Time Travel

The Impossibility of Time Travel

Is time travel possible? Most of us would probably say no. And yet modern science accepts at least one kind of time travel. According to the theory of relativity, travelers moving at different speeds experience time at different rates. An astronaut who traveled to a distant star at close to the speed of light could return to the earth hundreds or thousands of years into the future, while having aged only a few years in the process. Similarly, someone in a very strong gravitational field – near a black hole, say – would age more slowly than someone back on earth. Thus, time travel to the future is certainly possible.

But could one travel to the past? Backwards time travel, the kind that is usually found in science fiction, is an even more interesting prospect than travel to the future. It is, however, associated with certain paradoxes, and as a result has seemed to many to be logically impossible.

There are two main kinds of time travel paradoxes. The first type involve changes to the past, the second involve what are known as “causal loops.” The famous Grandfather Paradox is an example of the first type.

The Grandfather Paradox

Suppose a time traveler goes back in time and kills his grandfather when the latter was only a child. If his grandfather dies in childhood, then the time traveler cannot be born. But if the time traveler is never born, how can he have traveled back in time in the first place?

There are, of course, many possible variations on this paradox. A time traveler could simply prevent his parents from ever meeting (as almost happened in the movie Back to the Future), or he could kill his own younger self, or he could even change the entire course of evolution before human beings had a chance to develop.

Grandfather-type paradoxes are actually part of a more general problem with backwards time travel. For consider a time traveler who does not bring about any obviously paradoxical scenario, such as killing his own grandfather. It nevertheless seems inevitable that he will cause some changes. If nothing else, he will displace certain air molecules, photons, and so on. But now, any change to the past is itself a paradox, for it implies that something both happened and did not happen at a particular moment in history. In fact, an even simpler case can be made against the possibility of time travel. The time traveler will be visiting a past that did not originally include him. It follows that he both was and was not present at a particular moment in time. And that is obviously impossible. Thus, all time travel to the past appears to be ruled out.

There are at least two possible replies to this paradox. One popular solution says that travelers into the past create a new time line, parallel to but distinct from the set of events that originally took place. This solution does not really work, however, because in such a case there is no longer any reason to regard the new set of events as literally being in the past. For instance, suppose the inventor of a time machine decides to use his invention to prevent the assassination of President Kennedy. He steps into the time machine in present-day Dallas and a moment later steps out on what looks like the morning of November 22, 1963. The newspaper confirms the date, everyone in the city is anticipating the President's visit, and so on. But this is not the November 22, 1963 that is recorded in the history books and in the memories of those who are old enough to remember that day. On the “original” November 22, 1963, our time traveler was not in Dallas, he did not buy this particular copy of the newspaper, and he did not surprise Oswald as the latter waited in ambush. This morning never existed before in the history of the universe. The time traveler, then, did not actually go back to November 22, 1963, i.e., he did not return to the date when Kennedy was in fact assassinated. So in that case, why would we claim that he went back in time? What he did was go to a parallel universe, one in which another set of events, some very similar to or even exactly like those that occurred in our universe, take place. There is no reason to regard this set of events as being either in our past or in our future. They are simply in another temporal continuum. This, then, is not genuine time travel to the past. (This is not to say that the events in this parallel continuum are not temporally related to events in our past. For instance, one might suppose that the universe branches into two separate time lines at the exact moment before the time traveler arrives, so that the events taking place around our time traveler really are all within a short amount of time from certain events that took place in our past. But this is not enough to make those events be in our past, for they are still in a separate time line.)

The second way to avoid these time travel paradoxes says that travelers into the past merely play out their role in history. In this case, if our time traveler stepped out of his time machine on the morning of November 22, 1963, it really would be that day in our past. He was there on that date originally, only of course he didn't know this until he decided to get into his time machine and take the trip. He really did buy that newspaper to confirm the date, and he really did try to prevent Oswald from assassinating President Kennedy. But of course he wasn't successful. Or perhaps (conspiracy theorists, take notice) he did prevent Oswald from shooting, but there was another gunman around. What our time traveler cannot do is change any of what happened. In particular, he cannot prevent the assassination.

Physicists have shown that, at least where simple classical systems are concerned, the only trajectories that are consistent with the laws of nature are ones that are non-paradoxical. The laws of physics therefore seem to rule out the possibility of paradoxes. For instance, suppose an inventor tries to create a grandfather-type paradox as follows. He connects a time machine to a pool table so that a ball going into pocket A at time t will exit from pocket B at some time before t. Now suppose the inventor attempts to knock a ball into A at just the right angle and speed so that it will exit from B and collide with its former self with sufficient force to prevent it from reaching A. If the inventor could accomplish this, we would have a paradox on our hands, for if, as a result of the collision, the ball never reaches A, then it cannot exit from B.

