Births, deaths, and other time travel paradoxes
I DOUBT that any phenomenon, real or imagined, has inspired more perplexing, convoluted, and ultimately futile philosophical analysis than time travel has.
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.”
“In fact, H. G. Wells did imagine it in The Time Machine (1895), 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 unusual distinction for a philosopher of having received one electoral vote for President of the United States. But his textbook, first published in 1953, remained standard through four editions and 40 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.” 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 70-year-old, Benjamin grows younger every day, until infancy and oblivion. Fitzgerald would have admitted the logical impossibility. The story has many offspring.)
Time is necessarily simple for Hospers. If you imagine that one day you are in the 20th 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 spacetime continuum. This was in 1949.
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 ’30s. 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 to have the privilege of walking home with Gödel.
“Why can’t he go back and kill his grandfather? Because he did not.”
For Einstein’s 70th 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 time-like lines,” or, as a physicist today would say, closed time-like curves (CTCs). These are circular highways lacking on ramps or off ramps. A time-like line is a set of points separated only by time: same place, different times. A closed time-like curve loops back upon 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.2)
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 time-like 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.
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.
Reichenbach is confused, too (that would be Hans Reichenbach, author of The Direction of Time), and so is Capek (Milic Capek, “Time and Relativity Theory: Arguments for a Theory 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. 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.
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.
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 his first 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 accordion-like 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 rollercoaster.
Admit it: You didn’t help build the pyramids.
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.
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 a peculiar Austrian accent by the 37-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.
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 trans-millennial translation) the efficient, the formal, the material, and the final. Some of these are hard to recognize as causes.
“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...”
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.”
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 retro-causality. Effects undo their causes.
“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 branch of Nuclear Physics devoted to “theoretical, phenomenological, and experimental high energy physics, quantum field theory, and statistical systems”). 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.
The “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.”
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. “The a priori is greatly neglected. Logic is very powerful.”7 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. Turn to Page 14
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.”
Photo: james gleick
James Gleick is an award-winning science writer and best-selling author of Chaos: Making a New Science, Genius: The Life and Science of Richard Feynman, and The Information: A History, a Theory, a Flood. His books have been translated into 30 languages.
Excerpted from Time Travel:? A History by James Gleick © 2016. Published by Pantheon.? All rights reserved.