The Paradoxes - Time Travel: A History (2016)

Time Travel: A History (2016)


The Paradoxes

This seems to be a paradox. But one must not think ill of the paradox, for the paradox is the passion of thought, and the thinker without the paradox is like the lover without passion: a mediocre fellow.

—Søren Kierkegaard (1844)

PROPOSITION: Time travel is impossible, because you’d be able to go back and kill your grandfather, in which case you, the murderer, would never have been born; and so on, and so on.

We’ve been here before. We are in the domain of logic, which is, let’s remember, a country distinct from the domain of reality. Its inhabitants speak a dialect of their own, resembling natural language and often quite understandable, but full of pitfalls. A thing can be logically possible yet empirically impossible. If the logicians give us permission to build a time machine, we may still not be able to build it.

I doubt that any phenomenon, real or imagined, has inspired more perplexing, convoluted, and ultimately futile philosophical analysis than time travel has. (Some possible contenders, determinism and free will, are bound up anyway in the arguments over time travel.) The disputation was well under way while H. G. Wells was still alive to be bemused by it. In his classic textbook, An Introduction to Philosophical Analysis, John Hospers tackles the question: “Is it logically possible to go back in time—say, to 3000 B.C., and help the Egyptians build the pyramids? We must be very careful about this one.” The possibility is easy to state—we habitually use the same words to talk about time as we do when talking about space—and it’s easy to imagine. “In fact, H. G. Wells did imagine it in The Time Machine, and every reader imagines it with him.” (Hospers misremembers The Time Machine: “a person in 1900 pulls a lever on a machine and suddenly is surrounded by the world of many centuries earlier.”) Hospers was a bit of a kook, actually, who achieved the distinction, unusual for a philosopher, of having received one electoral vote for president of the United States.*1 His textbook, first published in 1953, remained standard through four editions and forty years.

His answer to the rhetorical question is an emphatic no. Time travel à la Wells is not just impossible, it is logically impossible. It is a contradiction in terms. In an argument that runs for four dense pages, Hospers proves this by power of reason.

“How can we be in the 20th century A.D. and the 30th century B.C. at the same time? Here already is one contradiction….It is not logically possible to be in one century of time and in another century of time at the same time.” You may pause to wonder (though Hospers doesn’t) whether a trap is lurking in that deceptively common expression “at the same time.” The present and the past are different times, therefore they are not the same time, nor at the same time. Q.E.D.

That was suspiciously easy. The point of the time-travel fantasy, however, is that the lucky time travelers have their own clocks. Their time can keep running forward, while they travel back to a different time as recorded by the universe at large. Hospers sees this but resists it. “People can walk backward in space, but what would ‘going backward in time’ literally mean?” he asks.

And if you continue to live, what can you do but get one day older every day? Isn’t “getting younger every day” a contradiction in terms—unless, of course, it is meant figuratively, as in “My dear, you’re getting younger every day,” where it is still taken for granted that the person, while looking younger every day, is still getting older every day?

(He gives no hint of being aware of F. Scott Fitzgerald’s short story in which Benjamin Button does precisely that. Born as a seventy-year-old, Benjamin grows younger every day, until infancy and oblivion. Fitzgerald admitted the logical impossibility. The story has many offspring.)

Time is simple for Hospers. If you imagine that one day you are in the twentieth century and the next day your time machine carries you back to ancient Egypt, he retorts, “Isn’t there a contradiction here again? For the next day after January 1, 1969, is January 2, 1969. The day after Tuesday is Wednesday (this is analytic—‘Wednesday’ is defined as the day that follows Tuesday)” and so on. And he has one final argument, the last nail in time travel’s logical coffin. The pyramids were built before you were born. You didn’t help. You didn’t even watch. “This is an unchangeable fact,” says Hospers and adds, “You can’t change the past. That is the crucial point: the past is what happened, and you can’t make what happened not have happened.” We’re still in a textbook about analytical philosophy, but you can almost hear the author shouting:

Not all the king’s horses or all the king’s men could make what has happened not have happened, for this is a logical impossibility. When you say that it is logically possible for you (literally) to go back to 3000 B.C. and help build the pyramids, you are faced with the question: did you help them build the pyramids or did you not? The first time it happened you did not: you weren’t there, you weren’t yet born, it was all over before you came on the scene.

