On the (Im)possibility of time travel

by Patrick Toner

Ben Brown has offered some arguments against the possibility of time travel. I will show here that they are unsuccessful. This requires going through them one by one, and that process shall occupy the bulk of my response. I will conclude with a brief explanation of why I agree with Brown’s conclusion despite finding his arguments faulty.

Brown begins by considering a causal paradox. He suggests that we’ve all seen examples of it in works of science fiction: “A person does thing X1 at time T1, which has as its direct result that he travels back in time and does thing X2 in time T2; but it turns out that X2 was actually the direct cause of his doing X1, and thus he would never have traveled to time T2 and done X2.” Brown’s argument that this is unacceptable seems sound, but his conclusion that this scenario renders time travel logically impossible simply does not follow. Any theory of time travel that allows the traveler to undercut the conditions that allowed him to travel back in time in the first place may very well be logically impossible. But to avoid the contradiction Brown here points out, the time travel advocate has only to accept that, foibles of science fiction writers aside, such scenarios really are impossible: theories that allow them are just bad theories.1   The range of the time traveler’s activities could be quite restricted—perhaps the time traveler can’t exert any causal influence while he’s in the past. So Brown’s causal paradox is no reason to claim that time travel is impossible. Rather, it illustrates a consequence time travel theorists should be careful to avoid.

Brown’s second argument is more involved, and answering it will require a bit of preliminary terminological clarification. Let’s start by distinguishing two types of persistence: endurance and perdurance.2   Endurantists and perdurantists agree that (at least some) objects persist, or last, over time. (I existed in 1975, and I exist now: I have persisted.) They disagree about how objects persist. Endurantists hold that persisting objects are wholly present at all times in which they exist. Perdurantists believe that persisting objects are, rather, spread out in time. They have temporal parts, and are not wholly present at any given moment of time. So assume that perdurantism is true: what accounts for my existing in both 1975 and 2002 is that I have a temporal part in 1975 and a temporal part in 2002; I am the “space-time worm” made up of all of my temporal parts.3   The perdurantist claims that temporal parts are like spatial parts. Time, like space, is extended. Just as spatially extended objects have spatial parts in different places, persisting objects have temporal parts in different times.4

Next, we need to distinguish two views about time. Eternalism—the claim that all times are ontologically on par; that the present is no more real than the past or the future—stands in contrast to presentism, according to which the past is no more, and the future is not yet; only the present exists. Thus, the dispute between eternalists and presentists is a dispute about the ontological status of other times (than the present). Presentists think that only the present exists, while eternalists think all times exist.

Brown correctly notes that time travel requires eternalism.5   He does not, however, distinguish endurance and perdurance. He argues as if there were no such distinction—and this accounts for the failure of his second argument. Brown thinks that if I were to travel back to 1985 and meet “myself” there, the person I meet would “obviously not (be) me despite the fact that we have the same DNA.” Brown offers no argument in support of this claim; he expects us to take it as obvious that I can’t be wholly in two places at the same time. Fair enough. I’ll take it as obvious.

For the perdurantist, however, my traveling back to 1985 and meeting myself there leads to none of the absurdities Brown suggests it must. The perdurantist would say that I meet myself in virtue of being a space-time worm that has zigzagged back upon itself. The “persons” who meet are simply temporal parts of me, and not persons at all. The perdurantist, thus, doesn’t claim that I can be wholly in two places at once. He claims only that I have parts in two places at once; but that’s a different story, and not obviously problematical.6  

Nor is there, pace Brown, a problem with handling moral responsibility. I am morally responsible for any acts committed by any of my temporal parts. I don’t evade moral responsibility for a sin by saying “hey, it was my foot that did it.” I’m responsible for what any of my spatial parts do. The same is true of my temporal parts. The problems Brown discusses are, therefore, only problems for the endurantist. So this argument shows that time travel requires a perdurantist ontology; not that time travel is impossible.7

Brown’s next argument is piggybacked onto this one, but it has a rather perplexing twist. Although he presents it as an argument against time travel, it is in fact an argument against eternalism. He writes that “such a theory of time travel would imply that there are a really real infinite number of human persons, all simultaneously existing as we speak.” But what he has in mind here is the “timeline” view (mentioned above), according to which all times are equally real. And the “timeline” view is eternalism. If this argument is successful, Brown accomplishes much more than showing time travel is impossible. He shows that eternalism is false. The argument, however, does not work.

