by James Gleick
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.
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“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.”
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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.