Physics of the Impossible Part 9

Alcubierre speculates that a journey in his proposed starship would resemble a journey taken on the Millennium Falcon in Star Wars. "My guess is they would probably see something very similar to that. In front of the ship, the stars would become long lines, streaks. In back, they wouldn't see anything-just black-because the light of the stars couldn't move fast enough to catch up with them," he says.

The key to the Alcubierre drive is the energy necessary to propel the s.p.a.cecraft forward at faster-than-light velocities. Normally physicists begin with a positive amount of energy in order to propel a starship, which always travels slower than the speed of light. To move beyond this strategy so as to be able to travel faster than the speed of light one would need to change the fuel. A straightforward calculation shows that you would need "negative ma.s.s" or "negative energy," perhaps the most exotic ent.i.ties in the universe, if they exist. Traditionally, physicists have dismissed negative energy and negative ma.s.s as science fiction. But we now see that they are indispensable for faster-than-light travel, and they might actually exist.

Scientists have looked for negative matter in nature, but so far without success. (Antimatter and negative matter are two entirely different things. The first exists and has positive energy, but a reversed charge. Negative matter has not yet been proven to exist.) Negative matter would be quite peculiar, because it would be lighter than nothing. In fact, it would float. If negative matter existed in the early universe, it would have drifted into outer s.p.a.ce. Unlike meteors that come crashing down onto planets, drawn by a planet's gravity, negative matter would shun planets. It would be repelled, not attracted, by large bodies such as stars and planets. Hence, although negative matter might exist, we expect to find it only in deep s.p.a.ce, certainly not on Earth.

One proposal to find negative matter in outer s.p.a.ce involves using the phenomenon called "Einstein lenses." When light travels around a star or galaxy its path is bent by its gravity, according to general relativity. In 1912 (even before Einstein fully developed general relativity) he predicted that a galaxy might be able to act like the lens of a telescope. Light from a distant object moving around a nearby galaxy would converge as it pa.s.sed around the galaxy, like a lens, forming a characteristic ring pattern when the light finally reached the Earth. These phenomena are now called "Einstein rings." In 1979 the first of these Einstein lenses was observed in outer s.p.a.ce. Since then, Einstein lenses have become an indispensable tool for astronomers. (For example, it was once thought that it would be impossible to locate "dark matter" in outer s.p.a.ce. [Dark matter is a mysterious substance that is invisible but has weight. It surrounds the galaxies and is perhaps ten times as plentiful as ordinary visible matter in the universe.] But NASA scientists have been able to construct maps of dark matter since dark matter bends light as the light pa.s.ses through, in the same way that gla.s.s bends light.) Therefore it should be possible to use Einstein lenses to search for negative matter and wormholes in outer s.p.a.ce. They should bend light in a peculiar way, which should be visible with the Hubble s.p.a.ce Telescope. So far, Einstein lenses have not detected the image of negative matter or wormholes in outer s.p.a.ce, but the search is continuing. If one day the Hubble s.p.a.ce Telescope detects the presence of negative matter or a wormhole via Einstein lenses, it could set off a shock wave in physics.

Negative energy is different from negative matter in that it actually exists, but only in minute quant.i.ties. In 1933 Hendrik Casimir made a bizarre prediction using the laws of the quantum theory. He claimed that two uncharged parallel metal plates will attract each other, as if by magic. Normally parallel plates are stationary, since they lack any net charge. But the vacuum between the two parallel plates is not empty, but full of "virtual particles," which dart in and out of existence.

For brief periods of time, electron-antielectron pairs burst out of nothing, only to be annihilated and disappear back into the vacuum. Ironically, empty s.p.a.ce, which was once thought to be devoid of anything, now turns out to be churning with quantum activity. Normally tiny bursts of matter and antimatter would seem to violate the conservation of energy. But because of the uncertainty principle, these tiny violations are incredibly short-lived, and on average energy is still conserved.

Casimir found that the cloud of virtual particles will create a net pressure in the vacuum. The s.p.a.ce between the two parallel plates is confined, and hence the pressure is low. But the pressure outside the plates is unconfined and larger, and hence there will be a net pressure pushing the plates together.

Normally the state of zero energy occurs when these two plates are at rest and sitting far apart from each other. But as the plates come closer together, you can extract energy out of them. Thus, because kinetic energy has been taken out of the plates, the energy of the plates is less than zero.

This negative energy was actually measured in the laboratory in 1948, and the results confirmed Casimir's prediction. Thus, negative energy and the Casimir effect are no longer science fiction but established fact. The problem, however, is that the Casimir effect is quite small; it takes delicate, state-of-the-art measuring equipment to detect this energy in the laboratory. (In general, the Casimir energy is proportional to the inverse fourth power of the distance of separation between the plates. This means that the smaller the distance of separation, the larger the energy.) The Casimir effect was measured precisely in 1996 by Steven Lamoreaux at the Los Alamos National Laboratory, and the attractive force is 1/30,000 the weight of an ant.

