An essential requirement for the possibility of time travel is the presumption that future and past were somehow real. But according to one popular view only the present is real, and to suppose that the past or future are also real is to suppose that the past and the future are also present — a contradiction. According to this sort of Heraclitean metaphysical conception, the future is genuinely open: there is no realm of determinate future fact, no denizens of the future to identify or talk about, though of course — in the fullness of time — there will be. Travel to the future on this view would be ruled out because there is simply nowhere to go.

The past, though, is spoken of as fixed and determinate and not subject to change. Travel into the past would appear to make it accessible in a way that would enable the traveler to effect changes — that is, to change things that are fixed and determinate and so not subject to change. Aristotle endorsed this popular view when he said that changing the past is beyond even the power of God. It was for this reason, Aristotle said, that ‘no one deliberates about the past, but about what is future and capable of being otherwise’ (NichomacheanThis is called the “no destination” objection to time travel.

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This view rejects the possibility of travelling to future because future is non-existent, therefore there is nowhere to travel to. Travel to past is also rejected, as the traveler cannot possibly go back in time and change it.To travel is to change position with time. Travel through space is the successive occupancy of spatial positions. Similarly, time travel requires the successive occupancy of temporal positions. But that seems to amount to either the trivial claim that each successive moment is occupied at the moment at which it is occupied, or the contradictory claim that there are some instants which might be followed not by the succeeding moment, but a quite different moment altogether. (Ayer 1956, p. 158).

It is well known that chronological discrepancies arise in connection with the special and general theories of relativity, quite independently of the question of time travel. But relativistic chronological discrepancies are benign in way that time travel discrepancies are not.What would count as a case of travelling into the past? We can conceive that after a certain time having experiences which are exactly like those of 1920. It is just this kind of thought experiment that makes time travel conceivable. But we would not be compelled to treat such experiences as decisive evidence of having traveled into the past. They might be taken as evidence of serious cognitive disorder, for example.

David Lewis has argued that time travel stories are perfectly coherent and it is instructive to examine his defense of the possibility of time travel. Lewis does not reject, but accept the reality of future and past. The world we live in, according to Lewis, is a Parmenidean world: ‘a four-dimensional manifold of events’ and the occupants of the world are four-dimensional aggregates of stages — ‘timelike streaks’ (1976, p. 145). However a time traveler is not like other aggregates; ‘if he travels towards the past he is a zig-zag streak’ (1976, p. 146). There might also be stretched out streaks which are travelers into the future.

This Parmenidean ontology of temporal stages removes the ‘no destination’ objection to time travel. Time travel requires that two events are separated by unequal amounts of time. One way that our experience of time may not correspond to physical time is because it may be intermittent. This type of discrepancy between objective time and psychological time provides a sense in which time travel into the future is unproblematic. These cases illustrate that experience may not coincide with elapsed time measured by clocks. The time travel envisaged by Lewis however involves the possibility of travel to the past and that raises serious difficulties.Lewis believes that denying the reality of past and future events is as parochial as denying the reality of distant places. Pastness, presentness and futurity are not objective features of reality but reflect only the perspective on the facts which is the standpoint of the experiencing subject.

The experience of a changing present does not reflect a change in facts at all, but only a change of chronological perspective, just as a change in spatial location effects a change in spatial perspective. On this view the temporal modalities of past, present and future do not mark any metaphysically significant distinction, whatever their importance may be for knowledge and practice. The commonly held conviction that there is a significant distinction between the past and the future is closely tied to the idea that cause cannot succeed its effect. The future seems to be causally accessible while the past is not. That indeed is one of the platitudes about what distinguishes the past and the future. It is no accident that those (like Lewis) who defend the possibility of time travel are leery about any deep metaphysical asymmetry between past and future.

If we accept this metaphysical framework it may seem, as Lewis suggests, the problems raised by time travel are oddities rather than absurdities. Having explained the consistency of time travel with his four-dimensional ontology, Lewis goes on to elucidate how the sequence of stages from which an individual is composed could be reversed in time. This involves reverse causation — a discrepancy between the direction of cause and the direction of time. Finally he provides a heroic attempt to defuse the threat of empirical paradox which arises because it seems that time travel would involve (or raise the possibility of) changing the past. There are also some related subsidiary problems which Lewis addresses, such as a puzzle about closed causal loops. Lewis believes that none of these difficulties are fatal to a coherent account of time travel.Time travel requires more than the possibility of successive events being separated by unequal amounts of time. It also requires a Parmenidean world which is extended in time analogously to the way that it is extended in space.

