Time Travel Paradoxes
This essay will investigate some typical paradoxes involved with time travel and attempt to determine whether or not they actually prohibit travel through time.
Is Time Travel Possible?
First, I want to take a brief detour into a couple of, while not practical, at least logically consistent methods of time travel allowed by Einstein’s special relativity theory. Of course, theoretical physicists are still debating whether or not there is any possible way to actually travel in time or whether it is even permissible according to the laws of nature but we won’t need to delve that deep into the subject. This is fortunate because their discussions typically involve the use of highly complex mathematics and so preclude most of us from participating. I intend to leave the mathematics to the experts and instead focus on a couple of the more accessible notions to have emerged. Let’s begin with some of the basics.
Einstein’s theory of special relativity (‘special’ because it excludes considerations of gravity) and subsequent extremely precise experiments have shown that time is undisputedly relative. By this what I mean is that time can pass at different rates for different observers. However, this doesn’t mean that you might wake up one morning and find that it takes you only fifty minutes to watch an hour long television programme. What it does mean is that for two observers undergoing motion relative to each other, the rate of passage of time (as they measure it to be for the other) will be different.
If I were to stay on Earth (motionless relative to you) while you rocketed off into space at a speed nearing the speed of light and I was to somehow compare the passage of your time with mine, I would find that your clocks are all moving slower than mine. Literally. It is important to note that this is not due to a defect in our timekeeping devices, it is not that the clocks are malfunctioning; time itself is moving slower. This miraculous finding was not just predicted by special relativity but has also been verified experimentally by scientists using precise measurements of clocks flown in planes and satellites.
Of course, you wouldn’t feel the slowing down of your time. How could you ever know that time has slowed down or sped up? If it is time itself that has slowed down, not just certain timekeeping devices, then everything has slowed down. Everything that used to take an hour now only takes fifty nine minutes (as I see it from Earth), but even your thoughts have slowed down so you could never be aware of the difference.
This immediately gives us two possible methods for achieving time travel. By travelling at near light speeds (effectively making our time pass slower) we can travel into the future and by travelling faster than light we can travel back in time to the past.
Travel at Near Light Speeds
This is a curious phenomenon. The faster that you travel (relative to some external reference point) the slower time will pass (as measured by someone at that external reference point). This of course means that if you are gone for say, ten years in your time, a hundred years may have passed for your friend at the motionless reference point. This is the basis for the twin paradox and in this way you can ‘travel’ into the future.
There is an obvious limitation inherent with this option. Only travel to the future is possible. Because the important thing here is the motion relative between two reference frames, the only kind of motion that can be brought about is a velocity increase. Even if you were to lift off in your rocket and immediately slow down coming to a complete standstill (say, relative to the sun), you would see Earth speeding away from you at a blistering thirty kilometres per second. If you were to shoot into reverse, the relative speed would increase. The only way you could reduce the relative motion between you and the Earth would be to maintain the same speed, flying alongside it at thirty kilometres per second. Unfortunately, this merely reduces the relative motion differential to zero. Time is passing at the same rate for both of you, so no one is going anywhen!
It is also doubtful whether we would be willing to call this true time travel. After all, one hasn’t actually actively travelled through time. It’s more like passive time travelling. You didn’t enter a time machine which somehow warped time propelling you into the future. Time (your time, that is) was only warped according to someone’s perspective from Earth. Not only that, you didn’t even have full control over the process. First, you couldn’t travel into the future to see what you would do in ten years because during that time you would have to be in the rocket where time would be passing just the way it always does. Second, to actually go forward in time you would have to decide who or what you wish to see in the future and make sure they are in the external reference frame. Third, as I pointed out above, once you view the future you cannot decide you don’t like it, change your mind and go back. It’s a one way trip only. Finally, according to my briefly sketched example, in order to see what time would be like in one hundred years you had to give up ten years of your own life. Although you could alter either of those figures by increasing or decreasing your speed, you would still be operating within the parameters laid down by physics. There is less freedom in the process than we might suppose there should be in true time travel. It is more like bending the rules of time a little rather than actually transcending them.