Since Alcubierre first proposed his theory, physicists have discovered a number of strange properties. The people inside the starship are causally disconnected from the outside world. This means that you cannot simply press a b.u.t.ton at will and travel faster than light. You cannot communicate through the bubble. There has to be a preexisting "highway" through s.p.a.ce and time, like a series of trains pa.s.sing by on a regular timetable. In this sense, the starship would not be an ordinary ship that can change directions and speeds at will. The starship would actually be like a pa.s.senger car riding on a preexisting "wave" of compressed s.p.a.ce, coasting along a preexisting corridor of warped s.p.a.ce-time. Alcubierre speculates, "We would need a series of generators of exotic matter along the way, like a highway, that manipulate s.p.a.ce for you in a synchronized way."

Actually, even more bizarre types of solutions to Einstein's equations can be found. Einstein's equations state that if you are given a certain amount of ma.s.s or energy, you can compute the warping of s.p.a.ce-time that the ma.s.s or energy will generate (in the same way that if you throw a rock into a pond, you can calculate the ripples that it will create). But you can also run the equations backward. You can start with a bizarre s.p.a.ce-time, the kind found in episodes of The Twilight Zone. (In these universes, for example, you can open up a door and find yourself on the moon. You can run around a tree and find yourself backward in time, with your heart on the right side of your body.) Then you calculate the distribution of matter and energy a.s.sociated with that particular s.p.a.ce-time. (This means that if you are given a bizarre collection of waves on the surface of a pond, you can work backward and calculate the distribution of rocks necessary to produce these waves). This was, in fact, the way in which Alcubierre derived his equations. He began with a s.p.a.ce-time consistent with going faster than light, and then he worked backward and calculated the energy necessary to produce it.

WORMHOLES AND BLACK HOLES.

Besides stretching s.p.a.ce, the second possible way to break the light barrier is by ripping s.p.a.ce, via wormholes, pa.s.sageways that connect two universes. In fiction, the first mention of a wormhole came from Oxford mathematician Charles Dodgson, who wrote Through the Looking Gla.s.s under the pen name Lewis Carroll. The Looking Gla.s.s of Alice is the wormhole, connecting the countryside of Oxford with the magical world of Wonderland. By placing her hand through the Looking Gla.s.s, Alice can be transported instantly from one universe to the next. Mathematicians call these "multiply connected s.p.a.ces."

The concept of wormholes in physics dates back to 1916, one year after Einstein published his epic general theory of relativity. Physicist Karl Schwarzschild, then serving in the Kaiser's army, was able to solve Einstein's equations exactly for the case of a single pointlike star. Far from the star, its gravitational field was very similar to that of an ordinary star, and in fact Einstein used Schwarzschild's solution to calculate the deflection of light around a star. Schwarzschild's solution had an immediate and profound impact on astronomy, and even today it is one of the best-known solutions of Einstein's equations. For generations, physicists used the gravitational field around this pointlike star as an approximation to the field around a real star, which has a finite diameter.

But if you took this pointlike solution seriously, then lurking at the center of it was a monstrous pointlike object that has shocked and amazed physicists for almost a century-a black hole. Schwarzschild's solution for the gravity of a pointlike star was like a Trojan Horse. On the outside it looked like a gift from heaven, but on the inside there lurked all sorts of demons and ghosts. But if you accepted one, you had to accept the other. Schwarzschild's solution showed that as you approached this pointlike star, bizarre things happened. Surrounding the star was an invisible sphere (called the "event horizon") that was a point of no return. Everything checked in, but nothing could check out, like a Roach Motel. Once you pa.s.sed through the event horizon, you never came back. (Once inside the event horizon, you would have to travel faster than light to escape back outside the event horizon, and that would be impossible.) As you approached the event horizon, your atoms would be stretched by tidal forces. The gravity felt by your feet would be much greater than the gravity felt by your head, so you would be "spaghettified" and then ripped apart. Similarly, the atoms of your body would also be stretched and torn apart by gravity.

To an outside observer watching you approach the event horizon, it would appear that you were slowing down in time. In fact, as you hit the event horizon, it would appear that time had stopped!

Furthermore, as you fell past the event horizon, you would see light that has been trapped and circulating around this black hole for billions of years. It would seem as if you were watching a motion picture film, detailing the entire history of the black hole, going back to its very origin.

And finally, if you could fall straight through to the black hole, there would be another universe on the other side. This is called the Einstein-Rosen Bridge, first introduced by Einstein in 1935; it is now called a wormhole.

Einstein and other physicists believed a star could never evolve naturally into such a monstrous object. In fact, in 1939 Einstein published a paper showing that a circulating ma.s.s of gas and dust will never condense into such a black hole. So although there was a wormhole lurking in the center of a black hole, he was confident that such a strange object could never form by natural means. In fact, astrophysicist Arthur Eddington once said that there should "be a law of nature to prevent a star from behaving in this absurd way." In other words, the black hole was indeed a legitimate solution of Einstein's equations, but there was no known mechanism that could form one by natural means.

