The Cosmic Landscape

by Leonard Susskind

Higgs bosons emit Z-bosons

  There is more, but it involves particles that we will meet only in later chapters.

  As I have explained, protons and neutrons are not on the list of elementary particles because they are composed of the simpler quarks, but for some purposes it is useful to forget the quarks and think of nucleons as elementary particles. This will require us to add some additional vertices. For example, a proton can emit a photon. (In reality one of the hidden quarks produced the photon, but the net effect is as if the proton did it.) In a similar way, one of the two d-quarks in a neutron can emit a W-boson and become a u-quark, thus turning the neutron into a proton. In effect there is a vertex in which a neutron becomes a proton while emitting a W-boson.

  Now we are ready to draw the Feynman diagram that explains the beta rays that Becquerel discovered emanating from his uranium. The diagram looks a good deal like a QED diagram except that the W-boson is exchanged, where in a QED diagram, the photon would be exchanged. Indeed, the weak interactions are very closely related to the electric forces due to photons.

  Take your slit cardboard square and start at the bottom. The neutron (which might be inside a nucleus) emits a negatively charged W-boson and becomes a proton. The W-boson goes a short way (about 10–16 centimeters) and splits into two particles: an electron and a neutrino “moving backward in time,” or more mundanely, an antineutrino. That’s what Becquerel would have seen in 1896 had he a powerful enough microscope. Later we will see the importance of this kind of process in creating the chemical elements of which we are made.

  The Laws of Physics

  You should now have a clear idea of what I mean by the Laws of Physics. I wish I could tell you that they are elegant, as some physicists would claim. But the unvarnished truth is that they are not. There are too many particles, too many vertex diagrams, and too many coupling constants. I haven’t even told you yet about the random collection of masses that characterize the particles. The whole thing would be a very unappealing concoction if it were not for one thing: it describes the properties of elementary particles, nuclei, atoms, and molecules with incredible precision.

  But there is a cost. It can be accomplished only by introducing about thirty “constants of nature”—masses and coupling constants—whose values have no other justification than that they “work.”17 Where do these numbers come from? Physicists don’t pull the various numbers from thin air or even from mathematical calculation in some master theory. They are the results of many years of experimental particle physics done at accelerator laboratories in many countries. Many of them, like the fine structure constant, have been measured with great precision, but the bottom line is, as I said, that we don’t understand why they are what they are.

  The Standard Model is the culmination and distillation of more than half a century of particle physics. When combined with Feynman’s graphical rules, it provides accurate descriptions of all elementary-particle phenomena, including the ways particles combine to form nuclei, atoms, molecules, gases, liquids, and solids. But it is far too complicated to be the paragon of simplicity that we hope would be the hallmark of a truly fundamental theory—a final theory—of nature.

  Unlike the laws of men, the Laws of Physics really are laws. We can choose to obey the law or disregard it, but an electron has no choice. These laws are not like the traffic laws or the tax laws that change from state to state and year to year. Perhaps the most important experimental fact, a fact that makes physics possible altogether, is that the constants of nature really are constant. Experiments at different times and places require exactly the same Feynman diagrams and give exactly the same values for each coupling constant and mass. When the fine structure constant was measured in Japan in the 1990s, it had exactly the same value as it had in Brookhaven, Long Island, in 1960 or at Stanford in the 1970s.

  Indeed, when physicists are pursuing the study of cosmology, they tend to take completely for granted that the laws of nature are the same everywhere in the universe. But it needn’t be so. One can certainly conceive of a world in which the fine structure constant changes as time goes on or in which some other constant varies from one location to another. From time to time physicists have questioned the assumption that the constants are absolutely constant, but thus far strong evidence suggests that they really are the same in every part of the observed universe: not the gigantic megaverse, but that part of the universe that we can see with the various kinds of telescopes at our disposal.

