Many Worlds in One: The Search for Other Universes

by Vilenkin, Alex

  Anthropic predictions are not like that. The best we can hope for is to calculate the statistical bell curve. Even if we calculate it very precisely, we will only be able to predict some range of values at a specified confidence level. Further improvements in the calculation will not lead to a dramatic increase in the accuracy of the prediction. If the observed value falls within the predicted range, there will still be a lingering doubt that this happened by sheer dumb luck. If it doesn’t, there will be doubt that the theory might still be correct, but we just happened to be among a small percentage of observers at the tails of the bell curve.

  It’s little wonder that, given a choice, physicists would not give up their old paradigm in favor of anthropic selection. But nature has already made her choice. We only have to find out what it is. If the constants of nature vary from one part of the universe to another, then, whether we like it or not, the best we can do is to make statistical predictions based on the principle of mediocrity.

  The observed value of the cosmological constant gives a strong indication that there is indeed a huge multiverse out there. It is within the range of values predicted from anthropic considerations, and there seem to be no credible alternatives. The evidence for the multiverse is, of course, indirect, as it will always be. This is a circumstantial case, where we are not going to hear eyewitness accounts or see the murder weapon. But if, with some luck, we make a few more successful predictions, we may still be able to prove the case beyond a reasonable doubt.

  15

  A Theory of Everything

  What I am really interested in is whether God could have made the world in a different way; that is, whether the necessity of logical simplicity leaves any freedom at all.

  —ALBERT EINSTEIN

  IN SEARCH OF THE FINAL THEORY

  The anthropic picture of the world hinges on the assumption that the constants of nature can vary from one place to another. But can they really? This is a question about the fundamental theory of nature: Will it yield a unique set of constants, or will it allow a wide range of possibilities?

  We don’t know what the fundamental theory is, and there is no guarantee that it really exists, but the quest for the final, unified theory inspires much of the current research in particle physics. The hope is that beneath the plurality of particles and the differences between the four basic interactions, there is a single mathematical law that governs all elementary phenomena. All particle properties and the laws of gravitation, electromagnetism, and strong and weak interactions would follow from this law, just as all theorems of geometry follow from Euclid’s five axioms.

  The kind of explanation for the particle properties that physicists hope to find in the final theory is well illustrated by how the chemical properties of the elements were explained in quantum mechanics. Early in the last century, atoms were thought to be the fundamental building blocks of matter. Each type of atom represents a different chemical element, and chemists had accumulated a colossal amount of data on the properties of the elements and their interactions with one another. Ninety-two different elements were known at the time—a bit too many, you might say, for the fundamental building blocks. Thankfully, the work of the Russian chemist Dmitry Mendeleyev in the late nineteenth century revealed some regularity in this mountain of data. Mendeleyev arranged elements in a table in order of increasing atomic weight and noticed that elements with similar chemical properties appeared at regular intervals throughout the table.ba Nobody could explain, however, why the elements followed this periodic pattern.

  By 1911 it became clear that atoms were not fundamental after all. Ernest Rutherford demonstrated that an atom consisted of a swarm of electrons orbiting a small, heavy nucleus. A quantitative understanding of the atomic structure was achieved in the 1920s, with the development of quantum mechanics. It turned out, roughly, that electron orbits form a series of concentric shells around the nucleus. Each shell can hold only up to a certain number of electrons. So, as we add more electrons, the shells gradually fill up. The chemical properties of an atom are determined mainly by the number of electrons in its outermost shell. As a new shell is filling up, the properties of the elements follow closely those of the preceding shell.bb This explains the periodicity of Mendeleyev’s table.

  For a few brief years it seemed that the fundamental structure of matter was finally understood. Paul Dirac, one of the founders of quantum mechanics, declared in his 1929 paper that “the underlying physical laws necessary for the mathematical theory of a larger part of physics and the whole of chemistry are thus completely known.” But then, one by one, new “elementary” particles began to pop up.

  To start with, the atomic nuclei turned out to be composite, consisting of protons and neutrons held together by the strong nuclear force. Then the positron was discovered, and following that the muon.bc When protons were smashed into one another in particle accelerators, new types of short-lived particles showed up. This did not necessarily mean that protons were made of those particles. If you smash two TV sets together, you can be sure that the things flying out in the debris are the parts the TV sets were originally made of. But in the case of colliding protons, some of the resulting particles were heavier than the protons themselves, with the extra mass coming from the kinetic energy of motion of the protons. So, these collision experiments did not reveal much about the internal structure of the proton, but simply extended the particle zoo. By the end of the 1950s, the number of particles exceeded that of the known chemical elements.bd One of the pioneers of particle physics, Enrico Fermi, said that if he could remember the names of all the particles, he would become a botanist.1