Time travel in this sense is nothing more than slowing the rate of passage of time relative to an external reference frame. It’s a little like time travel cheating. Before we liken it to time travel we should probably compare it to undergoing some form of cryogenic freezing. A cryo-specimen is certainly able to witness and live much further into the future than she should ordinarily be able to but we wouldn’t call it time travel anymore than we would say the bread in our freezer has travelled through time to appear in my toaster for breakfast.
Travelling Faster than Light
If you were able to somehow travel from one point to another faster than the speed of light, Einstein’s special relativity predicts that there would be some frames of reference in which your progress would be seen as travelling backwards in time. The basic upshot of this is that according to the laws of physics as we know them at the moment, genuine time travel into the past is theoretically possible. It isn’t all as peachy as that however.
The first, and least significant, problem is that again we are constrained by only being able to time travel in one direction. Although, if we have the ability to surpass the light speed barrier then we should also have access to the above ‘cryo-temporal’ method of time travel into the future so this is not a major limitation.
The biggest and ultimately damning objection to the notion of faster than light speed travel is that it is categorically impossible. The same theory that tempts us with travelling back in time to meet the man who first thought of it absolutely prohibits it as a physical possibility. Note that this does not just mean that we currently lack the capabilities or knowledge that would allow us to reach such velocities; reaching those velocities is actually, physically impossible.
The reason for this begins to take us beyond the scope of this essay but it can be briefly explained as follows. As someone’s (or something’s) speed approaches the speed of light there are more than just temporal distortions. Time slows down (for an external observer) but matter also shrinks in the direction of the motion and mass increases. Mass increases so much in fact that as one nears the speed of light mass nears an infinite quantity. In order to propel this ever increasing volume of mass, one requires more and more energy. Ultimately, to break the light speed barrier, one’s mass would actually become infinite and therefore require an infinite amount of energy to accelerate it by even the tiniest fraction. This is not a case of a technological limitation, it is a physical limitation imposed by the laws of physics as we know them. Ultimately, at least barring a major revision (although perhaps ‘upheaval’ is a more appropriate term) to our understanding, this method of time travel must forever remain the prerogative of science fiction authors.
Before we leave this section I feel I should briefly mention the possibility of using constructs known as wormholes for time travel. As with anything related to time travel, science fiction has played a much more instrumental role in promoting wormholes than actual science and the result is probably some distortion in truth.
Wormholes are purely hypothetical regions of the universe where spacetime is warped in a way permitting travel through not just space but time as well. At this stage the conjecture surrounding the existence of wormholes, whether they are even physically possible and if they are whether they could be made stable enough to permit matter or information to pass through is just too great to allow us to come to anything even remotely resembling a conclusion.
It will suffice for me to mention them in passing as a potential, logical, (physical?), theoretically proposed method for legitimate time travel, but because of the vast amount of speculation surrounding them, I don’t plan to spend any more time on them here.
To summarise where we are so far, the laws of physics seem to offer a couple of loopholes that can be exploited for (species of) time travel. At least, as far as we know, they don’t forbid it. We know for certain that time is not an absolute quantity, as was once thought. We have learnt that time is relative to speed and frame of reference, and physicists have discovered nothing in their equations to bar travel through time.
But just because something is theoretically feasible doesn’t mean it is physically possible. The methods we investigated above for time travel were in the first case dissatisfying, in the second, categorically impossible and in the third, still too speculative. The laws of physics, while not being entirely moot on the issue are certainly not tipping their hand too early in the game. Fortunately there are other ways to tackle the question of the feasibility of time travel.
If it can be shown that time travel generates irresolvable paradoxes then that might be, if not sufficient cause to forever banish time travel to the annals of science fiction, at least an indication that it might eventually prove itself to be forbidden by the laws of physics.
I will investigate three instances of time travel that typically exemplify three different species of paradox; reversals of causation, causal loops and the grandfather paradox.
Reversals of Causation
Causality is a hallowed tradition for us physical beings and although philosophers may occasionally find themselves at odds with it, both cause and effect are undeniably useful concepts in our daily lives. A fundamental feature of causality is the notion that causes precede their effects, always. Indeed, it makes no sense for this order to be reversed; if an effect could precede its cause then it would no longer be the effect at all. Because of this, we are understandably suspicious of anything which fails to follow the established (by everyday experience) norms.
Enter time travel.