Any such trajectory is ruled out by the laws of physics, however. Therefore, something will always prevent the ball from colliding with itself in such a way that a paradox results. To understand how that can be, we just need to keep in mind that time travelers (including time traveling billiard balls) merely play out their role in history. We therefore must take into account from the very beginning the role played by the ball coming out of B. It is a mistake to ignore that information when we describe the ball moving along the table toward A.

A correct description of the sequence of events will therefore be something like the following. The inventor tries to knock the ball into A at just the right angle and speed to create a paradox. As the ball is moving along the table, however, a slightly older version of itself exits through B. It collides with the younger version of the ball, but in such a way that it only slightly alters the direction of the younger ball. The younger ball reaches A, but at a slightly different angle than that originally planned by the inventor. This slightly different angle accounts for the different angle that the older ball has as it comes out of B, and therefore for the fact that it does not collide as planned (and prevent itself from reaching A). What the ball cannot do is prevent itself from reaching A, since it did come out of B.

This second solution does work to the extent that it shows time travel is not logically ruled out by grandfather-type paradoxes. But whether or not this approach works for the actual world – and in particular, whether it works in the case of human time travelers – is something we will have to return to later in the essay.

Causal Loops

A second type of time travel paradox is the closed causal loop. The classic example is the one in which you one day receive the instructions on how to build a time machine from a mysterious stranger. You follow the instructions and then use the time machine to go back in time, where, disguised as a mysterious stranger, you proceed to give your younger self instructions on how to build a time machine. But where did the knowledge of how to build such a machine come from in the first place?

Perhaps just as odd are causal loops that involve material objects. For example, suppose that as a child you are visited by someone who appears to be yet another mysterious stranger, and this stranger gives you a gold ring. You keep the ring for many years, until, as an adult, you travel back in time and give the ring to yourself as a child. So where did the ring originally come from?

Causal loops may be disturbing, but they do not appear to present us with logical impossibilities. The above scenarios do not include any internal inconsistencies of the sort that we find with the grandfather-type paradoxes. The gold ring and the time machine instructions simply exist uncaused. That is certainly out of the ordinary, and most people find it too hard to accept such a thing. But, as the philosopher David Lewis pointed out, it is not any more logically impossible for a gold ring to exist uncaused than it is for God, or for the universe as a whole, to exist uncaused.

This is not to say that causal loops do not present any problems. First of all, even if it is logically possible, it doesn’t seem very likely that things like gold rings or time machine instructions could exist without a cause. Second, there is a problem regarding changes that occur over the lifetime of any object that forms a causal loop. We will address this problem in the final section of the article. Before doing so, however, let’s consider a third common argument against backwards time travel, one that is much simpler than the above two.

Where Are the Time Travelers?

If time travel to the past is possible, then it will probably be discovered some day. But then time travelers should be visiting us. So where are they? And where were all the time tourists at major historical events, such as the Crucifixion or Columbus’ arrival in America?

Like the above arguments, this one is also inconclusive. Perhaps it is possible that one can travel back in time, but not to any time prior to the construction of the time machine one is using. Some candidates for time machines, such as wormholes (hypothetical shortcuts through spacetime), imply exactly this. Or it could be that it takes great amounts of energy to travel back in time, and that the further back one wishes to go, the more energy is required. Or perhaps such time travel is in principle physically possible, but never becomes feasible, due to insurmountable technical problems. Somewhat less convincing is the possibility that visitors from the future are among us but simply choose not to reveal themselves. (Some have even suggested that UFO’s could be such visitors!) Whatever one thinks of these explanations, it must be admitted that the absence of time travelers does not by itself prove the impossibility of time travel.

But Is Backwards Time Travel Actually Possible?

As we have seen, the kind of time travel where travelers merely play out their role in history is at least logically possible. There are ways to make any story involving such travel internally consistent. That, of course, does not mean that it is actually possible, i.e., that the laws of nature allow it. And there are good reasons to doubt its possibility. Problems arise with both the grandfather-type paradoxes and with causal loops. For although neither logically rules out time travel to the past, both require very unusual scenarios in order to remain non-paradoxical. And the real question is whether we have any reason for believing that such unusual scenarios can ever come about.

Consider the causal loop involving the gold ring once again. At the time that the ring is given to the child, it is in some definite state. Call it state x. It then takes some time (many years in the original example) before the ring is taken to the past and given to the child. During this elapsed time, the ring undergoes certain changes. In other words, it ages. It may get slightly scratched, and so on. How, then, can it be back in state x when it is given to the child? Remember that there is only one state that the ring can be in at the time it is given to the child, for that is a unique event. If the ring were the slightest bit different – if even one electron in the ring were out of place – it would be a case of changing the past (I’m ignoring complications arising from the Uncertainty Principle here, but I don’t believe that introducing them would help anyway). Just by touching the ring, one rubs off some of its atoms. These atoms would then have to somehow end up back in the ring before it is taken back in time.