The perdurantist eternalist partly avoids the problem Brown mentions—the problem of an actual infinity of persons—by denying that my past temporal parts are persons; they are, rather, temporal parts of a person. That’s not enough to avoid Brown’s argument, though, because he doesn’t object to the actual infinity of persons specifically, but, rather, actual infinity simpliciter (for things other than God). So if the perdurantist eternalist view produces an actual infinity of temporal parts, then Brown’s argument here still applies. Of course, in order for the argument to be successful, Brown has to show two things. First, that only God can be actually infinite. Second, that the perdurantist eternalist view really does produce an actual infinity. He offers arguments for neither required premise. Even if I grant the first—I don’t have any settled views on that question, so I’m willing to grant it for the sake of argument—I just don’t see how Brown can make the second stick.

Imagine that, in the history of the universe, there are thirty million human beings. Each of these human beings has lots of temporal parts. Let’s arbitrarily select an enormously high number—200,000,000,000,000. Now let’s multiply thirty million by two hundred trillion. (Well, you folks do it. I’ll trust you to get the right answer.) Have we gotten to infinity yet? Not quite. How many people with how many temporal parts would we need to have before we came up with an infinite number of parts? Let’s try one hundred billion human beings, each of whom has a googolplex temporal parts. Multiply. Infinity? Nope. And so forth. We can never reach infinity this way, no matter how high the numbers we start out with.

Perhaps this isn’t the angle Brown is thinking of, though. He may be assuming that the “timeline” is infinitely divisible. So if there is a temporal part that occupies time span T (say T is one second long), then that temporal part is divisible into smaller time spans, and so on ad infinitum (just as, in geometry, any segment of a line is infinitely divisible). While this is a commonsensical (and common) assumption, it is not necessarily true. Consider the possibility that there are fundamental temporal parts that last an instant—a non-divisible instant. These parts should be thought of as similar to the fundamental particles of matter, which are extended but not divisible. As long as non-divisible instantaneous temporal parts are possible—and I don’t see how they can be shown not to be—then Brown’s argument can be avoided.8

The fourth argument is simply the first argument restated and generalized, so it can be dealt with in the same way we dealt with the first argument. In his fifth argument, Brown cites Aristotle’s definition of time, and argues that, given such a definition, time travel leads to contradictions. This argument is by no means decisive, as Brown seems to recognize. (He states it as a conditional. “If you grant this….”) Brown produces the contradictions by stipulating a definition that rules out time travel. But why should the time travel advocate accept Aristotle’s definition of time? Brown gives him no reason to. An eternalist perdurantist will have a notion of time that is not inconsistent with time travel, since for him, change is an entirely different sort of phenomenon than it is for Aristotle. While some see the fact that eternalist perdurantism rules out “change” in the usual sense as a decisive argument against the view,9 others are happy enough to say goodbye to that notion of change. After all, it is thought that special relativity entails eternalism—and we wouldn’t want our dated conceptions of “change” to stand in the way of the triumphant march of scientific progress.10   At any rate, Brown’s considerations about problems of change are hardly compelling.

The final argument is this:

Presumably, when one says that time travel is possible one means that a person can go back, for example, to the real, true, genuine 1776. But if you’ve traveled back to the real 1776, then what are you doing there? You didn’t exist in 1776, so to say that you are in the real 1776 is to say that it’s not the real 1776, which is yet another contradiction.

This argument is unsound, for—given that he’s assumed for reductio the actual accomplishment of time travel—it has a false premise. If I’ve traveled back to 1776, then I did indeed exist in 1776—the real, true, genuine 1776. So the contradiction is not produced.

Brown’s last point is a suggestion rather than an argument. We are asked to consider what ramifications time travel would have “for morality, heaven and hell, God, angels, etc.” I’m not sure what ramifications Brown has in mind—indeed, I can’t see a significant problem arising from any of the directions mentioned here.11   Perhaps in a later article, Brown will provide some of his reasons for making this suggestion.

Brown’s arguments for the impossibility of time travel fail. However, I think he is right that time travel is impossible. And Brown is on the right track—as I said above, when he notes that time travel is possible only if eternalism is true. But eternalism is not true; presentism is true. Therefore, time travel is impossible. Obviously, it is both substantive and controversial to claim that presentism is true; I won’t argue in support of that claim here. However, it should be clear enough that it’s impossible for me to travel to the past if the past doesn’t exist, just as it’s impossible for me to travel to Planet X if Planet X doesn’t exist. The time traveler needs a destination. If presentism is true, there is no time but the present, and therefore, there is no destination.

If you’re not happy with the bare claim that presentism is true, then just take the lesson as a conditional: if presentism is true, time travel is impossible.  

If eternalism is true, however, time travel may be possible. While eternalism (combined with perdurantism) doesn’t rule out the possibility, neither does it entail it. Surely, though, endurantist eternalists find themselves faced with some of the problems raised by Brown in his essay: that combination of views is incompatible with the possibility of time travel. For what it’s worth, though, there are much stronger reasons for rejecting that combination of views than that they conflict with the possibility of time travel—which is, obviously enough, a worry only for those who think time travel is possible.12

Patrick Toner earned his BA at Franciscan University in 2000, and may have completed his MA in philosophy there in 2002, though he’s not entirely sure. He lives in Charlottesville, VA with his wife Shannon, and their kids Ben and Ellie. He is in his second year in the philosophy Ph.D. program at the University of Virginia.

