There was a conference for time travelers at M.I.T. earlier this spring.

I'm still hoping to attend, and although the odds are slim, they are apparently not zero despite the efforts and hopes of deterministically minded physicists who would like to eliminate the possibility of your creating a paradox by going back in time and killing your grandfather.

"No law of physics that we know of prohibits time travel," said Dr. J. Richard Gott, a Princeton astrophysicist.

Dr. Gott, author of the 2001 book "Time Travel in Einstein's Universe: The Physical Possibilities of Travel Through Time," is one of a small breed of physicists who spend part of their time (and their research grants) thinking about wormholes in space, warp drives and other cosmic constructions, that "absurdly advanced civilizations" might use to travel through time.

It's not that physicists expect to be able to go back and attend Woodstock, drop by the Bern patent office to take Einstein to lunch, see the dinosaurs or investigate John F. Kennedy's assassination.

In fact, they're pretty sure those are absurd dreams and are all bemused by the fact that they can't say why. They hope such extreme theorizing could reveal new features, gaps or perhaps paradoxes or contradictions in the foundations of Physics As We Know It and point the way to new ideas.

"Traversable wormholes are primarily useful as a 'gedanken experiment' to explore the limitations of general relativity," said Dr. Francisco Lobo of the University of Lisbon.

If general relativity, Einstein's theory of gravity and space-time, allows for the ability to go back in time and kill your grandfather, asks Dr. David Z. Albert, a physicist and philosopher at Columbia University, "how can it be a logically consistent theory?"

In his recent book "The Universe in a Nutshell," Dr. Stephen W. Hawking wrote, "Even if it turns out that time travel is impossible, it is important that we understand why it is impossible."

When it comes to the nature of time, physicists are pretty much at as much of a loss as the rest of us who seem hopelessly swept along in its current. The mystery of time is connected with some of the thorniest questions in physics, as well as in philosophy, like why we remember the past but not the future, how causality works, why you can't stir cream out of your coffee or put perfume back in a bottle.

But some theorists think that has to change.

Just as Einstein needed to come up with a new concept of time in order to invent relativity 100 years ago this year, so physicists say that a new insight into time - or beyond it - may be required to crack profound problems like how the universe began, what happens at the center of black hole or how to marry relativity and quantum theory into a unified theory of nature.

Space and time, some quantum gravity theorists say, are most likely a sort of illusion - or less sensationally, an "approximation" - doomed to be replaced by some more fundamental idea. If only they could think of what that idea is.

"By convention there is space, by convention time," Dr. David J. Gross, director of the Kavli Institute for Theoretical Physics and a winner of last year's Nobel Prize, said recently, paraphrasing the Greek philosopher Democritus, "in reality there is. ... ?" his voice trailing off.

The issues raised by time travel are connected to these questions, Dr. Lawrence Krauss, a physicist at Case Western Reserve University in Cleveland and author of the book "The Physics of Star Trek," said. "The minute you have time travel you have paradoxes," Dr. Krauss said, explaining that if you can go backward in time you confront fundamental issues like cause and effect or the meaning of your own identity if there can be two of you at once. A refined theory of time would have to explain "how a sensible world could result from something so nonsensical."

"That's why time travel is philosophically important and has captivated the public, who care about these paradoxes," he said.

At stake, said Dr. Albert, the philosopher and author of his own time book, "Time and Chance," is "what kind of view science presents us of the world."

"Physics gets time wrong, and time is the most familiar thing there is," Dr. Albert said.

We all feel time passing in our bones, but ever since Galileo and Newton in the 17th century began using time as a coordinate to help chart the motion of cannonballs, time - for physicists - has simply been an "addendum in the address of an event," Dr. Albert said.

"There is a feeling in philosophy," he said, "that this picture leaves no room for locutions about flow and the passage of time we experience."

Then there is what physicists call "the arrow of time" problem. The fundamental laws of physics don't care what direction time goes, he pointed out. Run a movie of billiard balls colliding or planets swirling around in their orbits in reverse and nothing will look weird, but if you run a movie of a baseball game in reverse people will laugh.

Einstein once termed the distinction between past, present and future "a stubborn illusion," but as Dr. Albert said, "It's hard to imagine something more basic than the distinction between the future and the past."

The Birth of an Illusion

Space and time, the philosopher Augustine famously argued 1,700 years ago, are creatures of existence and the universe, born with it, not separately standing features of eternity. That is the same answer that Einstein came up with in 1915 when he finished his general theory of relativity.

That theory explains how matter and energy warp the geometry of space and time to produce the effect we call gravity. It also predicted, somewhat to Einstein's dismay, the expansion of the universe, which forms the basis of modern cosmology.

But Einstein's theory is incompatible, mathematically and philosophically, with the quirky rules known as quantum mechanics that describe the microscopic randomness that fills this elegantly curved expanding space-time. According to relativity, nature is continuous, smooth and orderly, in quantum theory the world is jumpy and discontinuous. The sacred laws of physics are correct only on average.

