Physics of the Impossible

by Michio Kaku

  If one analyzes the last few centuries in physics, one of the most important achievements of the last century was to summarize all fundamental physics into two great theories: the quantum theory (represented by the Standard Model) and Einstein’s theory of general relativity (describing gravity). Remarkably, together they represent the sum total of all physical knowledge at a fundamental level. The first theory describes the world of the very small, the subatomic quantum world where particles perform a fantastic dance, darting in and out of existence and appearing two places at the same time. The second theory describes the world of the very large, such as black holes and the big bang, and uses the language of smooth surfaces, stretched fabrics, and warped surfaces. The theories are opposites in every way, using different mathematics, different assumptions, and different physical pictures. It’s as if nature had two hands, neither of which communicated with the other. Furthermore, any attempt to join these two theories has led to meaningless answers. For half a century any physicist who tried to mediate a shotgun wedding between the quantum theory and general relativity found that the theory blew up in their faces, producing infinite answers that made no sense.

  All of this changed with the advent of the superstring theory, which posits that the electron and the other subatomic particles are nothing but different vibrations of a string, acting like a tiny rubber band. If one strikes the rubber band, it vibrates in different modes, with each note corresponding to a different subatomic particle. In this way, superstring theory explains the hundreds of subatomic particles that have been discovered so far in our particle accelerators. Einstein’s theory, in fact, emerges as just one of the lowest vibrations of the string.

  String theory has been hailed as a “theory of everything,” the fabled theory that eluded Einstein for the last thirty years of his life. Einstein wanted a single, comprehensive theory that would summarize all physical law, that would allow him to “read the Mind of God.” If string theory is correct in unifying gravity with the quantum theory, then it might represent the crowning achievement of science going back two thousand years ago to when the Greeks asked what matter was made of.

  But the bizarre feature of superstring theory is that these strings can only vibrate in a specific dimension of space-time; they can only vibrate in ten dimensions. If one tries to create a string theory in other dimensions, the theory breaks down mathematically.

  Our universe, of course, is four-dimensional (with three dimensions of space and one of time). This means that the other six dimensions must have collapsed somehow, or curled up, like Kaluza’s fifth dimension.

  Recently physicists have given serious thought to proving or disproving the existence of these higher dimensions. Perhaps the simplest way to prove the existence of higher dimensions would be to find deviations from Newton’s law of gravity. In high school we learn that the gravity of the Earth diminishes as we go into outer space. More precisely, gravity diminishes with the square of the distance of separation. But this is only because we live in a three-dimensional world. (Think of a sphere surrounding the Earth. The gravity of the Earth spreads out evenly across the surface of the sphere, so the larger the sphere, the weaker the gravity. But since the surface of the sphere grows as the square of its radius, the strength of gravity, spread out over the surface of the sphere, must diminish as the square of the radius.)

  But if the universe had four spatial dimensions, then gravity should diminish as the cube of the distance of separation. If the universe had n spatial dimensions, then gravity should diminish as the n-1-th power. Newton’s famous inverse-square law has been tested with great accuracy over astronomical distances; that is why we can send space probes soaring past the rings of Saturn with breathtaking accuracy. But until recently Newton’s inverse-square law had never been tested at small distances in the laboratory.

  The first experiment to test the inverse-square law at small distances was performed at the University of Colorado in 2003 with negative results. Apparently there is no parallel universe, at least not in Colorado. But this negative result has only whetted the appetite of other physicists, who hope to duplicate this experiment with even greater accuracy.

  Furthermore, the Large Hadron Collider, which will become operational in 2008 outside Geneva, Switzerland, will be looking for a new type of particle called the “sparticle,” or superparticle, which is a higher vibration of the superstring (everything you see around you is but the lowest vibration of the superstring). If sparticles are found by the LHC, it could signal a revolution in the way we view the universe. In this picture of the universe, the Standard Model simply represents the lowest vibration of the superstring.

  Kip Thorne says, “By 2020, physicists will understand the laws of quantum gravity, which will be found to be a variant of string theory.”

  In addition to higher dimensions, there is another parallel universe predicted by string theory, and this is the “multiverse.”

  THE MULTIVERSE

  There is still one nagging question about string theory: why should there be five different versions of string theory? String theory could successfully unify the quantum theory with gravity, but there were five ways in which this could be done. This was rather embarrassing, since most physicists wanted a unique “theory of everything.” Einstein, for example, wanted to know if “God had any choice in making the universe.” His belief was that the unified field theory of everything should be unique. So why should there be five string theories?

  In 1994 another bombshell was dropped. Edward Witten of Princeton’s Institute for Advanced Study and Paul Townsend of Cambridge University speculated that all five string theories were in fact the same theory—but only if we add an eleventh dimension. From the vantage point of the eleventh dimension, all five different theories collapsed into one! The theory was unique after all, but only if we ascended to the mountaintop of the eleventh dimension.

  In the eleventh dimension a new mathematical object can exist, called the membrane (e.g., like the surface of a sphere). Here was the amazing observation: if one dropped from eleven dimensions down to ten dimensions, all five string theories would emerge, starting from a single membrane. Hence all five string theories were just different ways of moving a membrane down from eleven to ten dimensions.

