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Lewis1976 - AMERICAN PHILOSOPHICAL QUARTERLY Volume 13...

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Unformatted text preview: AMERICAN PHILOSOPHICAL QUARTERLY Volume 13, Number 2, April 1976 VI. THE PARADOXES OF TIME TRAVEL DAVID LEWIS IME travel, I maintain, is possible. The paradoxes of time travel are oddities, not impossibilities. They prove only this much, which few would have doubted: that a possible world Where time travel took place would be a most strange world, different in fundamental ways from the world we think is ours. I shall be concerned here with the sort of time travel that is recounted in science fiction. Not all science fiction writers are clear-headed, to be sure, and, inconsistent time travel stories have often been written. But some writers have thought the problems through with great care, and their stories are perfectly consistent.1 If I can defend the consistency of some science fiction stories of time travel, then I suppose parallel defenses might be given of some contro- versial physical hypotheses, such as the hypothesis that time is circular or the hypothesis that there are particles that travel faster than light. But I shall not explore these parallels here. What is time travel? Inevitably, it involves a V discrepancy between time and time. Any traveler departs and then arrives at his destination; the time elapsed from departure to arrival (positive, or perhaps zero) is the duration of the journey. But if he is a time traveler, the separation in time between departure and arrival does not equal the duration of his journey. He departs; he travels for an hour, let us say; then he arrives. The time he reaches is not the time one hour after his departure. It is later, if he has traveled toward the future; earlier, if he has traveled to ward the past. If he has traveled far toward the past, it is earlier even than his departure. How can it be that the same two events, his departure and his arrival, are separated by two unequal amounts of time? ‘ It is tempting to reply that there must be two independent time dimensions; that for time~ travel to be possible, time must be not a line but a plane? Then a pair of events may have two unequal separations if they are separated more in one of the time dimensions than in the other. The lives of common people occupy straight diagonal lines across the plane of time, sloping at a rate of exactly one hour of time, per hour of timez. The life of the time traveler occupies a bent path, of varying slope. On closer inspection, however, this account seems not to give us time travel as we know it from the stories. When the traveler revisits the days of his childhood, will his playmates be there to meet him? No; he has not reached the part of the plane of time where they are. He is no longer separated from them along one of the two dimensions of time, but he is still separated from them along the other. I do not say that twodimensional time is impossible, or that there is no way to square it with the usual conception of what time travel would be like. Nevertheless I shall say no more about twodimensional time. Let us set it aside, and see how time travel is possible even in one-dimensional time. The world—the time traveler's world, or ours —is a four-dimensional manifold of events. Time is one dimension of the four, like the spatial dimensions except that the prevailing laws of nature discriminate between time and the others —or rather, perhaps, between various timelike dimensions and various spacelike dimensions. (Time remains onedimensional, since no two timelike dimensions are orthogonal.) Enduring things are timelike streaks: wholes composed of temporal parts, or stages, located at various times and places. Change is qualitative differ— 11 have particularly in mind two of the time travel stories of Robert A. Heinlein: “By His Bootstraps" in R. A. Heinlein, The Menace from Earth (Hicksville, N.Y., 1959), and “—All You Zombies—,” in R. A. Heinlein, The Unpleasant Profession of Jonathan Hang (Hicksville, N.Y., 1959). 2 Accounts of time travel in two-dimensional time are found in Jack W. Meiland, "A Two-Dimensional Passage Model of Time for Time Travel," Philosophical Studies, vol. 26- (1974), pp. 153—173; and in the initial chapters of Isaac Asimov, The End of Eternity (Garden City, N.Y., 1955). Asimov’s dcnouement, however, seems to require some different conception of time travel. — ' l4'5 146 AMERICANT’HILOSQPHICAL QUARTERLY ence between different stages—different temporal parts—of some enduring thing, just as a “change” in scenery from east to west is a qualitative dif~ ference between the eastern and western spatial parts of the landscape. If this paper should change your mind about the possibility of time travel, there will be a difference of opinion be- tween two different temporal parts of you, the stage that started reading and the subsequent stage that finishes. If change is qualitative difference between temporal parts of