Until the pair are married in a theory of so-called quantum gravity, physics has no way to investigate what happens in the Big Bang, when the entire universe is so small that quantum rules apply.

Looked at closely enough, with an imaginary microscope that could see lengths down to 10^-33 centimeters, quantum gravity theorists say, even ordinary space and time dissolve into a boiling mess that Dr. John Wheeler, the Princeton physicist and phrasemaker, called "space-time foam." At that level of reality, which exists underneath all our fingernails, clocks and rulers as we know them cease to exist.

"Everything we know about stops at the Big Bang, the Big Crunch," said Dr. Raphael Bousso, a physicist at the University of California, Berkeley.

What happens to time at this level of reality is anybody's guess. Dr. Lee Smolin, of the Perimeter Institute for Theoretical Physics in Waterloo, Ontario, said, "There are several different, very different, ideas about time in quantum gravity."

One view, he explained, is that space and time "emerge" from this foamy substrate when it is viewed at larger scales. Another is that space emerges but that time or some deeper relations of cause and effect are fundamental.

Dr. Fotini Markopoulou Kalamara of the Perimeter Institute described time as, if not an illusion, an approximation, "a bit like the way you can see the river flow in a smooth way even though the individual water molecules follow much more complicated patterns."

She added in an e-mail message: "I have always thought that there has to be some basic fundamental notion of causality, even if it doesn't look at all like the one of the space-time we live in. I can't see how to get causality from something that has none; neither have I ever seen anyone succeed in doing so."

Physicists say they have a sense of how space can emerge, because of recent advances in string theory, the putative theory of everything, which posits that nature is composed of wriggling little strings.

Calculations by Dr. Juan Maldacena of the Institute for Advanced Study in Princeton and by others have shown how an extra dimension of space can pop mathematically into being almost like magic, the way the illusion of three dimensions can appear in the holograms on bank cards. But string theorists admit they don't know how to do the same thing for time yet.

"Time is really difficult," said Dr. Cumrun Vafa, a Harvard string theorist. "We have not made much progress on the emergence of time. Once we make progress we will make progress on the early universe, on high energy physics and black holes.

"We are out on a limb trying to understand what's going on here."

Dr. Bousso, an expert on holographic theories of space-time, said that in general relativity time gets no special treatment.

He said he expected both time and space to break down, adding, "We really just don't know what's going to go."

"There is a lot of mysticism about time," Dr. Bousso said. "Time is what a clock measures. What a clock measures is more interesting than you thought."

A Brief History of Time Travel

"If we could go faster than light, we could telegraph into the past," Einstein once said. According to the theory of special relativity - which he proposed in 1905 and which ushered E=mc² into the world and set the speed of light as the cosmic speed limit - such telegraphy is not possible, and there is no way of getting back to the past.

But, somewhat to Einstein's surprise, in general relativity it is possible to beat a light beam across space. That theory, which Einstein finished in 1916, said that gravity resulted from the warping of space-time geometry by matter and energy, the way a bowling ball sags a trampoline. And all this warping and sagging can create shortcuts through space-time.

In 1949, Kurt Gödel, the Austrian logician and mathematician then at the Institute for Advanced Study, showed that in a rotating universe, according to general relativity, there were paths, technically called "closed timelike curves," you could follow to get back to the past. But it has turned out that the universe does not rotate very much, if at all.

Most scientists, including Einstein, resisted the idea of time travel until 1988 when Dr. Kip Thorne, a gravitational theorist at the California Institute of Technology, and two of his graduate students, Dr. Mike Morris and Dr. Ulvi Yurtsever, published a pair of papers concluding that the laws of physics may allow you to use wormholes, which are like tunnels through space connecting distant points, to travel in time.

These holes, technically called Einstein-Rosen bridges, have long been predicted as a solution of Einstein's equations. But physicists dismissed them because calculations predicted that gravity would slam them shut.

Dr. Thorne was inspired by his friend, the late Cornell scientist and author Carl Sagan, who was writing the science fiction novel "Contact," later made into a Jodie Foster movie, and was looking for a way to send his heroine, Eleanor Arroway, across the galaxy. Dr. Thorne and his colleagues imagined that such holes could be kept from collapsing and thus maintained to be used as a galactic subway, at least in principle, by threading them with something called Casimir energy, (after the Dutch physicist Hendrik Casimir) which is a sort of quantum suction produced when two parallel metal plates are placed very close together. According to Einstein's equations, this suction, or negative pressure, would have an antigravitational effect, keeping the walls of the wormhole apart.

If one mouth of a wormhole was then grabbed by a spaceship and taken on a high-speed trip, according to relativity, its clock would run slow compared with the other end of the wormhole. So the wormhole would become a portal between two different times as well as places.

Dr. Thorne later said he had been afraid that the words "time travel" in the second paper's title would create a sensation and tarnish his students' careers, and he had forbidden Caltech to publicize it.