Imagine that Bill, a thirty year old intrepid time traveller, is getting ready to head back in time to witness a historic, momentous occasion; the day he was born. He starts up the time machine but just before he actually ‘takes off’ you casually stroll up, reach in the window (or whatever opening exists on his machine) and punch him square in the eye. The result of this (apart from possibly seriously affecting your relationship with Bill) is that Bill gets a black eye thirty years before you punched him, i.e. an effect occurs before its cause. Problem.
A causal loop describes a situation where a time traveller travels back in time and instigates a loop of events, the poles of which turn out to be the cause and effect of each other, hence the paradox.
A scientist, let’s call him Billy, fascinated by time travel, meets a good looking man in a café who claims to be from the future. This man tells Billy how to build a time machine. Billy follows the man’s instructions and finally succeeds in doing so. Years later a much older Billy, while doing a little wandering through time meets his younger self in a café. During the course of their conversation he imparts information about how to build the time machine. The paradox becomes apparent when we try to determine the source of the information. Young Billy got the idea for the time machine from old Billy but where did old Billy get the information from which allowed him to build the machine and go back in time in the first place?
The Grandfather Paradox
This paradox is probably the most famous of all time travel paradoxes and describes a special kind of causal loop where the protagonist, let’s call him William, goes back in time and kills his grandfather. The obvious paradox arises when we realise that if William kills his grandfather, his father and consequently he himself, were never born. If William never existed then who killed his grandfather?
If these three paradoxes turn out to be truly irresolvable this will have a serious impact on our thoughts about time and time travel. If we can’t find a way to explain them then we may be forced into refuting time travel on purely logical grounds. Let us now turn to some popular solutions that have been offered to resolve the paradoxes.
In this section I will outline two standard methods that are often cited as ways of circumventing the problems paradoxes create.
The Novikov Self-Consistency Principle
I must confess that I have never fully been able to grasp the logic behind this principle, for there seems to be none. Igor Novikov proposed his principle to solve time travel paradoxes but it is so arbitrary and contrived that to my way of thinking it resolves nothing.
The principle simply states that the probability of someone changing the past in a way that would create an irresolvable paradox is zero. It may still be possible to change the past, just not in any ways that would create paradoxes.
If we apply this principle to the grandfather paradox, we might find that William is able to successfully go back in time but for some reason or another he finds that he is unable to kill his grandfather. Perhaps William miscalculated and his grandfather wasn’t where he expected him to be, perhaps his gun misfired, perhaps at the moment of truth he couldn’t go through with it. It doesn’t matter what it is, but every time that William tries (if he should try more than once) he will find himself unable to kill his grandfather. The death of William’s grandfather results in an obvious paradox but it need not be so straightforward.
In theory, William could, out of sheer annoyance, have moved his gun a few inches to the left, lined up another target in his sights and pulled the trigger. As long as the new victim’s death doesn’t result in a paradox, that is, as long as the circumstances which led to William going back in time (all of them) remain intact, then there is no reason to suppose that William would be prevented from killing him. This produces another problem though. We can imagine that the new target is actually a friend of your grandfather’s, Smith, who is going to introduce your father to your mother tomorrow. In this case, killing Smith would also result in a paradox so again (according to Novikov’s principle) something must intervene or go wrong to frustrate William.
We might then suggest that William try waiting until Smith has discharged his duty and facilitated William’s father’s meeting his mother. Would he be able to kill the unwitting Smith then? What if it is true that if Smith is killed, William’s father would be so affected it would cause him to rethink his life’s purpose in such a way that he would later renounce the world and become a monk, obviously not marrying William’s mother? Then we should have found that William would have been unable to kill Smith as well.
At this point we find ourselves confronting two issues. The first is how could… (who?) the universe(?) have known that the murder of Smith would lead to a paradox and so have known that William had to be thwarted? This also reveals an even prior issue. Who or what is preventing William from creating the paradox? The second problem is that we have unwittingly stepped out onto a slippery slope. Let’s resume the thought experiment and find out where our downward slide eventually deposits us.
So, we know that William can’t kill his grandfather and he can’t kill Smith. So who can he kill? Or to rephrase the question in an equivalent way, whose death wouldn’t affect any of the circumstances which will eventually lead to William inventing a time machine and using it to appear just where he is right now, rifle in hand, mystified, and a little annoyed that no one is dying?