Although the dispute about whether the world is ultimately composed of persisting substance individuals or individuals which are aggregates of temporal stages is important, I will examine the plausibility of time travel stories mainly from within the Parmenidean four-dimensionalist metaphysical framework. While I believe that an ontology of individuals extended in time as well as in space is defective, that will not be a primary focus of concern in what follows. Let us grant that the world is a four-dimensional manifold of events and that we are aggregates of stages or streaks extended in time as well as in space. Could the aggregates of person stages from which are constituted be zig-zagged or stretched in the way that Lewis says time travel requires?One difficulty for zig-zag aggregates, not widely remarked upon, is what may be called the double occupancy problem. Tim, we supposed, stepped into the time machine on 1 January 1994, adjusted the dial, and precisely at noon set off into the past.

For observers outside it seems that the machine simply vanishes when Tim presses the button. But how can the “movement” into the past possibly get started? We know that at times later than noon there is no machine present, since it has disappeared into the past. But what of the moments just before noon? At those times there seem to be not one but two machines — one going backwards and the other forwards — each apparently occupying (or attempting to occupy) the same location! That is, it seems that as the machine sets out into the past it will collide with itself, or on a four-dimensionalist view the Tim-at-noon stage has earlier and later stages at the same space-time location. This is a difficulty which is glossed over in Lewis’s account — though in fairness it should be added that it is glossed over in other accounts as well.

All individuals, for Lewis, are aggregates of the temporal parts (or stages) of which they are composed. But a traveler into the past is a topological anomaly unlike other aggregates. It sounds as though the time travelling individual is a perfectly orderly, if unusually oriented, aggregate of stages.

But it is quite mysterious how some stage of an individual can have an earlier and a later stages at the same space-time location. This problem can be avoided by locating the successor stage of Tim-at-noon somewhere else, but then this stage will be discontinuous with Tim’s earlier stages. Time reversal would then involve discontinuity. And as Lewis notes: ‘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’ (1976, p. 147). The advantage of spatio-temporal continuity for individual identity is that it is a one-one relation. Discontinuity threatens to compromise identity by raising the possibility of one-many relations.

This discontinuity is concealed in the account because Lewis explicates the zig-zag with the help of a spatial analogy of a railway doubling back on itself. In that case the doubling back is unproblematic because there is more than one dimension for the railway track to follow. But although Lewis does not rule out two-dimensional time altogether, he explicitly excludes it from the discussion and identifies his concern with travel in one-dimensional time (1976, p. 145). In one-dimensional time it is quite unclear how there could be an aggregate of stages which doubles back without discontinuity. You can’t bend word-lines back inone-dimensional time without breaking them. There are parallels sometimes drawn from physics, such as Feynman’s famous conjecture that positrons are electrons travelling backwards in time, but they are of no help here.

Evaluating Feynman’s proposal would take us too far afield, but it should be noted that the supposed positron-electron aggregate is not a smooth and continuous “world-line” of a single particle, but at best distinct particle stages punctuated by violent events. The problems concerning the identity of quantum particles however are notoriously intractable and I will say no more about them. To make the story about Tim coherent we have to introduce another time series. There must be more than one chronological separation between two events. Time travel, Lewis says, ‘involves a discrepancy between time and time’ (1976, p.

145). That is, time travel requires that the temporal interval separating successive events is not necessarily unique: successive events may be separated by distinct temporal intervals. Since a temporal interval may be identified with a uniform causal process which occurs during that interval — that is to say, with a clock — this amounts to the claim that successive events can be separated by different networks of causal links. The so-called ‘twin paradox’ proposed by Paul Langevin, concerning the possibility of differential ageing implied by the general theory of relativity, is a famous illustration of the possibility of a plurality of chronological metrics. The networks of causal separation required for time travel involve something much more radical that the time dilation sanctioned by physics, though it may be that the chronological pluralism of relativity softens us up for the sort of time travel story recounted by Lewis.

Although the same interval of duration may be recorded by distinct, non-equivalent temporal metrics, these discrepant metrics are topologically contemporaneous. Thus in the relativistic ‘twin paradox’, one twin may return having aged less, but there are important theoretical constraints on the permissible deviation in the alternative chronologies. In particular he cannot return younger than when he departed, or arrive back before he departed. Time may be dilated but not contracted; and in particular because the separation between distant events can never be reduced to zero it follows that it can never be reversed. A clock in another inertial frame can appear to be running slow, and in an accelerated inertial frame will actually run slow. But it won’t stop and a fortiori it won’t run backwards. The time travel discussed by Lewis however involves more than a different chronological perspectives on the same stretch of duration.

