H. G. Wells published his first novel, *The Time Machine*, in 1895, just a few years before Queen Victoria's six-decade reign over the U.K. ended. An even more durable dynasty was also drawing to a close: the 200-year-old Newtonian era of physics. In 1905 Albert Einstein published his special theory of relativity, which upset Isaac Newton's applecart and, to Wells's presumed delight, allowed something that had been impossible under Newton's laws: time travel into the future. In Newton's universe, time was steady everywhere and everywhen; it never sped up or slowed down. But for Einstein, time was relative.

Time travel is not only possible, it has already happened, though not exactly as Wells imagined. The biggest time traveler to date is Sergei K. Krikalev, according to J. Richard Gott, an astrophysicist at Princeton University. Over the course of his long career, which began in 1985, the Russian cosmonaut spent a little over 803 days in space. As Einstein proved, time passes more slowly for objects in motion than for those at rest, so as Krikalev hurtled along at 17,000 miles an hour onboard the *Mir* space station, time did not flow at the same rate for him as it did on Earth. While Krikalev was in orbit, he aged 1/48 of a second less than his fellow earthlings. From another perspective, he traveled 1/48 of a second into the future.

The time-travel effect is much easier to see with longer distances and higher speeds. If Krikalev left Earth in 2015 and made a round-trip to Betelgeuse—a star that is about 520 light-years from Earth—at 99.995 percent the speed of light, by the time he returned to Earth he would be only 10 years older. Sadly, everyone he knew would be long dead because 1,000 years would have passed on Earth; it would be the year 3015. “Time travel to the future, we know we can do,” Gott says. “It's just a matter of money and engineering!”

Jumping a few nanoseconds—or centuries—into the future is relatively straightforward, despite practical challenges. But going *backward* in time is harder. Einstein's special theory of relativity forbade it. After another decade of work, Einstein unveiled his general theory of relativity, which finally lifted that restriction. How someone would actually travel back in time, however, is a vexing problem because the equations of general relativity have many solutions. Different solutions assign different qualities to the universe—and only *some* of the solutions create conditions that permit time travel into the past.

Whether any of those solutions describes our own universe is an open question, which raises even more profound investigations: Just how much tweaking of fundamental physics would it take to allow backward time travel? Does the universe itself somehow prevent such journeys even if Einstein's equations do not rule them out? Physicists continue to speculate, not because they imagine time travel will ever be practical but because thinking about the possibility has led to some surprising insights about the nature of the universe we inhabit, including, perhaps, how it came to be in the first place.

## A new way of looking at time

With his special theory of relativity, Einstein made time malleable in a way that must have pleased Wells, who presciently believed that we inhabit a universe in which three-dimensional space and time are knit together into a four-dimensional whole. Einstein arrived at his revolutionary results by exploring the implications of two fundamental ideas. First, he argued that even though all motion is relative, the laws of physics must look the same for everyone anywhere in the universe. Second, he realized that the speed of light must be similarly unchanging from all perspectives: if everyone sees the same laws of physics operating, they must also arrive at the same result when measuring the speed of light.

To make light a universal speed limit, Einstein had to jettison two commonsense notions: that all observers would agree on the measurement of a given length and that they would also agree on the duration of time's passage. He showed that a clock in motion, whizzing past someone at rest, would tick more slowly than a stationary clock at the person's side. And the length of a ruler moving swiftly by would shorten. Yet for anyone who was traveling at the same speed as the clock and ruler, the passage of time and the length of the ruler would appear normal.

At ordinary speeds, the time-and-space-distorting effects of special relativity are negligible. But for anything moving at a hefty fraction of the speed of light, they are very real. For example, many experiments have confirmed that the decay rate of unstable particles called muons slows by an order of magnitude when they are traveling at close to the speed of light. The speeding muons, in effect, are minuscule time travelers—subatomic Krikalevs—hopping a few nanoseconds into the future.

## Gödel's strange universe

Those speedy clocks and rulers and muons are all racing forward in time. Can they be thrown into reverse? The first person to use general relativity to describe a universe that permits time travel into the past was Kurt Gödel, the famed creator of the incompleteness theorems, which set limits on the scope of what mathematics can and cannot prove. He was one of the towering mathematicians of the 20th century—and one of the oddest. His many foibles included a diet of baby food and laxatives.

Gödel presented this model universe as a gift to Einstein on his 70th birthday. The universe Gödel described to his skeptical friend had two unique properties: It rotated, which provided centrifugal force that prevented gravity from crunching together all the matter in the cosmos, creating the stability Einstein demanded of any cosmic model. But it also allowed for time travel into the past, which made Einstein deeply uneasy. In Gödel's cosmos, space travelers could set out and eventually reach a point in their own past, as if the travelers had completed a circuit around the surface of a giant cylinder. Physicists call these trajectories in spacetime “closed timelike curves.”