All this changed with the advent of a paper by J. Robert Oppenheimer and his student Hartland Snyder, written that same year, showing that black holes can indeed be formed by natural means. They a.s.sumed that a dying star had used up its nuclear fuel and then collapsed under gravity, so that it imploded under its own weight. If gravity could compress the star to within its event horizon, then nothing known to science could prevent gravity from squeezing the star to a point-particle, the black hole. (This implosion method may have given Oppenheimer the clue for building the Nagasaki bomb just a few years later, which depends on imploding a sphere of plutonium.) The next breakthrough came in 1963, when New Zealand mathematician Roy Kerr examined perhaps the most realistic example of a black hole. Objects spin faster as they shrink, in much the same way that skaters spin faster when they bring in their arms close to their body. As a result black holes should be spinning at fantastic rates.

Kerr found that a spinning black hole would not collapse into a pointlike star, as Schwarzschild a.s.sumed, but would collapse into a spinning ring. Anyone unfortunate enough to hit the ring would perish; but someone falling into the ring would not die, but would actually fall through. But instead of winding up on the other side of the ring, he or she would pa.s.s through the Einstein-Rosen Bridge and wind up in another universe. In other words, the spinning black hole is the rim of Alice's Looking Gla.s.s.

If he or she were to move around the spinning ring a second time, he or she would enter yet another universe. In fact, repeated entry into the spinning ring would put a person in different parallel universes, much like hitting the "up" b.u.t.ton on an elevator. In principle, there could be an infinite number of universes, each stacked on top of each other. "Pa.s.s through this magic ring and-presto!-you're in a completely different universe where radius and ma.s.s are negative!" Kerr wrote.

There is an important catch, however. Black holes are examples of "nontransversable wormholes" that is, pa.s.sing through the event horizon is a one-way trip. Once you pa.s.s through the event horizon and the Kerr ring, you cannot go backward through the ring and out through the event horizon.

But in 1988 Kip Thorne and colleagues at Cal Tech found an example of a transversable wormhole, that is, one through which you could pa.s.s freely back and forth. In fact, for one solution, the travel through a wormhole would be no worse than riding on an airplane.

Normally gravity would crush the throat of the wormhole, destroying the astronauts trying to reach the other side. That is one reason that faster-than-light travel through a wormhole is not possible. But the repulsive force of negative energy or negative ma.s.s could conceivably keep the throat open sufficiently long to allow astronauts a clear pa.s.sage. In other words, negative ma.s.s or energy is essential for both the Alcubierre drive and the wormhole solution.

In the last few years an astonishing number of exact solutions have been found to Einstein's equations that allow for wormholes. But do wormholes really exist, or are they just a figment of mathematics? There are several major problems facing wormholes.

First, to create the violent distortions of s.p.a.ce and time necessary to travel through a wormhole, one would need fabulous amounts of positive and negative matter, on the order of a huge star or a black hole. Matthew Visser, a physicist at Washington University, estimates that the amount of negative energy you would need to open up a 1-meter wormhole is comparable to the ma.s.s of Jupiter, except that it would need to be negative. He says, "You need about minus one Jupiter ma.s.s to do the job. Just manipulating a positive Jupiter ma.s.s of energy is already pretty freaky, well beyond our capabilities into the foreseeable future."

Kip Thorne of the California Inst.i.tute of Technology speculates that "it will turn out that the laws of physics do allow sufficient exotic matter in wormholes of human size to hold the wormhole open. But it will also turn out that the technology for making wormholes and holding them open is unimaginably far beyond the capabilities of our human civilization."

Second, we do not know how stable these wormholes would be. The radiation generated by these wormholes might kill anyone who enters. Or perhaps the wormholes would not be stable at all, closing as soon as one entered them.

Third, light beams falling into the black hole would be blue shifted; that is, they would attain greater and greater energy as they came close to the event horizon. In fact, at the event horizon itself, light is technically infinitely blue shifted, so the radiation from this infalling energy could kill anyone in a rocket.

Let us discuss these problems in some detail. One problem is to ama.s.s enough energy to rip the fabric of s.p.a.ce and time. The simplest way to do this is to compress an object until it becomes smaller than its "event horizon." For the sun, this means compressing it down to about 2 miles in diameter, whereupon it will collapse into a black hole. (The Sun's gravity is too weak to compress it naturally down to 2 miles, so our sun will never become a black hole. In principle, this means that anything, even you, can become a black hole if you were sufficiently compressed. This would mean compressing all the atoms of your body to smaller than subatomic distances-a feat that is beyond the capabilities of modern science.) A more practical approach would be to a.s.semble a battery of laser beams to fire an intense beam at a specific spot. Or to build a huge atom smasher to create two beams, which would then collide with each other at fantastic energies, sufficient to create a small tear in the fabric of s.p.a.ce-time.

PLANCK ENERGY AND PARTICLE ACCELERATORS.

One can calculate the energy necessary to create an instability in s.p.a.ce and time: it is of the order of the Planck energy, or 1019 billion electron volts. This is truly an unimaginably large number, a quadrillion times larger than the energy attainable with today's most powerful machine, the Large Hadron Collider (LHC), located outside Geneva, Switzerland. The LHC is capable of swinging protons in a large "doughnut" until they reach energies of trillions of electron volts, energies not seen since the big bang. But even this monster of a machine falls far short of producing energy anywhere near the Planck energy.