  Someday we may be able to go to distant galaxies and measure the constants directly in those places. But even now we continually receive messages from remote regions of the universe. Astronomers routinely study the light from far-off sources and disentangle the spectral lines that were emitted or absorbed by distant atoms.18 The relations between individual spectral lines are intricate, but they are always the same, no matter where and when the light originated. Just about any change in the local Laws of Physics would change the details, so we have excellent evidence that the laws are the same in all parts of the observed universe.

  These rules—a list of particles, a list of masses and coupling constants, and Feynman’s methods—that I call the Laws of Physics are extremely powerful. They govern almost every aspect of physics, chemistry, and ultimately, biology, but the rules do not explain themselves. We have no theory that tells us why the Standard Model is the right thing and not something else. Could other things have been the Laws of Physics? Might the list of elementary particles, the masses, and the coupling constants be different in other parts of the universe that we cannot observe? Might the Laws of Physics be different in very distant times and places? If so, what governs the way they change? Are there deeper laws that tell us what laws are possible and what are not? These are the questions that physicists are starting to grapple with at the beginning of the twenty-first century. They are the questions about which The Cosmic Landscape is concerned.

  One thing may be puzzling you about this chapter. I haven’t once mentioned the most important force in the universe—the force of gravity. Newton discovered the elementary theory of gravity that bears his name. Einstein also delved deeply into the meaning of gravity in the General Theory of Relativity. Even though the laws of gravity are far more important in determining the fate of the universe than all the others, gravity is not considered to be part of the Standard Model. The reason is not that gravity is unimportant. Of all the forces of nature, it will play the largest role in this book. My reason for separating it from the other laws is that the relationship between gravity and the microscopic world of quantum mechanical elementary particles is not yet understood. Feynman himself tried to apply his methods to gravity and gave up in disgust. In fact he once advised me to never get involved in the subject. That was like telling a small boy to stay out of the cookie jar.

  In the next chapter I will tell you about the “mother of all physics problems.” It is a grim tale of what goes wrong when gravity is combined with these Laws of Physics. It is also a tale of extreme violence. The Laws of Physics as we have understood them predict an extraordinarily lethal universe. Evidently we are missing something.

  CHAPTER TWO

  The Mother of All Physics Problems

  New York City, 1967

  I first learned about the “mother of all physics problems” one crisp fall day in New York City in an unlikely place: Washington Heights. Located three miles north of Columbia University, the Heights is part of Manhattan but in many ways resembles the South Bronx, where I grew up. Once, it had been a middle-class Jewish neighborhood, but most of the Jews had left and were replaced by Latin Americans, especially working-class Cubans. It was a great neighborhood for inexpensive Cuban restaurants. My favorite was a Cuban-Chinese place.

  People familiar with the area know that there is a group of unusual Byzantine-looking buildings on Amsterdam Avenue at about 187th Street. The streets nearby are filled with young Orthodox Jewish students and rabbis; the local student hangout at that time was a falafel
joint called MacDovid’s. The odd buildings are the campus of Yeshiva University, the oldest Jewish institution of higher learning in the United States. It specializes in the education of rabbis and Talmudic scholars, but in 1967, it also had a graduate school of physics and mathematics called the Belfer Graduate School of Science.

  I had just come from a year of postdoctoral work in Berkeley to be an assistant professor in the Belfer School. The exotic Yeshiva buildings didn’t look anything like the Berkeley or Harvard campus, or any other campus for that matter. Finding the Physics Department would be a challenge. A bearded fellow on the street directed me toward the top of one building, where there was a turret or onion dome of some kind. This didn’t look promising, but it was the only job I had, so I entered and climbed the spiral staircase. At the top was an open door to a very small, dark office containing a massive bookcase filled with large, leather-bound volumes, all of whose titles were written in Hebrew. In the office sat a rabbinical-looking, gray-bearded gentleman reading some ancient tome. The sign said:

  Physics Department

  Professor Posner

  “Is this the Physics Department?” I asked, uncomprehendingly.