Admit it: you didn’t help build the pyramids. That’s a fact, but is it a logical fact? Not every logician finds these syllogisms self-evident. Some things cannot be proved or disproved by logic. The words Hospers deploys are more slippery than he seems to notice, beginning with the word time. And in the end, he’s openly assuming the thing he’s trying to prove. “The whole alleged situation is riddled with contradictions,” he concludes. “When we say we can imagine it, we are only uttering the words, but there is nothing in fact even logically possible for the words to describe.”

Kurt Gödel begged to differ. He was the century’s preeminent logician, the logician whose discoveries made it impossible ever to think of logic in the same way. And he knew his way around a paradox.

Where a logical assertion of Hospers sounds like this—“It is logically impossible to go from January 1 to any other day except January 2 of the same year”—Gödel, working from a different playbook, sounded more like this:

That there exists no one parametric system of three-spaces orthogonal on the x0-lines follows immediately from the necessary and sufficient condition which a vector field v in a four-space must satisfy, if there is to exist a system of three-spaces everywhere orthogonal on the vectors of the field.

He was talking about world lines in Einstein’s space-time continuum. This was in 1949. Gödel had published his greatest work eighteen years earlier, when he was a twenty-five-year-old in Vienna: mathematical proof that extinguished once and for all the hope that logic or mathematics might assemble a complete and consistent system of axioms, powerful enough to describe natural arithmetic and either provably true or provably false. Gödel’s incompleteness theorems were built on a paradox and leave us with a greater paradox.*2 We know that complete certainty must always elude us. We know that for certain.

Now Gödel was thinking about time—“that mysterious and self-contradictory being which, on the other hand, seems to form the basis of the world’s and our own existence.” Having escaped Vienna after the Anschluss by way of the Trans-Siberian Railway, he settled at the Institute for Advanced Study in Princeton, where he and Einstein intensified a friendship that had begun in the early thirties. Their walks together, from Fuld Hall to Olden Farm, witnessed enviously by their colleagues, became legendary. In his last years Einstein told someone that he still went to the Institute mainly um das Privileg zu haben, mit Gödel zu Fuss nach Hause gehen zu dürfen, to have the privilege of walking home with Gödel. For Einstein’s seventieth birthday, in 1949, his friend presented him with a surprising calculation: that his field equations of general relativity allow for the possibility of “universes” in which time is cyclical—or, to put it more precisely, universes in which some world lines loop back upon themselves. These are “closed timelike lines,” or as a physicist today would say, closed timelike curves (CTCs). They are circular highways lacking on-ramps or off-ramps. A closed timelike curve loops back on itself and thus defies ordinary notions of cause and effect: events are their own cause. (The universe itself—entire—would be rotating, something for which astronomers have found no evidence, and by Gödel’s calculations a CTC would have to be extremely large—billions of light-years—but people seldom mention these details.)*3

If the attention paid to CTCs is disproportionate to their importance or plausibility, Stephen Hawking knows why: “Scientists working in this field have to disguise their real interest by using technical terms like ‘closed timelike curves’ that are code for time travel.” And time travel is sexy. Even for a pathologically shy, borderline paranoid Austrian logician. Almost hidden inside the bouquet of computation, Gödel provided a few words of almost-plain English:

In particular, if P, Q are any two points on a world line of matter, and P precedes Q on this line, there exists a time-like line connecting P and Q on which Q precedes P; i.e., it is theoretically possible in these worlds to travel into the past, or otherwise influence the past.

Notice, by the way, how easy it had already become for physicists and mathematicians to speak of alternative universes. “In these worlds…,” Gödel writes. The title of his paper, when he published it in Reviews of Modern Physics, was “Solutions of Einstein’s Field Equations of Gravitation,” and a “solution” is nothing less than a possible universe. “All cosmological solutions with non-vanishing density of matter,” he writes, meaning all possible universes that aren’t empty. “In this paper I am proposing a solution” = Here’s a possible universe for you. But does this possible universe actually exist? Is it the one we’re living in?

Gödel liked to think so. Freeman Dyson, then a young physicist at the Institute, told me many years later that Gödel would ask him, “Have they proved my theory yet?” There are physicists today who will tell you that if a universe has been proved not to contradict the laws of physics, then yes, it is real. A priori. Time travel is possible.

