B003CTEFLQ EBOK

by Michio Kaku

  At one point in the 1950s, physicists despaired of making sense of subatomic particles because new ones were being discovered all the time. J. Robert Oppenheimer, in disgust, once said, “The Nobel Prize in Physics should be given to the physicist who does not discover a new particle that year.” These subatomic particles were given so many strange Greek names that Enrico Fermi said, “If I had known that there would be so many particles with Greek names, I would have become a botanist rather than a physicist.” But in string theory, if one had a super microscope and could peer directly into an electron, one would find not a point particle, but a vibrating string. When the superstring vibrates in a different mode or note, it changes into a different subatomic particle, like a photon or a neutrino. In this picture, the subatomic particles that we see in nature can be viewed as the lowest octave of the superstring. Thus, the blizzard of subatomic particles discovered over the decades are simply notes on this superstring. The laws of chemistry, which seem so confusing and arbitrary, are the melodies played out on superstrings. The universe itself is a symphony of strings. And the laws of physics are nothing but harmonies of the superstring.

  Superstring theory can also encompass all of Einstein’s work on relativity. As the string moves in space-time, it forces the surrounding space around it to curve, precisely as Einstein had predicted back in 1915. In fact, superstring theory is inconsistent unless it can move in a space-time consistent with general relativity. As physicist Edward Witten has said, even if Einstein had never discovered the theory of general relativity, it might have been rediscovered via the string theory. Witten says, “String theory is extremely attractive because gravity is forced upon us. All known consistent string theories include gravity, so while gravity is impossible in quantum field theory as we have known it, it’s obligatory in string theory.”

  However, string theory makes some other quite surprising predictions. Strings can only consistently move in ten dimensions (one dimension of time and nine dimensions of space). In fact, string theory is the only theory which fixes the dimensionality of its own space-time. Like the Kaluza-Klein theory of 1921, it can unify gravity with electromagnetism by assuming that higher dimensions can vibrate, creating forces that can spread throughout three dimensions like light. (If we add an eleventh dimension, then string theory allows for the possibility of membranes vibrating in hyperspace. This is called “M-theory,” which can absorb string theory and provide new insights into the theory from the vantage point of the eleventh dimension.)

  What would Einstein think of superstring theory if he were alive today? The physicist David Gross said, “Einstein would have been pleased with this, at least with the goal, if not the realization…. He would have liked the fact that there is an underlying geometrical principle—which unfortunately, we don’t really understand.” The essence of Einstein’s unified field theory, as we saw, was to create matter (wood) out of geometry (marble). Gross commented on this: “To build matter itself out of geometry—that in a sense is what string theory does….[It’s] a theory of gravity in which particles of matter as well as the other forces of nature emerge in the same way that gravity emerges from geometry.” It is instructive to go back to Einstein’s early work on the unified field theory, from the vantage point of string theory. The key to Einstein’s genius was that he was able to isolate the key symmetries of the universe that unify the laws of nature. The symmetry that unifies space and time is the Lorentz transformation, or rotations in four dimensions. The symmetry behind gravity is general covariance, or arbitrary coordinate transformations of space-time.

  However, on Einstein’s third try at a great unifying theory, he failed, mainly because he lacked the symmetry that would unite gravity and light, or unite marble (geometry) with wood (matter). He, of course, was acutely aware that he lacked a fundamental principle that would guide him through the thicket of tensor calculus. He once wrote, “I believe that in order to make real progress one must again ferret out some general principle from nature.”

  But that is precisely what the superstring provides. The symmetry underlying the superstring is called “supersymmetry,” a strange and beautiful symmetry that unifies matter with forces. As mentioned earlier, subatomic particles have a property called “spin,” acting as if they were spinning tops. The electron, proton, neutron, and quarks that make up the matter in the universes all have spin 1/2 and they are called “fermions,” named after Enrico Fermi, who explored the properties of particles with half-integral spin. The quanta of forces, however, are based on electromagnetism (with spin 1) and gravitation (with spin 2). Notice that they have integral spin, and are called “bosons” (after the work of Bose and Einstein). The key point is that in general, matter (wood) is made of fermions with half-integral spin, while forces (marble) are made of bosons with integral spin. Supersymmetry unifies fermions and bosons. This is the essential point, that supersymmetry allows for a unification of wood and marble, as Einstein wished. In fact, supersymmetry allows for a new type of geometry that has even surprised the mathematicians, called “superspace,” which makes possible “supermarble.” In this new approach, we must generalize the old dimensions of space and time to include new fermionic dimensions, which then allows us to create a “superforce” out of which all forces originated at the instant of creation.

  Thus, some physicists have speculated that one must generalize Einstein’s original principle of general covariance to read: the equations of physics must be super covariant (i.e., maintain the same form after a super covariant transformation).