Well, he might try skipping to another city and trying his luck there. Let’s say he selects a woman named Sally as his new target. He finds out where she lives and has perched himself in a tree behind her house with a view directly into her living room. As soon as she comes home he is set to (finally) get down to some killing. He gets comfortable and settles into his wait but unfortunately he apparently gets a little too comfortable and falls asleep (it’s a comfortable tree). When he wakes up, it’s past midnight and Sally has already gone to bed. Thwarted again! No matter. He has all the time in the world; he has a time machine for God’s sakes! He figures he’ll catch her at breakfast.
The sun rises on an alert William, hands steady, settled, fully primed for the mission. Sally walks into the living room and right into the middle of William’s crosshairs. He finger slowly starts to squeeze the trigger… when all of a sudden a bird, thinking the rifle is some kind of odd, black branch, alights on the barrel, startling William and upsetting his balance.
Several hours later, William regains consciousness lying on his back staring up into the branches of the tree. It turns out that had Sally died that day, she wouldn’t have worked so hard that she died of stress exactly two years and fifteen days later. Her funeral wouldn’t have taken place exactly three days later at 2:15pm and a man called Jones (who had just picked up a part time job at the funeral home) wouldn’t have met Sally’s grieving mother who wouldn’t have remarked to him in passing how she wished she could go back in time to warn her daughter not to work so hard. Jones (a science major) wouldn’t have lain awake that night contemplating Sally’s mother’s comment and wouldn’t have changed his major to relativity theory. He then wouldn’t have landed the job at the university where William met him and wouldn’t have taught him in exactly the way he did which led to William’s breakthrough discovery. Paradox.
You see where this is going. It ties in with chaos theory, the old image of a butterfly flapping its wings causing a tornado hundreds of miles away. It’s feasible that any change at all, no matter how insignificant, could create effects which ripple outwards from the source irrevocably changing a vast number of events all over the world. How big do these changes need to be to constitute a paradox? We might allow that a change resulting in the shop where William bought the clothes he is now wearing closing would not result in a paradox; he would still be able to come back in time and kill his target, albeit while wearing different clothes. But there must be a significant number of events that contributed to William growing up the way he did, with the attitude and personality and motivations he has. Even if we allow for a fairly robust theory of human development in which most of what we become and do would have happened as it did regardless of extenuating factors, we would probably still be forced to admit that a number of small changes (more than we might at first suppose) could have had serious ‘butterfly effect’ ramifications.
Okay, it’s time to collect some of the threads we’ve been weaving and see what conclusions we can draw.
First, Novikov’s self-consistency principle appears to be completely arbitrary and to a certain degree specious. In order to avoid any paradoxes he is just stating that events that might lead to a paradox are forbidden. He does not offer any further explanations or details in support of his claim. He might as well be claiming that God created the universe because no one else could have.
Second, the only possible way I can imagine his principle working in practice is to also postulate the existence of a being beyond time and space with almost unlimited powers able to intervene in our reality at any time, in any way. This being would also have to be possessed of total omniscience for it would need to be able to immediately survey a staggering number of life histories and the myriad complex interactions they engage in over a period of what could amount to millions of years in order to foresee any potential paradoxical situations and act to ensure they never take place. If you are going to go to such theoretical lengths to avoid time travel paradoxes you are probably better advised to postulate that time travel is simply prohibited by the laws of physics. There are far fewer leaps of faith to be made that way. I think any appeal to the universe itself as a kind of impersonal, automatic ‘paradox-denying’ framework is ultimately futile. Interventions of the kind we are talking about are not the kinds of things that avail themselves of non-sentient processes. The kind of interventions Novikov requires must be oriented towards highly specific goals, i.e. preventing William from killing his grandfather, and they must be capable of calculating incredibly complex causality permutations to determine permissible and forbidden acts.