That’s setting the bar fairly low. Einstein was more cautious. Yes, he acknowledged, “such cosmological solutions of the gravitation equations…have been found by Mr. Gödel.” But he added mildly, “It will be interesting to weigh whether these are not to be excluded on physical grounds.” In other words, don’t follow the math out the window.*4 Einstein’s caution did little to diminish the popularity of Gödel’s closed timelike curves among fans of time travel—and in their number we must count logicians, philosophers, and physicists. They wasted little time in launching the hypothetical Gödel rocket ships.

“Suppose our Gödelian spacetime traveller decides to visit his own past and talk to his younger self,” wrote Larry Dwyer in 1973. He specifies:

at t1, T talks to his younger self

at t2, T enters his rocket to begin his journey to the past.

Let t1 = 1950; t2 = 1974

Not the most original start, but Dwyer is a philosopher writing in Philosophical Studies: An International Journal for Philosophy in the Analytic Tradition, a far cry from Astounding Stories. Dwyer has done his homework:

Science fiction contains an abundance of stories where the plot centres around certain individuals who, having operated complex mechanical devices, find themselves transported back to the past.

Besides reading the stories, he is reading the philosophical literature, beginning with Hospers’s proof of the impossibility of time travel. He thinks Hospers is just confused. Reichenbach is confused, too (that would be Hans Reichenbach, author of The Direction of Time), and so is Čapek (Milič Čapek, “Time in Relativity Theory: Arguments for a Philosophy of Becoming”). Reichenbach argued for the possibility of “self encounters”—the “younger ego” meets the “older ego,” for whom “the same occurrence takes place a second time,” and though this may appear paradoxical it is not illogical. Dwyer begs to differ: “It is this sort of talk that has given rise to so much confusion in the literature.” Čapek is drawing diagrams with “impossible” Gödelian world lines. Likewise Swinburne, Whitrow, Stein, Gorovitz (“Gorovitz’s problems, of course, are all of his own making”) and indeed Gödel himself, who misconstrues his own theory.

They all make the same error, according to Dwyer. They imagine that a time traveler could change the past. That cannot happen. Dwyer can live with other difficulties created by time travel: backward causation (effects preceding their causes) and entity multiplication (time travelers and time machines crossing paths with their doubles). But not this. “Whatever else time travel may entail,” he says, “it does not involve changing the past.” Consider old T, using his Gödelian spacetime loop to travel back from 1974 to 1950, when he meets young T.

The encounter is of course recorded twice in the mental history of the time traveller; while young T’s reaction to his encounter with T may be one of fear, scepticism, joy, etc., T, for his part, may or may not recall his feelings when, in his youth, he was confronted by a person claiming to be his older self. Now of course it would be self contradictory to say that T does something to young T which, by his memory, he knows does not happen to him.

Of course.

Why can’t T go back and kill his grandfather? Because he did not. It’s that simple.

EXCEPT—of course—it’s never that simple.

Robert Heinlein, having created his multitude of Bob Wilsons in 1939, punching one another before self-explaining the mysteries of time travel, revisited the paradoxical possibilities twenty years later in a story that outdid all its predecessors. It was titled “ ‘—All You Zombies—’ ” and published in Fantasy and Science Fiction after a Playboy editor turned it down because the sex made him queasy (it was 1959).*5 The story has a transgender plot element, a bit forward for the era but necessary to accomplish the time-travel equivalent of a quadruple axel: the protagonist is his (/her) own mother, father, son, and daughter. The title is also the punchline: “I know where I came from—but where did all you zombies come from?”

Could anyone top this? In purely numerical terms—sure. In 1973 David Gerrold, who had been a young television writer for the short-lived (and, later, long-lived) Star Trek, published a novel, The Man Who Folded Himself, featuring a college student named Daniel who receives a Timebelt from a mysterious “Uncle Jim,” complete with instructions. Uncle Jim urges him to keep a diary, and a good thing, too, because life quickly gets complicated. We soon struggle to keep track as the cast of characters expands accordionlike to include Don, Diane, Danny, Donna, ultra-Don, and Aunt Jane—all of whom are (as if you didn’t know) the same person, on a looping temporal roller coaster.