  Superstring theory allows us to reanalyze Einstein’s old work on the unified field theory, but in an entirely new light. When we begin to analyze the solutions to the superstring equations, we encounter many of the bizarre spaces that Einstein pioneered back in the 1920s and 1930s. As we saw earlier, he was working with generalizations of Riemannian space, which today can correspond to some spaces found in string theory. Einstein was looking at these bizarre spaces one after the other, in agonizing fashion (including complex spaces, spaces with “torsion,” “twisted spaces,” “antisymmetric spaces,” etc.), but he got lost because he lacked any guiding physical principle or picture to lead him out of the tangle of mathematics. This is where supersymmetry comes in—it acts as an organizing principle that allows us to analyze many of these spaces from a different perspective.

  But is supersymmetry the symmetry that eluded Einstein for the last three decades of his life? The key to Einstein’s unified field theory is that it was to be made of pure marble, that is, pure geometry. The ugly “wood” that infested his original relativity theory was to be absorbed into geometry. Supersymmetry might hold the key to a theory of pure marble. In this theory, one can introduce something called “superspace,” in which space itself becomes supersymmetrized. In other words, there is the possibility that the final unified field theory will be made of “supermarble,” out of a new “supergeometry.”

  Physicists now believe that at the instant of the big bang, all the symmetries of the world were unified, as Einstein believed. The four forces we see in nature (gravity, electromagnetism, and the strong and weak nuclear force) were unified into a single “superforce” at the instant of creation, and only later broke apart as the universe cooled. Einstein’s quest for the unified field theory seemed impossible, only because today we see the four forces of the world horribly broken into four pieces. If we can turn back the clock 13.7 billion years, to the original big bang, we would see the cosmic unity of the universe displayed in full glory, as Einstein imagined.

  Witten claims that string theory will one day dominate physics the same way that quantum mechanics dominated physics for the past half-century. However, there are still many formidable obstacles. The critics of the theory point out some of its weak spots. First, it is impossible to test directly. Since superstring theory is a theory of the universe, the only way to test it is to re-create the big bang, that is, create energies in an atom smasher that approximate the beginning of t
he universe. To do this would require an atom smasher the size of a galaxy. This is out of the question, even for an advanced civilization. However, most physics is done indirectly, so there are high hopes that the Large Hadron Collider (LHC) to be built outside of Geneva, Switzerland, will have enough energy to probe the theory. The LHC, when it is turned on in the near future, will accelerate protons to trillions of electron volts, sufficient to smash atoms apart. When examining the debris of such fantastic collisions, physicists hope to find a new kind of particle, the superparticle or “sparticle,” which would represent a higher resonance or octave of the superstring.

  There is even some speculation that dark matter may be made of sparticles. For example, the partner of the photon, called the “photino,” is neutral in charge, stable, and has mass. If the universe were filled with a gas of photinos, we would not be able to see it, but it would act very much like dark matter. One day, if we ever identify the true nature of dark matter, it may provide an indirect proof of superstring theory.

  Yet another way to test the theory indirectly is to analyze gravity waves from the big bang. When the LISA gravity wave detectors are launched into space in the next decade, they may eventually pick up gravity waves emitted one-trillionth of a second after the instant of creation. If these agree with predictions made from the string theory, the data might confirm the theory once and for all.

  M-theory may also explain some of the puzzles that surround the old Kaluza-Klein universe. Recall that one serious objection to the Kaluza-Klein universe was that these higher dimensions could not be seen in the laboratory, and in fact must be much smaller than an atom (otherwise, atoms would float into these higher dimensions). But M-theory gives us a possible solution to this by assuming that our universe itself is a membrane floating in an infinite eleven-dimensional hyperspace. Thus, subatomic particles and atoms would be confined to our membrane (our universe), but gravity, being a distortion of hyperspace, can flow freely between universes.

  This hypothesis, as strange as it may seem, can be tested. Ever since Isaac Newton, physicists have known that gravity decreases as the inverse square of the distance. In four spatial dimensions, gravity should decrease as the inverse cube of the distance. Thus, by measuring tiny deviations from a perfect inverse square law, one may detect the presence of other universes. Recently, it was conjectured that if there is a parallel universe only a millimeter away from our universe, it might be compatible with Newtonian gravity and also might be detectable with the LHC. This in turn has created a certain amount of excitement among physicists, realizing that one aspect of superstring theory might be testable soon, either by looking for sparticles or by looking for parallel universes a millimeter from ours.

  These parallel universes might provide yet another explanation for dark matter. If there is a parallel universe nearby, we will not be able to see it or feel it (since matter is confined to our membrane universe) but we would be able to feel its gravity (which can travel between universes). To us, this would appear as if invisible space had some form of gravity, much like dark matter. In fact, some superstring theorists have speculated that perhaps dark matter can be explained as the gravity produced by a nearby parallel universe.

  But the real problem of proving the correctness of superstring theory is not experiment. We don’t have to build gigantic atom smashers or space satellites to verify the theory. The real problem is purely theoretical: if we are smart enough to completely solve the theory, we should be able to find all its solutions, which should include our universe, with its stars, galaxies, planets, and people. So far, no one on Earth is smart enough to completely solve these equations. Perhaps tomorrow, or perhaps decades from now, someone may announce that they have completely solved the theory. At that time, we will be able to tell whether it is a theory of everything, or a theory of nothing. Because string theory is so precise, without any adjustable parameters, there is nothing in between.