  The breakthrough that introduced order into this unruly crowd of particles was made in the early 1960s, independently, by Murray Gell-Mann of Caltech and Yuval Ne’eman, an Israeli military officer who took leave to complete his Ph.D. in physics. They noticed that all strongly interacting particles fell into a certain symmetric pattern. Gell-Mann and independently George Zweig of CERN (the European Centre for Nuclear Research) later showed that the pattern could be neatly accounted for if all these particles were composed of more fundamental building blocks, which Gell-Mann called quarks. This reduced the number of elementary particles, but not by much: quarks come in three “colors” and six “flavors,” so there are eighteen different quarks and as many antiquarks. Gell-Mann was awarded the 1969 Nobel Prize for uncovering the symmetry of strongly interacting particles.

  In a parallel development, a somewhat similar symmetry was discovered for the particles interacting through weak and electromagnetic forces. The key role in the formulation of this electroweak theory was played by Harvard physicists Sheldon Glashow and Steven Weinberg and the Pakistani physicist Abdus Salam. They shared the 1979 Nobel Prize for this work. Classification of particles according to symmetries played a role analogous to that of the periodic table in chemistry. In addition, three types of “messenger” particles, which mediate the three basic interactions, were identified: photons for the electromagnetic force, W and Z particles for the weak force, and eight gluons for the strong force. All these ingredients provided a basis for the Standard Model of particle physics.

  The development of the Standard Model was completed in the 1970s. The resulting theory gave a precise mathematical scheme that could be used to determine the outcomes of encounters between any known particles. This theory has been tested in countless accelerator experiments, and as of now it is supported by all the data. The Standard Model also predicted the existence and properties of W and Z particles and of an additional quark—all later discovered. By all these accounts, it is a phenomenally successful theory.

  And yet, the Standard Model is obviously too baroque to qualify as the ultimate theory of nature. The model contains more than sixty elementary particles—not a great improvement over the number of elements in Mendeleyev’s table. It includes nineteen adjustable parameters, which had to be determined from experiments but are completely arbitrary as far as the theory is conce
rned. Furthermore, one important interaction—gravity—is left out of the model.2 The success of the Standard Model tells us that we are on the right track, but its shortcomings indicate that the quest should continue. 3

  THE PROBLEM WITH GRAVITY

  The omission of gravity in the Standard Model is not just an oversight. On the face of it, gravity appears to be similar to electromagnetism. Newton’s gravitational force, for example, has the same inverse square dependence on the distance as Coulomb’s electric force. However, all attempts to develop a quantum theory of gravity along the same lines as the theory of electromagnetism, or other interactions in the Standard Model, encountered formidable problems.

  The electric force between two charged particles is due to a constant exchange of photons. The particles are like two basketball players who pass the ball back and forth to one another as they run along the court. Similarly, the gravitational interaction can be pictured as an exchange of gravitational field quanta, called gravitons. And indeed, this description works rather well, as long as the interacting particles are far apart. In this case, the gravitational force is weak and the spacetime is nearly flat. (Remember, gravity is related to the curvature of spacetime.) The gravitons can be pictured as little humps bouncing between the particles in this flat background.

  At very small distances, however, the situation is completely different. As we discussed in Chapter 12, quantum fluctuations at short distance scales give the spacetime geometry a foamlike structure (see Figure 12.1). We have no idea how to describe the motion and interaction of particles in such a chaotic environment. The picture of particles moving through a smooth spacetime and shooting gravitons at one another clearly does not apply in this regime.

  Effects of quantum gravity become important only at distances below the Planck length—an unimaginably tiny length, 1025 times smaller than the size of an atom. To probe such distances, particles have to be smashed at tremendous energies, far beyond the capabilities of the most powerful accelerators. On much larger distance scales, which are accessible to observation, quantum fluctuations of spacetime geometry average out and quantum gravity can be safely ignored. But the conflict between Einstein’s general relativity and quantum mechanics cannot be ignored in our search for the ultimate laws of nature. Both gravity and quantum phenomena have to be accounted for in the final theory. Thus, leaving gravity out is not an option.

  THE HARMONY OF STRINGS

  Most physicists now place their hopes on a radically new approach to quantum gravity—the theory of strings. This theory provides a unified description for all particles and all their interactions. It is the most promising candidate we have ever had for the fundamental theory of nature.

  According to string theory, particles like electrons or quarks, which seem to be pointlike and were thought to be elementary, are in fact tiny vibrating loops of string. The string is infinitely thin, and the length of the little loops is comparable to the Planck length. The particles appear to be structureless points because the Planck length is so tiny.