So many variations on a theme. The paradoxes multiply almost as fast as the time travelers, but when you look closely, they are all the same. There is just one paradox, wearing different costumes to suit the occasion. Sometimes it is called the bootstrap paradox—a tribute to Heinlein, whose Bob Wilson pulled himself by his bootstraps into his own future. Or the ontological paradox, a conundrum of being and becoming, a.k.a. “Who’s your daddy?” People and objects (pocket watches, notebooks) exist without origin or cause. Jane of “ ‘—All You Zombies—’ ” is her own mother and father, begging the question of where her genes came from. Or: in 1935 an American stockbroker finds a Wellsian time machine (“polished ivory and gleaming brass”) hidden by palm leaves in the Cambodian jungle (“the land of mystery”); he throws the lever and arrives back in 1925, where the machine is polished up and cached in the palm leaves.*6 That is its life cycle: a ten-year closed timelike curve. “But where did it come from originally?” the stockbroker asks a yellow-robed Buddhist. The wise man explains as if to a dunce: “There never was any ‘originally.’ ”*7

Some of the cleverest loops involve pure information. “Mr. Buñuel, I had a nice idea for a movie for you.” A book on how to build a time machine arrives from the future. See also: predestination paradox. Trying to change what’s bound to happen somehow helps make it happen. In The Terminator (1984), a cyborg assassin (played with an idiosyncratic Austrian accent by a thirty-seven-year-old bodybuilder, Arnold Schwarzenegger) travels back in time to kill a woman before she can give birth to the man who is destined to lead a future resistance movement; the cyborg’s failure leaves detritus that makes its own creation possible; etc.

In a way, of course, the predestination paradox predates time travel by several millennia. Laius, hoping to defy the prophecy of his own murder, leaves baby Oedipus in the wilderness to die. Tragically, his plan backfires. The idea of the self-fulfilling prophecy is ancient, though the term is new, coined by the sociologist Robert Merton in 1948 to describe an all-too-real phenomenon: “a false definition of the situation evoking a new behavior which makes the originally false conception come true.” (For example, a warning of gasoline shortages causes panic buying that leads to gasoline shortages.) People have always wondered whether they can escape destiny. Only now, in the era of time travel, we ask whether we can change the past.

All the paradoxes are time loops. They all force us to think about causality. Can an effect precede its cause? Of course not. Obviously. By definition. “A cause is an object followed by another,” David Hume kept saying. If a child receives a measles inoculation and then suffers a seizure, the inoculation may or may not have caused the seizure. The one thing everyone knows for sure is that the seizure didn’t cause the inoculation.

But we’re not very good at understanding causes. The first person on record as trying to analyze cause and effect by power of ratiocination was Aristotle, who created layers of complexity that have caused confusion ever after. He distinguished four distinct types of causes, which can be named (making allowances for the impossibility of transmillennial translation) the efficient, the formal, the material, and the final. Some of these are hard for us to recognize as causes. The efficient cause of a sculpture is the sculptor, but the material cause is the marble. Both are needed before the sculpture can exist. The final cause is the purpose for which it is made—its beauty, let’s say. Considered chronologically, final causes seem to come later. What is the cause of an explosion: the dynamite? the spark? the bank robber? the safecracking? This line of thought tends to strike modern people as pettifogging. (On the other hand, some professionals find Aristotle’s vocabulary pitiably primitive. They would not want to discuss causal relations without mentioning immanence, transcendence, individuation, adicity, hybrid causes, probabilistic causes, and causal chains.) Either way, we do well to remember that nothing, when we look closely, has a single unambiguous incontrovertible cause.

Would you accept the assertion that the cause of a rock is that same rock an instant earlier?

“All reasonings concerning matters of fact seem to be founded on the relation of Cause and Effect,” said Hume, but he discovered that the reasonings were never easy or certain. Is the sun the cause of a rock’s warming? Is an insult the cause of a person’s anger? Only one thing could be said for sure: “A cause is an object followed by another.” If an effect doesn’t necessarily follow from a cause, was it a cause at all? The arguments echoed down the corridors of philosophy and continue to echo, despite Bertrand Russell’s attempt to settle the matter once and for all in 1913 with an appeal to modern science. “Oddly enough, in advanced sciences such as gravitational astronomy, the word ‘cause’ never occurs,” he wrote. Time for philosophers to get with the program. “The reason why physics has ceased to look for causes is that, in fact, there are no such things. The law of causality, I believe, like much that passes muster among philosophers, is a relic of a bygone age, surviving, like the monarchy, only because it is erroneously supposed to do no harm.”

