Introduction
In this essay I intend to explore the concept of time travel from a philosophical point of view. In addition to time travel being a subject that is inherently interesting to fans of science fiction, it raises a number of deeper philosophical and scientific issues and enables us to examine these issues from a different perspective. Among the issues raised are the reconciliation of different kinds of possibility - psychological, epistemic, logical, metaphysical and physical – as well as the reality, or otherwise, of time and tense, and, perhaps most interestingly, what factors constrain our freedom to act as we wish.
I believe that by considering time travel, we may learn something about the world that we live in, and we can also use what we know through a philosophical investigation of our world to determine to what extent, if any, time travel is possible, and if it is, what implications this has for us.
I will suggest that time travel is possible on at least some of the levels of possibility mentioned above, but perhaps not on others. I will further suggest that if it is possible, the world in which it occurs, will seem very odd indeed. Since we have yet to see time travel instantiated in the actual world, it remains to be seen whether it is our world that is that odd.
I will initially discuss different types of possibility. I believe that this is necessary because time travel may be possible at certain levels of possibility and not at others. I will then discuss different methods of time travel that have been discussed by writers on the subject. Some of the problems and paradoxes have more impact on some types than others, so it is necessary to distinguish them. I will also briefly discuss different philosophical takes on time itself and suggest that if time travel is possible, it is more likely to take place in a time structure that is real and untensed. I will then go on to discuss some of the problems that have been posed for the proponents of time travel and attempt to show that while they have problematic implications, they do not preclude its logical or metaphysical possibility. I will then go on to suggest how by an appeal to a particular instantiation of the multiverse theory the paradoxes associated with time travel may be completely eliminated.
Possibilities of time travel
When discussing the possibility of time travel we should consider that there are different kinds of possibility: psychological and epistemic, as well as logical, metaphysical and physical possibility.[1] Time travel is possible at a psychological level. By this I mean that we can clearly understand what it means for someone to travel in time and interact with people from different eras. This is, however, no guide to the kind of possibility we are interested in when considering the possibility of time travel. Humans are able to conceptualise many ideas that cannot be actualised: for example, attempts have been made to square the circle and redefine the value of pi. It is possible to conceive of such things, but they are not possible in any philosophically interesting sense.
Rather, we should concern ourselves with whether time travel is logically, metaphysically or physically possible.[2] Of these categories logical possibility is the broadest. Time travel is logically possible if it is not precluded by the laws of logic. These laws are open to dispute, but one clear case is that logical contradictions are not logically possible. So, for example, it is not logically possible that ‘it is the case both that Ferdy is a female fox and that Ferdy is not a female fox’ (Lowe 1998: 14-15). I shall argue that we have no reason to suppose that time travel in this sense is not possible, but that in order to avoid a logical contradiction time travel is subject to certain constraints which I will outline in the course of this essay.
Metaphysical possibility covers a narrower range of possibility, sometimes identified with broad logical possibility. It is concerned with the essential nature of things. For instance, it is metaphysically impossible for water to be anything other than H20. If there is a logically possible world in which time travel occurs, we can say that it is metaphysically possible. It may be the case that time travel is logically possible but not metaphysically possible. What is and is not metaphysically possible is open to dispute and I do not need to discuss this, but adopting this metaphysics, my discussion will bring out some of the constraints on the type of possible world that time travel will takes place in.
I take physical (or actual) possibility to be what is possible in this world, the world in which we find ourselves (or more weakly in nearby possible worlds in which uncontroversial counterfactual assumptions are made – namely those nearby worlds that have the same laws of nature). If time travel is physically possible, then clearly it is metaphysically and logically possible. But if it is logically possible, it does not entail its actual possibility. As such, logic and metaphysics inform what is actually possible.[3]
Another kind of possibility, raised by Horwich (1987), is epistemic possibility. He suggests that certain types of knowledge about time travel may be precluded to humans, for example, perfect precognition. Since the notion of time travel raises the possibility of knowing what one is going to do, or what one has done, and as a result of this knowledge attempting to change what happens, we should concern ourselves with whether it is possible to know such facts. I will discuss this further when I discuss the paradoxes of time travel.