  “Yes it is,” he said, “and I am the physics professor. Who are you?”

  “I’m the new guy, the new assistant professor, Susskind.” A kindly but very puzzled look came over his face.

  “Oy vey, they never tell me anything. What new guy?”

  “Is the chairman here?” I sputtered.

  “I am the chairman. In fact I am the only physics professor, and I don’t know anything about a new guy.” At that time I was twenty-six years old with a wife and two small children, and it was beginning to look like I might be unemployed.

  Confused and embarrassed, I slunk out of the building and started to cross the street, when I saw a guy I knew from college named Gary Gruber. “Hey Gruber, what’s going on here? I just came from the Physics Department. I thought it was full of physicists, but there seems to be only an old rabbi named Posner.”

  Gruber found this much more amusing than I did. He laughed and said, “ I think you probably want the graduate department, not the undergraduate. It’s around the corner on One hundred eighty-fourth Street. I’m a graduate student there.” Sweet relief! I walked over to 184th and looked on the side of the street that Gruber had indicated, but I could see nothing that looked like a graduate school of science. The street was just a row of seedy-looking storefronts. One of them advertised: “Abogado—Bail Bonds.” Another was empty and boarded up. The biggest storefront was an establishment of the kind that caters bar mitzvahs and Jewish weddings. It looked like it was no longer in business, but a small establishment that prepared kosher food was still in the basement. I passed it once, but on the second pass, I looked a little closer. Sure enough, a small sign next to the caterer’s said:

  Belfer Graduate School

  and pointed up a broad flight of stairs. The stairs had an old stained and worn carpet, and from the lower floor the smell of food floated up. I wasn’t sure if I liked the look of this place any better than the last. I climbed up to a big room that I could see was once a ballroom for weddings and bar mitzvahs. Now it was a large space with sofas, comfortable chairs, and much to my relief, blackboards. Blackboards meant physicists.

  Surrounding the space were about twenty offices. The entire school was housed in this one-time ballroom. It would have been very depressing except that several people were having a lively physics conversation at one of the boards. What’s more, I recognized some of them. I saw Dave Finkelstein, who had arranged my new job. Dave was a charismatic and brilliant theoretical physicist who had just written a paper on the use of topology in quantum field theory that was to become a classic of theoretical physics. I also saw P. A. M. Dirac, arguably the greatest theoretical physicist of the twentieth century after Einstein. Dave introduced me to Yakir Aharonov, whose discovery of the Aharonov-Bohm effect had made him famous. He was talking to Roger Penrose, who is now Sir Roger. Roger and Dave were two of the most important pioneers in the theory of black holes. I saw an open door with a sign that said Joel Lebowitz. Joel, a very well-known mathematical physicist, was arguing with Elliot Lieb, whose name was also familiar. It was the most brilliant collection of physicists that I had ever seen assembled in one place.

  They were talking about vacuum energy. Dave was arguing that the vacuum was full of zero-point energy and that this energy ought to affect the gravitational field. Dirac didn’t like vacuum energy because whenever physicists tried to calculate its magnitude, the answer would come out infinite. He thought that if it came out infinite, the mathematics must be wrong and that the right answer is that there is no vacuum energy. Dave pulled me into the conversation, explaining as he went. For me this conversation was a fateful turning point—my introduction to a problem that would obsess me for almost forty years and that eventually led to The Cosmic Landscape.

  The Worst Prediction Ever

  The part of the mind—I guess we call it the ego—that gets pleasure from being proved right is especially well developed in theoretical physicists. To make a theory of some phenomenon followed by a clever calculation and then finally to have the result confirmed by an experiment provides a tremendous source of satisfaction. In some instances the experiment takes place before the calculation, in which case it’s not predicting but, rather, explaining a result, and it’s almost as good. Even very good physicists now and then make wrong predictions. We tend to forget about them, but one wrong prediction just will not go away. It is by far the all-time worst calculation of a numerical result that any physicist ever made. It was not the work of any one person, and it was so wrong that no experiment was ever needed to prove it so. The problem is that the wrong result seems to be an inevitable consequence of our best theory of nature, quantum field theory.