  Will superstring theory or M-theory allow us to unify the laws of nature into a simple, coherent whole, as Einstein once said? At this point, it is too early to say. We are reminded of Einstein’s words: “The creative principle resides in mathematics. In a certain sense, therefore, I hold it true that pure thought can grasp reality, as the ancients dreamed.” Perhaps a young reader of this book will be inspired by this quest for a unification of all physical forces to complete this program.

  So how should we re-evaluate Einstein’s true legacy? Instead of saying that he should have gone fishing after 1925, perhaps a more fitting tribute might be as follows: All physical knowledge at the fundamental level is contained in two pillars of physics, general relativity and the quantum theory. Einstein was the founder of the first, was the godfather of the second, and paved the way for the possible unification of both.

  Notes

  Preface

  “A pop icon on a par…”: Brian, p. 436.

  “In the remaining 30 years of his life…”: Pais, Einstein Lived Here, p. 43.

  Chapter 1. Physics before Einstein

  “If A is success, I should say…”: Pais, Einstein Lived Here, p. 152.

  “Everyone who had real contact…”: French, p. 171.

  “tortured man, an extremely neurotic…”: Cropper, p. 19.

  “is the most profound and the most fruitful that physics…”: Ibid., p. 173.

  “The idea of the time of magnetic action…”: Ibid., p. 163.

  “We can scarcely avoid the conclusion…”: Ibid., p. 164.

  Chapter 2. The Early Years

  “A sound skull is needed…”: Brian, p. 3.

  “It doesn’t matter;…”: Clark, p. 27.

  “Classmates regarded Albert as a freak…”: Brian, p. 3.

  “Yes, that is true….”: Pais, Subtle Is the Lord, p. 38.

  “It is, in fact, nothing short…”: Cropper, p. 205.

  “A wonder of such nature…”: Schilpp, p. 9.

  “Through the reading of popular books…”: Ibid., p. 5.

  “In all these years I never…”: Pais, Subtle Is the Lord, p. 38.

  “At the age of 12,…”: Schilpp, p. 9.

  “Soon the flight of his mathematical genius…”: Sugimoto, p. 14.

  “philosophical nonsense…”: Brian, p. 7.

  “I love the Swiss…”: Clark, p. 65.

  “Whoever approached him was captivated…”: Folsing, p. 39.

  “Many a young or elderly woman…”: Ibid., p. 44.

  “Beloved sweetheart…”: Brian, p. 12; Folsing, p. 42.

  “a work which I read with breathless attention.”: Schilpp, p. 15.

  “such a principle resulted from a paradox upon which…”: Ibid., p. 53.

  “All physical theories, their mathematical expression notwithstanding,…”: Calaprice, p. 261.

  “most fascinating subject at the time…”: Clark, p. 55.

  “You are a smart boy, Einstein,…”: Pais, Subtle Is the Lord, p. 44; Brian, p. 31.

  “You’re enthusiastic, but hopeless at physics….”: Folsing, p. 57.

  “something very great”: Sugimoto, p. 19.

  “I can go anywhere I want—…”: Folsing, p. 71.

  “My sweetheart has a very wicked tongue…”: Brian, p. 31.

  “This Miss Maric is causing me…”: Ibid., p. 47.

  “By the time you’re 30, she’ll be an old witch.”: Ibid.

  “What’s to become of her?”: Ibid., p. 25.

  “who cannot gain entrance to a good family.”: Ibid.

  “I would have found [a job]…”: Thorne, p. 69.

  “By the mere existence of his stomach,…”: Schilpp, p. 3.

  “I am nothing but a burden to my relatives…”: Pais, Subtle Is the Lord, p. 41.

  “pissing ink”: Brian, p. 69.

  “worldly monastery.”: Ibid., p. 52.

  “Many years later, he still recalled…”: Ibid., p. 53.

  “sad fate did not permit [her father]…”: Ibid.

  “The door of the flat was ope
n to allow the floor,…”: Sugimoto, p. 33.

  “private lessons in mathematics and physics.”: Ibid., p. 31.

  “These words of Epicurus applied to us:…”: Brian, p. 55.

  Chapter 3. Special Relativity and the “Miracle Year”

  “The germ of the special relativity theory…”: Folsing, p. 166.

  “A storm broke loose in my mind.”: Brian, p. 61.

  “The solution came to me suddenly…”: Ibid. p. 63

  “I owe more to Maxwell than to anyone.”: Ibid., p. 152. Many biographies trace Einstein’s ideas back to the Michelson-Morley experiment. But as Einstein himself made clear on several occasions, this experiment only peripherally affected his thinking. He was led to relativity theory via Maxwell’s equations. The entire thrust of his original paper was to show that Maxwell’s equations had a hidden symmetry revealed by his relativity theory, and that this should be elevated to a universal principle of physics.

  “Thank you, I’ve completely solved the problem.”: Folsing, p. 155; Pais, Subtle Is the Lord, p. 139.

  “one of the most remarkable volumes in the whole…”: Cropper, p. 206.