Earman_on_time_travel

Earman_on_time_travel - Time Travel 6.1 Introduction Over...

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Unformatted text preview: Time Travel 6.1 Introduction Over the last few years leading physics journals, such as Physical Review, Physical Review Letters, Journal qf Mathematical Physics, and Classical and Quantum Gravity, have been publishing articles dealing with time travel and time machines.1 Why? Have physicists decided to set up in competition with science fiction writers and Hollywood producers? More seriously, does this research cast any light on the sorts of problems and puzzles that have featured in the philosophical literature on time travel? The last question is not easy to answer. The philosophical literature on time travel is full of sound and fury, but the significance remains opaque. Most of the literature focuses on two matters, backward causation and the paradoxes of time travel.2 PrOperly understood, the first is irrelevant to the type of time travel most deserving of serious attention; and the latter, while always good for a chuckle, are a crude and unilluminating means of approaching some delicate and deep issues about the nature of physical possibility. The overarching goal of this chapter is to refocus attention on what I take to be the important unresolved problems about time travel and to use the recent work in physics to sharpen the formulation of these issues.3 The plan of this chapter is as follows. Section 6.2 distinguishes two main types of time travel—Wellsian and Godelian. The Wellsian type is inextricably bound up with backward causation. By contrast, the Godelian type does not involve backward causation, at least not in the form that arises in Wellsian stories of time travel. This is not to say, however, that Godelian time travel is unproblematic. This chapter is devoted largely to attempts, first, to get a more accurate fix on what the problems are and second, to provide an assessment of the different means of dealing with these problems. Section 6.3 provides a brief excursion into the hierarchy of causality conditions on relativistic spacetimes and introduces the concepts needed to assess the problems and prospects of Godelian time travel. Section 6.4- tevieWS the known examples of general relativistic cosmological models allowing Godelian time travel. Since Godel’s (1949a) discovery, it Time Travel 16 I has been found that closed timelike curves (CTCs) exist in a wide variety of solutions to EFE. This suggests that if classical general relativity theory is to be taken seriously, so must the possibility of Godelian time travel. Section 6.5 introduces the infamous grandfather paradox of time travel. It is argued that such paradoxes involve both less and more than initially meets the eye. Such paradoxes cannot possibly show that time travel is conceptually or physically impossible. Rather, the parading of the paradoxes is a rather ham-handed way of making the point that local data in spacetimes with CTCs are constrained in unfamiliar ways. The shape and status of these constraints has to be discerned by other means. Section 6.6 poses the problem of the status of the consistency constraints in terms of an apparent incongruence between two concepts of physical possibility that diverge when CTCs are present. Section 6.7 considers various therapies for the time travel malaise caused by this incongruence. The preferred therapy would provide an account of laws of nature on which the consistency constraints entailed by CTCs are themselves laws. I offer an account of laws that holds out the hope of implementing the preferred therapy. This approach is investigated by looking at recent work in physics concerning the nature of consistency constraints for both non-self—interacting systems (section 6.8) and self-interacting systems (section 6.9) in spacetimes with CTCs. Section 6.10 investigates a question that is related to but different from the question of whether time travel is possible; namely, is it possible to build a time machine that will produce CTCs where none existed before? Some concluding remarks are given in section 6.11. An appendix reviews Godel’s attempt to use his solution to EFE to prove the ideality of time. 6.2 Types of time travel; backward causation Two quite different types of time travel feature in the science fiction and the philosophical literature, though the stories are often so vague that it is hard to tell which is intended (or whether some altogether different mechanism is supposed to be operating). In what I will call the Wellsian type!“ the time travel takes place in a garden variety spacetimHay, Newtonian spacetime of classical physics or Minkowski spacetime of special relativistic physics. So the funny business in this kind of time travel does not enter in terms of spatiotemporal structure but in two other places: the structure of the world lines of the time travellers and the causal relations among the events on these world lines. Figure 6.