Time Travel - Is it Possible? Glenn Mason-Riseborough (17/10/1997) Introduction. What is time? This is one of those fundamental questions that humans have continuously asked throughout ... time. The asymmetry between the number of space dimensions (3) and the number of time dimensions (1) effects our experience to such an extent that we believe (rightly or wrongly) that they are fundamentally different. Intuitively, we say that time is that thing that always seems to pass constantly in the background, whatever we do, wherever we choose to go in space. So we ask the questions: Can we travel in time? Can we go back in time and visit people who died thousands of years ago? Can we go forward in time and visit people who are yet to be born? Science-fiction stories often discuss these questions and in fact Lewis (1986), in his discussion on time travel defines it as that which is described in science-fiction stories on time travel (1) . In this view, Lewis sees time travel as some kind of journey in which the time between departure and arrival is not equal to the duration of the journey. In my opinion, this is a naive view which does not really address the question of what we mean by time. In this essay, I will initially discuss a number of scenarios which show the logical possibility of time travel from a naive view of time. I will then show the insufficiency of this naive view before examining the shortcomings of Lewis’ (1986) argument. I will then discuss the view that time is ideal and look at some attempts at finding a definition of time which fits in with our intuitive feelings of the importance of the present. Special relativity (STR) and time dilation. One of the more curious and counter-intuitive results to come out of STR is the result which is known as time dilation. With the development of this theory, the intuitive idea that time is constant across all inertial reference frames is no longer accepted as true. Einstein’s speed of light postulate tells us that the speed of light in a vacuum, measured in any inertial reference frame, is constant regardless of the difference in velocity between the light source and observer. A scenario is as follows (see Fig. 1): there are two observers, one (OE) on Earth, and the other (OS) on a spacecraft moving at constant velocity; they are both observing a clock (2) on the spacecraft. This clock is designed such that it registers a ‘tick’ as a pulse of light emitted from a light source which then reflects off a mirror and is detected by a light detector next to the light source. It is clear that both observers see the pulse of light as travelling different relative distances. OS sees the light moving strictly up and down in one dimension (since he is at rest relative to the clock), whereas OE observes the pulse to have an additional horizontal component which takes into account the spacecraft’s horizontal velocity. Clearly we have a situation in which OE sees the light travel further than OS does (calculated using Pythagoras’ theorem) but still at the same speed. Thus, we must conclude that the time for both observers is different (3) . and hence, in a certain sense time travel already exists in everyday life. For example, if an spacecraft takes off then travels at an average speed of 0.0002c (216,000 km/h) (4) for an hour as measured by a clock on the spacecraft, then after this period has elapsed, a clock on Earth will have recorded that one hour and 7.2 ? 10-5 seconds have elapsed. Thus, (using Lewis’ definition of time travel) we can say that the travel time (as measured by the clock in the spacecraft) is less than the difference between the arrival and departure times (as measured by the clock on earth) and thus the spacecraft has travelled forward in time 7.2 ? 10-5 seconds (or the Earth has travelled back in time 7.2 ? 10-5 seconds). At this point we need to question our usage of two different inertial reference frames to calculate time. Clearly, if we used only one (most sensibly we would use the proper time interval ( )) we would not have arrived at a discrepancy between journey length and the difference between arrival and departure times. Using two different inertial reference frames shows us the possibility of time travel, however using only one does not. Our naive view of time is insufficient to choose which of these interpretations is better. The ubiquitous time machine. In almost any account of time travel the ‘time machine’ is conveniently used to aid the time traveller in his journey. We have no idea how this machine works in practice, but for a philosophical discussion this does not seem to matter. The next scenario I will discuss was given by Putnam (1962 cited in Weingard, 1973) and uses just such a device. In this scenario a time traveller is watched in his journey by some observer who is not travelling through time in any ‘unusual’ manner (5) (Fig. 2 shows the world line of the traveller from this observer’s point of view). In this situation the traveller stepped into the time machine at time t2 and transported himself back to time t1. At time t0 the observer sees the traveller (T1) at location A; at time t1 there is the creation of two additional travellers at location B, one of which is travelling in reverse (T2) (from the observers