The nature of time
One of the main objections to the possibility of time travel is the so-called no destinations objection. This has its origins in McTaggart’s contention that time, as the dimension of change, requires an A series, that an A series leads to a contradiction, and that time is therefore unreal. A refinement of this idea, presentism, regards only present time as real: the past and the future are not. This is a threat to the possibility of time travel because simply put, if the past and future are not real, then time travel is impossible because there is no when to which to travel.[4]
However, this cannot be the case. This is one situation where scientific investigation can inform our metaphysical views. We know that time travel into the future is physically possible. The general theory of relativity predicts that the clocks on board an object that accelerates to sufficiently fast speed (or which moves into a sufficiently strong gravitational field) will move at different rates to those in a stationary frame of reference.[5] The clocks on board a spaceship moving at relativistic speeds will move more slowly than those located back on Earth.
If such a spaceship were to travel from Earth to a nearby star and then return, it would effectively have travelled into the Earth’s future. For every hour that passed on board ship, more than one hour would pass back on Earth. Such predictions have been tested experimentally by placing very accurate atomic clocks on board a concorde flying at supersonic speeds and comparing them to similar clocks that remained stationary on the ground. The differences predicted by relativity theory have been measured.
So any argument that time travel is impossible because there are no destinations must be revised if not rejected entirely because time travel to the future is possible.[6] Dowe (2000) has suggests that a presentist view may still be possible if we revise the theory to allow that the destination time exists or comes into existence when the time-traveller arrives at his destination. But since relativity theory suggests that time passes at different rates for objects in different frames of reference, (that is for any object undergoing acceleration relative to another), a vast multitude of different presents is entailed. This seems to raise very similar problems as those which presentism solves by the abolition of the past and the future.
The alternative view to presentism is that past, present and future are all real (although our epistemic relationship to the past and the future clearly differ).[7] From the time-traveller’s point of view, this makes life much easier as there is no question that the relevant destination exists. This view is favoured by Lewis (1976), who is an advocate of the possibility of time travel. However, this is not entirely unproblematic as allowing the reality of the future raises the issue of whether the future is open, determined or fixed. Fewer questions are raised by allowing the reality of the past because intuitively we believe the past to be fixed in a way that the future is not.[8] Since we have seen that time travel to the future is actually possible, I do not intend to address the ontological status of the future here. The remainder of this essay is concerned with travel to the past.
Methods of time travel
One question worthy of consideration is what form time travel might take. I will distinguish between two kinds of time travel: sliding and jumping. Let us suppose that our time-traveller is travelling from 2003 back to 1963 to find out who actually killed President Kennedy. On a sliding view, when the time-traveller presses his button to activate his time machine, he stays in our universe but travels backwards towards his destination taking a finite non-zero time to arrive there. Put another way, there is spatio-temporal continuity connecting the time-traveller in 2003 to 1963.[9] As he travels he will see the outside world moving backwards at an accelerated rate (assuming that while travelling he can visually interact with the non time-travelling world). If a non time-travelling observer were to observe the time machine throughout the entire forty-year period, he would see the time-traveller appear from nowhere in 1963 and then observe him moving apparently backwards at one fortieth normal speed until the year 2003 at which point he would disappear.
On a time jump scenario, the time-traveller disappears, leaving our space-time in 2003 and reappearing in 1963. The journey may or may not involve some passage of time from the point of view of the traveller, but for the non-time travelling observer the time machine leaves our universe and reappears elsewhen. There is a spatio-temporal discontinuity.
Physical theories suggest both may be true. Gödel concluded that certain solutions to the field equations in general relativity suggest that travel to the past may be possible on a time jump view via wormholes in space-time. Richard Feynman, by contrast, suggested that a particular sub-atomic particle - a positron - may simply be an electron moving backwards in time. This is analogous to the sliding view. From our non time-travelling perspective, we observe electrons and positrons colliding and annihilating each other. From the electron’s perspective the electron becomes a positron and starts moving backwards in time at the point at which we see them annihilate each other. This example brings to the fore one of the oddities associated with the sliding view of time travel, namely that different temporal parts of an object exist in two places at the same time. I believe that this is simply an oddity, however, it does raise a real problem, and I now propose to examine some of the problems associated with time travel. I believe that none of these problems is fatal for the concept of time travel itself. They do however raise problems with particular modes of time travel.