something, then what doesn’t have temporal parts can't change. For instance, numbers can’t change; nor can the events of any moment of time, since they cannot be subdivided into dissimilar temporal parts. (We have set aside the case of twodimensional time, and hence the possibility that an event might be momentary along one time dimension but di— visible along the other.) It is essential to dis- tinguish change from “Cambridge change,” which can befall anything. Even a number can “change” from being to not being the rate of exchange between pounds and dollars. Even a momentary event can “change” from being a year ago to being a year and a day ago, or from being forgotten to being remembered. But these are not genuine changes. Not just any old re~ versal in truth value of a time-sensitive sentence about something makes a change in the thing itself. A time traveler, like anyone else, is a streak through the manifold of space-time, a whole composed of stages located at various times and places. But he is not a streak like other streaks. If he travels toward the past he is a zig-zag streak, doubling back on himself. If he travels toward the future, he is a stretched~out streak. And if he travels either way instantaneously, so that there are no intermediate stages between the stage that departs and the stage that arrives and his journey has zero duration, then he is a broken streak. I asked how it could be that the same two events were separated by two unequal amounts of time, and I set aside the reply that time might have two independent dimensions. Instead I re- ply by distinguishing time itself, external time as I shall also call it, from the personal time of a particular time traveler: roughly, that which is measured by his wristwatch. His journey takes an hour of his personal time, let us say; his .J wristwatch reads an hour later at arrival than at departure. But the arrival is more than an hem after the departure in external time, if he travels toward the future; or the arrival is before the departure in external time (or less than an hour after), if he travels toward the past. That is only rough. I do not wish to define personal time operationally, making Wrist. watches infallible by definition. That which is measured by my own wristwatch often disagrees with external time, yet I am no time traveler; What my misregulated wristwatch measures is neither time itself nor my personal time. Instead of an operational definition, we need a func. tional definition of personal time: it is that which occupies a certain role in the pattern of events that comprise the time traveler's life. If you take the stages of a common person, they manifest certain regularities with respect to ex- ternal time. Properties change continuously as you go along, for the most part, and in familiar ways. First come infantile stages. Last come senile ones. Memories accumulate. Food digests. Hair grows. Wristwatch hands move. If you take the stages of a time traveler instead, they do not manifest the common regularities with respect to external time. But there is one way to assign coordinates to the time traveler's stages, and one way only (apart from the arbitrary choice of a zero point), so that the regularities that hold with respect to this assignment match those that commonly hold with respect to external time. With respect to the correct assignment properties change continuously as you go along, for the most part, and in familiar ways. First come in- fantile stages. Last come senile ones. Memories accumulate. Food digests. Hair grows. Wrist watch hands move. The assignment of coordi- nates that yields this match is the time traveler’s personal time. It isn’t really time, but it plays the role in his life that time plays in the life of a common person. It’s enough like time so that we can—with due caution—transplant our temporal vocabulary to it in discussing his affairs. We can say without contradiction, as the time traveler prepares to set out, “Soon he will be in the past.” We mean that a stage of him is slightly later in his personal time, but much earlier in external time, than the stage of him that is present as we say the sentence. We may assign locations in the time traveler's personal time not only to his stages themselves buFalsoito the events that go on around him. THE PARADOXES OF TIME TRAVEL Soon Caesar will die, long ago; that is, a stage slightly later in the time traveler’s personal time than his present stage, but long ago in external time, is simultaneous with Caesar’s death. We could even extend the assignment of personal time to events that are not part of the time traveler‘s life, and not simultaneous with any of his stages. If his funeral in ancient Egypt is separated from his death by three days of ex- ternal time and his death is separated from his birth by three score years and ten of his personal time, then we may add the two intervals and say that his funeral follows his birth by three score years and ten and three days of extended per- sonal time. Likewise a