The third point I raised was that of the slippery slope. It turns out that we are probably able to halt that before we run into too many problems. The fear was that in prohibiting changes which result in a paradox we might find chaos theory ultimately prohibits any kind of change at all. Without a more detailed discussion of cause and effect, which is really beyond the scope of this essay, we can probably safely conclude that the ripple effects of any cause are greater than we might at first imagine but not so great that any and all past changes affected by a time traveller would result in paradoxes. Even if some kind of Novikov self-consistency principle is in effect, a time traveller to the past would probably be able to make some changes, she would probably just have to make sure she was well clear of her ancestors and anyone close to them.
Parallel Universes /Alternate Timelines
This possible solution to time travel paradoxes hinges on something known as the ‘many-worlds interpretation’ which is a postulate of quantum mechanics first proposed by a clever fellow called Hugh Everett in 1957. What this notion suggests is that at each moment in time an almost infinite number of new universes or timelines are created, in each of which something different takes place.
Imagine you had an accident. In this universe you escaped without injury and continued to live your life. In a second universe you died and events proceeded accordingly. In a third, you lost a limb. In a fourth, you got a concussion and so in, ad nauseum.
How does this allow us to cash out our time travel paradoxes? Well, what it means is that instead of travelling back (or forward) in time in this universe thereby creating a paradox where, say, an effect precedes a cause, you actually jump into a different universe (even though you might jump into the time stream in that different universe at a different time, earlier or later than the time in the original universe) so that the effect always occurs after the cause because despite the potential time difference between universes, the time you left the first universe will always precede the time you arrive in the second universe.
Let’s say you leave universe A in 2011 and arrive in universe B in 1999. If you had stayed only in universe A, this may have resulted in a paradox but since you actually jumped universes, you also jumped time streams and these two time streams are like chalk and cheese; mutually exclusive and unable to be meaningfully compared to each other. The times you left universe A and arrived in universe B are merely nominal. Any cause in universe A will always be prior to an effect in universe B for you, because you were in universe A before you were in universe B, irrespective of what the nominal date is. Equally, you could kill your grandfather in universe B because it isn’t your ‘real’ grandfather. Your ‘real’ grandfather, the one that if you killed would result in a paradox, is alive and happy in universe A and therefore doesn’t affect your being alive today in universe B killing a man who looks and acts suspiciously like your universe A grandfather.
This is a cute and pleasing result for resolving our paradoxes and apparently the mathematics in support of it is fairly stable. While it may be cute, it is unfortunately anything but tidy. Any physicist will tell you that the quest for unifying theories is a quest for symmetry and simplicity. Every fundamental law that has been discovered is tidy and elegant. By this, they mean that a wide variety of phenomena can be explained and accounted for by a comparatively small and simple equation or set of equations. The universe also seems to abide by something called ‘Occam’s razor,’ a postulate which recommends tending towards the theory which makes the fewest assumptions. A theory which advocates the creation of a near infinite number of universes every second seems incredibly wasteful and redundant. Granted, things in nature are sometimes redundant and wasteful, but through the laws of physics which govern all matter, there does seem to be a kind of organising tendency to nature. We, as complex, organised beings are ample proof of that. Not only that, the redundancies we see in nature tend to be fairly minor compared to a universe which creates endless copies of itself. Even if we allow that there are untold trillions of stars out there, that number would very quickly pale in comparison to a series of universes constantly propagating themselves. That just can’t be a viable alternative.
So, the two resolutions we looked at above seem to be inadequate in overcoming time travel paradoxes. Fortunately, there are a couple of other ideas we can find solace in. Allow me to introduce the following.
Tweaked Parallel Universes
Recall that the problem with the parallel universe or many-worlds interpretation was that it seemed unbelievably wasteful and redundant. We might be able to ameliorate the theory somewhat by saying that a new universe is only created when someone attempts to travel through time. Perhaps something about the logistics of warping time causes an unavoidable fission of the universe into two identical copies.
Perhaps travelling backwards or forwards in time in any one universe is impossible but it may be possible to jump into parallel universes which are only created when the need for one arises; i.e. when someone warps time. It may be that the energy required to warp time is so great that it fractures the universe itself into a pair of universes.
Interesting and as explained above, this overcomes all of our time travel paradoxes. My gut instinct is that this is still reaching for straws. It seems kind of incredible that an entire universe could be split into identical copies. Bear in mind that we aren’t talking about just Earth or the solar system or even our galaxy. We’re talking about the entire universe. This solution overcomes all paradoxes but I still don’t feel like it’s the one we are looking for.