Russell had in mind the hyper-Newtonian view of science described a century earlier by Laplace—the Universe Rigid—in which all that exists is locked together in a machinery of physical laws. Laplace spoke of the past as the cause of the future, but if the whole machine chugs along in lockstep, why should we imagine any particular gear or lever to be more causal than any other piece? We may consider the horse to be the cause of the carriage’s motion, but that is mere prejudice. Like it or not, the horse, too, is fully determined. Russell had noticed that when physicists write down their laws in mathematical language, time has no inherent directionality. “The law makes no difference between past and future,” he wrote. “The future ‘determines’ the past in exactly the same sense in which the past ‘determines’ the future.”

“But,” we are told, “you cannot alter the past, while you can to some extent alter the future.” This view seems to me to rest upon just those errors in regard to causation which it has been my object to remove. You cannot make the past other than it was—true….If you already know what the past was, obviously it is useless to wish it different. But also you cannot make the future other than it will be….If you happen to know the future—e.g. in the case of a forthcoming eclipse—it is just as useless to wish it different as to wish the past different.

And yet, Russell notwithstanding, scientists can no more abandon causation than anyone else. Cigarette smoking causes cancer, whether or not any particular cigarette causes any particular cancer. The burning of oil and coal in the air causes climate change. A mutation in a single gene causes phenylketonuria. The collapse of a burned-out star causes a supernova. Hume was right: “All reasonings concerning matters of fact seem to be founded on the relation of Cause and Effect.” Sometimes it’s all we talk about. The lines of causality are everywhere, some short and some long, some firm and others tenuous, invisible, interwoven, and inescapable. They all run in one direction, from past to future.

Let’s say that one day in 1811, in the town of Teplice, northwestern Bohemia, a man named Ludwig inks a note on a stave in his sketchbook. On an evening in 2011, a woman named Rachel blows a horn in Boston Symphony Hall, with a measurable effect: the air in that room vibrates with a predominant wavelength of 444 cycles per second. Who can deny that, at least in part, the note on paper caused the atmospheric vibrations two centuries later? Using the laws of physics, the path of influence from those molecules in Bohemia to the molecules in Boston would be challenging to compute, even given Laplace’s mythical “intelligence which could comprehend all the forces.” Yet we can see an unbroken causal chain. A chain of information, if not matter.

Russell did not end the conversation when he declared notions of causality to be relics of a bygone age. Not only do philosophers and physicists continue to wrangle over cause and effect, they add new possibilities to the mix. Retrocausation is now a topic: also known as backward causation or retro-chronal causation. Michael Dummett, a distinguished English logician and philosopher (and reader of science fiction), seems to have given this branch its start with his 1954 paper, “Can an Effect Precede Its Cause?” followed ten years later with his less tentative “Bringing About the Past.” Among the questions he raised was this. Suppose he hears on the radio that his son’s ship has sunk in the Atlantic. He prays to God that his son should be among the survivors. Has he blasphemed by asking God to undo what has been done? Or is this prayer functionally identical to praying in advance for his son’s safe passage?

What might inspire modern philosophers, against all precedent and tradition, to consider the possibility that effects might precede causes? The Stanford Encyclopedia of Philosophy offers this answer: “Time Travel.” Indeed, all the time-travel paradoxes, births and murders alike, stem from retrocausality. Effects undo their causes.

The first main argument against the causal order being the temporal order is that temporally backwards causation is possible in cases such as time travel. It seems metaphysically possible that a time traveler enters a time machine at time t1, thus causing her to exit the time machine at some earlier time t0. Indeed, this looks to be nomologically possible, since Gödel has proved that there are solutions to Einstein’s field equations that permit looping pathways.

Not that time travel settles the matter. “A variety of incoherencies might be alleged here,” the encyclopedia cautions, “including the incoherency of changing what is already fixed (causing the past), of being both able and unable to kill one’s own ancestors, or of generating a causal loop.” Brave writers are willing to risk an incoherency or two. Philip K. Dick ran the clocks backward (as it were) in Counter-Clock World, and so did Martin Amis in Time’s Arrow.

We do seem to be traveling in circles.

