Physics of the Impossible

by Michio Kaku

  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 God, questions that are relevant even today. If God is omnipotent and all-powerful, he wrote, then is He bound by the passing of time? In other words, does God, like the rest of us mortals, have to rush because He is late for an appointment? Saint Augustine eventually concluded that God 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 space. If we can move forward and backward in space, 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 documents to a British ambassador 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 Dickens 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 classic 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 mass 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 spaceship 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 passed, 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 space. 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 space 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 passed 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 space.

  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 albums.

  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 embarrassing 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 analyses 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 space. But since space 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, passing 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 Gödel 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 Institute for Advanced Study, Gödel 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 Stockum in 1936, before Gödel’s time traveling solution, but van Stockum 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 assumed 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 space 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 mass-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 space-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. Assume that a Type III civilization is able to string a wormhole between these two chambers (possibly extracting one from the space-time foam). Next, take the first chamber and send it into space 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 pass 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 machin
es 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 assault? 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 thorniest 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.)