This is, I believe, by far the best solution to our time travel paradoxes. The problem with all of the paradoxes is that ‘time’ as in a ‘river of time’ is treated as a constant; something a time traveller can hop out of and re-enter wherever (whenever) he wishes. Giving time a privileged position like this is unwarranted in light of Einstein’s revelation that time is relative.
So what happens is when we think about Bill from 2011 going back to 1940, we imagine that the events of the ‘first’ 1940 (when Bill hadn’t time travelled) are erased and replaced by events from the ‘second’ 1940 (when Bill has time travelled). The implicit assumption is that there is only one timeline, flowing inexorably at a constant rate. There is therefore only one 1940 and one 1950 and so on. This is a mistake. And it’s what leads to the paradoxes. Only one privileged timeline is not enough ‘space’ to fit in all of the possible events we can imagine in time travel and so we find paradoxes arising, which must occur inevitably… but only because of the way we treat time.
Let’s carefully follow the state of affairs as Bill sees them with relation to the grandfather paradox.
Bill, born in 1980, lives a normal life until Dec 31, 2011 when he decides that he wants to kill his grandfather before his grandfather gave birth to his father to test Novikov’s self consistency theory. Fortunately, he somehow came into possession of a time machine around the same time and so jumps in with his gun and travels back to 1940. At this time his grandfather is 20 years old and his father won’t be born for another 10 years; plenty of time to pull off his cosmos altering crime.
Bill successfully completes the trip and heads straight to the local milk bar where he knows his grandfather likes to hang out. He walks around comparing the twenty-something’s faces to a picture he brought along of his grandfather when he was 20. A few moments later he spots his grandfather, pulls out his gun and shoots the man in the heart. There is no mistake, no misfire, no intervention; his grandfather falls to the floor dead. Bill looks at his hand wondering if he will start to disintegrate like he had seen in some popular time travel movies. Nothing like that happens. In fact, nothing out of the ordinary at all happens. He flees the scene and hides in an alley a few blocks away to process the last few minutes.
According to classic temporal theory, Bill’s successful act of killing his grandfather should have meant that he was no longer born and so couldn’t have travelled back in time to kill his grandfather in the first place. The paradox. How could he have killed his grandfather if he had never been born? And how could he have been born if had killed his grandfather? The problem is that both of the ‘if’ postulates in those two statements are true. He has never been born and he has killed his grandfather. The timeline possibilities (we need two representations to account for the paradox) for this event looks like this:
‘GF’ stands for the grandfather.
Important note: These two timelines do not represent two different temporal streams or parallel universes. I have only duplicated them for clarity to illustrate the paradox.
As you can see, both of these timelines cannot logically be true. Now if we focus on time as an unchanging constant then we find ourselves in a paradox. Bill leaves the temporal stream in 2011 and re-enters in 1930 totally screwing up later events. In essence what this interpretation is doing is erasing timeline (1) because it ‘precedes’ timeline (2). Bill goes back to 1930 and essentially overwrites the events that had happened according to timeline (1). This interpretation holds that there can only be one 1930 and in it the grandfather is killed and Bill is consequently not born. The paradox arises because the timeline (1) event (Bill going back in time) is necessary for timeline (2) but if the grandfather dies in timeline (2) then timeline (1) cannot have happened.
Let’s re-analyse it making Bill the primary focus. In this diagram there is no single timeline covering everyone. Rather, we will be treating each person as having their own personal timeline which can operate independently of other peoples.
It’s not that easy to understand from my diagrams so I will attempt to go through what happened slowly. In the first two diagrams we see the normal timelines of Bill and his grandfather. The grandfather lives a long life giving birth to Bill’s father who in turn gives birth to Bill in 1980. At this point Bill’s timeline starts up and flows along with his grandfather’s until Dec 31, 2011. At this point things get a bit hairy. Rather than Bill leaving the time stream and re-entering at 1930, which is what we saw in the classical interpretation, we see in the second diagram Bill’s timeline continuing to flow in a rightward direction. The only difference is that instead of going from 2011 to 2012, he goes from 2011 to 1930. However, everyone else’s time streams have been warped and realigned themselves with what should be Bill’s Jan 1, 2012 at the 1930 point on their timelines. We see this through the grandfather’s new timeline which has shifted to the right. Bill sees himself in 1930 only because everybody else’s time streams have moved. It’s as if Bill held his time stream locked and forced everybody else’s to move around him. That’s what I mean by saying that Bill is the focus, not time.