bystander might truly say, three years after the last departure of another famous time traveler, that “he may even now—if I may use the phrase—be wandering on some plesiosaurus-hauntcd oolitic coral reef, or beside the lonely saline seas of the Triassic Age."3 If the time traveler does wander on an oolitic coral reef three years after his departure in his personal time, then it is no mistake to say with respect to his extended personal time that the wandering is taking place “even now". We may liken intervals of external time to distances as the crow flies, and intervals of per- sonal time to distances along a winding path. The time traveler's life is like a mountain rail- way. The place two miles due east of here may also be nine miles down the line, in the west bound direction. Clearly we are not dealing here with two independent dimensions. Just as dis- tance along the railway is not a fourth spatial dimension, so a time traveler's personal time is not a second dimension of time. How far down the line some place is depends on its location in three-dimensional space, and likewise the loca- tions of events in personal time depend on their locations in one—dimensional external time. Five miles down the line from here is a place where the line goes under a trestle; two miles further is a place where the line goes over a trestle; these places are one and the same. The trestle by which the line mosses over itself has two different locations along the line, five miles down from here and also seven. In the same Way, an event in a time traveler’s life may have more than one location in his personal time. If 147 he doubles back toward the past, but not too far, he may be able to talk to himself. The con- versation involves two of his stages, separated in his personal time but simultaneous in external time. The location of the conversation in per- sonal time should be the location of the stage involved in it. But there are two such stages; to share the locations of both, the conversation must be assigned two different locations in per— sonal time. The more .we extend the assignment of per- sonal time outwards from the time traveler’s stages to the surrounding events, the more will such events acquire multiple locations. It may happen also, as we have already seen, that events that are not simultaneous in external time will be assigned the same location in personal time— or rather, that at least one of the locations of one will be the same as at least one of the loca- tions of the other. So extension must not be carried too far, lest the location of events in ex- tended personal time lose its utility as a means of keeping track of their roles in the time traveler's history. . A time traveler who talks to himself, on the telephone perhaps, looks for all the world like two different people talking to each other. It isn’t quite right to say that the whole of him is in two places at once, since neither of the two stages involved in the conversation is the whole of him, or even the whole of the part of him that is located at the (external) time of the con- versation. What's true is that he, unlike the rest of us, has two different complete stages located at the same time at different places. What reason have I, then, to regard him as one person and not two? What unites his stages, including the simultaneous ones, into a single person? The problem of personal identity is especially acute if he is the sort of time traveler whose journeys are instantaneous, a broken streak consisting of several unconnected segments. Then the natural way to regard him as more than one person is to take each segment as a different person. No one of them is a time traveler, and the peculiarity of the situation comes to this: all but one of these several people vanish into thin air, all but another one appear out of thin air, and there are remarkable resemblances between one at his 3 G. Wells, The Time Machine, An Invention (London. 1895), epilogue. The passage is criticized as contradic» wry In Donald C. Williams, "The M th of Passa e." The journal of Philoso h , vol. 48 195] , . 463. Y S P y P r48 appearance and another at his vanishing. Why isn't that at least as good a description as the one I gave, on which the several segments are all parts of one time traveler? I answer that what unites the stages (or seg- ments) of a time traveler is the same sort of mental, or mostly mental, continuity and con- nectedness that unites anyone else. The only difference is that whereas a common person is connected and continuous with respect to ex— ternal time, the time traveler is connected and continuous only with respect to his own personal time. Taking the stages in order, mental (and bodily) change is mostly gradual rather than sudden, and at no point is there sudden change in too many different respects all at once. (We can include position in external time among the respects we keep track of, if we like. It may change discontinuoust with respect to personal time if not too much else changes discon- tinuously along with it.) Moreover, there is not too much change altogether. Plenty of traits and traces last a lifetime. Finally, the connectedness and the continuity are not accidental. They are explicable; and further, they are explained by the fact that the properties of each stage depend causally on those of the stages just before in personal time, the dependence being such as tends to keep things the same.