The next particle accelerator after the LHC will be the International Linear Collider (ILC). Instead of bending the path of subatomic particles into a circle, the ILC will shoot them down a straight path. Energy will be injected as the particles move along this path, until they attain unimaginably large energies. Then a beam of electrons will collide with antielectrons, creating a huge burst of energy. The ILC will be 30 to 40 kilometers long, or ten times the length of the Stanford Linear Accelerator, currently the largest linear accelerator. If all goes well, the ILC is due to be completed sometime in the next decade.

The energy produced by the ILC will be .5 to 1.0 trillion electron volts-less than the 14 trillion electron volts of the LHC, but this is deceptive. (In the LHC, the collisions between the protons take place between the const.i.tuent quarks making up the proton. Hence the collisions involving the quarks are less than 14 trillion electron volts. That is why the ILC will produce collision energies larger than those of the LHC.) Also, because the electron has no known const.i.tuent, the dynamics of the collisions between electron and antielectron are simpler and cleaner.

But realistically, the ILC, too, falls far short of being able to open up a hole in s.p.a.ce-time. For that, you would need an accelerator a quadrillion times more powerful. For our Type 0 civilization, which uses dead plants for fuel (e.g., oil and coal), this technology is far beyond anything we can muster. But it may become possible for a Type III civilization.

Remember, a Type III civilization, which is galactic in its use of energy, consumes 10 billion times more energy than a Type II civilization, whose consumption is based on the energy of a single star. And a Type II civilization in turn consumes 10 billion times more energy than a Type I civilization, whose consumption is based on the energy of a single planet. In one hundred to two hundred years, our feeble Type 0 civilization will reach Type I status.

Given that projection, we are a long, long way from being able to achieve the Planck energy. Many physicists believe that at extremely tiny distances, at the Planck distance of 10-33 centimeters, s.p.a.ce is not empty or smooth but becomes "foamy" it is frothing with tiny bubbles that constantly pop into existence, collide with other bubbles, and then vanish back into the vacuum. These bubbles that dart in and out of the vacuum are "virtual universes," very similar to the virtual particles of electrons and antielectrons that pop into existence and then disappear.

Normally, this quantum s.p.a.ce-time "foam" is completely invisible to us. These bubbles form at such tiny distances that we cannot observe them. But quantum physics suggests that if we concentrate enough energy at a single point, until we reach the Planck energy, these bubbles can become large. Then we would see s.p.a.ce-time frothing with tiny bubbles, each bubble a wormhole connected to a "baby universe."

In the past these baby universes were considered an intellectual curiosity, a strange consequence of pure mathematics. But now physicists are seriously thinking that our universe might have originally started off as one of these baby universes.

Such thinking is sheer speculation, but the laws of physics allow for the possibility of opening a hole in s.p.a.ce by concentrating enough energy at a single point, until we access the s.p.a.ce-time foam and wormholes emerge connecting our universe to a baby universe.

Achieving a hole in s.p.a.ce would, of course, require major breakthroughs in our technology, but again, it might be possible for a Type III civilization. For example, there have been promising developments in something called a "Wakefield tabletop accelerator." Remarkably, this atom smasher is so small that it can be placed on top of a table yet generate billions of electron volts of energy. The Wakefield tabletop accelerator works by firing lasers onto charged particles, which then ride on the energy of that laser. Experiments done at the Stanford Linear Accelerator Center, the Rutherford Appleton Laboratory in England, and the ecole Polytechnique in Paris show that enormous accelerations are possible over small distances using laser beams and plasma to inject energy.

Yet another breakthrough was made in 2007, when physicists and engineers at the Stanford Linear Accelerator Center, UCLA, and USC demonstrated that you can double the energy of a huge particle accelerator in just 1 meter. They started with a beam of electrons that are fired down a 2-mile-long tube in Stanford, reaching an energy of 42 billion electron volts. Then these high-energy electrons were sent through an "afterburner," which consisted of a plasma chamber only 88 centimeters long, where the electrons pick up an additional 42 billion electron volts, doubling their energy. (The plasma chamber is filled with lithium gas. As the electrons pa.s.s through the gas, they create a plasma wave that creates a wake. This wake in turn flows to the back of the electron beam and then shoves it forward, giving it an extra boost.) In this stunning achievement, the physicists improved by a factor of three thousand the previous record for the amount of energy per meter they could accelerate an electron beam. By adding such "afterburners" to existing accelerators, one might in principle double their energy, almost for free.

Today the world record for a Wakefield tabletop accelerator is 200 billion electron volts per meter. There are numerous problems scaling this result to longer distances (such as maintaining the stability of the beam as laser power is pumped into it). But a.s.suming that we could maintain a power level of 200 billion electron volts per meter, this means that an accelerator capable of reaching the Planck energy would have to be 10 light-years long. This is well within the capability of a Type III civilization.

Wormholes and stretched s.p.a.ce may give us the most realistic way of breaking the light barrier. But it is not known if these technologies are stable; if they are, it would still take a fabulous amount of energy, positive or negative, to make them work.