  (To visualize this, imagine a beach ball with a rubber band stretched around the equator. Imagine taking a pair of scissors and cutting the beach ball twice, once above and once below the rubber band, thereby lopping off the top and bottom of the beach ball. All that is left is the rubber band, a string. In the same way, if we curl up the eleventh dimension, all that is left of a membrane is its equator, which is the string. In fact, mathematically there are five ways in which this slicing can occur, leaving us with five different string theories in ten dimensions.)

  The eleventh dimension gave us a new picture. It also meant that perhaps the universe itself was a membrane, floating in an eleven-dimensional space-time. Moreover, not all these dimensions had to be small. In fact, some of these dimensions might actually be infinite.

  This raises the possibility that our universe exists in a multiverse of other universes. Think of a vast collection of floating soap bubbles or membranes. Each soap bubble represents an entire universe floating in a larger arena of eleven-dimensional hyperspace. These bubbles can join with other bubbles, or split apart, and even pop into existence and disappear. We might live on the skin of just one of these bubble universes.

  Max Tegmark of MIT believes that in fifty years “the existence of these ‘parallel universes’ will be no more controversial than the existence of other galaxies—then called ‘island universes’—was 100 years ago.”

  How many universes does string theory predict? One embarrassing feature of string theory is that there are trillions upon trillions of possible universes, each one compatible with relativity and the quantum theory. One estimate claims that there might be a googol of such universes. (A googol is 1 followed by 100 zeros.)

  Normally comm
unication between these universes is impossible. The atoms of our body are like flies trapped on flypaper. We can move freely about in three dimensions along our membrane universe, but we cannot leap off the universe into hyperspace, because we are glued onto our universe. But gravity, being the warping of space-time, can freely float into the space between universes.

  In fact, there is one theory that states that dark matter, an invisible form of matter that surrounds the galaxy, might be ordinary matter floating in a parallel universe. As in H. G. Wells’s novel The Invisible Man, a person would become invisible if he floated just above us in the fourth dimension. Imagine two parallel sheets of paper, with someone floating on one sheet, just above the other.

  In the same way there is speculation that dark matter might be an ordinary galaxy hovering above us in another membrane universe. We could feel the gravity of this galaxy, since gravity can ooze its way between universes, but the other galaxy would be invisible to us because light moves underneath the galaxy. In this way, the galaxy would have gravity but would be invisible, which fits the description of dark matter. (Yet another possibility is that dark matter might consist of the next vibration of the superstring. Everything we see around us, such as atoms and light, is nothing but the lowest vibration of the superstring. Dark matter might be the next higher set of vibrations.)

  To be sure, most of these parallel universes are probably dead ones, consisting of a formless gas of subatomic particles, such as electrons and neutrinos. In these universes the proton might be unstable, so all matter as we know it would slowly decay and dissolve. Complex matter, consisting of atoms and molecules, probably would not be possible in many of these universes.

  Other parallel universes might be just the opposite, with complex forms of matter far beyond anything we can conceive of. Instead of just one type of atom consisting of protons, neutrons, and electrons, they might have a dazzling array of other types of stable matter.

  These membrane universes might also collide, creating cosmic fireworks. Some physicists at Princeton believe that perhaps our universe started out as two gigantic membranes that collided 13.7 billion years ago. The shock waves from that cataclysmic collision created our universe, they believe. Remarkably, when the experimental consequences of this strange idea are explored they apparently match the results from the WMAP satellite currently orbiting the Earth. (This is called the “Big Splat” theory.)

  The theory of the multiverse has one fact in its favor. When we analyze the constants of nature, we find that they are “tuned” very precisely to allow for life. If we increase the strength of the nuclear force, then the stars burn out too quickly to give rise to life. If we decrease the strength of the nuclear force, then stars never ignite at all and life cannot exist. If we increase the force of gravity, then our universe dies quickly in a Big Crunch. If we decrease the strength of gravity, then the universe expands rapidly into a Big Freeze. In fact, there are scores of “accidents” involving the constants of nature that allow for life. Apparently, our universe lives in a “Goldilocks zone” of many parameters, all of which are “fine-tuned” to allow for life. So either we are left with the conclusion that there is a God of some sort who has chosen our universe to be “just right” to allow for life, or there are billions of parallel universes, many of them dead. As Freeman Dyson has said, “The universe seemed to know we were coming.”

  Sir Martin Rees of Cambridge University has written that this fine tuning is, in fact, convincing evidence for the multiverse. There are five physical constants (such as the strength of the various forces) that are fine-tuned to allow for life, and he believes that there are also an infinite number of universes in which the constants of nature are not compatible with life.

  This is the so-called “anthropic principle.” The weak version simply states that our universe is fine-tuned to allow for life (because we are here to make this statement in the first place). The strong version says that perhaps our existence was a by-product of design or purpose. Most cosmologists would agree to the weak version of the anthropic principle, but there is considerable debate over whether the anthropic principle is a new principle of science that could lead to new discoveries and results, or whether it is simply a statement of the obvious.