Problems associated with time travel
The first problem, alluded to above, and discussed as far as I am aware for the first time by Grey (1999:60), is the double occupancy problem, which applies solely to the sliding mode of travel. Consider the moment that the time-traveller presses the button on his time machine to start moving into the past. From his point of view he will start moving backwards in time and the outside world will start moving in reverse. From the point of view of the external observer, as we approach the point at which the button is pressed, there will be two time machines, one moving forwards in time, and one moving backwards.
This raises the obvious difficulty that if the time machine is stationary in space, the forward and backward-moving temporal parts of the machine will occupy the same space at the same time. The moment that the time machine starts moving backwards it would find that the space that it takes up is already occupied by the forward-in-time moving part of the time machine that is already there! This is a distinct question as to whether two objects, such as a statue and a lump of bronze, can exist in the same place at the same time. It is simply whether different temporal parts of the same object can exist in the same place at the same time and appears to be metaphysically and a fortiori physically impossible.
This problem is analogous to Feynman’s proposition that a positron is merely an electron moving backwards in time. In such a case, the non time-travelling observer sees an electron and a positron coming together and annihilating each other. Dowe (2000: 445) uses this analogy to suggest a solution to the problem: that the time machine must be moving. However, the analogy does not hold up. An electron is a point like object (subject to quantum mechanical uncertainty in relation to its position). For an object extended in space, such as a putative time machine, even if it is moving there will be a time when one part of the object overlaps another part. In order to avoid this, space and time would need to be discrete and discontinuous so that there is a time t1 at which the whole of the time machine is in a particular region of space S1, and an immediately subsequent instant t2, at which the whole of the time machine is in region S2. Regions S1 and S2 must be spatially separated such that there is no point that is in both regions and this is simply not the case with moving objects. I do not wish to discuss whether space and time are ultimately discrete or continuous, but even if they were discrete - composed of indivisible units - an object of greater than one spatial unit would be unable to move from a region S1 to a region S2 in one time unit unless it were no more than one spatial unit in size. Such a small time machine would make human time travel very difficult indeed! I cannot see any way of resolving this difficulty.
Another potential problem associated with sliding to the past is the measurement of elapsed time.[10] How is the time-traveller to know how much time has passed during his voyage into the past? In the normal world we measure time by reference to certain types of change.[11] The length of a day was in times past defined by reference to the Earth’s rotation and its position relative to the Sun; hours, minutes and seconds were subdivisions of the day. With technological progress the accuracy with which we were able to measure time improved and now basic unit of time measurement is the second, which is defined in relation to so many vibrations of a caesium atom.[12] The caesium atom is used because of its accuracy – its vibration rate is constant - but of course this constancy is in relation to the movement of other objects in the universe, which also move with regularity, such as other atoms as well as the stars, pulsars, galaxies, etc. So in a universe with a large number of objects, we can confidently use the constancy of the rates of change of some objects with respect to others as a means of measuring the passage of time. However, in a universe with a very limited number of objects this confidence is undermined. If we imagine a universe with three objects A, B, and C and suppose that we observe C’s movement appearing to slow down relative to A and B, would we be justified in treating C as a poor reference by which to measure the passage of time? Would not an equally justified conclusion be that A and B’s movement were getting faster?[13]
Insofar as this relates to time travel, in a time machine that is moving backwards, the number of objects that the time-traveller has available to measure change and thus the passage of his personal time is likely to be extremely limited compared to the non time-traveller. How could a time-traveller know whether a clock in his machine was reliable or not? Lewis (1976: 146) suggests a functional measure of time: it is that which occupies a certain role in the pattern of events that comprise the time-traveller’s life: ‘Memories accumulate. Food digests. Nails grow. Wristwatch hands move.’ He says that this kind of measurement of time is sufficiently like our normal measurement that we can apply our temporal vocabulary to the time-traveller. However, this does not answer the question that I have asked. It is not clear to me that these measures can be treated as reliable for the reasons I have stated. In such a situation the boundary between what constitutes the flow of time, and the means by which we measure it seems to have become a little blurred.