Lewis introduces the notion of ‘personal’ time which may diverge from ‘external’ time (1976, p. 146). Five minutes of personal time might correspond to 100 years of external time. Lewis envisages however that personal time can run backwards with respect to external time. During the course of the journey the time traveler could observe external time clocks running in reverse. Backwards chronologies however arewithout any empirical (theoretical or experiential) support. We can of course imagine sequences of events running in reverse, but that is very different from the actual reversal of physical process.

Time travel into the past requires more than chronological discrepancy, which is in any case a relativistic feature of our world. As Lewis (1976, p. 148) says it ‘necessarily involves reverse causation’ and Lewis analyses causation in terms of counterfactual dependence. Time travel therefore involves events which are related so that an earlier event depends on a later event.

for its occurrence. Local causal reversal however generates the possibility of empirical paradox and is, I suggest, at odds with some deep convictions about human agency. I willcome back to this when we consider Lewis’s discussion of whether Tim can kill his grandfather. Trouble in fact arises, as we shall see, even if we suppose that it is not individuals but information signals which are sent into the past. These problems are bound up with a metaphysical conviction that while the future may be hostage to contingency the past cannot be.It is not a priori or necessary that causal priority is the same as temporal priority. Temporal priority concerns the totality of events; causal priority is concerned with particular sequences of related events. It may be that a particular causal sequence could run temporally “upstream”, as it were.

While this may not be contradictory, it is, we shall see, extremely problematic. We know quite generally that once an effect has occurred then its cause must have occurred. But if the cause were later than the effect, then once the effect has occurred then its cause would have to be unstoppable. However we also believe, in general, that we are able to intervene in the world to bring about or to prevent contingent happenings. If the cause of some event is located in the future then such interventions are subject to clear constraints, and in some cases will turn out to be impossible. It is a familiar feature of our experience that something that already exists can bring into being something which did not exist before.

But, as Ayer (1956, p. 171) has argued, it quite unclear how something which does not yet exist could now exert a causal influence. We are causally dependent on our ancestors, but not on our descendants. (I will consider below a problem which arises for supposing that some individuals might be their own ancestors.) A problem which arises in connection with reverse causation is the possibility of causal loops, that is ‘closed causal chains in which some of the causal links are normal in direction and others reversed’ (Lewis 1976, p. 148).

These are queer customers, but Lewis rejects that as an objection on the grounds that an infinite past or the decay of radioactive elements are just as inexplicable as closed causal loops. However the situation with closed causal loops, I suggest, is worse. Whereas spontaneous radioactive decay appears to leave something mysteriously unexplained without the possibility of appealing to something further, the case of closed causal loops raises the possibility of empirical contradiction. The fundamental difficulty of reverse causation is making sense of how what has not yet happened could affect what is happening now. On the one hand we believe that if something has not happened yet then maybe it will not. Perhaps something will derail the causal train. But if what has not yet happened is necessary for what has already happened then happen it must.

We are all fatalists about the past, but reverse causation extends the same considerations to the future. Lewis notes the close parallel with fatalism (1976, p. 151) in his discussion of whether it is possible for Tim to act to change the past and it is to this issue that we shall now turn. A popular theme in science fiction is the case of the traveler whose journey into the past is not merely possible but necessary — in order perhaps to secure some significant fact about the present, such as the time traveler’s own existence. It may be that the traveler, for example, is one of his or her own ancestors. In the story devised by Jonathan Harrison (1979) the principal character, ‘Dum’, turns out to be his own parent.

In a more complicated story ‘All You Zombies’ by Robert Heinlein (1960) the principal character (who undergoes a sex-change) turns out to be both of his own parents. There is a prima facie difficulty being one’s own parent, or more generally one’s own ancestor. It seems to involve an individual having incompatible degrees of genetic relatedness to him or herself. The genetic constitution of an individual remains constant over that individual’s lifetime. But each parent provides their offspring with one half of their genetic complement.