} illustrates two variants ofthe Wellsian theme. Figure 6.1a shows the time traveller a1 cruising along in his time machine. At e1 he sets the time travel dial to “minus 200 years," throws the switch, and presto he and the machine disappear. Two hundred years prior to e, (as measured in Newtonian absolute time or the inertial time of the frame in which all is at rest) a person exactly resembling the time traveller both in terms of physical appearance and mental states pops into existence at .92. Even if we swallow 162 names, onunans, WHIMPERS, AND snmnxs tT 81 e3 at E ‘31 5 ‘32 B3 02w, ea e4 (0) (b) Fig. 6.1 Two lbrms of Wellsian time travel these extraordinary occurrences, the description given so far does notjustify the appellation of“time travel.” That appellation requires that although at, is discontinuous with at}, 0:2 is in some appropriate sense a continuation ofal. Whatever else that sense involves, it seems to require that events on 0t1 cause the events on 09;. Thus enters backward causation in which causes are later than their effects. Figure 6.]b also involves funny world line structure, but now instead of being discontinuous, the world line “bends backwards” on itself, the arrows involves no time travel. As described in external time, the sequence of events is as follows. At 54 a pair ol‘middle-aged twins is spontaneously created; the [33 twin ages in the normal way while his [32 brother gets progressively younger; meanwhile, a third person ,3, who undergoes normal biological aging and who is the temporal mirror image of ,8; is cruising for a fateful meeting with {32; when 51 and 132 meet at as they annihilate one another. Once again, the preference for the time travel description seems to require a causal significance for the arrows on the world line segments so that, for example, later events on ,3! (as measured in external time) cause earlier events on [32 (again as measured in external time). these paradoxes here except to say that they bear analogies to the paradoxes ofGodelian time travel that will receive detailed treatment below. But aside from such paradoxes, there is the prior matter of whether the phenomena represented in Fig. 6.1 are physically possible, even when shorn oftheir time Time Trams! 163 travel/backward causation interpretations. In Fig. 6.1a, for example, the creation ex while at .92 and the extinction ad nihilum at 91 are at odds with well entrenched conservation principles. Of course, the scenario can be modified so that conservation of mass—energy is respected: at 81 the time traveler and the time machine dematerialize as before but now their mass is replaced by an equivalent amount of energy, while at e; a non-material form of energy is converted into an equivalent amount of ponderable matter. But this emended scenario is much less receptive to a time travel/backward causation reading. For the causal resultants oft:1 can be traced forwards in time in the usual way while the causal antecedents of :2 can be traced backwards in time, thus weakening the motivation for seeing a causal link going from 9, to 22. At first blush Godclian time travel would seem to have three advantages over Wellsian time travel. First, on the most straightforward reading of physical possibilityecompatibility with accepted laws of physics—Godelian time travel would seem to count as physically possible, at least as regards the laws of the general theory of relativity (GTR). Second, unlike stories of Wellsian time travel, Giidelian stories are not open to a rereading on which no time travel takes place. And third, no backward causation is involved. On further analysis, however, the first advantage turns out to be something of a mirage since (as discussed below in sections 6.5 through 6.8) Godelian time travel produces a tension in the naive conception of physical possibility. And the second and third advantages are gained in a manner that could lead one to object that Godelian time travel so-called is not time travel after all. To begin the explanation of the claims, I need to say in some detail what is meant by Godelian time travel. This type of time travel does not involve any funny business with discontinuous world lines or world lines that are “bent backwards" on themselves. Rather, the funny business all derives‘ from the structure of the spacetime which, of course, cannot be Newtonian or Minkowskian. The funny spacetimes contain continuous and even infinitely differentiable timelike curves such that ifone traces along such a curve, always moving in the future direction as defined by the globally defined external time orientation. one eventually returns to the very same spacetime location from whence one began. There is no room here for equivocation or alternative descriptions; hence the second advantage. (More cautiously and more precisely, there are some spacetimes admitting Giidelian time travel in the form of closed, future-directed timelike curves, and the curves cannot be unrolled into open curves on which events are repeated over and over ad infinitum—at least such a