point of view entropy will be decreasing for this traveller) and one which looks very similar to, but slightly older than T1 (T3). At time t2, T2 and T1 collide and annihilate each other and only T3 remains. This scenario may be interpreted in two different ways. The first suggests that the traveller did travel in time as indicated by his world line and thus time travel is logically possible. The second view interprets this scenario such that the traveller simply disappeared at t2 after colliding with some strange system (which was created at time t1). Also created at time t1 was some person who bears a striking resemblance to the traveller (6) . Again we cannot know which interpretation we should accept—our naive view of time is too limited. Gödel’s R-universe. Deduced from the general theory of relativity (GTR), Gödel (1949, cited in Yourgrau, 1991) discovered that there is a non- standard universe which he called a rotating universe (or R- universe). In this universe the ‘compass of inertia’ rotates everywhere relative to matter and it is not possible to fit the co- moving frames into a single, consistent, cosmic time. What this means is that in these worlds there exists world lines which are curved to such an extent that they return to their starting points. Hence, in these worlds travelling in time would be equivalent to travelling in space. In the same way that we can travel around the Earth and end up where we first started, a person in an R- universe would simply be able to arrive back at the present by heading into the future for a sufficient length of time. It is interesting to note that our universe may easily be an R-universe (with a relatively small curvature), it is simply an empirical issue to determine whether or not this is the case. Discussion and summary of the naive view of time travel. From a naive viewpoint, our three arguments above all show in different ways that time travel is not only logically possible but (in the case of the first and third arguments) may also be a physical reality of our universe. From a certain perspective time dilation can be seen as a form of time travel where two objects are moving at different speeds relative to each other. The time machine scenario shows that time travel is logically possible, although not logically necessary as there can be other interpretations of the events. Gödel’s R-universe showed us that time travel may be seen in exactly the same way as ordinary space travel is seen. Lewis (1986) argues strongly in favour of the view that time travel is possible, although he does not go as far as saying that it exists in our universe. All he says is that the “possible world in which time travel took place would be a most strange world, different in fundamental ways from the world we think is ours” (Lewis, 1986, p67). Lewis’ reason for this view is entirely different from the arguments I have given which support time travel. His argument relies heavily on the assumption that there is some absolute time (which Lewis calls ‘external time’) which is distinct from ‘personal time.’ Time travel is then a discrepancy between personal time and external time. In this respect I cannot support his contentions since the results of STR insist that there can be no absolute frame of reference—all measurements (except for light) in space-time are relative to each other (7) . In addition, even if absolute time existed, it would be imperceptible and immeasurable and of no use to us whatsoever. Time is ideal. In my view, the solution becomes clear when we look at space- time from a completely different perspective. The case that Gödel (1949, cited in Yourgrau, 1991) argues is that time is merely ideal, an illusion; we may say that relativity has explained away time. Our view of time arises out of our subjective view of one particular dimension of four-dimensional space-time. His view (as I understand it) is that the problem of time in an R- universe destroys the objectivity of temporal succession. No longer can we say that time exists objectively separate from space, but it is simply one dimension of space-time in which we can travel through. Any special temporal succession is meaningless and thus time travel in the sense that it is different to some expected temporal succession becomes meaningless. It is analogous to saying that because I am walking at this speed in this direction, any difference that you make from me in speed or direction is space travel. We are both travelling in space just like we are both travelling in time. Thus, under this interpretation the question of the logical possibility of time travel becomes meaningless. Is the subjective aspect of intuitive time important? Having said in the previous section that time is ideal, we need to qualify this with a further conditional regarding the nature of time. McTaggart (1908, cited in Yourgrau, 1991) was the first person to explicitly state a fundamental distinction between different aspects of the temporal; these he called the A-series and the B-series. The A-series characterises time in terms of past, present and future—this idea recognises the flux of the now. On the other hand, the B-series shows the geometrical relationship between events in time in terms of before and after. Thus, for