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<h2 class="hd hd-2 unit-title">An inconsistent time travel story</h2>
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<p><span style="font-family: 'book antiqua', palatino;">Telling a consistent time travel story is harder than one might think. </span></p>
<p><span style="font-family: 'book antiqua', palatino;">The Hollywood film <a href="https://www.youtube.com/watch?v=qvsgGtivCgs" target="[object Object]">Back to the Future</a> is an example of an entertaining but <em>inconsistent</em> time travel story. </span></p>
<p><span style="font-family: 'book antiqua', palatino;">Here is a quick summary. On October 25, 1985, George McFly is unhappy. George’s son, Marty, then travels back in time to 1955 and meets his father as a young man. As a result of their meeting, George conquers his fears, and blossoms into a bold and courageous man. When Marty returns to October 25, 1985, he is faced with a very different situation from the one that was described at the beginning of the film. George leads a happy life.</span></p>
<p><span style="font-family: 'book antiqua', palatino;">It is not hard to see why this story is inconsistent. At the beginning of the film we are told that, at a certain time <span class="math inline">\(t\)</span>, George is unhappy. At the end of the film we are told that, at <span class="math inline">\(t\)</span>, George is happy. In other words: what we are told at the beginning of the film conflicts with what we are told at the end of the film. </span></p>
<p><span style="font-family: 'book antiqua', palatino;">(The fact that we are told one thing <em>at the beginning</em> of the film, and the other <em>at the end</em> of the film doesn’t help. Notice, for example, that we wouldn’t count a witness as consistent if she says one thing at the beginning of her testimony and the opposite at the end of her testimony.)</span></p>
<p><span style="font-family: 'book antiqua', palatino;">For a time travel story to be consistent, it must never make conflicting statements about what the world of the story is like at a given time. If at some point in the story we are told that, at time <span class="math inline">\(t\)</span>, George is unhappy, then the story is never allowed to renege on this commitment: it cannot later tell us that, at time <span class="math inline">\(t\)</span>, George is happy. And this is so regardless of whether there is any time travel in the story. </span></p>
<p><span style="font-family: 'book antiqua', palatino;">So: if, according to the story, Marty travels back in time and tries to improve George's situation at <span class="math inline">\(t\)</span>, then the story must have it turn out that somehow or other George is unhappy at <span class="math inline">\(t\)</span> in spite of the attempted interference.</span></p>
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<h3 class="hd hd-2">Video Review: Consistent and Inconsistent Time Travel Stories</h3>
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<h4><span style="font-family: 'book antiqua', palatino;">A Changing-timeline interpretation</span></h4>
<p><span style="font-family: 'book antiqua', palatino;">One way of restoring consistency to <em>Back to the Future</em> is to interpret the story as involving a "change in George’s timeline". Before the change, George’s timeline is such that he is born, grows up and ends up unhappy. After the change, George’s timeline is such that he is born, grows up and ends up happy. (See figure below.)</span></p>
<p><span style="font-family: 'book antiqua', palatino;">On this interpretation, the story relies on two different senses of time. It relies on the ordinary notion of time when it describes changes <em>within</em> George’s timeline: when it says that he is born, grows up, and ends up happy or unhappy. It uses a different, non-ordinary sense of time when it says that the timeline itself "changes": that George’s development through ordinary time, as it is described at the beginning of the story, is different from his development through ordinary time, as it is described later in the story.</span></p>
<p><span style="font-family: 'book antiqua', palatino;">To avoid confusion, let us use "super-time" to talk about time in this second sense. </span></p>
<p><span style="font-family: 'book antiqua', palatino;">We are therefore considering an interpretation of <em>Back to the Future</em> according to which facts about how George evolves in ordinary time "change" across super-time. At an initial super-time, George lives his life within ordinary time in a way that ends badly; at a later super-time, he lives his life within ordinary time in a way that ends happily. </span></p>