Sliding types of time travel, then, have certain difficulties associated with them, most notably the double occupancy problem. What of time jumps? Because of the spatio-temporal discontinuity, these are not subject to the double occupancy problem. However, the problem of measuring how much time has elapsed during the journey may be a problem here too, even if the jump appears instantaneous to the traveller – is the time jump instantaneous or does time, in fact, stop during the journey?[14]
One further problem, peculiar to jump jumps, raised by Lewis (1976: 148), is that of personal identity. Since all that the non time-travelling world sees is the older part of the time-traveller appearing in 1963, and continuing to live his life, while some later time, the younger part of the time-traveller is born, grows up, until he enters his time machine and disappears, how are we to distinguish between the genuine time-traveller and the case in which our time-traveller has been annihilated in 2003 and been replaced by an exactly similar person ex nihilo in 1963? Lewis (1976: 148) answers thus,
‘what unites the stages (or segments) of a time-traveller is the same sort of mental, or mostly mental, continuity and connectedness that unites anyone else. The only difference is that whereas a common person is connected and continuous with respect to external time, the time-traveller is connected and continuous only with respect to his own personal time.’
Lewis raises the possibility of a counterfeiting demon creating someone, Fred, in mid-life, who appears out of thin air, lives for a while and then dies. At a later date the demon destroys another person, Sam, who at the time of his destruction is exactly like Fred (either by chance or through the demon’s moulding) at the moment of his creation. In combination Fred and Sam are very much like a single time-traveller whose personal time starts at Sam’s birth, goes on till Sam’s death, then immediately on from there to Fred’s creation and then his death. However, according to Lewis, they do not have the right kind of causal connectedness necessary. Fred’s early stages are not dependent on Sam’s later stages. So this is not a case of time travel.
While I agree with Lewis’ conclusion, I think that a little more needs saying. From a God’s eye view, Lewis’ explanation is correct. However, from the perspective of the time-traveller himself or the external observer there is little to distinguish the two cases. For those of us inhabiting the universe, we have no a priori rules that we can apply: as far as we are aware there has yet to be a single case of time travel and so the question arises how would we act in such a situation. I submit that if we were to encounter someone who appeared in the past – let us call him, Samorfred - who is physically identical to Sam, with Sam’s memories, and claiming to be Sam, we have, unless evidence to the contrary is provided, good reasons to suppose that it is Sam. This does not prove, of course that it is Sam, and matters of proof may be important: if Sam had killed someone before his departure, would his counterpart be liable for the murder?[15] However, I do not think that the problem of personal identify is in any way threatening to the notion of time travel and as such little else needs to be said on the subject.
Paradoxes
The problems addressed so far raise difficulties with particular forms of time travel, but do not threaten its overall logical or metaphysical possibility. Travel to the future does not entail any paradox, just a certain strangeness in that people are able to age at different rates. Time travel to the past however, does appear truly paradoxical, because it appears that we should be able to change the past. The principal paradox is identified in Lewis’ paradigmatic example (1976: 149):
‘Consider Tim. He detests his grandfather, whose success in the munitions trade built the family fortune that paid for Tim’s machine. Tim would like nothing so much as to kill Grandfather, but alas he is too late. Grandfather died in his bed in 1957, while Tim was a young boy. But when Tim has built his time machine and travelled to 1920, suddenly he realizes that he is not too late after all. He buys a rifle; he spends long hours in target practice; he shadows Grandfather to learn the route of his daily walk to the munitions works; he rents a room along the route; and there he lurks, one winter day in 1921, rifle loaded, hate in his heart, as Grandfather walks closer, closer…’
This is the paradox. If one could travel to the past, one could presumably change the past. In this example, doing so would mean that Tim’s grandfather dies in 1921, not 1957. Since he dies in 1921, he never has children, so Tim is never born, ensuring that he does not travel back to 1921 and does not kill his grandfather… So Tim both does and does not kill his grandfather, and consequently both does and does not exist. This is a plain contradiction. It is logically impossible that Tim can change the past by killing his grandfather, so Tim cannot kill his grandfather.