reinterpretation cannot be made without doing damage to the local topological features of the spacetime; see section 6.3.) As for the third advantage, consider a spacetime 1V1, gab containing a CTC y that is instantiated by, say, a massive particle. Pick a point pEy and choose a small neighborhood N of‘p. UN is chosen wisely, all the causal relations in the restricted spacetime N, gabm will be “normal.” So if qEN is also on y and is chronologically later than [7, one would judge unequivocally that events 164 BANGS, CRUNCHES, WHIMPERS, AND SHRIEKS at p cause those at q and not vice versa. But in the encompassing spacetime one might be tempted to say that backward causation is involved since, although (1 is chronologically later than [3, events at q causally influence those at}? because 12 emerges from N and loops around to rejoin p. But the situation here is quite different from that in Wellsian time travel. In universes with Gédelian time travel it is consistent to assume—and, in fact, is implicitly assumed in standard relativistic treatments—that all causal influences in the form of energy—momentum transfers propagate forward in time with a speed less than or equal to that of light. So in the case at issue, events at q causally influence those at )9 because q chronologically precedes p and because there is a continuous causal process linking q to p and involving always future- directed causal propagation of energyimomentum. Of course, one could posit that there is another kind of causal influence, not involving energyfi momentum transfer, by which events at q affect those atp backwards in time, so that even if the future-directed segment of'y from g to ,0 were to disappear, events at q would still influence those at ,0. But the point is that Gédelian time travel need not implicate such a backward causal influence. We are now in a position to see why the second and third advantages have been purchased at a price. One can object that Gédelian time travel does not deliver time travel in the sense wanted since Godelian time travel so-called implies that there is no time in the usual sense in which to “go back.” In Godel’s (1949a) universe, for example, there is no serial time order for events, since every spacetime point p chronologically precedes itself; nor is there a single time slice which would permit one to speak of the Gédel universe at a given time (see section 6.3). I feel that there is a good deal of justice to this complaint. But I also feel that the phenomenon of“time travel” in the Gédel universe and in other general relativistic cosmologies is a worthy object of investigation, whether under the label of “time travel” or under another. The bulk of this chapter is devoted to that investigation. Before starting on that task, it is worth mentioning for sake of completeness other senses of time travel that appear in the literature. For example, Chapman (1982) and Zemach (1968} devise various scenarios built around the notion of“two times.” One interpretation of such schemes would involve the replacement of the usual relativistic conception of spacetime as a four-dimensional manifold equipped with a Lorentz metric of signature (+ + + —) (three space dimensions plus one time dimension) with a five- dimensional manifold equipped with a metric of signature (+ + + — —) (three space dimensions and two time dimensions). This scheme is worthy of investigation in its own right, but I will confine attention here to standard relativistic spacetimes. 6.3 The causal structure of relativistic space-times There is an infinite hierarchy of causality conditions that can be imposed on relativistic spacetimes (Carter 1971). I will mention only sufficiently many of 170 BANGS, GRUNCHES, WHIMPERS, AND SHRIEKS adopt will depend in large measure on whether it is possible to achieve a peaceful coexistence with CTCs. It is to that matter I now turn. 6.5 The paradoxes of time travel The darling of the philosophical literature on deelian time travel is the “grandfather paradox” and its variants. Example: Kurt travels into the past and shoots his grandfather at a time before grandpa became a father, thus preventing Kurt from being born, with the upshot that there is no Kurt to travel into the past to kill his grandfather so that Kurt is born after all and travels into the past . . . (Though the point is obvious, it is nevertheless worth emphasizing that killing one‘s grandfather is overkill. If initially Kurt was not present in the vicinity of some early segment of his grandfather’s world line, then traveling along a trajectory that will take him into that vicinity, even if done with a heart innocent of any murderous intention, is enough to produce an antinomy. This remark will be important for the eventual unraveling of the real significance of the grandfather paradox.) On one level it is easy to understand the fascination that such paradoxes have exercised—they are cute and their formal elucidation calls for the sorts of apparatus that is the stock-in-trade of philosophy. But at a deeper level