  QUANTUM THEORY

  In addition to higher dimensions and the multiverse, there is yet another type of parallel universe, one that gave Einstein headaches and one that continues to bedevil physicists today. This is the quantum universe predicted by ordinary quantum mechanics. The paradoxes within quantum physics seem so intractable that Nobel laureate Richard Feynman was fond of saying that no one really understands the quantum theory.

  Ironically, although the quantum theory is the most successful theory ever proposed by the human mind (often accurate to within one part in 10 billion), it is built on a sand of chance, luck, and probabilities. Unlike Newtonian theory, which gave definite, hard answers to the motion of objects, the quantum theory can give only probabilities. The wonders of the modern age, such as lasers, the Internet, computers, TV, cell phones, radar, microwave ovens, and so forth, are all based on the shifting sands of probabilities.

  The sharpest example of this conundrum is the famous “Schrödinger’s cat” problem (formulated by one of the founders of the quantum theory, who paradoxically proposed the problem in order to smash this probabilistic interpretation). Schrödinger railed against this interpretation of his theory, stating, “If one has to stick to this damned quantum jumping, then I regret having ever been involved in this thing.”

  The Schrödinger’s cat paradox is as follows: a cat is placed in a sealed box. Inside a gun is pointed at the cat (and the trigger is then connected to a Geiger counter next to a piece of uranium). Normally when the uranium atom decays it sets off the Geiger counter and then the gun and the cat is killed. The uranium atom can either decay or not. The cat is either dead or alive. This is just common sense.

  But in the quantum theory, we don’t know for sure if the uranium has decayed. So we have to add the two possibilities, adding the wave function of a decayed atom with the wave function of an intact atom. But this means that, in order to describe the cat, we have to add the two states of the cat. So the cat is neither dead nor alive. It is represented as the sum of a dead cat and a live cat!

  As Feynman once wrote, quantum mechanics “describes nature as absurd from the point of view of common sense. And it fully agrees with experiment. So I hope you can accept nature as She is—absurd.”

  To Einstein and Schrödinger, this was preposterous. Einstein believed in “objective reality,” a commonsense, Newtonian view in which objects existed in definite states, not as the sum of many possible states. And yet this bizarre interpretation lies at the heart of modern civilization. Without it modern electronics (and the very atoms of our body) would cease to exist. (In our ordinary world we sometimes joke that it’s impossible to be “a little bit pregnant.” But in the quantum world, it’s even worse. We exist simultaneously as the sum of all possible bodily states: unpregnant, pregnant, a child, an elderly woman, a teenager, a career woman, etc.)

  There are several ways to resolve this sticky paradox. The founders of the quantum theory believed in the Copenhagen School, which said that once you open the box, you make a measurement and can determine if the cat is dead or alive. The wave function has “collapsed” into a single state and common sense takes over. The waves have disappeared, leaving only particles. This means that the cat now enters a definite state (either dead or alive) and is no longer described by a wave function.

  Thus there is an invisible barrier separating the bizarre world of the atom and the macroscopic world of humans. For the atomic world, everything is described by waves of probability, in which atoms can be in many places at the same time. The larger the wave at some location, the greater the probability of finding the particle at that point. But for large objects these waves have collapsed and objects exist in definite states, and hence common sense prevails.


  (When guests would come to Einstein’s house, he would point to the moon and ask, “Does the moon exist because a mouse looks at it?” In some sense, the answer of the Copenhagen School might be yes.)

  Most Ph.D. physics textbooks religiously adhere to the original Copenhagen School, but many research physicists have abandoned it. We now have nanotechnology and can manipulate individual atoms, so atoms that dart in and out of existence can be manipulated at will, using our scanning tunneling microscopes. There is no invisible “wall” separating the microscopic and macroscopic world. There is a continuum.

  At present there is no consensus on how to resolve this issue, which strikes at the very heart of modern physics. At conferences, many theories heatedly compete with others. One minority point of view is that there must be a “cosmic consciousness” pervading the universe. Objects spring into being when measurements are made, and measurements are made by conscious beings. Hence there must be cosmic consciousness that pervades the universe determining which state we are in. Some, like Nobel laureate Eugene Wigner, have argued that this proves the existence of God or some cosmic consciousness. (Wigner wrote, “It was not possible to formulate the laws [of the quantum theory] in a fully consistent way without reference to consciousness.” In fact, he even expressed an interest in the Vedanta philosophy of Hinduism, in which the universe is pervaded by an all-embracing consciousness.)

  Another viewpoint on the paradox is the “many worlds” idea, proposed by Hugh Everett in 1957, which states that the universe simply splits in half, with a live cat in one half and a dead cat in the other. This means that there is a vast proliferation or branching of parallel universes each time a quantum event occurs. Any universe that can exist, does. The more bizarre the universe, the less likely it is, but nonetheless these universes exist. This means there is a parallel world in which the Nazis won World War II, or a world where the Spanish Armada was never defeated and everyone is speaking in Spanish. In other words, the wave function never collapses. It simply continues on its way, merrily splitting off into countless universes.