The key is to realise that Bill never left his time stream. That’s impossible. If you are alive, you must be in your time stream, whether you are warping time or not. As a kind of corroboration of this, even though we imagine Bill to have gone back in time a good 81 years, we intuitively think his age stays at 31, the age he was when he left in 2011. He doesn’t suddenly lose 81 years to become -50. Why? He never left his time stream. He warped everyone else’s and caused them to align with his at a different place. If Bill decides not to return to the future, he will continue to age normally turning 41 in 1940 and 81 in 1980, the year he was born although he will now never see that. He no longer has parents because he has erased them, but don’t make the mistake of thinking he never had any. That’s a paradox. He did, it’s just that his time stream is the only one that includes them. To everyone else, he just appeared one day in 1930 at 31 years of age.
Another point to note is that while there was only one 1910, there were actually two 1930s. In the first of them Bill’s grandfather survived, in the second he didn’t. Here’s the catch. Only Bill is aware of any duplicates. Everyone else only recalls the second 1930, the one where Bill’s grandfather dies, because their timelines no longer include the first 1930. There were also two 1940s. In one of them, Bill’s father was born, in the second he wasn’t. There were two 1980s. In the first, Bill was born, in the second he wasn’t. In fact, there were two of every moment from 1930 to 2011. Bill is the only one to know this fact because his is the only intact timeline i.e. a timeline not overwritten. Of course, Bill won’t have any direct recollection of any events prior to the first 1980 because he wasn’t born until then so his timeline doesn’t include them, but he would have learned about some of what happened through stories and history (now defunct and meaningless to everyone except Bill).
This notion resolves not only the grandfather paradox but also the reversal of causation paradox. In the latter we can see that if Bill were to sustain an injury just prior to his trip so that the bruise (effect) occurred in the past, before the cause, this is only an illusion of perception. In reality, because Bill’s timeline is still intact, and because Bill’s timeline is the only one of any consequence regarding events in his life, clearly the cause precedes the effect, although if anyone else was aware of the facts it would seem to them as though the opposite was the case. Looking only at the nominal dates, yes, the bruise appears in 1930 while the injury appeared in 2011 but those dates are irrelevant. Bill’s timeline is still moving forward, irrespective of what date label we give it.
Unfortunately, the case of causal loops involving the time traveller travelling to a time in his or her own past is not so straightforward. In fact, it turns out that a time traveller cannot visit themselves in either the past or the future. Because the time traveller is not actually stepping outside of time (as is assumed in the classical interpretation) but rather warping everyone else’s around hers, there can always be only one of her at any ‘time.’ Imagine the following scenario:
In these diagrams we can see that Kate, born in 1980 lives a normal life until she turns 30. On Dec 31, 2010 Kate uses a time machine to go back in time to 2000, when she was only 20. Now, because she doesn’t leave her own timeline, Kate can’t actually meet her younger self because her own past always, categorically occurs earlier on her own personal timeline. Remember she is manipulating everyone else’s timelines, warping them to hers.
The tricky part happens in the second year 2000 when Kate appears in everybody else’s time as a 30 year old woman. To everyone else she would appear to have aged ten years in a single night. Although Kate actually lived the full ten years, her timeline is the only one to have recorded that decade. Everyone else’s first decade of the 21st century has been erased and is being overwritten by Kate. It’s important to realise that in the year 2000, the twenty year old Kate didn’t disappear and the 30 year old Kate didn’t appear. It could seem like that to everyone else because one day Kate is 20 and the next she’s 30, but in fact what happened is everyone’s timelines re-aligned to Kate’s at their year 2000. Kate actually hasn’t gone anywhere (or anywhen), she has merely shifted everyone else’s timelines creating the illusion that she ‘travelled’ through time.