In fact, their paper made time travel safe for serious scientists, and other theorists, including Dr. Frank Tipler of Tulane University and Dr. Hawking, jumped in. In 1991, for example, Dr. Gott of Princeton showed how another shortcut through space-time could be manufactured using pairs cosmic strings - dense tubes of primordial energy not to be confused with the strings of string theory, left over by the Big Bang in some theories of cosmic evolution - rushing past each other and warping space around them.

Harnessing the Dark Side

These speculations have been bolstered (not that time machine architects lack imagination) with the unsettling discovery that the universe may be full of exactly the kind of antigravity stuff needed to grow and prop open a wormhole. Some mysterious "dark energy," astronomers say, is pushing space apart and accelerating the expansion of the universe. The race is on to measure this energy precisely and find out what it is.

Among the weirder and more disturbing explanations for this cosmic riddle is something called phantom energy, which is so virulently antigravitational that it would eventually rip planets, people and even atoms apart, ending everything. As it happens this bizarre stuff would also be perfect for propping open a wormhole, Dr. Lobo of Lisbon recently pointed out. "This certainly is an interesting prospect for an absurdly advanced civilization, as phantom energy probably comprises of 70 percent of the universe," Dr. Lobo wrote in an e-mail message. Dr. Sergey Sushkov of Kazan State Pedagogical University in Russia has made the same suggestion.

In a paper posted on the physics Web site arxiv.org/abs/gr-qc/0502099, Dr. Lobo suggested that as the universe was stretched and stretched under phantom energy, microscopic holes in the quantum "space-time foam" might grow to macroscopic usable size. "One could also imagine an advanced civilization mining the cosmic fluid for phantom energy necessary to construct and sustain a traversable wormhole," he wrote.

Such a wormhole he even speculated, could be used to escape the "big rip" in which a phantom energy universe will eventually end.

But nobody knows if phantom, or exotic, energy is really allowed in nature and most physicists would be happy if it is not. Its existence would lead to paradoxes, like negative kinetic energy, where something could lose energy by speeding up, violating what is left of common sense in modern physics.

Dr. Krauss said, "From the point of view of realistic theories, phantom energy just doesn't exist."

But such exotic stuff is not required for all time machines, Dr. Gott's cosmic strings for example. In another recent paper, Dr. Amos Ori of the Technion-Israel Institute of Technology in Haifa describes a time machine that he claims can be built by moving around colossal masses to warp the space inside a doughnut of regular empty space into a particular configuration, something an advanced civilization may be able to do in 100 or 200 years.

The space inside the doughnut, he said, will then naturally evolve according to Einstein's laws into a time machine.

Dr. Ori admits that he doesn't know if his machine would be stable. Time machines could blow up as soon as you turned them on, say some physicists, including Dr. Hawking, who has proposed what he calls the "chronology protection" conjecture to keep the past safe for historians. Random microscopic fluctuations in matter and energy and space itself, they argue, would be amplified by going around and around boundaries of the machine or the wormhole, and finally blow it up.

Dr. Gott and his colleague Dr. Li-Xin Li have shown that there are at least some cases where the time machine does not blow up. But until gravity marries quantum theory, they admit, nobody knows how to predict exactly what the fluctuations would be.

"That's why we really need to know about quantum gravity," Dr. Gott said. "That's one reason people are interested in time travel."

Saving Grandpa

But what about killing your grandfather? In a well-ordered universe, that would be a paradox and shouldn't be able to happen, everybody agrees.

That was the challenge that Dr. Joe Polchinski, now at the Kavli Institute for Theoretical Physics in Santa Barbara, Calif., issued to Dr. Thorne and his colleagues after their paper was published.

Being a good physicist, Dr. Polchinski phrased the problem in terms of billiard balls. A billiard ball, he suggested, could roll into one end of a time machine, come back out the other end a little earlier and collide with its earlier self, thereby preventing itself from entering the time machine to begin with.

Dr. Thorne and two students, Fernando Echeverria and Gunnar Klinkhammer, concluded after months of mathematical struggle that there was a logically consistent solution to the billiard matricide that Dr. Polchinski had set up. The ball would come back out of the time machine and deliver only a glancing blow to itself, altering its path just enough so that it would still hit the time machine. When it came back out, it would be aimed just so as to deflect itself rather than hitting full on. And so it would go like a movie with a circular plot.

In other words, it's not a paradox if you go back in time and save your grandfather. And, added Dr. Polchinski, "It's not a paradox if you try to shoot your grandfather and miss."

"The conclusion is somewhat satisfying," Dr. Thorne wrote in his book "Black Holes and Time Warps: Einstein's Outrageous Legacy." "It suggests that the laws of physics might accommodate themselves to time machines fairly nicely."

Dr. Polchinski agreed. "I was making the point that the grandfather paradox had nothing to do with free will, and they found a nifty resolution," he said in an e-mail message, adding, nevertheless, that his intuition still tells him time machines would lead to paradoxes.

Dr. Bousso said, "Most of us would consider it quite satisfactory if the laws of quantum gravity forbid time travel."

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Four-Dimensional Reality

Manipulating Time