A closed timelike curve is any path through spacetime that loops back on itself. In Gödel's rotating cosmos, such a curve would circle around the entire universe, like a latitude line on Earth's surface. Physicists have concocted a number of different types of closed timelike curves, all of which allow travel to the past, at least in theory. A journey along any of them would be disappointingly ordinary, however: Through the portholes of your spaceship, you would see stars and planets—all the usual sights of deep space. More important, time—as measured by your own clocks—would tick forward in the usual way; the hands of a clock would not start spinning backward even though you would be traveling to a location in spacetime that existed in your past.

“Einstein was already aware of the possibility of closed timelike curves back in 1914,” says Julian Barbour, an independent theoretical physicist who lives near Oxford, England. As Barbour recalls, Einstein said, “My intuition strives most vehemently against this.” The curves' existence would create all kinds of problems with causality—how can the past be changed if it has already happened? And there is the hoary grandfather paradox: What happens to a time traveler who kills his or her grandfather before the grandfather meets the grandmother? Would the demented traveler ever be born?

Fortunately for fans of causality, astronomers have found no evidence that the universe is rotating. Gödel himself apparently pored over catalogs of galaxies, looking for clues that his theory might be true. Gödel might not have devised a realistic model of the universe, but he did prove that closed timelike curves are completely consistent with the equations of general relativity. The laws of physics do not rule out traveling to the past.

## An annoying possibility

Over the past few decades cosmologists have used Einstein's equations to construct a variety of closed timelike curves. Gödel conjured an entire universe that allowed them, but more recent enthusiasts have warped spacetime only within parts of our universe.

In general relativity, planets, stars, galaxies and other massive bodies warp spacetime. Warped spacetime, in turn, guides the motions of those massive bodies. As the late physicist John Wheeler put it, “Spacetime tells matter how to move; matter tells spacetime how to curve.” In extreme cases, spacetime might bend enough to create a path from the present back to the past.

Physicists have proposed some exotic mechanisms to create such paths. In a 1991 paper, Gott showed how cosmic strings—infinitely long structures thinner than an atom that may have formed in the early universe—would allow closed timelike curves where two strings intersected. In 1983 Kip S. Thorne, a physicist at the California Institute of Technology, began to explore the possibility that a type of closed timelike curve called a wormhole—a kind of tunnel joining two different locations in spacetime—might allow for time travel into the past. “In general relativity, if you connect two different regions of space, you're also connecting two different regions of time,” says Sean M. Carroll, a colleague of Thorne's at Caltech.

The entrance into a wormhole would be spherical—a three-dimensional entrance into a four-dimensional tunnel in spacetime. As is the case with all closed timelike curves, a trip through a wormhole would be “like any other journey,” Carroll says. “It's not that you disappear and are reassembled at some other moment of time. There is no respectable theory where that kind of science-fiction time travel is possible.” For all travelers, he adds, “no matter what they do, time flows forward at one second per second. It's just that your local version of ‘forward’ might be globally out of sync with the rest of the universe.”

Although physicists can write equations that describe wormholes and other closed timelike curves, all the models have serious problems. “Just to get a wormhole in the first place, you need negative energy,” Carroll says. Negative energy is when the energy in a volume of space spontaneously fluctuates to less than zero. Without negative energy, a wormhole's spherical entrance and four-dimensional tunnel would instantaneously implode. But a wormhole held open by negative energy “seems to be hard, probably impossible,” Carroll says. “Negative energies seem to be a bad thing in physics.”

Even if negative energy kept a wormhole open, just when you would be on the verge of turning that into a time machine, “particles would be moving through the wormhole, and every particle would loop back around an infinite number of times,” Carroll says. “That leads to an infinite amount of energy.” Because energy deforms spacetime, the entire thing would collapse into a black hole—an infinitely dense point in spacetime. “We're not 100 percent sure that that happens,” Carroll says. “But it seems to be a reasonable possibility that the universe is actually preventing you from making a time machine by making a black hole instead.”

Unlike black holes, which are a natural consequence of general relativity, wormholes and closed timelike curves in general are completely artificial constructs—a way of testing the bounds of the theory. “Black holes are hard to avoid,” Carroll says. “Closed timelike curves are very hard to make.”

Even if wormholes are physically implausible, it is significant that they fit in with the general theory of relativity. “It's very curious that we can come so close to ruling out the possibility of time travel, yet we just can't do it. I also think that it's annoying,” Carroll says, exasperated that Einstein's beautiful theory might allow for something so seemingly implausible. But by contemplating that annoying possibility, physicists may gain a better understanding of the kind of universe we live in. And it may be that if the universe did not permit backward time travel, it never would have come into existence.