Perhaps an advanced Type III civilization might already have this technology. It might be millennia before we can even think about harnessing power on this scale. Because there is still controversy over the fundamental laws governing the fabric of s.p.a.ce-time at the quantum level, I would cla.s.sify this as a Cla.s.s II impossibility.

12: TIME TRAVEL.

If time travel is possible, then where are the tourists from the future?

-STEPHEN HAWKING.

"[Time travel] is against reason," said Filby.

"What reason?" said the Time Traveler.

-H. G. WELLS.

In the novel Ja.n.u.s Equation, writer G. Spruill explored one of the harrowing problems with time travel. In this tale a brilliant mathematician whose goal is to discover the secret of time travel meets a strange, beautiful woman, and they become lovers, although he knows nothing about her past. He becomes intrigued about finding out her true ident.i.ty. Eventually he discovers that she once had plastic surgery to change her features. And that she had a s.e.x change operation. Finally, he discovers that "she" is actually a time traveler from the future, and that "she" is actually himself, but from the future. This means that he made love to himself. And one is left wondering, what would have happened if they had had a child? And if this child went back into the past, to grow up to become the mathematician at the beginning of the story, then is it possible to be your own mother and father and son and daughter?

CHANGING THE PAST.

Time is one of the great mysteries of the universe. We are all swept up in the river of time against our will. Around AD 400, Saint Augustine wrote extensively about the paradoxical nature of time: "How can the past and future be, when the past no longer is, and the future is not yet? As for the present, if it were always present and never moved on to become the past, it would not be time, but eternity." If we take Saint Augustine's logic further, we see that time is not possible, since the past is gone, the future does not exist, and the present exists only for an instant. (Saint Augustine then asked profound theological questions about how time must influence G.o.d, questions that are relevant even today. If G.o.d is omnipotent and all-powerful, he wrote, then is He bound by the pa.s.sing of time? In other words, does G.o.d, like the rest of us mortals, have to rush because He is late for an appointment? Saint Augustine eventually concluded that G.o.d is omnipotent and hence cannot be constrained by time and would therefore have to exist "outside of time." Although the concept of being outside of time seems absurd, it's one idea that is recurring in modern physics, as we will see.) Like Saint Augustine, all of us have at some time wondered about the strange nature of time and how it differs from s.p.a.ce. If we can move forward and backward in s.p.a.ce, why not in time? All of us have also wondered what the future may hold for us, in the time beyond our years. Humans have a finite lifetime, but we are intensely curious about events that will happen long after we are gone.

Although our longing to travel in time is probably as ancient as humanity, apparently the very first written time travel story is Memoirs of the Twentieth Century, written in 1733 by Samuel Madden, about an angel from the year 1997 who journeys over 250 years into the past to give doc.u.ments to a British amba.s.sador that describe the world of the future.

There would be many more such stories. The 1838 short story "Missing One's Coach: An Anachronism," written anonymously, is about a person waiting for a coach who suddenly finds himself a thousand years in the past. He meets a monk from an ancient monastery and tries to explain to him how history will progress for the next thousand years. Afterward he suddenly finds himself just as mysteriously transported back to the present, except that he has missed his coach.

Even the 1843 Charles d.i.c.kens novel, A Christmas Carol, is a kind of time travel story, since Ebenezer Scrooge is taken into the past and into the future to witness the world before the present and after his death.

In American literature the first appearance of time travel dates back to Mark Twain's 1889 novel, A Connecticut Yankee in King Arthur's Court. A nineteenth-century Yankee is wrenched backward through time to wind up in King Arthur's court in AD 528. He is taken prisoner and is about to be burned at the stake, but then he declares he has the power to blot out the sun, knowing that an eclipse of the sun would happen on that very day. When the sun is eclipsed, the mob is horrified and agrees to set him free and grant him privileges in exchange for the return of the sun.

But the first serious attempt to explore time travel in fiction was H. G. Wells's cla.s.sic The Time Machine, in which the hero is sent hundreds of thousands of years into the future. In that distant future, humanity itself has genetically split into two races, the menacing Moorlocks who maintain the grimy underground machines, and the useless, childlike Eloi who dance in the sunlight in the world above, never realizing their awful fate (to be eaten by the Moorlocks).

Since then, time travel has become a regular feature of science fiction, from Star Trek to Back to the Future. In Superman I, when Superman learns that Lois Lane has died, he decides in desperation to turn back the hands of time, rocketing himself around the Earth, faster than the speed of light, until time itself goes backward. The Earth slows down, stops, and eventually spins in the opposite direction, until all clocks on the Earth beat backward. Floodwaters rage backward, broken dams miraculously heal themselves, and Lois Lane comes back from the dead.

From the perspective of science, time travel was impossible in Newton's universe, where time was seen as an arrow. Once fired, it could never deviate from its past. One second on the Earth was one second throughout the universe. This conception was overthrown by Einstein, who showed that time was more like a river that meandered across the universe, speeding up and slowing down as it snaked across stars and galaxies. So one second on the Earth is not absolute; time varies when we move around the universe.