<p><span style="font-family: 'book antiqua', palatino;">The problem with this way of thinking about the story is that it is not clear that there is good sense to be made of super-time. Notice, in particular, that none of us has ever experienced changes in super-time. When we experience change in everyday life, it is always by experiencing ordinary change—by observing sand trickling through an hourglass, or listening to leaves rustling in the wind—and ordinary change involves differences across ordinary time, not differences across super-time.</span></p>
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<p><span style="font-family: 'book antiqua', palatino;"><img src="/assets/courseware/v1/5b435e62405e9518799e81a2e87a5f54/asset-v1:MITx+24.118x+2T2020+type@asset+block/TimeTravelFig1.jpg" type="saveimage" target="[object Object]" hight="50%" width="50%" /></span></p>
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<p><span style="font-family: 'book antiqua', palatino;">Whether or not the notion of super-time can ultimately be made sense of, it will not be our concern here. When I speak about time in this lecture I will always be concerned with ordinary time. And when I speak of time travel, what I mean is extraordinary travel within ordinary time, not changes in the world’s timeline across super-time.</span></p>
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<h3 class="hd hd-2">Question: Couldn't the Timeline change?</h3>
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<h4><span style="font-family: 'book antiqua', palatino;">A world-travel interpretation</span></h4>
<p><span style="font-family: 'book antiqua', palatino;">There is a different way of trying to make <em>Back to the Future</em> consistent. </span></p>
<p><span style="font-family: 'book antiqua', palatino;">One could think of the film as a story about travel <em>between</em> worlds, rather than a story of time travel within a single world. The idea is that, when Marty travels back to 1955, he travels to the 1955 of a <em>different universe</em>, and then comes back to the 1985 of that other universe. Accordingly, George remains miserable in the 1985 of the original universe, while his alternative-universe counterpart is happy in his own, other-worldly 1985.</span></p>
<p><span style="font-family: 'book antiqua', palatino;">A world-travel story of this kind is certainly consistent.</span></p>
<p><span style="font-family: 'book antiqua', palatino;"> Notice, however, that on this interpretation of <em>Back to the Future</em> we should feel very differently about events in the film than the film itself encourages us to feel. For instance, the film is supposed to have a happy ending. But on the world-travel interpretation, the ending is tragic, since it has Marty traveling to the 1985 of the alternate universe. He seems to think he’s been reunited with his real family, and is happy to be home. But he is mistaken about this. He is in fact meeting alternate-universe copies of his real family for the first time. His real family is still miserable back in his home universe. They are probably even more miserable now that Marty has disappeared.</span></p>
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<h3 class="hd hd-2">Video Review: A World-Travel Interpretation</h3>
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<h4><span style="font-family: book antiqua,palatino;">Conclusion</span></h4>
<p><span style="font-size: 12pt; font-family: 'book antiqua', palatino;"><em>Back to the Future</em> is inconsistent, assuming it is interpreted as an ordinary-time travel story, rather than a super-time story or a world-travel story. </span></p>
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<h3 class="hd hd-2">Video Exercises: Consistent and Inconsistent Time Travel Stories</h3>
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<h2 class="hd hd-2 unit-title">A consistent time travel story</h2>
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<p><span style="font-size: 12pt; font-family: 'book antiqua', palatino;"> I have argued that <em>Back to the Future</em> is inconsistent, assuming it is interpreted as an ordinary-time travel story, rather than a super-time story or a world-travel story. </span></p>
<p><span style="font-size: 12pt; font-family: 'book antiqua', palatino;">Not every time travel story is inconsistent, however. Good examples of consistent time travel stories include the films <a href="https://www.youtube.com/watch?v=CBNMEwNx9x4" target="[object Object]">Twelve Monkeys</a> and <a href="https://www.youtube.com/watch?v=9rUPZBibHAQ" target="[object Object]">The Time Traveler’s Wife</a>. Here is another example of a consistent time travel story:</span></p>
<blockquote>
<p><span style="font-family: 'book antiqua', palatino;">On the eve of your 21st birthday, an elderly stranger shows up at your doorstep and explains how to build a time machine. It takes you several years of hard work, but you eventually manage to construct a working version of the machine. You use it to lead a fascinating life of time travel. Towards the end of your life you use your time machine to travel to the eve of your 21st birthday and explain to your younger self how to build a time machine.</span></p>
</blockquote>