there is a meta-puzzle connected with the amount of attention lavished on them. For what could such paradoxes possibly show? (1) Could the grandfather paradox show that Godelian time travel is not logically or mathematically possible?9 Certainly not, for we have mathematically consistent models in which CTCs are instantiated by physical processes. (2) Could the grandfather paradox show that Godelian time travel is not conceptually possible? Perhaps so, but it is not evident what interest such a demonstration would have. The grandfather paradox does bring out a clash between Godelian time travel and what might be held to be conceptual truths about spatiotemporal/causal order. But in a similar way the twin paradox of special relativity theory reveals a clash between the structure of relativistic spacetimes and what were held to be conceptual truths about time lapse. The special and general theories of relativity have both produced conceptual revolutions. The twin paradox and the grandfather paradox help to emphasize how radical these revolutions are, but they do not show that these revolutions are not sustainable or contain inherent contradictions.(3) Could the grandfather paradox show that Godelian time travel is not physically possible? No, at least not if “physically possible” means compatibility with EFE and the energy conditions, for we have models which satisfy these laws and which contain CTCs. (4) Could the paradox show that although Godelian time travel is physically possible it is not physically realistic? This is not even a definite claim until the relevant sense of “physically realistic” is specified. And in the abstract it is not easy to see how the grandfather paradox would support that claim as opposed to the claim that time travel is flatly impossible. Additional factors such as the need Time Travel 17! for high accelerations to complete a time travel jOurney or the instability of Cauchy horizons connected with CTCs (see section 6.10) would seem to be needed to support the charge that Gédelian time travel is physically unrealistic. If anything, Such factors tend to mitigate the force of the paradoxes (see sections 6.6, 6.8, and 6.10). (5) Doesn’t the grandfather paradox at least demonstrate that there is a tension between time travel and free will? Of course Kurt cannot succeed in killing his grandfather. But one might demand an explanation of why Kurt doesn‘t succeed. He had the ability, the opportunity, and (let’s assume) the desire. What then prevented him from succeeding? Some authors pose this question in the rhetorical mode, suggesting that there is no satisfactory answer so that either time travel or free will must give way. But if the question is intended non-rhetorically, it has an answer of exactly the same form as the answer to analogous questions that arise when no CTCs exist and no time travel is in the offing. Suppose, for instance, that in the time travel scenario Kurt had his young grandfather in the sights ofa .30-30 rifle but didn’t pull the trigger. The reason the trigger was not pulled is that laws of physics and the relevant circumstances make pulling the trigger impossible at the relevant spacetime location. With CTCs present, global Laplacian determinism (which requires a Cauchy surface, as discussed in chapter 3) is inoperable. But local determinism makes perfectly good sense. In any spacetime M, gab, chronology- violating or not, and at any fie M one can always choose a small enough neighborhood N off) such that N,g,,,,|~ possesses a Cauchy surface 2 with pE]+(E). And the relevant initial data on 2 together with the coupled Einsteinimatter equations will uniquely determine the state at ,9. Taking p to be the location of the fateful event of Kurt’s pulling/not pulling the trigger and carrying through the details of the deterministic physics for the case in question shows why Kurt didn’t pull the trigger. Of course, one can go on to raise the usual puzzles about free will; namely, granting the validity of what was just said, is there not a way of making room for Kurt to have exercised free will in the sense that he could have done otherwise? At this point all of the well-choreographed moves come into play. There are those (the incompatibilists) who will respond with arguments intended to show that determinism implies that Kurt couldn’t have done otherwise, and there are others ( the compatibilists) Waiting to respond with equally well-rehearsed counterarguments to show that determinism and free will can coexist in harmony. But all of this has to do with the classic puzzles ofdeterminism and free will and not with CTCs and time travel per se. (6) Perhaps we have missed something. Suppose that Kurt tries over and over again to kill his grandfather. Of course, each time Kurt fails—sometimes because his desire to pull the trigger evaporates before the opportune moment, sometimes because although his murderous desire remains unabated his hand cramps before he can pull the trigge...
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