## Did the universe create itself?

General relativity describes the universe on the largest scales. But quantum mechanics provides the operating manual for the atomic scale, and it offers another possible venue for closed timelike curves—one that gets at the origin of the universe.

“On a very small scale—10–30 centimeter—you might expect the topology of spacetime to fluctuate, and random fluctuations might give you closed timelike curves if nothing fundamental prevents them,” says John Friedman, a physicist at the University of Wisconsin–Milwaukee. Could those quantum fluctuations somehow be magnified and harnessed as time machines? “There's certainly no formal proof that you *can't* have macroscopic closed timelike curves,” Friedman says. “But the community of people who have looked at these general questions would bet pretty heavily against it.”

There is no doubt that the creation of a loop in spacetime on either a quantum scale or a cosmic one would require some very extreme physics. And the most likely place to expect extreme physics, Gott says, is at the very beginning of the universe.

In 1998 Gott and Li-Xin Li, an astrophysicist now at Peking University in China, published a paper in which they argued that closed timelike curves were not merely possible but essential to explain the origin of the universe. “We investigated the possibility of whether the universe could be its own mother—whether a time loop at the beginning of the universe would allow the universe to create itself,” Gott says.

Gott and Li's universe “starts” with a bout of inflation—just as in standard big bang cosmology, where an all-pervasive energy field drove the universe's initial expansion. Many cosmologists now believe that inflation gave rise to countless other universes besides our own. “Inflation is very hard to stop once it gets started,” Gott says. “It makes an infinitely branching tree. We're one of the branches. But you have to ask yourself, Where did the trunk come from? Li-Xin Li and I said it could be that one of the branches just loops around and grows up to be the trunk.”

A simple two-dimensional sketch of Gott and Li's self-starting universe looks like the number “6,” with the spacetime loop at the bottom and our present-era universe as the top stem. A burst of inflation, Gott and Li theorized, allowed the universe to escape from the time loop and expand into the cosmos we inhabit today.

It is difficult to contemplate the model, but its main appeal, Gott says, is that it eliminates the need for creating a universe out of nothing. Yet Alexander Vilenkin of Tufts University, Stephen Hawking of the University of Cambridge and James Hartle of the University of California, Santa Barbara, have proposed models in which the universe does indeed arise out of nothing. According to the laws of quantum mechanics, empty space is not really empty but is filled with “virtual” particles that spontaneously pop into and out of existence. Hawking and his colleagues theorized that the universe burst into being from the same quantum-vacuum stew. But in Gott's view, the universe is not made out of nothing; it is made out of something—itself.

## A cosmic chess game

For now, there is no way to test whether any of those theories might actually explain the origin of the universe. The famed physicist Richard Feynman compared the universe to a great chess game being played by the gods. Scientists, he said, are trying to understand the game without knowing the rules. We watch as the gods move a pawn one space forward, and we learn a rule: pawns always move one space forward. But what if we never saw the opening of a game, when a pawn can move two spaces forward? We might also assume, mistakenly, that pawns always remain pawns—that they never change their identity—until we see a pawn transformed into a queen. “You would say that's against the rules,” Gott says. “You can't change your pawn into a queen. Well, yes, you can! You just never saw a game that extreme before. Time-travel research is like that. We're testing the laws of physics by looking at extreme conditions. There's nothing logically impossible about time travel to the past; it's just not the universe we're used to.” Turning a pawn into a queen could be part of the rules of relativity.

Such wildly speculative ideas may be closer to philosophy than to physics. But for now, quantum mechanics and general relativity—powerful, counterintuitive theories—are all we have to figure out the universe. “As soon as people start trying to bring quantum theory and general relativity into this, the first thing to say is that they really have no idea what they're doing,” says Tim Maudlin, a philosopher of science at New York University. “It's not really rigorous mathematics. It's one piece of mathematics that sort of looks like general relativity and another little piece of mathematics that sort of looks like quantum theory, mixed together in some not entirely coherent way. But this is what people have to do because they honestly don't know how to go forward in a way that makes sense.”

Will some future theory eliminate the possibility of time travel into the past? Or will the universe again turn out to be far stranger than we imagine? Physics has advanced tremendously since Einstein redefined our understanding of time. Time travel, which existed only in the realm of fiction for Wells, is now a proved reality, at least in one direction. Is it too hard to believe that some kind of symmetry exists in the universe, allowing us to travel backward in time? When I put the question to Gott, he replies with an anecdote:

“There's a story where Einstein was talking to a guy. The guy pulled a notebook out and scribbled something down. Einstein says, ‘What's that?’ The guy says, ‘A notebook. Whenever I have a good idea, I write it down.’ Einstein says, ‘I've never had any need for a notebook; I've only had three good ideas.’”

Gott concludes: “I think we're waiting for a new good idea.”