“THE RECENT RENAISSANCE of wormhole physics has led to a very disturbing observation,” wrote Matt Visser, a mathematician and cosmologist in New Zealand in 1994 in Nuclear Physics B (the forking path of Nuclear Physics devoted to “theoretical, phenomenological, and experimental high energy physics, quantum field theory and statistical systems”). Evidently the “renaissance” of wormhole physics was well established, though these supposed tunnels through spacetime remained (and remain) entirely hypothetical. The disturbing observation was this: “If traversable wormholes exist then it appears to be rather easy to transform such wormholes into time machines.” It was not just disturbing. It was extremely disturbing: “This extremely disturbing state of affairs has led Hawking to promulgate his chronology protection conjecture.”

Hawking is, of course, Stephen Hawking, the Cambridge physicist who by then had become the world’s most famous living scientist, in part because of his dramatic decades-long struggle with an inexorably paralyzing motor neuron disease and in part because of his flair for popularizing the knottiest problems of cosmology. No wonder he was attracted to time travel.

“Chronology Protection Conjecture” was the title of a paper he wrote in 1991 for Physical Review D. He explained the motivation as follows: “It has been suggested that an advanced civilization might have the technology to warp spacetime so that closed timelike curves would appear, allowing travel into the past.” Suggested by whom? An army of science-fiction writers, of course, but Hawking cited the physicist Kip Thorne (yet another Wheeler protégé) of the California Institute of Technology, who had been working with his graduate students on “wormholes and time machines.”

At some point the term “sufficiently advanced civilization” became a trope. As in: Even if we humans can’t do it, could a sufficiently advanced civilization? This is useful not just for SF writers but for physicists, too. So Thorne and Mike Morris and Ulvi Yurtsever wrote in Physical Review Letters in 1988, “We begin by asking whether the laws of physics permit an arbitrarily advanced civilization to construct and maintain wormholes for interstellar travel.” Not coincidentally, twenty-six years later, Thorne served as executive producer and science advisor for the 2014 big-budget movie Interstellar. “One can imagine an advanced civilization pulling a wormhole out of the quantum foam,” they wrote in the 1988 paper, and they included an illustration captioned “Spacetime diagram for conversion of a wormhole into a time machine.” They were contemplating wormholes with mouths in motion: a spaceship might enter one mouth and exit another mouth in the past. Fittingly, they concluded by posing a paradox, only this time it isn’t the grandfather who dies:

Can an advanced being measure Schrödinger’s cat to be alive at an event P (thereby “collapsing its wave function” onto a “live” state), then go backward in time via the wormhole and kill the cat (collapse its wave function onto a “dead” state) before it reaches P?

They left that question unanswered.

Hawking stepped in. He analyzed the wormhole physics as well as the paradoxes (“all sorts of logical problems, if you were able to change history”). He considered the possibility of evading the paradoxes “by some modification of the concept of free will,” but free will is seldom a happy topic for a physicist, and Hawking saw a better approach: what he proposed to call the chronology protection conjecture. A great deal of calculation was required, and when the calculating was done, Hawking was convinced: the laws of physics would protect history from the supposed time travelers. Notwithstanding Kurt Gödel, they must forbid the appearance of closed timelike curves. “It seems there is a chronology protection agency,” he wrote sci-fi-ishly, “which prevents the appearance of closed timelike curves and so makes the universe safe for historians.” And he concluded with a flourish—the kind of thing Hawking could get away with in the Physical Review. He had more than a theory. He had “evidence”:

There is also strong experimental evidence in favor of the conjecture from the fact that we have not been invaded by hordes of tourists from the future.

Hawking is one of those physicists who knows that time travel is impossible but also knows it’s fun to talk about. He points out that we are all traveling through time, one second at a time. He describes black holes as time machines, reminding us that gravitation slows the passage of time locally. And he often tells the story of the party he threw for time travelers—invitations sent only after the fact: “I sat there a long time, but no one came.”

In fact, the chronology protection conjecture had been floating about long before Stephen Hawking gave it a name. Ray Bradbury, for example, stated it in his 1952 story about time-traveling dinosaur hunters: “Time doesn’t permit that sort of mess—a man meeting himself. When such occasions threaten, Time steps aside. Like an airplane hitting an air pocket.” Notice that time has agency here: time doesn’t permit, and time steps aside. Douglas Adams offered his own version: “Paradoxes are just the scar tissue. Time and space heal themselves up around them and people simply remember a version of events which makes as much sense as they require it to make.”