As I discussed earlier, according to Einstein's special theory of relativity, time slows down inside a rocket the faster it moves. Science fiction writers have speculated that if you could break the light barrier, you could go back in time. But this is not possible, since you would have to have infinite ma.s.s in order to reach the speed of light. The speed of light is the ultimate barrier for any rocket. The crew of the Enterprise in Star Trek IV: The Voyage Home hijacked a Klingon s.p.a.ceship and used it to whip around the sun like a slingshot and break the light barrier to wind up in San Francisco in the 1960s. But this defies the laws of physics.

Nonetheless, time travel to the future is possible, and has been experimentally verified millions of times. The journey of the hero of The Time Machine into the far future is actually physically possible. If an astronaut were to travel near the speed of light, it might take him, say, one minute to reach the nearest stars. Four years would have elapsed on the Earth, but for him only one minute would have pa.s.sed, because time would have slowed down inside the rocket ship. Hence he would have traveled four years into the future, as experienced here on Earth. (Our astronauts actually take a short trip into the future every time they go into outer s.p.a.ce. As they travel at 18,000 miles per hour above the Earth, their clocks beat a tiny bit slower than clocks on the Earth. Hence, after a yearlong mission on the s.p.a.ce station, they have actually journeyed a fraction of a second into the future by the time they land back on Earth. The world record for traveling into the future is currently held by Russian cosmonaut Sergei Avdeyev, who orbited for 748 days and was hence hurled .02 seconds into the future.) So a time machine that can take us into the future is consistent with Einstein's special theory of relativity. But what about going backward in time?

If we could journey back into the past, history would be impossible to write. As soon as a historian recorded the history of the past, someone could go back into the past and rewrite it. Not only would time machines put historians out of business, but they would enable us to alter the course of time at will. If, for example, we were to go back to the era of the dinosaurs and accidentally step on a mammal that happens to be our ancestor, perhaps we would accidentally wipe out the entire human race. History would become an unending, madcap Monty Python episode, as tourists from the future trampled over historic events while trying to get the best camera angle.

TIME TRAVEL: PHYSICISTS' PLAYGROUND Perhaps the person who has distinguished himself the most on the dense mathematical equations of black holes and time machines is cosmologist Stephen Hawking. Unlike other students of relativity who often distinguish themselves in mathematical physics at an early age, Hawking was actually not an outstanding student as a youth. He was obviously extremely bright, but his teachers would often notice that he was not focused on his studies and never lived up to his full potential. But a turning point came in 1962, after he graduated from Oxford, when he first began to notice the symptoms of ALS (amyotrophic lateral sclerosis, or Lou Gehrig's disease). He was rocked by the news that he was suffering from this incurable motor neuron disease that would rob him of all motor functions and likely soon kill him. At first the news was extremely upsetting. What would be the use of getting a Ph.D. if he was going to die soon anyway?

But once he got over the initial shock he became focused for the first time in his life. Realizing that he did not have long to live, he began to ferociously tackle some of the most difficult problems in general relativity. In the early 1970s he published a landmark series of papers showing that "singularities" in Einstein's theory (where the gravitational field becomes infinite, like at the center of black holes and at the instant of the big bang) were an essential feature of relativity and could not be easily dismissed (as Einstein thought). In 1974 Hawking also proved that black holes are not entirely black, but gradually emit radiation, now known as Hawking radiation, because radiation can tunnel through the gravity field of even a black hole. This paper was the first major application of the quantum theory to relativity theory, and it represents his best known work.

As predicted, ALS slowly led to paralysis of his hands, legs, and even his vocal cords, but at a much slower rate than the doctors had originally predicted. As a result, he has pa.s.sed many of the usual milestones of normal people, fathering three children (he is now a grandfather), divorcing his first wife in 1991, four years later marrying the wife of the man who created his voice synthesizer, and filing for divorce from his second wife in 2006. In 2007 he made headlines when he went aboard a jet airplane that sent him into weightlessness, fulfilling a lifelong wish of his. His next goal is to blast off into outer s.p.a.ce.

Today he is almost totally paralyzed in his wheelchair, communicating to the outside world via movements of his eyes. Yet even with this crushing disability, he still cracks jokes, writes papers, gives lectures, and engages in controversy. He is more productive moving his two eyes than are teams of scientists who have full control over their bodies. (His colleague at Cambridge University, Sir Martin Rees, who was appointed Astronomer Royal by the Queen, once confided to me that Hawking's disability does prevent him from doing the tedious calculations necessary to keep at the top of his game. So instead he concentrates on generating new and fresh ideas rather than cranking out difficult calculations, which can be done by his students.) In 1990 Hawking read papers of his colleagues proposing their version of a time machine, and he was immediately skeptical. His intuition told him that time travel was not possible because there are no tourists from the future. If time travel were as common as taking a Sunday picnic in the park, then time travelers from the future should be pestering us with their cameras, asking us to pose for their picture alb.u.ms.

Hawking also raised a challenge to the world of physics. There ought to be a law, he proclaimed, making time travel impossible. He proposed a "Chronology Protection Conjecture" to ban time travel from the laws of physics in order to "make history safe for historians."