  1. For a seminal discussion of this issue, see David Lewis, “The Paradoxes of Time Travel,” American Philosophical Quarterly 13 (1976), 145-152. Lewis rejects the idea that a person could travel back in time and, for example, kill the person who made it possible for him to travel back in time. Thaxris, Lewis would reject the scenario Brown sets out in his first argument. (Lewis, incidentally, finds nothing objectionable about causal loops in general; he just seems to object to the most viciously circular.)  ↑
  2. The terminology I use here is David Lewis’s. Cf. On the Plurality of Worlds (Cambridge: Blackwell, 1986), 202. The terminology one prefers is of no great importance: however, the distinction itself is vital. Do not be misled, then, by those who use “endure” and “perdure” interchangeably. Cf. Norris Clarke, SJ, The One and the Many (Notre Dame, IN: University of Notre Dame Press, 2001), 125. Fr. Clarke typically uses “perdure” to mean (I think) what I mean by “endure,” but on the page cited, he switches between the two terms, with a use of “persist” thrown in for good measure. He can use the terminology however he prefers, of course; but on my usage here, the terms are not interchangeable. ↑
  3. I say “a” temporal part: this is merely for convenience. As far as I know, no perdurantist would claim that I had just one temporal part in 1975. I’ll have more to say about this later. ↑
  4. This view is often called “four dimensionalism,” because it treats time as a dimension in addition to the three spatial dimensions. “Four dimensionalism” is misleading, however, because it is possible for a non-spatially extended object to persist—and, of course, such an object would not be four dimensional. It is also misleading because it is typically used in such a way as to gloss over the distinction between the temporal issue—eternalism vs. presentism (about which more next)—and the persistence issue—perdurance vs. endurance. For these reasons, I avoid the term. ↑
  5. “To consider time travel possible is to consider time as a sort of continuum, like a line that goes on in both directions, each point ‘simultaneously’ existing.” ↑
  6. Of course, it can be objected that the problem with the story I’ve just told is that it requires my having two temporal parts at the same time; and isn’t that sort of like my having two spatial parts at the same place? That is, isn’t it contradictory? It might be if the temporal aspect were the only thing that distinguished temporal parts from one another, but that can’t be right, or there’d be only one temporal part per time—a part that includes everything that exists at that time. But that’s not the perdurance view; that view is that I have a temporal part at T, you have a temporal part at T, and so does everything else that exists at T. The parts, that is, are also distinguished by spatial location—not merely by temporality. This helps us avoid the objection. My two temporal parts at T can be differentiated in virtue of being in different places, even though they are at the same time.  ↑
  7. Ted Sider has beaten Brown to the punch in showing this, however. See Four Dimensionalism (Oxford: Clarendon Press, 2001), 101-109.  ↑
  8. Or, at any rate, Brown needs to get to work showing why these fundamental temporal parts are impossible in order to defend his needed premise and get his argument to go through.  ↑
  9. Cf. Peter Geach, “Some Problems about Time,” Proceedings of the British Academy 51 (1966).  ↑
  10. Ted Sider calls the apparent incompatibility of presentism and special relativity the “fatal blow to presentism.” (Op cit., 42.) More importantly, many people think that the dogma of Divine Eternity entails eternalism about time. I think that is an error. But my point is that there are reasons for accepting eternalism, and once one is an eternalist, perdurance necessarily follows. (Cf. n. 12 below.) Therefore, many Christians will be unconvinced by Brown’s considerations about the nature of time, as will many people of scientistic leanings. ↑
  11. He had mentioned the “morality” issue earlier, when he suggested that the “me” of 1992 can’t be the “me” of now, and so I can’t be morally responsible for the actions of “me” in 1992. I assume that’s what he has in mind here. However, as I said, the perdurantist has a fine solution to this problem. ↑
  12. Endurantism is, in fact, incompatible with eternalism; perdurance is the only live option for the eternalist. Likewise, the presentist must be an endurantist. For arguments in support of this claim, see Trenton Merricks, “Persistence, Parts, and Presentism,” Nous 33 (1999), 421-438; “Endurance and Indiscernibility,” Journal of Philosophy 91 (1994), 165-184; and “On the Incompatibility of Enduring and Perduring Entities,” Mind 104 (1995), 523-531. Also see E.J. Lowe, “Tense and Persistence,” in Questions of Time and Tense, R. Le Poidevin, ed. (Oxford: Clarendon Press, 1998), 43-59, esp. 56-58. ↑