An individual who was both parent and offspring would seem to have an incompatible degree of genetic relatedness to him or herself. The genetic composition objection is not quite decisive however. For it is not actually contradictory to suppose that the second gamete, provided by the other parent at conception, should restore precisely the complement of genes discarded in the meiotic cell division in which the first gamete was generated. That is, it is not impossible that a sexually reproducing parent be genetically identical with their offspring — though the likelihood of this is the sort of probability that a kettle has of freezing on a hot stove. In such a case the offspring would be genetically a clone of its parent. Self-parenting would be more straightforward if we lived in a world in which ontogenesis was Aristotelian, so that the genetic form was provided by just one parent.

But in a world, such as ours, in which a Mendelian process of genetic blending takes place the possibility is quite beyond belief. In the case of Harrison’s ‘Dum’, it was impossible (without gratuitously complicating the story) for him to have had a daughter, for example, and that is simply incredible. The very idea of time travel is quite bizarre from a Heraclitean metaphysical perspective.

It apparently involves the possibility of alternative successors to the present moment. It is as though the time traveller is somehow able to move away from the present so that former contemporaries come to “occupy” another epoch. But there is just nowhen else to go. The whole notion of time travel rests on a misguided spatial analogy which leads to a denial that there is any significant asymmetry between past and future.

Time however branches forward but not back. The past is the realm of determinate fact; the future is the realm of unrealized possibility. The past is fixed, the future is fluid.These are all expressions of the same Heraclitean metaphysical intuition that there is a fundamental asymmetry between past and future. On this intuition it is nonsensical to suppose that there could be real time reversal. The so-called ‘arrows’ of time — the thermodynamic, psychological and cosmological — are sometimes thought to provide time with direction.

As long as time is identified with one of the ‘arrows’ it seems that time reversal makes sense. But if temporal passage is the actualization of possibility, time reversal would involve the absurdity of “repotentialization” of the past (see Capek 1961 p. 347). The past however is not a realm of potentiality like the future. That is not to say that future might be other than that which it is going to be, nor that it might be anything at all.

It is to say that what it will be is not yet determinate. It is inchoate, unlike the past. Rather than developing these themes I have concentrated on some difficulties for time travel which arise from within a Parmenidean perspective. First, one of the requirements for time travel, the existence of alternative chronological orderings, designated ‘personal’ and ‘external’ time in Lewis’s analysis, is not sanctioned by the alternative metrics of physics. Lewis’s ‘personal’ time happens to coincide with the physical time order, although, were time travel to occur, it would diverge from it. It is a time order in which our experience is located but which might come apart from ‘external’ time.

This temporal dualism between experiential time and physical time has a disturbing Cartesian resonance. It much more plausible to suppose that there is only one time series, that of physical time, and that this is also the time of our experience. On the Lewis story there is only ever one stage of the traveler which is the causal successor of any antecedent stage. But the causal successor (for personal time) need not be the same as the temporal successor for other individuals (in external time). While external time provides us with an account of temporal succession we can define or make sense of another time series which is based on causal succession. This in turn was explained by Lewis’s counterfactual analysis of causation. I have not challenged that analysis directly, but we noted that it has rebarbative consequences.

Lewis says that zig-zag streaks have the same sort of mental continuity and connectedness that unite any other aggregate of person stages (1976, p. 148). But the problems raised by reverse causation make it difficult to suppose that the present could be dependent on the future in the way that it is dependent on the past. For the time traveler, something anomalous happens. It seems that nothing in our experience rules out the possibility of psychological time continuing in reverse. In that sense backwards experience seems to be perfectly coherent. There is no obvious contradiction, for example, in the description of Tim’s experience at the beginning of this paper.

It therefore seems that our conscious experience (the psychological arrow of time) just happens to align with objective physical time but that it need not. But this is not easy to make sense of at all. To make good sense of it we would need to provide an account of causal interactions at the boundary of a backwards travelling (or time reversed) physical system. The problems that this raises are quite intractable. The ‘double occupancy’ problem is one of these difficulties which illustrates that it is very difficult to make sense of continuous zig-zag streaks in space-time.

Travel to the past requires reverse causation. Reverse causation raises the possibility of causal loops and the attendant problems that arise, for instance, if someone were to be one of their ancestors. Although this may not be self-contradictory it does lead to intolerable restrictions on the range of possibility, and the range of efficacious choice available to an agent. Dum and Jocasta in Harrison’s story, for example, cannot have a daughter. Tim cannot shoot his grandfather or press a button, though he can shoot grandfather’s twin and press a physically indistinguishable button which is not wired up to send a detonating signal into the past.

These empirical paradoxes arise as soon as reverse causation is allowed because reverse causation makes past times causally accessible. They are some of the intolerable consequences of countenancing time travel. Bibliography: