Physics of the Impossible

by Michio Kaku

  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 naïvely 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 space-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 Class II impossibility.

  13: PARALLEL UNIVERSES

  “But do you really mean, sir,” said Peter, “that there could be other worlds—all over the place, just around the corner—like that?”

  “Nothing is more probable,” said the Professor…while he muttered to himself, “I wonder what they do teach them at these schools.”

  —C. S. LEWIS, THE LION, THE WITCH AND THE WARDROBE

  listen: there’s a hell of a good universe next door; let’s go

  —E. E. CUMMINGS

  Are alternate universes really possible? They are a favorite device for Hollywood scriptwriters, as in the Star Trek episode called “Mirror, Mirror.” Captain Kirk is accidentally transported to a bizarre parallel universe in which the Federation of Planets is an evil empire held together by brutal conquest, greed, and plunder. In that universe Spock wears a menacing beard and Captain Kirk is the leader of a band of ravenous pirates, advancing by enslaving their rivals and assassinating their superiors.

  Alternate universes enable us to explore the world of “what if” and its delicious, intriguing possibilities. In the Superman comics, for example, there have been several alternate universes in which Superman’s home planet, Krypton, never blew up, or Superman finally reveals his true identity as mild-mannered Clark Kent, or he marries Lois Lane and has superkids. But are parallel universes just the domain of Twilight Zone reruns, or do they have a basis in modern physics?

  Throughout history going back to almost all ancient societies, people have believed in other planes of existence, the homes of the gods or ghosts. The Church believes in heaven, hell, and purgatory. The Buddhists have Nirvana and different states of consciousness. And the Hindus have thousands of planes of existence.

  Christian theologians, at a loss to explain where heaven might be located, have often speculated that perhaps God lives in a higher dimensional plane. Surprisingly, if higher dimensions did exist, many of the properties ascribed to the gods might become possible. A being in a higher dimension might be able to disappear and reappear at will or walk through walls—powers usually ascribed to deities.

  Recently the idea of parallel universes has become one of the most hotly debated topics in theoretical physics. There are, in fact, several types of parallel universes that force us to reconsider what we mean by what is “real.” What is at stake in this debate about various parallel universes is nothing less than the meaning of reality itself.

  There are at least three types of parallel universes that are intensely discussed in the scientific literature:

  a. hyperspace, or higher dimensions,

  b. the multiverse, and

  c. quantum parallel universes.

  HYPERSPACE

  The parallel universe that has been the subject of the longest historical debate is one of higher dimensions. The fact that we live in three dimensions (length, width, height) is common sense. No matter how we move an object in space, all positions can be described by these three coordinates. In fact, with these three numbers
we can locate any object in the universe, from the tip of our noses to the most distant of all galaxies.

  A fourth spatial dimension seems to violate common sense. If smoke, for example, is allowed to fill up a room, we do not see the smoke disappearing into another dimension. Nowhere in our universe do we see objects suddenly disappearing or drifting off into another universe. This means that any higher dimensions, if they exist at all, must be smaller than an atom.

  Three spatial dimensions form the fundamental basis of Greek geometry. Aristotle, for example, in his essay “On Heaven,” wrote, “The line has magnitude in one way, the plane in two ways, and the solid in three ways, and beyond these there is no other magnitude because the three are all.” In AD 150 Ptolemy of Alexandria offered first “proof” that higher dimensions were “impossible.” In his essay “On Distance,” he reasoned as follows. Draw three lines that are mutually perpendicular (like the lines forming the corner of a room). Clearly, he said, a fourth line perpendicular to the other three cannot be drawn, hence a fourth dimension must be impossible. (What he actually proved was that our brains are incapable of visualizing the fourth dimension. The PC on your desk calculates in hyperspace all the time.)

  For two thousand years, any mathematician who dared to speak of the fourth dimension potentially suffered ridicule. In 1685 mathematician John Wallis polemicized against the fourth dimension, calling it a “Monster in Nature, less possible than a Chimera or Centaure.” In the nineteenth century Karl Gauss, the “prince of mathematicians,” worked out much of the mathematics of the fourth dimension but was afraid to publish because of the backlash it would cause. But privately Gauss conducted experiments to test whether flat, three-dimensional Greek geometry really described the universe. In one experiment he placed his assistants on three mountaintops. Each one had a lantern, thereby forming a huge triangle. Gauss then measured the angles of each corner of the triangle. To his disappointment, he found that the interior angles all summed up to 180 degrees. He concluded that if there were deviations to standard Greek geometry, they must be so small that they could not be detected with his lanterns.

  Gauss left it to his student, Georg Bernhard Riemann, to write down the fundamental mathematics of higher dimensions (which were then imported wholesale decades later into Einstein’s theory of general relativity). In one powerful sweep, in a celebrated lecture Riemann delivered in 1854, he overthrew two thousand years of Greek geometry and established the basic mathematics of the higher, curved dimensions that we use even today.

  After Riemann’s remarkable discovery was popularized in Europe in the late 1800s, the “fourth dimension” became quite a sensation among artists, musicians, writers, philosophers, and painters. Picasso’s cubism, in fact, was partly inspired by the fourth dimension, according to art historian Linda Dalrymple Henderson. (Picasso’s paintings of women with eyes facing forward and nose to the side was an attempt to visualize a fourth-dimensional perspective, since one looking down from the fourth dimension could see a woman’s face, nose, and the back of her head simultaneously.) Henderson writes, “Like a Black Hole, the ‘fourth dimension’ possessed mysterious qualities that could not be completely understood, even by the scientists themselves. Yet, the impact of ‘the fourth dimension’ was far more comprehensive than that of Black Holes or any other more recent scientific hypothesis except Relativity Theory after 1919.”

  Other painters drew from the fourth dimension, as well. In Salvador Dali’s Christus Hypercubius, Christ is crucified in front of a strange, floating three-dimensional cross, which is actually a “tesseract,” an unraveled four-dimensional cube. In his famous Persistence of Memory, he attempted to represent time as the fourth dimension, and hence the metaphor of melted clocks. Marcel Duchamps’s Nude Descending a Staircase was an attempt to represent time as the fourth dimension by capturing the time-lapse motion of a nude walking down a staircase. The fourth dimension even pops up in a story by Oscar Wilde, “The Canterville Ghost,” in which a ghost haunting a house lives in the fourth dimension.

  The fourth dimension also appears in several of H. G. Wells’s works, including The Invisible Man, The Plattner Story, and The Wonderful Visit. (In the latter, which has since been the basis of scores of Hollywood movies and science fiction novels, our universe somehow collides with a parallel universe. A poor angel from the other universe falls into our universe after being accidentally shot by a hunter. Horrified by all the greed, pettiness, and selfishness of our universe, the angel eventually commits suicide.)

  The idea of parallel universes was also explored, tongue-in-cheek, by Robert Heinlein in The Number of the Beast. Heinlein imagines a group of four brave individuals who romp across parallel universes in a mad professor’s interdimensional sports car.

  In the TV series Sliders, a young boy reads a book and gets the inspiration to build a machine that would allow him to “slide” between parallel universes. (The book that the young boy was reading was actually my book, Hyperspace.)

  But historically the fourth dimension has been considered a mere curiosity by physicists. No evidence has ever been found for higher dimensions. This began to change in 1919 when physicist Theodor Kaluza wrote a highly controversial paper that hinted at the presence of higher dimensions. He started with Einstein’s theory of general relativity, but placed it in five dimensions (one dimension of time and four dimensions of space; since time is the fourth space-time dimension, physicists now refer to the fourth spatial dimension as the fifth dimension). If the fifth dimension were made smaller and smaller, the equations magically split into two pieces. One piece describes Einstein’s standard theory of relativity, but the other piece becomes Maxwell’s theory of light!

  This was a stunning revelation. Perhaps the secret of light lies in the fifth dimension! Einstein himself was shocked by this solution, which seemed to provide an elegant unification of light and gravity. (Einstein was so shaken by Kaluza’s proposal that he mulled it over for two years before finally agreeing to have this paper published.) Einstein wrote to Kaluza, “The idea of achieving [a unified theory] by means of a five-dimensional cylinder world never dawned on me…At first glance, I like your idea enormously…The formal unity of your theory is startling.”

  For years physicists had asked the question: if light is a wave, then what is waving? Light can pass through billions of light-years of empty space, but empty space is a vacuum, devoid of any material. So what is waving in the vacuum? With Kaluza’s theory we had a concrete proposal to answer this problem: light is ripples in the fifth dimension. Maxwell’s equations, which accurately describe all the properties of light, emerge simply as the equations for waves traveling in the fifth dimension.

  Imagine fish swimming in a shallow pond. They might never suspect the presence of a third dimension, because their eyes point to the side, and they can only swim forward and backward, left and right. A third dimension to them might appear impossible. But then imagine it rains on the pond. Although they cannot see the third dimension, they can clearly see the shadows of the ripples on the surface of the pond. In the same way, Kaluza’s theory explained light as ripples traveling on the fifth dimension.

  Kaluza also gave an answer as to where the fifth dimension was. Since we see no evidence of a fifth dimension, it must have “curled up” so small that it cannot be observed. (Imagine taking a two-dimensional sheet of paper and rolling it up tightly into a cylinder. From a distance, the cylinder looks like a one-dimensional line. In this way, a two-dimensional object has been turned into a one-dimensional object by curling it up.)

  Kaluza’s paper initially created a sensation. But in the coming years, objections were found to his theory. What was the size of this new fifth dimension? How did it curl up? No answers could be found.

  For decades Einstein would work on this theory in fits and starts. After he passed away in 1955, the theory was soon forgotten, becoming just a strange footnote to the evolution of physics.

  STRING THEORY

  All this ha
s changed with the coming of a startling new theory, called the superstring theory. By the 1980s physicists were drowning in a sea of subatomic particles. Every time they smashed an atom apart with powerful particle accelerators, they found scores of new particles spitting out. It was so frustrating that J. Robert Oppenheimer declared that the Nobel Prize in Physics should go to the physicist who did not discover a new particle that year! (Enrico Fermi, horrified at the proliferation of subatomic particles with Greek-sounding names, said, “If I could remember the names of all these particles, I would have become a botanist.”) After decades of hard work, this zoo of particles could be arranged into something called the Standard Model. Billions of dollars, the sweat of thousands of engineers and physicists, and twenty Nobel Prizes have gone into painfully assembling, piece by piece, the Standard Model. It is a truly remarkable theory, which seems to fit all the experimental data concerning subatomic physics.

  But the Standard Model, for all its experimental successes, suffered from one serious defect. As Stephen Hawking says, “It is ugly and ad hoc.” It contains at least nineteen free parameters (including the particle masses and the strength of their interactions with other particles), thirty-six quarks and antiquarks, three exact and redundant copies of sub-particles, and a host of strange-sounding subatomic particles, such as tau neutrinos, Yang-Mills gluons, Higgs bosons, W bosons, and Z particles. Worse, the Standard Model makes no mention of gravity. It seemed hard to believe that nature, at its most supreme, fundamental level, could be so haphazard and supremely inelegant. Here was a theory only a mother could love. The sheer inelegance of the Standard Model forced physicists to reanalyze all their assumptions about nature. Something was terribly wrong.