As we discussed earlier, Kate’s age doesn’t change because she never leaves her own timeline. To use classical terminology, she leaves on Dec 31, 2010 as a thirty year old woman and appears in the nominal Jan 1, 2000 at the same age. Using more accurate terminology according to my new perspective, Kate warps time on Dec 31, 2010 as a thirty year old woman causing everyone else’s timelines to shift ten years to the right effectively reversing time for her.
General Comments on Time Travel
In light of the preceding discussion we can now make some more general comments about time travel:
1. This model is actually quite similar to the way Kant viewed one of his faculties of the mind, sensibility. We grasp the physical world through sensibility and we do so through two forms, space and time. These two forms operate in the mind of each individual, rather than being a part of the external world. He made the mistake of following Newton in thinking they were absolute, not relative, but he was the first to take space and time as something that we impose on an unordered, formless external reality. In very much the same way, I am suggesting that time exists for each of us independently of anyone else, through what I have called individual timelines.
2. Time travel is only theoretically possible because everyone has an individual timeline. The notion of leaving one’s timeline appears to me to be pure science fiction or new age mumbo jumbo. Leaving your timeline would mean you exist outside of time, a notion I find utterly repulsive. It also smacks of some kind of transcendent consciousness displacement which I believe deserves no credence in theoretical or practical discussions.
3. Time travel is nothing more than rearranging all other timelines while holding your own motionless.
4. The particular time (date) we are experiencing now is nothing more than a sort of consensus among everyone’s timelines. This is what makes time travel (theoretically) possible. I can get in a time machine in 2010 and appear in 1950 only because everyone else’s timelines agree that it is 1950. What makes it 1950 is not any kind of grand, unchanging universal timeline that measures the flow of time. Rather, it is 1950 only because everyone’s timelines have shifted (except the time traveller’s of course) so that 1950 is in the present.
5. The present can be envisioned as a thin band stretching across all timelines and steadily progressing to the right. This is crucial to the notion of time travel.
6. In order to time travel each timeline would have to be a kind of recording device able to be rewound (or fast forwarded) and replayed. This would mean that the past is not forever gone, but always capable of being recalled, something like a video tape.
7. Time travel to the future is also possible. It would simply involve shifting everyone’s timelines to the left. Although I do perceive some problems with this I think they aren’t anything that can’t be overcome.
The prime question I set out to answer with this essay was whether time travel paradoxes preclude the possibility of time travel. If we are unable to conceive of situations in which the paradoxes are rendered inert then that alone may be enough to settle the question with a negative answer.
We first looked at possibilities of time travel through Einstein’s theory of special relativity and wormholes. They turned out to be quite unsatisfactory, but we did conclude that physicists can’t rule time travel out of their equations just yet.
Next, we looked at three typical paradoxes of time travel; reversals of causation, causal loops and the grandfather paradox. The theorised resolutions to these included Novikov’s self-consistency principle and parallel universes. The former seemed too ad hoc and failed to really explain anything while the latter seemed incredibly wasteful and ugly; something which runs contrary to all successful physical theories.
We discovered that by amending the parallel universe theory so that parallel universes are only created in response to a time travel event the theory could be made less extravagant and more plausible but it still seemed a little hard to swallow.
Finally, I suggested the notion of individual timelines as a means of overcoming the paradoxes. This different way of thinking about time erased all of the paradoxes and revealed some interesting points about time travel including things like it is impossible to travel through time to visit yourself and time travel is actually a misnomer; ‘warping time’ would be more appropriate.
Of course, this individual timeline theory spawns a whole host of other questions including, what exactly is a timeline? Do only living things have timelines or does everything have a timeline? Could it ever be possible to manipulate the timelines of everything in the universe? Could the time traveller achieve the same outcome by just shifting his or her own timeline relative to all others? This is not the place to address these questions but it certainly makes for interesting thinking.
Ultimately, the individual timeline theory gives us a theoretically plausible means of overcoming potential paradoxes thereby fulfilling the aim of this essay. While the theory can’t comment on the physical possibility or impossibility of time travel it has shown us that at least paradoxes haven’t sounded the death toll on time travel yet.
 Something that I will not investigate in any detail here.
 I judge that a fuller discussion of causality and consequence is unwarranted at this point. For the purposes of this essay I think we have enough information to make a reasonable conclusion.
 I won’t follow this idea up in this essay.