<p><span style="font-family: 'book antiqua', palatino;">According to this narrative, there are causal loops. (For instance: your building a time machine late in life is a cause of your traveling back in time to give your younger self information about how to build a time machine, which is a cause of your building a time machine late in life.) </span></p>
<p><span style="font-family: 'book antiqua', palatino;">That means that the scenario depicted by the story is weird. But weirdness is not the same as logical inconsistency, and what’s at issue here is whether the story is logically consistent. </span></p>
<p><span style="font-family: 'book antiqua', palatino;">In spite of its causal loops, there is nothing logically inconsistent about our story: there is no time [mathjaxinline]t[/mathjaxinline] and proposition [mathjaxinline]p[/mathjaxinline] such that at one point in the narrative we are told that [mathjaxinline]p[/mathjaxinline] is the case at [mathjaxinline]t[/mathjaxinline], and at a different point in the narrative we are told that [mathjaxinline]p[/mathjaxinline] is not the case at [mathjaxinline]t[/mathjaxinline].</span></p>
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<h3 class="hd hd-2">Question: Isn't that 'Consistent' Case Paradoxical?</h3>
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<span style="font-family: 'book antiqua', palatino;">Determine whether each of the following stories can be interpreted as
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<span style="font-family: 'book antiqua', palatino;">You are an avid gambler. You are at the races, and decide to bet all your savings on Easy Goer. Tragically, Master Charlie wins the race, by a nose. Because of your recklessness, you end
up leading a life of hardship. Towards the end of your life, however,
you catch a lucky break: an old aunt bequeathes you a time machine.</span>
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<span style="font-family: 'book antiqua', palatino;">You travel back to the time in which you had placed the disastrous bet, and head straight for the tracks. You see your younger self standing in
line, eagerly awaiting the chance to bet on Easy Goer. You
approach him and whisper into his ear "Master Charlie". Your younger self is receptive,
and bets his money on Master Charlie. He wins big, and spends the rest of his life in luxury and style.</span>
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<p>
<span style="font-family: 'book antiqua', palatino;"><em>Pixit</em>, the innovative pig-sitting app, is the latest start-up to disrupt the markets. You travel back in time to a time when <em>Pixit</em> shares were cheap and buy as many of them as you can. You place the share certificates in a box and burry the box in an empty lot&#8212;the empty lot where you know your home will be built a few years later. You then travel back to the present day, run to your back yard and dig up the chest. The chest is a little moldy, but the certificates are still there!</span>
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<h2 class="hd hd-2 unit-title">The Grandfather Paradox</h2>
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<p><span style="font-family: book antiqua,palatino;">Bruno hates his grandfather, and not without reason. Grandfather was a gambler and a drunk, and he orchestrated a large scale fraud, which left hundreds of people in poverty. Nothing would please Bruno more than killing Grandfather. Unfortunately, Grandfather died many years ago, long before Bruno was born. </span><br /><br /><span style="font-family: book antiqua,palatino;">Bruno is undeterred. He builds a time machine and travels to September 13, 1937, a time before Grandfather had children, and before the fraud. Grandfather is on his morning walk. Bruno has climbed up a church steeple, and positioned himself at the belfry with a sniper's rifle. He aims the rifle with the precision of an expert gunman. Grandfather stops to tie his shoelaces. The church bells starts tolling. Noon has arrived. Bruno caresses the trigger. Grandfather stands still for a moment. A breeze ruffles some nearby leaves. Bruno prepares to shoot...</span><br /><br /><span style="font-family: book antiqua,palatino;">What happens next? Suppose Bruno kills Grandfather. Then Grandfather will never have children. (Assume no funny business: no rising from the dead, no frozen sperm, etc.) So Bruno's mother will never be born. So Bruno will never be born. So he won't go back in time. So he won't kill Grandfather after all. Contradiction! But if Bruno doesn't kill Grandfather, what stops him? There is Bruno on the belfry with his rifle. Killing Grandfather is his lifelong ambition. He has a clear shot...</span><br /><br /><span style="font-family: book antiqua,palatino;">We seem to have been left with a paradox. On the one hand, we know that Bruno won't succeed, on pain of contradiction. On the other, we're at a loss to explain what could possibly stop him.</span><br /><br /></p>
