheel on the back. For those whose notions of time travel were formed in the 1980s, it would be a souped-up stainless steel sports car. Details of operation vary from model to model, but they all have one thing in common: When someone actually travels through time, the machine ostentatiously dematerializes, only to reappear many years in the past or future. And most people could tell you that such a time machine would never work, even if it looked like a DeLorean.
They would be half right: That is not how time travel might work, but time travel in some other form is not necessarily off the table. Since time is kind of like space (the four dimensions go hand in hand), a working time machine would zoom off like a rocket rather than disappearing in a puff of smoke. Einstein described our universe in four dimensions: the three dimensions of space and one of time. So traveling back in time is nothing more or less than the fourth-dimensional version of walking in a circle. All you would have to do is use an extremely strong gravitational field, like that of a black hole, to bend space-time. From this point of view, time travel seems quite difficult but not obviously impossible.
These days, most people feel comfortable with the notion of curved space-time. What they trip up on is actually a more difficult conceptual problem, the time travel paradox. This is the worry that someone could go back in time and change the course of history. What would happen if you traveled into the past, to a time before you were born, and murdered your parents? Put more broadly, how do we avoid changing the past as we think we have already experienced it? At the moment, scientists don’t know enough about the laws of physics to say whether these laws would permit the time equivalent of walking in a circle—or, in the parlance of time travelers, a “closed timelike curve.” If they don’t permit it, there is obviously no need to worry about paradoxes. If physics is not an obstacle, however, the problem could still be constrained by logic. Do closed timelike curves necessarily lead to paradoxes?These days, most people feel comfortable with the notion of curved space-time. What they trip up on is actually a more difficult conceptual problem, the time travel paradox. This is the worry that someone could go back in time and change the course of history. What would happen if you traveled into the past, to a time before you were born, and murdered your parents? Put more broadly, how do we avoid changing the past as we think we have already experienced it? At the moment, scientists don’t know enough about the laws of physics to say whether these laws would permit the time equivalent of walking in a circle—or, in the parlance of time travelers, a “closed timelike curve.” If they don’t permit it, there is obviously no need to worry about paradoxes. If physics is not an obstacle, however, the problem could still be constrained by logic. Do closed timelike curves necessarily lead to paradoxes?
If they do, then they cannot exist, simple as that. Logical contradictions cannot occur. More specifically, there is only one correct answer to the question “What happened at the vicinity of this particular event in space-time?” Something happens: You walk through a door, 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, once 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 space-time with closed timelike curves than you can change events that already happened in ordinary space-time, with no closed timelike curves.
As we will see, the time travel paradox—the possibility of changing our past—seems intractable only because it conflicts with our notion of ourselves as beings with free will. Consistent stories are possible, even in space-times with closed timelike curves.
To illustrate this point, imagine that you stumble upon a time machine in the form of a gate. When you pass through it in one direction, it takes you exactly one day into the past; if you pass through in the other direction, it takes you exactly one day into the future. You walk up to the gate, where you see an older version of yourself waiting for you. The two of you exchange pleasantries. Then you leave your other self behind as you walk through the gate into yesterday. But instead of obstinately wandering off, you wait around a day to meet up with the younger version of yourself (you have now aged into the older version you saw the day before) 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 person walk out of the rear side of the gate, emerging from one day in the future. That’s no surprise; it just means that you will see that person enter the front side of the gate tomorrow. But as you keep watch, you notice that he simply loiters around for one day, and when precisely 24 hours have passed, the traveler walks calmly through the front of the gate. Nobody ever approached from elsewhere. That 24-hour period constitutes the entire life span of this time traveler. He experiences the same thing over and over again, although he doesn’t realize it himself, since he does not accumulate new memories along the way. Every trip through the gate is precisely the same to him. That may strike you as weird or unlikely, but there is nothing paradoxical or logically inconsistent about it.
The real question is this: What happens if we try to cause trouble? That is, what if we choose not to go along with the plan? Let’s say you meet a day-older version of yourself just before you cross through the front of the gate and jump backward in time, as if you will hang around for a day to greet yourself in the past. But once you actually do jump backward in time, you still seem to have a choice about what to do next. You can obediently fulfill your apparent destiny, or you can cause trouble by wandering off. What is to stop you from deciding to wander? That seems like it would create a paradox. Your younger self bumped into your older self, but your older self decides not to cooperate, apparently violating the consistency of the story.
We know what the answer is: That cannot happen. If you met up with an older version of yourself, we know with absolute certainty that once you age into that older self, you will be there to meet your younger self. That is because, from your personal point of view, that meet-up happened, and there is no way to make it un-happen, any more than we can change the past without any time travel complications. There may be more than one consistent set of things that could happen at the various events in space-time, but one and only one set of things actually does occur. Consistent stories happen; inconsistent ones do not. The vexing part is understanding what forces us to play along.
The issue that troubles us, when you get down to it, is free will. We have a strong feeling that we cannot be predestined to do something we choose not to do. That becomes a difficult feeling to sustain if we have already seen ourselves doing it.
Of course, there are some kinds of predestination we are willing to accept. 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. The much more detailed kind of predestination implied by closed timelike curves, where it seems that we simply cannot make certain choices (like walking away after meeting a future version of ourselves), is bothersome.