‘ To see the purpose of my final requirement of causal continuity, let us see how it excludes a case of counterfeit time travel. Fred was created out of thin air, as if in the midst of life; he lived a while, then died. He was created by a demon, and the demon had chosen at random what Fred was to be like at the moment of his creation. Much later someone else, Sam, came to resemble Fred as he was when first created. At the very moment when the resemblance became perfect, the demon destroyed Sam. Fred and Sam together are very much like a single person: a time traveler whose personal time starts at Sam's birth, goes on to Sam’s destruction and Fred’s creation, and goes on from there to Fred's death. Taken in this order, the stages of Fred-cum-Sam have the proper connectedness and continuity. But they lack causal continuity, so Fred-cum- Sam is not one person and not a time traveler. 4I discuss the relation between personal identi AMERICANP PHILOSOPHICAL QUARTERLY Perhaps it was pure coincidence that Fred at his creation and Sam at his destruction were exactly alike; then the connectedness and continuity of Fred-cum-Sam across the crucial point are acd. dental. Perhaps instead the demon remembered what Fred was like, guided Sam toward perfect resemblance, watched his progress, and destroyed him at the right moment. Then the connected. ness and continuity of Fred-cum-Sam has a causal explanation, but of the wrong sort. Either way, Fred's first stages do not depend causally for their properties on Sam’s last stages. 80 the case of Fred and Sam is rightly disqualified as a ease of personal identity and as a case of time travel. We might expect that when a time traveler visits the past there will be reversals of causation. You may punch his face before he leaves, causing his eye to blacken centuries ago. Indeed, travel into the past necessarily involves reversed causa. tion. For time travel requires personal identity —he who arrives must be the same person who departed. That requires causal continuity, in which causation runs from earlier to later stages in the order of personal time. But the orders of personal and external time disagree at some point, and there we have causation that runs from later to earlier stages in the order of ex ternal time. Elsewhere I have given an analysis of causation in terms of chains of counterfactual dependence, and I took care that my analysis would not rule out causal reversal a primals I think I can argue (but not here) that under my analysis the direction of counterfactual depen- dence and causation is governed by the direction of other de facto asymmetries of time. If so, then reversed causation and time travel are not ex- cluded altogether, but can occur only where there are local exceptiOns to these asymmetries. As I said at the outset, the time traveler’s world would be a most strange one. Stranger still, if there are local—but only local —causal reversals, then there may also be causal loops: closed causal chains in which some of the causal links are normal in direction and others are reversed. (Perhaps there must be loops if there is reversal; I am not sure.) Each event on the loop has a causal explanation, being caused by events elsewhere on the loop. That is not to ty and mental connectedness and continuity at greater length in “Survival and Identity" in The Identity of Persons, ed. by Amelie Rorty (forthcoming). 5 "Causation." The Journal of Philosophy. vol. 70 (1973).:pp. 556-567; the analysis relies on the analysis of counter- factuals given in my Counter-factual: (Oxford, 1973). THE PARADOXES OF TIME TRAVEL I49 say that the loop as a whole is caused or ex- plicable. It may not be. Its inexplicability is especially remarkable if it is made up of the 5955 of causal processes that transmit information. Recall the time traveler who talked to himself. He talked to himself about time travel, and in the course of the conversation his older self told his younger self how to build a time machine. That information was available in no other way. His older self knew how because his younger self had been told and the information had been preserved by the causal processes that constitute recording, storage, and retrieval of memory traces. His younger self knew, after the con- versation, because his older self had known and the information had been preserved by the causal processes that constitute telling. But where did the information come from in the first place? Why did the whole alfair happen? There is simply no answer. The parts of the loop are explicable, the whole of...
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