  The string in little loops is highly taut, and this tension causes the loops to vibrate, in a way similar to the vibrating strings in a violin or piano. Different vibration patterns on a straight string are illustrated in Figure 15.1. In these patterns, which correspond to different musical notes, the string has a wavy shape, with several complete half-waves fitting along its length. The larger the number of half-waves, the higher the note. Vibration patterns of loops in string theory are similar (see Figure 15.2), but now different patterns correspond to different types of particles, rather than different notes. The properties of a particle—for example, its mass, electric charge, and charges with respect to weak and strong interactions—are all determined by the exact vibrational state of the string loop. Instead of introducing an independent new entity for each type of particle, we now have a single entity—the string—of which all particles are made.

  Figure 15.1. Vibration patterns of a straight string.

  Figure 15.2. A schematic representation of vibration patterns of a string loop.

  The messenger particles—photons, gluons, W, and Z—are also vibrating little loops, and particle interactions can be pictured as string loops splitting and joining. What is most remarkable is that the spectrum of string states necessarily includes the graviton—the particle mediating gravitational interactions. The problem of unifying gravity with other interactions does not exist in string theory: on the contrary, the theory cannot be constructed without gravity.

  The conflict between gravity and quantum mechanics has also disappeared. As we have just discussed, the problem was due to quantum fluctuations of the spacetime geometry. If particles are mathematical points, the fluctuations go wild in the vicinity of the particles and the smooth spacetime continuum turns into a violent spacetime foam. In string theory, the little loops of string have a finite size, which is set by the Planck length. This is precisely the distance scale below which quantum fluctuations get out of control. The loops are immune to such sub-Planckian fluctuations: the spacetime foam is tamed just when it is about to start causing trouble. Thus, for the first time we have a consistent quantum theory of gravity.

  The idea that particles may secretly be strings was suggested in 1970 by Yoichiro Nambu of the University of Chicago, Holger Nielsen of the Niels Bohr Institute, and Leonard Susskind, then at Yeshiva University. String theory was first meant to be a theory of strong interactions, but it was soon found that it predicted the existence of a massless boson, which had no counterpart among the strongly interacting particles. The key realization that the massless boson had all the properties of the graviton was made in 1974 by John Schwarz of Caltech and Joel Scherk of the École Normale Supérieure. It took another ten years for Schwarz, working in collaboration with Michael Green of Queen Mary College in London, to resolve some subtle mathematical issues and show that the theory was indeed consistent.

  String theory has no arbitrary constants, so it does not allow any tinkering or adjustments. All we can do is to uncover its mathematical framework and see whether or not it corresponds to the real world. Unfortunately, the mathematics of the theory is incredibly complex. Now, after twenty years of assault by hundreds of talented physicists and mathematicians, it is still far from being fully understood. At the same time, this research revealed a mathematical structure of amazing richness and beauty. This, more than anything else, suggests to the physicists that they are probably on the right track.4

  THE LANDSCAPE

  As I have just mentioned, string theory has no adjustable parameters. This is not an exaggeration: I mean none at all. Even the number of the dimensions of space is rigidly fixed by the theory. The problem is that it gives the wrong answer: it requires that space should have nine dimensions instead of three.

  This sounds very embarrassing: Why should we even consider a theory that is in such blatant conflict with reality? The conflict, however, can be avoided if the extra six dimensions are curled up or, as physicists say, compactified . A soda straw is a simple example of compactification: it has one large dimension along the straw and another curled up in a small circle. When viewed from a distance, the straw looks like a one-dimensional line, but close by we can see that its surface is in fact a two-dimensional cylinder (see Figure 15.3). Quite similarly, the compact extra dimensions will not be visible if they are sufficiently small. In string theory, they are not expected to be much larger than the Planck length.5

  The main problem with extra dimensions is that it is not clear exactly how they are to be compactified. If there were a single extra dimension, there would be only one way to compactify it: to curl it up into a circle. Two extra dimensions can be compactified as a sphere, as a doughnut, or as a more complicated surface with a large number of “handles” (Figure 15.4). As you go to higher dimensions, the number of possibilities multiplies. The vibrational states of the strings depend on the size and shape of extra dimensions, so each new compactification corresponds to a new vacuum with diff
erent types of particles, having different masses and different interactions.

  Figure 15.3. A soda straw has a two-dimensional cylindrical surface. It has a large dimension along the straw and a small dimension curled up in a circle.

  The hope of string theorists was that in the end the theory would yield a unique compactification describing our world and we would finally have an explanation for the observed values of all the particle physics parameters. 6 On the wave of excitement that followed some mathematical breakthroughs in the 1980s, it seemed that this goal might be just around the corner, and string theory was heralded as the future “theory of everything”—a tall order for a theory that was yet to make its first observational prediction! But gradually, a very different picture was beginning to emerge: the theory appeared to allow thousands of different compactifications.

  Figure 15.4. Different ways to compactify two extra dimensions. The large, noncompact dimensions are not shown.