One can ask the question whether this conclusion does not apply just to the past, but to the present and future as well? We cannot change the present from what it is and we cannot change the future from what it will be. This does not mean that we cannot influence events now. What we do now influences the future, enabling certain possibilities and ruling out others. However, we cannot change the future from what it will be. The problem comes into stark relief when we consider the past, since we have a different epistemic relationship with the past than that which we have with the future: we can have a certain sort knowledge of the past that we do not have of the future. If a non time-travelling Tim were to plan to kill someone at some point in the future, we should not say that he could not. In contrast, we know that he is precluded from killing his grandfather in the past, yet it is our conviction that Tim can kill his grandfather. His inability to do so violates the so-called Autonomy Principle:
‘Suppose an agent, T, within a local region of spacetime, S is able to bring about some configuration of matter with features F. Then in any local region, S’, sufficiently similar to S (with respect to the region’s intrinsic characteristics), an agent, T1 sufficiently similar to T, must also be able to bring about configuration of matter with the feature, F.’[16]
In other words, Tim knows that he can kill has grandfather, and the possibility of his creating a logical contradiction will not prevent him from so doing. Some take this as evidence that time travel to the past is impossible, reasoning as follows.
- If time travel to the past were possible, then contradictions would be possible.
- Contradictions are impossible.
- Therefore time travel is impossible.
If we are to allow time travel we must deny the claim in the first premise, that contradictions would be possible. Lewis suggests that the problem is to do with an equivocation in the meaning of the word ‘can’. Tim can kill his grandfather in the sense that he has the capacity to kill his grandfather, but he doesn’t. He cannot kill his grandfather because it is logically impossible to change the past. He suggests by analogy that an ape cannot speak Finnish because it does not have the correct anatomy, whereas he, Lewis, can because he is a human with the correct vocal capacities. ‘But don’t take me along to Helsink as your interpreter: I can’t speak Finnish,’ he says (1976: 150). His speaking Finnish is compossible with facts about his anatomy but not with other facts about his knowledge of the Finnish language. Similarly, Tim’s killing his grandfather is compossible with one set of facts, but not compossible with another, wider, set of facts.
However, this answer is unlikely to provide comfort to those, like me, who intuitively find this explanation unsatisfying. The reason is that there is a disanalogy between the two examples. We are able to provide reasons why the ape cannot speak Finnish: it has the wrong anatomy, an inappropriate larynx for speaking a human language and insufficient intelligence to understand more than a few simple words. We are also able to provide reasons why Lewis cannot speak Finnish: he has not been taught how to speak it, he is not good at learning languages, he has neither the time not the inclination to learn, and so on.
Are we able to do the same in the time travel example? It seems that we can provide an explanation as to why Tim can kill his grandfather: he has the training, the physical strength and the inclination. These explanations come from outside the structure of the time-travel element of the story. When it comes to saying why he cannot, however, it seems that the only explanation we can provide is that he cannot because he does not: a circular explanation. We are forced back onto the horns of the time-travelling dilemma. The paradox is unresolved.
If we allow that Tim cannot kill his grandfather, then what would actually happen? Suppose Tim repeatedly tries to kill his grandfather. On each attempt he is bound to fail. Horwich (1987: ch.7) discusses such attempts.[17] Tim would notice that his gun jams; he might forget to be in the correct position one morning; his grandfather might take an alternative route to work. In other words we see a string of increasingly improbable coincidences. We do not see such coincidences in the non time-travelling world and therefore he suggests we should not allow them in Tim’s case. He goes on to suggest that there are alternative explanations that are compatible with time travel being logically possible. These include what I take to be some sort of hard determinism in which the initial conditions of the universe are such that those who travel to the past are not concerned with bilking. Another is that those who travel to the past are simply psychologically uninterested in attempting to change the past. A third is that space-time is such the energy requirements for time travel make impractical travel to a past that is sufficiently recent to allow such attempts.
I do not wish to deal with these alternative explanations here. I concede that they may all be adequate explanations as to how time travel could happen without leading to logical contradictions. Moreover, the third of them – the excessive energy requirement required for time travel – is compatible with what we know of the physical universe. Instead, I wish to consider whether there is any other way of resolving the problem that the more Tim tries to kill his grandfather, the more he will encounter coincidences that prevent him from so doing as it seems to me that this is the principal oddity of the grandfather paradox and Horwich’s appeal to alternative explanations are simply ways of avoiding it.