Strictly speaking, it is not impossible for the ring to be in exactly the same state after many years. But it is so unlikely as to be virtually impossible. Add to this our suspicions regarding rings (or perhaps even worse, time machine instructions) existing uncaused, and causal loops seem to be all but ruled out. But if time travel to the past is possible, what’s to prevent someone from bringing about this sort of situation? In other words, why couldn’t a time traveler succeed in giving a ring to his former self?

A similar problem occurs when we try to avoid grandfather-type paradoxes where human beings are involved. Let’s return to the example of the time traveler attempting to prevent the Kennedy assassination. Suppose he realizes that he has failed in his attempt. All he needs to do at this point is study the situation, find out why he failed, and go back in time again to try once more. But in order to be merely playing his role in history, he would have to fail again! No matter how many times he did this, he would have to fail. If he was sufficiently persistent, he might keep going back to that particular time and place, so that there would be hundreds of him around (each of a slightly different age), a whole army of the same individual trying to prevent the assassination. Why wouldn't he be able to achieve his goal? (Furthermore, there is the strange fact that on his first attempt, he should already have seen all his other selves around, which would certainly have affected his original plans.)

The answer, according to the proponent of backwards time travel, is that he can’t succeed because that is not what happened. That is certainly true: no time traveler will ever prevent the Kennedy assassination. Likewise, if no ring ever returns to a former state of itself, then no ring can ever form a causal loop – so no time traveler will ever be able to give a ring to his former self. But why not? It seems that in order to maintain the possibility of backwards time travel, one must suppose that time travelers would in some cases be unable to perform what appear to be simple, everyday kinds of actions.

A proponent of backwards time travel might claim that common sense notions regarding what is and isn’t possible to do – in other words, common sense views on freedom of the will – have to be altered. By the “common sense view” here, I just mean the belief that humans are free in the sense that they can choose from among different possible courses of action, or, to put it another way, that we have what is termed “libertarian free will.”

But now if time travel to the past is possible, then the future from which a time traveler comes is already determined in the sense that it is the only future that is actually possible. Any other logically possible future is ruled out by the fact that the time traveler did not come from it.* But a determined future is incompatible with libertarian free will, for if there is only one possible future, then one is not free to choose what actions to perform from among different possibilities. Thus, if travel to the past is possible, there is no such thing as libertarian free will.

As long as one is willing to accept determinism in this sense, travel to the past might seem to present no serious difficulties. For if human beings are not free in the libertarian sense, then neither is the time traveler. The time traveler, therefore, is really in the same boat as everyone else: he can only do what is already determined he will do. It is the case that he will fail to prevent Kennedy’s assassination. Nothing else is possible for him. No matter how many times he tries, he is destined to fail. Or perhaps the simple fact is that he is destined not to try over and over. He simply will not have the desire to do so. After all, his desires are likewise determined.

But does this really solve the problem? I don’t think so. The question that remains is, how plausible is this solution? In other words, given what we know about the world around us, including about human behavior, how likely is it that time travel is actually possible? I believe the likelihood is, in any practical sense, zero.

Suppose we grant to the proponent of time travel that human beings do not have libertarian free will. It does not follow that time travelers shouldn’t be able to carry out what I above called “simple, everyday kinds of actions.”

First of all, we have very good reasons for supposing that, given a chance to travel back in time, some human beings would desire to do such things as prevent the Kennedy assassination, give rings to their former selves, and so on. I regard this as obvious given what we know of human behavior, including what each of us, or at least most of us, know about our own desires.

Of course this is not conclusive proof. After all, even if the reader believes that right now, given the chance to travel back in time, he or she would have the desire to perform one of the above experiments, the situation might change if he or she were actually given the chance to travel in time. It is certainly logically possible that no time traveler would have the desire to do any of the above things. But remember, we are not concerned with mere logical possibility here. We are considering what we have reason to believe is actually the case, given what we know about the world. And there is no reason (other than an ad hoc one) to suppose that time travelers would not have such desires.

But then the only explanation left is to suppose that time travelers who desire to perform acts such as the above are unable to carry out their plans. In other words, something must always prevent a time traveler from killing their own grandfather, interfering with Oswald, and so on. Now, once again, this is certainly logically possible. Maybe the universe is organized in such a way that time travelers who desire to shoot at their own grandfathers will either miss, or their gun will jam, and so on. But given what we know about the world around us, this seems extremely unlikely as well. Again, we have no reason for supposing that such a thing is true other than the ad hoc one to allow the possibility of time travel. Time travel to the past therefore appears to be logically possible but not actually possible.

Notes:

* The kind of determinism suggested by time travel is essentially the same as that suggested by the theory of relativity. For a brief explanation of relativistic determinism, see http://www.kiekeben.com/relativistic.html ^

Other sites:

NOVA - Time Travel

Time Travel (Preston and Hammonds)

Time Travel (John Gribbin)

Time Travel Paradoxes (Kelley L. Ross)