Perhaps that seems a bit magical. Scientists prefer to credit the laws of physics. Gödel thought a robust, paradox-free universe was simply a matter of logic. “Time travel is possible, but no person will ever manage to kill his past self,” he told a young visitor in 1972.*8 “The a priori is greatly neglected. Logic is very powerful.” At some point chronological protection became part of the ground rules. It even became a cliché. In her 2008 story “The Region of Unlikeness,” Rivka Galchen can take all that old stage business for granted:

Science fiction writers have arrived at analogous solutions to the grandfather paradox: murderous grandchildren are inevitably stopped by something—faulty pistols, slippery banana peels, their own consciences—before the impossible deed can be carried out.

Region of unlikeness comes from Augustine: “I perceived myself to be far off from Thee, in the region of unlikeness”—in regione dissimilitudinis. He is not fully realized. Nor are any of us, bound as we are in time and space. “I beheld the other things below Thee, and I perceived that they neither altogether are, nor altogether are not.” God is eternity, remember, and we are not, much to our sorrow.

Galchen’s narrator falls into a friendship with two older men, philosophers maybe, scientists, it’s all a bit vague. The relationships are not well defined. The narrator feels that she is a bit undefined herself. The men speak in riddles. “Oh, time will tell,” one of them says. And: “Time is our tragedy, the substance we have to wade through as we try to move closer to God.” They vanish from her life for a while. She watches the obituary pages. An envelope appears mysteriously in her mailbox—diagram, billiard balls, equations. She thinks of an old joke: “Time flies like an arrow and fruit flies like a banana.” One thing becomes clear: everyone in this story knows a lot about time travel. A fateful loop—the same paradox as ever—begins to emerge from the shadows. Some rules are explained: that “contrary to popular movies, travel into the past didn’t alter the future, or, rather, that the future was already altered, or, rather, that it was all far more complicated than that.” Fate seems to be tugging at her, in a gentle way. Can anyone evade destiny? Look what happened to Laius. All she can say is, “Surely our world obeys rules still alien to our imagination.”

WE BEGIN AGAIN. A woman stands at the end of a “pier”—the open-air observation platform at Orly Airport (la grande jetée d’Orly), overlooking a sea of concrete on which the great metal jetliners rest, pointed like arrows toward the future. The sun is pale in a charcoal sky. We hear shrill jet blasts, a ghostly choir, murmuring voices. The woman almost smiles as the wind ruffles her hair. A child holds on to the railing, watching the planes on a warm Sunday. He sees the woman raise her hands to her face in horror and sees also, out of the corner of his eye, a blur, a falling shape. Later, he knew he had seen a man die, the narrator intones. Not long afterward, World War III begins. A nuclear holocaust destroys Paris, and the rest of the world, too.

This is La jetée, a 1962 film by Chris Marker—the pen name of Christian François Bouche-Villeneuve, born in 1921, a philosophy student, a resistance fighter with the Maquis, and then a roving journalist and photographer.*9 He was rarely photographed without a mask and lived to be ninety-one. In the fifties, after he worked with Alain Resnais on his Holocaust documentary Night and Fog, Resnais said: “A theory is making the rounds, and not without some grounds, that Marker could be an extra-terrestrial. He looks like a human, but perhaps he could be from the future or another planet.” Marker called La jetée a “photo-novel”: it is composed of still photographs, fading and dissolving, shifting points of view, to create, as one critic observed, the “illusion of a time-space continuum.” We are told that it is the story of a man marked by a memory from his childhood. The sudden roar, the woman’s gesture, the crumpling body, and the cries of the crowd on the jetty blurred by fear. The memory—and the marking—make him a candidate for time travel.

Now the world is dead and radioactive. Ruined churches, cratered streets. Survivors inhabit the tunnels and catacombs under Chaillot; a few men rule over prisoners in a camp. They despair. Their one hope lies in finding an emissary to send back to the past. Space was off limits. The only link with the means of survival passed through Time. A loophole in Time and then maybe it would be possible to reach food, medicine, sources of energy. Camp scientists experiment cruelly on one prisoner after another, driving them to madness or death, until finally they come to the nameless man “whose story we are telling.” What makes this man different from the others is his obsession with the past—with a particular image from the past. If they could imagine or dream of another time, perhaps they would be able to reenter it. The camp police spied even on dreams. The message here is that time travel is for the imaginative: an idea that recurs in the literature, for example in Jack Finney’s Time and Again. Time travel begins in the mind’s eye. Here, in La jetée, it’s a matter not just of transportation but of survival. The human mind balked. To wake up in another time meant to be born a second time, as an adult. The shock would be too much.