Suppose that every month during our lives we make a decision that is a straight two-way choice. If we live for seventy years we will make 840 such choices before we die. Further suppose that each choice affects the future choices available, so that by making one choice we rule out all of the outcomes that the other choices would have led to. Each choice, then, takes us down a branch on a tree of possibilities. By the time we reach the end of our lives, the total number of potential outcomes for our lives is 2840, a number which according to my calculator is 253 digits long. The chances of reaching any particular outcome are, ceteris paribus, 1/2840, odds less likely than the oddest of coincidences. Just to get a feel for how unlikely any particular outcome is, it is similar to someone playing the national lottery and winning the jackpot on 36 consecutive occasions.
Yet we do not think that the scenario I have outlined is in any way odd or unlikely. We certainly don’t think that our journey through life is beset with coincidence and I believe that I have been very conservative with the number of choices we make during our lives. This is because the relevant coincidence is not the occurrence of a multitude of unlikely events, but rather it is our foreknowledge of future events combined with the belief that we are free agents. If at birth we had been given a letter that we were told to open on our deathbed and which, when we did so, correctly outlined each of the choices we had made throughout our lives, we should indeed be very surprised – and we would probably make a hasty exit at that stage![18] If this is the case then the major paradox of time travel, the grandfather paradox, is a specific instance of a more generalised problem - nothing to do with time travel – namely to what extent is it possible to act freely in a fixed or determined universe? Normally this problem is not apparent to us, precisely because we lack foreknowledge. Instances of time travel raise the possibility of such foreknowledge and this I would suggest that this is the true problem. If we routinely went through life with accurate predictions being made concerning our futures we would have a very different conception of the relationship between foreknowledge and our freedom of action than we do. If this is so, then in my view a universe in which time travel were possible would requires us to revise our notions of what it means to be free.[19]
Possible solutions
One way of avoiding the paradoxes associated with time travel, and retaining freedom, is to appeal to the multiverse. So far the types of time travel we have been discussing have been unidimensional - the time-traveller goes back to his own past, which he cannot change. Abbruzzese suggests an alternative, multidimensional view in which the time-traveller goes to an alternative universe. So when Tim travels back to the year 1920, he in fact travels to a 1920 in a different universe. In this universe he is free to act as he wishes without creating a paradox. He can and does kill his grandfather (or rather his grandfather’s counterpart). Of course, in that universe he will then never be born, but this doesn’t matter as he has been born in his own universe. The difficulty with this, as Abbruzzese rightly points out, is that this does not appear to be time travel at all, but rather trans-dimensional travel. The time-traveller would not be interacting with his ancestors, but with their trans-dimensional counterparts.
However, with a slight modification, we can obtain the paradox-avoiding benefits of the multiverse while retaining the concept of time travel. The solution is to posit a branching multiverse, similar to the idea suggested by Everett in relation to quantum theory. On this scenario, on each occasion where there is a choice or the possibility of a different outcome, the universe splits into two, one in which one outcome is realised, and another in which the other outcome is realised. When Tim arrives back in 1920, he travels back along his own branch, but the moment he does anything different, a new branch is created, and, of course, on this branch he is free to kill his grandfather. Of course this will mean that there are branches in which Tim exists and those in which he does. This scenario raises many of the same problems that Abruzzese identifies with his version of the multiverse – and empirically the two may be indistinguishable. But I believe that on this scenario, we are justified in calling what Tim does time travel.[20]
Conclusions
In this essay I have discussed some of the problems and paradoxes associated with time travel. I have attempted to show that the notion raises some peculiar consequences, but with the exception of the double occupancy problem raising seemingly insuperable difficulties with sliding modes of travel, there is nothing that as a matter of logic prevents time travel from being possible. In the case in which we are presented with an agent who is able in ways that might appear incompatible with the past we may notice a string of increasingly unlikely coincidences. The reason we don’t notice such coincidences in the actual world is as a result of our different epistemic relationship with the future. We are just as unable to do other than what we will do in the future as we are in the past.