The embarra.s.sing thing, however, was that no matter how hard physicists tried, they could not find a law to prevent time travel. Apparently time travel seems to be consistent with the known laws of physics. Unable to find any physical law that makes time travel impossible, Hawking recently changed his mind. He made headlines in the London papers when he said, "Time travel may be possible, but it is not practical."

Once considered to be fringe science, time travel has suddenly become a playground for theoretical physicists. Physicist Kip Thorne of Cal Tech writes, "Time travel was once solely the province of science fiction writers. Serious scientists avoided it like the plague-even when writing fiction under pseudonyms or reading it in privacy. How times have changed! One now finds scholarly a.n.a.lyses of time travel in serious scientific journals, written by eminent theoretical physicists...Why the change? Because we physicists have realized that the nature of time is too important an issue to be left solely in the hands of science fiction writers."

The reason for all this confusion and excitement is that Einstein's equations allow for many kinds of time machines. (Whether they will survive the challenges from the quantum theory, however, is still in doubt.) In Einstein's theory, in fact, we often encounter something called "closed time-like curves," which is the technical term for paths that allow for time travel into the past. If we followed the path of a closed time-like curve, we would set out on a journey and return before we left.

The first time machine involves a wormhole. There are many solutions of Einstein's equations that connect two distant points in s.p.a.ce. But since s.p.a.ce and time are intimately intertwined in Einstein's theory, this same wormhole can also connect two points in time. By falling down the wormhole, you could journey (at least mathematically) into the past. Conceivably, you could then journey to the original starting point and meet yourself before you left. But as we mentioned in the previous chapter, pa.s.sing through the wormhole at the center of a black hole is a one-way trip. As physicist Richard Gott has said, "I don't think there's any question that a person could travel back in time while in a black hole. The question is whether he could ever emerge to brag about it."

Another time machine involves a spinning universe. In 1949 mathematician Kurt G.o.del found the first solution of Einstein's equations involving time travel. If the universe spins, then, if you traveled around the universe fast enough, you might find yourself in the past and arrive before you left. A trip around the universe is therefore also a trip into the past. When astronomers would visit the Inst.i.tute for Advanced Study, G.o.del would often ask them if they ever found evidence that the universe was spinning. He was disappointed when they told him that there was clearly evidence that the universe expanded, but the net spin of the universe was probably zero. (Otherwise, time travel might be commonplace, and history as we know it would collapse.) Third, if you walk around an infinitely long, rotating cylinder, you also might arrive before you left. (This solution was found by W. J. van Stock.u.m in 1936, before G.o.del's time traveling solution, but van Stock.u.m was apparently unaware that his solution allowed for time travel.) In this case, if you danced around a spinning May Pole on May Day, you might find yourself in the month of April. (The problem with this design, however, is that the cylinder must be infinite in length and spin so fast that most materials would fly apart.) The most recent example of time travel was found by Richard Gott of Princeton in 1991. His solution was based on finding gigantic cosmic strings (which may be leftovers from the original big bang). He a.s.sumed that two large cosmic strings were about to collide. If you quickly traveled around these colliding cosmic strings, you would travel back in time. The advantage of this type of time machine is that you would not need infinite spinning cylinders, spinning universes, or black holes. (The problem with this design, however, is that you must first find huge cosmic strings floating in s.p.a.ce and then make them collide in a precise fashion. And the possibility of going back in time would last only a brief period.) Gott says, "A collapsing loop of string large enough to allow you to circle it once and go back in time a year would have to have more than half the ma.s.s-energy of an entire galaxy."

But the most promising design for a time machine is the "transversable wormhole," mentioned in the last chapter, a hole in s.p.a.ce-time in which a person could freely walk back and forth in time. On paper, transversable wormholes can provide not only faster-than-light travel, but also travel in time. The key to transversable wormholes is negative energy.

A transversable wormhole time machine would consist of two chambers. Each chamber would consist of two concentric spheres, which would be separated by a tiny distance. By imploding the outer sphere, the two spheres would create a Casimir effect and hence negative energy. a.s.sume that a Type III civilization is able to string a wormhole between these two chambers (possibly extracting one from the s.p.a.ce-time foam). Next, take the first chamber and send it into s.p.a.ce at near light-speed velocities. Time slows down in that chamber, so the two clocks are no longer in synchronization. Time beats at different rates inside the two chambers, which are connected by a wormhole.

If you are in the second chamber, you can instantly pa.s.s through the wormhole to the first chamber, which exists at an earlier time. Thus you have gone backward in time.

There are formidable problems facing this design. The wormhole may be quite tiny, much smaller than an atom. And the plates may have to be squeezed down to Planck-length distances to create enough negative energy. Lastly, you would be able to go back in time only to the point when the time machines were built. Before then, time in the two chambers would be beating at the same rate.

PARADOXES AND TIME CONUNDRUMS.

Time travel poses all sorts of problems, both technical as well as social. The moral, legal, and ethical issues are raised by Larry Dwyer, who notes, "Should a time traveler who punches his younger self (or vice versa) be charged with a.s.sault? Should the time traveler who murders someone and then flees into the past for sanctuary be tried in the past for crimes he committed in the future? If he marries in the past can he be tried for bigamy even though his other wife will not be born for almost 5,000 years?"