Credit 11.1

He lies in a hammock. A mask, with electrodes, covers his eyes. A large hypodermic needle injects drugs into his veins, while background voices whisper in German. He suffers. They continue. On the tenth day, images begin to ooze, like confessions. A peacetime morning. A peacetime bedroom—a real bedroom. Real children. Real birds. Real cats. Real graves. On the sixteenth day he is on the pier at Orly. Empty.

Sometimes he sees a woman, who might be the one he seeks. She is standing on the pier, or driving a car, smiling. A headless body is carved in ruined stone. These are images from a timeless world. He recovers from his trance, but the experimenters send him back again.

This time, he is close to her, speaks to her. She welcomes him without surprise. They are without plans, without memories. Time builds itself simply around them, their only landmarks the flavor of the moment and the markings on the walls. They explore a natural history museum, filled with animals from other times. For her, he is a man of mystery—vanishing periodically, wearing a curious necklace, dog tags from the war to come. She calls him her Ghost. It occurs to him that in his world, his time, she is already dead.

Many people, seeing La jetée with no foreknowledge, are not aware that they are seeing a series of still images. Then, twenty minutes into the film, the woman, asleep, her hair askew on her pillow, opens her eyes, looks directly at the viewer, breathes, and blinks. Time shudders, becomes momentarily real again. The frozen images have been timeless—memories, crystalized. Perhaps memory is the time traveler’s subject. Marker once said, “I will have spent my life trying to understand the function of remembering, which is not the opposite of forgetting, but its other side.” And he liked to quote George Steiner: “It is not the past that rules us—it is the image of the past.” Jetée is a pun, too: j’étais, I was.

The hero (if that’s what he is) carries out a mission not of his choosing. His masters send him not only to the past but then to the future, too. Humans have survived, and so, concealing his eyes behind military-style sunglasses, he begs them to do what is necessary to enable their own existence. They must help, he says. They must: their very survival proves it. Here is paradox again: the narrator says, “This sophism was taken for fate in disguise.” When he returns to the past, as we know he must—somewhere inside him, the memory of a twice-lived fragment of time—his destination is Orly Airport. It is Sunday. He knows that the woman will be at the end of the pier. The wind ruffles her hair. She almost smiles. As he runs toward her, it occurs to him that somewhere, too, holding on to the railing, will be the child he once was. And then: There was no way to escape Time. He understands. On ne s’évadait pas du Temps. The future has followed him here. Only at the last instant does he realize whose death he had witnessed as a child.

*1 A rebellious elector in Virginia refused to cast his ballot for the vote winners, Richard Nixon and Spiro Agnew, in 1972 and voted instead for John Hospers, on the Libertarian line.

*2 Gödel’s proof “is more than a monument,” said John von Neumann, “it is a landmark which will remain visible far in space and time….The subject of logic has completely changed its nature and possibilities with Gödel’s achievement.”

*3 Also, the Gödelian universe does not expand, whereas most cosmologists are pretty sure that ours does.

*4 Gödel’s biographer Rebecca Goldstein remarked, “As a physicist and a man of common sense, Einstein would have preferred that his field equations excluded such an Alice-in-Wonderland possibility as looping time.”

*5 The Heinlein story inspired a 2014 film, Predestination, with Ethan Hawke and Sarah Snook playing instances of the time traveler.

*6 Wells might have admired this descriptive flourish: “The general impression which the contrivance gave was that of unreality. The right-angles, at which various bars joined each other, did not seem to be quite ninety degrees. The perspective was distinctly off; for regardless from which side one viewed it, the more distant side always seemed to be the larger.”

*7 Ralph Milne Farley, “The Man Who Met Himself” (1935). Of course the man is in a ten-year loop, too. He uses the time to make money in the stock market.

*8 Rudy Rucker, a mathematician and, later, an author of science fiction.

*9 The self-description he ultimately settled on: “filmmaker, photographer, traveler.”