Gary Lorrison
Department of Philosophy
University of Durham
garylorrison@aol.com
References
Abbruzzese, John. 2001. On Using the Multiverse to Avoid the Paradoxes of Time Travel. Analysis. 61(1): 36 – 38.
Chambers, Timothy. 1999. Time Travel: How not to Defuse the Principal Paradox, Ratio 12(3): 296 – 301.
Dowe, Phil. 2000. The Case for Time Travel, Philosophy: The Journal of the Royal Institute of Philosophy, Volume 75, Issue 293: 441 -451.
Grey,William .1999. Troubles with Time Travel, Philosophy: The Journal of the Royal Institute of Philosophy, Volume 74, Issue 287: 55 -70.
Harrison, Joseph. 1971. Dr. Who and the Philosophers,. ???
Horwich, Paul. 1987. Asymmetries in Time: Problems in the Philsophy of Science. MIT Press, London.
Lowe, E.J. 1998. The Possibility of Metaphysics: Substance, Identity and Time. Clarendon Press. Oxford
Lowe, E.J. 1987. The Indexical Fallacy in McTaggart’s Proof of the Unreality of Time. Mind 9: 62-70
McTaggart, J.M.E. 1908. The Unreality of Time. Mind 17: 457-474
Oddie, Graham. 1990. Backwards Causation and the Permanence of the Past. Synthese 85(1): 71-93
Shoemaker, Sydney. 1969 Time without Change, Journal of Philosophy 66: 363 - 381
[1] The precise formulation of these different types of possibility is open to dispute and different interpretations, but for the purposes of this essay it is necessary merely to appreciate that they refer to different ways that we may understand something to be possible. Insofar as this needs clarifying I have attempted to do so.
[2] I adopt these concepts from Lowe (1998)
[3] The results of scientific experiments can also help us to decide between alternative metaphysical systems – for instance, the special and general theories of relativity have shaped discussion on the nature of time. The same may apply to logic. Quantum mechanics has led to the developments of new logics, which, while controversial, challenge our traditional concepts of logic.
[4] Oddly, McTaggart’s complete rejection of the reality of time seems less threatening, as past, present and future seem to be on an equal footing on his thesis.
[5] Sufficiency in this case is when relativistic effects become noticeable.
[6] It may be argued that such relativistic time travel is not true time travel, but I cannot see how such an argument could seriously be advocated.
[7] This would appear to require either a rejection of McTaggart’s requirement that time requires an A series, or that an A series implies that time is unreal – see for example, Lowe (1987).
[8] But see Oddie for an attempt to show that the past may not be fixed!
[9] Relativistic travel to the future is of the sliding variety.
[10] I am not yet sure that this is a real problem but submit that it is at least worthy of discussion as it does not appear to be addressed at great length in the literature on the subject.
[11] Of course, some philosophers maintain that time simply is change. I do not wish to address that issue here, but wish to point out that our measurements of time are all dependent on change of some sort.
[12] The duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom.
[13] I am sure that there is some relation between this point and Shoemaker’s (1969) attempt to show that time need not necessarily involve change, but I need to develop this idea further.
[14] Unless we have some a priori reason for supposing that time requires change it is not clear to me that we can distinguish the two cases.
[15] I have adopted this argument from Harrison: 1971
[16] I adopted this definition from Chambers 1999: 298
[17] Such attempts are known as bilking attempts. A bilking argument is an argument that concerns a closed causal chain of the sort described, in which by modifying one event in the chain, we introduce a contradiction into the chain.
[18] For a wonderful fictional account of just this, see Gabriel Garcia-Marquez’s One Hundred Years of Solitude.
[19] See my unpublished MA essay ‘Moral Responsibility and Determinism: An Analysis of Frankfurt Style Cases’ for a fuller discussion of the tensions between freedom and determinism.
[20] For reasons of space I have not dealt with the other major objection to backwards time travel: namely that it appears to necessitate reverse causation with effects preceding causes. I simply assert that if we are to rule out time travel on this basis we need to decide if the notion that causes should precede their effects is a priori or a posteriori. If a priori, then we must rule out backwards time travel. If a posteriori, then given a sufficiently strong philosophical argument we are able to allow time travel and accept the odd consequences outlined by Lewis and … among others as simply oddities permitted within the overall metaphysical structure.
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