But perhaps the th.o.r.n.i.e.s.t problems are the logical paradoxes raised by time travel. For example, what happens if we kill our parents before we are born? This is a logical impossibility. It is sometimes called the "grandfather paradox."

There are three ways to resolve these paradoxes. First, perhaps you simply repeat past history when you go back in time, therefore fulfilling the past. In this case, you have no free will. You are forced to complete the past as it was written. Thus, if you go back into the past to give the secret of time travel to your younger self, then it was meant to happen that way. The secret of time travel came from the future. It was destiny. (But this does not tell us where the original idea came from.) Second, you have free will, so you can change the past, but within limits. Your free will is not allowed to create a time paradox. Whenever you try to kill your parents before you are born, a mysterious force prevents you from pulling the trigger. This position has been advocated by the Russian physicist Igor Novikov. (He argues that there is a law preventing us from walking on the ceiling, although we might want to. Hence there might be a law preventing us from killing our parents before we are born. Some strange law prevents us from pulling the trigger.) Third, the universe splits into two universes. On one time line the people whom you killed look just like your parents, but they are different, because you are now in a parallel universe. This latter possibility seems to be the one consistent with the quantum theory, as I will discuss later when I talk about the multiverse.

The second possibility is explored in the movie Terminator 3, in which Arnold Schwarzenegger plays a robot from the future where murderous machines have taken over. The few remaining humans, hunted down like animals by the machines, are led by a great leader whom the machines have been unable to kill. Frustrated, the machines send a series of killer robots back to the past, before the great leader was born, to kill off his mother. But after epic battles, human civilization is eventually destroyed at the end of the movie, as it was meant to be.

Back to the Future explored the third possibility. Dr. Brown invents a plutonium-fired DeLorean car, actually a time machine for traveling to the past. Michael J. Fox (Marty McFly) enters the machine and goes back and meets his teenage mother, who then falls in love with him. This poses a sticky problem. If Marty McFly's teenage mother spurns his future father, then they never would have married, and Michael J. Fox's character would never have been born.

The problem is clarified a bit by Doc Brown. He goes to the blackboard and draws a horizontal line, representing the time line of our universe. Then he draws a second line, which branches off the first line, representing a parallel universe that opens up when you change the past. Thus, whenever we go back into the river of time, the river forks into two rivers, and one time line becomes two time lines, or what is called the "many worlds" approach, which we will discuss in the next chapter.

This means that all time travel paradoxes can be solved. If you have killed your parents before you were born, it simply means you have killed some people who are genetically identical to your parents, with the same memories and personalities, but they are not your true parents.

The "many worlds" idea solves at least one main problem with time travel. To a physicist, the number one criticism of time travel (besides finding negative energy) is that radiation effects will build up until either you are killed the instant you enter the machine or the wormhole collapses on you. Radiation effects build up because any radiation entering the time portal will be sent back into the past, where it will eventually wander around the universe until it reaches the present day, and then it will fall into the wormhole again. Since radiation can enter the mouth of the wormhole an infinite number of times, the radiation inside the wormhole can become incredibly strong-strong enough to kill you. But the "many worlds" interpretation solves this problem. If the radiation goes into the time machine and is sent into the past, it then enters a new universe; it cannot reenter the time machine again, and again, and again. This simply means that there are an infinite number of universes, one for each cycle, and each cycle contains just one photon of radiation, not an infinite amount of radiation.

In 1997, the debate was clarified a bit when three physicists finally proved that Hawking's program to ban time travel was inherently flawed. Bernard Kay, Marek Radzikowski, and Robert Wald showed that time travel was consistent with all the known laws of physics, except in one place. When traveling in time, all the potential problems were concentrated at the event horizon (located near the entrance to the wormhole). But the horizon is precisely where we expect Einstein's theory to break down and quantum effects to take over. The problem is that whenever we try to calculate radiation effects as we enter a time machine, we have to use a theory that combines Einstein's theory of general relativity with the quantum theory of radiation. But whenever we naively try to marry these two theories, the resulting theory makes no sense: it yields a series of infinite answers that are meaningless.

This is where a theory of everything takes over. All problems of traveling through a wormhole that have bedeviled physicists (e.g., the stability of the wormhole, the radiation that might kill you, the closing of the wormhole as you entered it) are concentrated at the event horizon, precisely where Einstein's theory made no sense.

Thus the key to understanding time travel is to understand the physics of the event horizon, and only a theory of everything can explain this. This is the reason that most physicists today would agree that one way to definitively settle the time travel question is to come up with a complete theory of gravity and s.p.a.ce-time.

A theory of everything would unite the four forces of the universe and enable us to calculate what would happen when we entered a time machine. Only a theory of everything could successfully calculate all the radiation effects created by a wormhole and definitively settle the question of how stable wormholes would be when we entered the time machine. And even then, we might have to wait for centuries or even longer to actually build a machine to test these theories.

Because the laws of time travel are so closely linked to the physics of wormholes, time travel seems to qualify as a Cla.s.s II impossibility.

13: PARALLEL UNIVERSES.