this aspect of time, events are located at specific immovable points on a continuum. We can clearly see that our arguments up until this point have been based entirely around the B-series (8) . We have not considered that the intuitive aspect of time may be relevant to our discussion. Gödel (unpublished, cited in Yourgrau, 1991) argued that if time is not an illusion, then it must include both the A-series and B-series aspects. This brings an additional complication to the argument. Should we believe our intuitive feelings on the importance of the present (9) , or should we only accept the proof that the equations tell us? Relativity theory has proved only that time is relative, it says nothing about its subjectivity. If the A-series is a necessary component of time, then we must accept that in some way time does flow, and there is the logical possibility of stepping out of this flow, or manipulating our speed through it. Conclusions. Is time travel logically possible? The best response I can give is ‘what do you mean by time?’ Naive approaches to time travel without first considering what we mean by time lead to ambiguity. If we use an intuitive definition that incorporates the A-series, then we may see time as a flowing of events which travel through the present. We may liken our travel through time to riding a standing wave on a river in which the future is constantly being created and revealing itself to us. The past is behind us, and we remember its passing as though we are looking back at it. Perhaps we may be able to leave our standing wave and travel up or down the river of time before finding another standing wave to ride. On the other hand, by accepting the inherent geometrical nature of B-theoretic time, we accept that the flow of time is illusion. Time is a dimension in space-time no different from any other dimension and as such everything in it exists completed. Our travel through time is equivalent to our travel through space and it is only the geometry of space-time which makes us believe there is any difference. References: Lewis, D. (1986). The paradoxes of time travel. In Collected papers Vol. II. Oxford: Oxford University Press. Weingard, R. (1973). On travelling backward in time. In P. Suppes (ed.) Space, time and geometry. Dordrech, Holland: D. Reidel Publishing. Yourgrau. P. (1991). The disappearance of time: Kurt Gödel and the idealistic tradition in philosophy. Cambridge: Cambridge University Press. Endnotes: 1 In particular, Lewis has in mind two stories written by Robert Heinlein—“By his bootstraps” in The menace from Earth and “—All your zombies—“ in The unpleasant profession of Jonathan Hoag. 2 We may consider a clock as a series of events, subjectively occurring regularly in time. Our first clocks would have been our internal processes (circadian rhythms, heartbeat, etc.) and the external events (light and dark) which influence them. Our newer clocks were an attempt to map regularly occurring features of the world onto our subjective experience. Hence, our clocks have evolved from sun rise and sun set observations, to observations of stars, to the atomic clock. All of these methods use the motion of a body as part of the measurement although (arguably) this is not the only way of measuring time. 3 The relative times are given by the formula where is the time of the ‘tick’ as measured by OS, is the time of the ‘tick’ as measured by OE, v is the relative speed between the spacecraft and Earth, and c is the speed of light in a vacuum 4 The Guinness Book of Records (1990) states the highest velocity attained by any space vehicle is 240,000 km/h, while the highest speed attained by a human is 39,897 km/h. 5 Perhaps all we can say is that the observer is travelling through time differently than the traveller is. 6 Weingard (1991) suggests a matter transmitter (whatever that is) is responsible for the disappearance and reappearance of the traveller rather than a time machine (whatever that is). The distinction is that there is no time travel taking place. 7 We need not accept STR’s denial of absolute time, in fact we could devise a system in which there was only absolute time. However, I think it is important to stay as true to our own universe as possible. It would be easy to imagine a world in which there were five time dimensions and four space dimensions and the inhabitants travel at will through all of them with equal ease. Then we could easily say that time travel is logically possible, but it would be trivially so, and not related to our own world view of time. 8 STR and GTR are entirely geometrical representations and thus B- theoretic. 9 My own opinion is that both the A-series (in the sense of the now) and B-series aspects of time are true. From this, I can say that we move neither in space nor time, we exist and have always existed in the instant which is now. The object that existed in this relative position ten seconds ago and had the same name as me is not me; the object that will exist in this relative position in ten seconds and will have the same name as me is not me. These objects are as much me as the object which exists 10 metres away from me. Thus, for me, time travel (and space travel) as I have defined it is not possible, either logically or actually.