  Before I tell you what the quantity is, let me tell you how wrong the prediction is. If the result of a calculation disagrees with an experiment by being 10 times too large or too small, we say that it was off by one order of magnitude; if wrong by a factor of 100, then it’s two orders of magnitude off; a factor of 1,000, three orders; and so on. Being wrong by one order of magnitude is bad; two orders, a disaster; three, a disgrace. Well, the best efforts of the best physicists, using our best theories, predict Einstein’s cosmological constant incorrectly by 120 orders of magnitude! That’s so bad that it’s funny.

  Einstein was the first to get burned by the cosmological constant. In 1917, one year after the completion of the General Theory of Relativity, Einstein wrote a paper that he later regretted as his worst mistake. The paper, titled “Cosmological Considerations on the General Theory of Relativity,” was written a few years before astronomers understood that the faint smudges of light called nebulae were actually distant galaxies. It was still twelve years till the American astronomer Edwin Hubble would revolutionize astronomy and cosmology, demonstrating that the galaxies are all receding away from us with a velocity that grows with distance. Einstein didn’t know in 1917 that the universe was expanding. As far as he or anyone else knew, the galaxies were stationary, occupying the same location for all eternity.

  According to Einstein’s theory the universe is closed and bounded, which first of all means that space is finite in extent. But it doesn’t mean that it has an edge. The surface of the earth is an example of a closed-and-bounded space. No point on earth is more than twelve thousand miles from any other point. Moreover, there is no edge to the earth: no place that represents the boundary of the world. A sheet of paper is finite, but it has an edge: some people would say four edges. But on the earth’s surface, if you keep going in any direction, you never come to the end of space. Like Magellan you will eventually come back to the same place.1

  We often say that the earth is a sphere, but to be precise, the term sphere refers only to the surface. The correct mathematical term for the solid earth is a ball. To understand the analogy between the surface of the earth and the universe
of Einstein, you must learn to think only of the surface and not the solid ball. Let’s imagine creatures—call them flatbugs—that inhabit the surface of a sphere. Assume that they can never leave that surface: they can’t fly, and they can’t dig. Let’s also assume that the only signals they can receive or emit travel along the surface. For example, they might communicate with their environment by emitting and detecting surface waves of some kind. These creatures would have no concept of the third dimension and no use for it. They would truly inhabit a two-dimensional closed-and-bounded world. A mathematician would call it a 2-sphere, because it is two-dimensional.

  We are not flatbugs living in a two-dimensional world. But according to Einstein’s theory, we live in a three-dimensional analog of a sphere. A three-dimensional closed-and-bounded space is more difficult to picture, but it makes perfect sense. The mathematical term for such a space is a 3-sphere. Just like the flatbugs, we would discover that we live in a 3-sphere by traveling out along any direction and eventually finding that we always return to the starting point. According to Einstein’s theory, space is a 3-sphere.

  In fact spheres come in every dimension. An ordinary circle is the simplest example. A circle is one-dimensional like a line: if you lived on it, you could move only along a single direction. Another name for a circle is a 1-sphere. Moving along the circle is much like moving along a line except that you come back to the same place after a while. To define a circle, start with a two-dimensional plane and draw a closed curve. If every point on the curve is the same distance from a central point (the center), the curve is a circle. Notice that we began with a two-dimensional plane in order to define the 1-sphere.

  The 2-sphere is similar except that you begin with three-dimensional space. A surface is a 2-sphere if every point is the same distance from the center. Perhaps you can see how to generalize this to a 3-sphere or, for that matter, a sphere of any dimension. For the 3-sphere we begin with a four-dimensional space. You can think of it as a space described by four coordinates instead of the usual three. Now just pick out all the points that are at a common distance from the origin. Those points all lie on a 3-sphere.