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<p><span style="font-family: book antiqua,palatino;">What should we conclude from the Grandfather Paradox? </span><br /><br /><span style="font-family: book antiqua,palatino;">One possible conclusion is that time travel is an inherently contradictory idea, like a figure that is both a circle and a square. </span></p>
<p><span style="font-family: book antiqua,palatino;">I think that would be mistake. The key observation is that there are perfectly consistent ways of filling in the details in Bruno's story. Suppose, for example, that we continue the story by saying that Bruno loses his nerve at the last minute and puts down the gun. Or by saying that Bruno gets distracted by a barking dog and aims a little too far to the right. In each case, we have a consistent time travel story, and in each case we have a perfectly acceptable explanation of why Bruno's assassination attempt fails.</span><br /><br /><span style="font-family: book antiqua,palatino;">You might think that this misses the point. Perhaps the real problem is not to explain why the assassination attempt fails on particular versions of the story. Perhaps the real problem is to explain why it <em>must</em> fail: why it fails on <em>any</em> consistent way of filling out the details. It seems to me, however, that here there is a fairly flatfooted explanation to be given. </span><br /><br /><span style="font-family: book antiqua,palatino;">Let me begin with an analogy. </span></p>
<p><span style="font-family: book antiqua,palatino;">Suppose you are allowed to paint each of the points on a sheet of paper any color you like. Could you draw a figure that is both a circle and a square? You cannot. And there is no reason to expect an interesting explanation of <em>why</em> you cannot. Presumably all there is to be said is that no distribution of ink-blots on a page yields a figure that is both a circle and a square, and therefore that any attempt to draw such a figure will fail. </span></p>
<p><span style="font-family: book antiqua,palatino;">Now imagine that God makes the world in a way that is analogous to drawing a picture. She starts with a grid of spacetime points, and "draws" on the grid by deciding which physical properties to fill each spacetime point with. In some regions God "draws" positive charge; in some She "draws" mass. Could God "draw" a world in which Bruno kills Grandfather before Grandfather has children. She cannot. And, as before, there is no reason to expect an interesting explanation of <em>why</em> She cannot. Perhaps all there is to be said is that no distribution of physical properties across spacetime yields a scenario in which Bruno kills Grandfather before Grandfather has children, so any attempt to "draw" such a scenario will fail. </span><br /><br /><span style="font-family: book antiqua,palatino;">With this as our background, let us return to our original question: why does Bruno's assassination attempt fail on <em>any</em> consistent way of filling out the details? I see no reason to expect a more interesting explanation than the following. We have seen that there is no coherent scenario---no world God could "draw"---in which Bruno kills Grandfather before Grandfather has children. So any coherent way of filling out the details of the story must be such that the assassination attempt fails.</span><br /><br /><span style="font-family: book antiqua,palatino;">I do not mean to suggest that these considerations set the Grandfather Paradox to rest. But I do think they show that explaining why the Paradox is supposed to be paradoxical is not as easy as one might think. We have seen that there is no reason to think that a fully spelled-out version of the story will fail to explain why Bruno's assassination attempt goes wrong. And we have seen that there is a (fairly uninteresting) explanation of why the assassination attempt will go wrong on any way of spelling out the details. So what is the problem supposed to be? I will use the remainder of this chapter to explore two possible answers:</span></p>
<ul>
<li><span style="font-family: book antiqua,palatino;">The Grandfather Paradox is problematic because it raises questions about whether the laws of physics could rule out paradoxical time travel in a principled way, but without banning it altogether.</span></li>
<li><span style="font-family: book antiqua,palatino;">The Grandfather Paradox is problematic because it shows that time travel is incompatible with free will.</span></li>
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<h2 class="hd hd-2 unit-title">[Bonus: The Time Travel Convention]</h2>
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<p>[<span style="font-family: 'book antiqua', palatino;">See <a href="https://www.youtube.com/watch?v=5OXQypOAbdI" target="[object Object]">here</a> for Tina Fey’s take on the Time Traveler’s Convention.]</span></p>
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