The Grand Design

by Stephen Hawking

  In this view, the universe appeared spontaneously, starting off in every possible way. Most of these correspond to other universes. While some of those universes are similar to ours, most are very different. They aren’t just different in details, such as whether Elvis really did die young or whether turnips are a dessert food, but rather they differ even in their apparent laws of nature. In fact, many universes exist with many different sets of physical laws. Some people make a great mystery of this idea, sometimes called the multiverse concept, but these are just different expressions of the Feynman sum over histories.

  To picture this, let’s alter Eddington’s balloon analogy and instead think of the expanding universe as the surface of a bubble. Our picture of the spontaneous quantum creation of the universe is then a bit like the formation of bubbles of steam in boiling water. Many tiny bubbles appear, and then disappear again. These represent mini-universes that expand but collapse again while still of microscopic size. They represent possible alternative universes, but they are not of much interest since they do not last long enough to develop galaxies and stars, let alone intelligent life. A few of the little bubbles, however, will grow large enough so that they will be safe from recollapse. They will continue to expand at an ever-increasing rate and will form the bubbles of steam we are able to see. These correspond to universes that start off expanding at an ever-increasing rate—in other words, universes in a state of inflation.

  As we said, the expansion caused by inflation would not be completely uniform. In the sum over histories, there is only one completely uniform and regular history, and it will have the greatest probability, but many other histories that are very slightly irregular will have probabilities that are almost as high. That is why inflation predicts that the early universe is likely to be slightly nonuniform, corresponding to the small variations in the temperature that were observed in the CMBR. The irregularities in the early universe are lucky for us. Why? Homogeneity is good if you don’t want cream separating out from your milk, but a uniform universe is a boring universe. The irregularities in the early universe are important because if some regions had a slightly higher density than others, the gravitational attraction of the extra density would slow the expansion of that region compared with its surroundings. As the force of gravity slowly draws matter together, it can eventually cause it to collapse to form galaxies and stars, which can lead to planets and, on at least one occasion, people. So look carefully at the map of the microwave sky. It is the blueprint for all the structure in the universe. We are the product of quantum fluctuations in the very early universe. If one were religious, one could say that God really does play dice.

  This idea leads to a view of the universe that is profoundly different from the traditional concept, requiring us to adjust the way that we think about the history of the universe. In order to make predictions in cosmology, we need to calculate the probabilities of different states of the entire universe at the present time. In physics one normally assumes some initial state for a system and evolves it forward in time employing the relevant mathematical equations. Given the state of a system at one time, one tries to calculate the probability that the system will be in some different state at a later time. The usual assumption in cosmology is that the universe has a single definite history. One can use the laws of physics to calculate how this history develops with time. We call this the “bottom-up” approach to cosmology. But since we must take into account the quantum nature of the universe as expressed by the Feynman sum over histories, the probability amplitude that the universe is now in a particular state is arrived at by adding up the contributions from all the histories that satisfy the no-boundary condition and end in the state in question. In cosmology, in other words, one shouldn’t follow the history of the universe from the bottom up because that assumes there’s a single history, with a well-defined starting point and evolution. Instead, one should trace the histories from the top down, backward from the present time. Some histories will be more probable than others, and the sum will normally be dominated by a single history that starts with the creation of the universe and culminates in the state under consideration. But there will be different histories for different possible states of the universe at the present time. This leads to a radically different view of cosmology, and the relation between cause and effect. The histories that contribute to the Feynman sum don’t have an independent existence, but depend on what is being measured. We create history by our observation, rather than history creating us.

  The idea that the universe does not have a unique observer-independent history might seem to conflict with certain facts we know. There might be one history in which the moon is made of Roquefort cheese. But we have observed that the moon is not made of cheese, which is bad news for mice. Hence histories in which the moon is made of cheese do not contribute to the present state of our universe, though they might contribute to others. That might sound like science fiction, but it isn’t.

  An important implication of the top-down approach is that the apparent laws of nature depend on the history of the universe. Many scientists believe there exists a single theory that explains those laws as well as nature’s physical constants, such as the mass of the electron or the dimensionality of space-time. But top-down cosmology dictates that the apparent laws of nature are different for different histories.

  Consider the apparent dimension of the universe. According to M-theory, space-time has ten space dimensions and one time dimension. The idea is that seven of the space dimensions are curled up so small that we don’t notice them, leaving us with the illusion that all that exist are the three remaining large dimensions we are familiar with. One of the central open questions in M-theory is: Why, in our universe, aren’t there more large dimensions, and why are any dimensions curled up?

  Many people would like to believe that there is some mechanism that causes all but three of the space dimensions to curl up spontaneously. Alternatively, maybe all dimensions started small, but for some understandable reason three space dimensions expanded and the rest did not. It seems, however, that there is no dynamical reason for the universe to appear four-dimensional. Instead, top-down cosmology predicts that the number of large space dimensions is not fixed by any principle of physics. There will be a quantum probability amplitude for every number of large space dimensions from zero to ten. The Feynman sum allows for all of these, for every possible history for the universe, but the observation that our universe has three large space dimensions selects out the subclass of histories that have the property that is being observed. In other words, the quantum probability that the universe has more or less than three large space dimensions is irrelevant because we have already determined that we are in a universe with three large space dimensions. So as long as the probability amplitude for three large space dimensions is not exactly zero, it doesn’t matter how small it is compared with the probability amplitude for other numbers of dimensions. It would be like asking for the probability amplitude that the present pope is Chinese. We know that he is German, even though the probability that he is Chinese is higher because there are more Chinese than there are Germans. Similarly, we know our universe exhibits three large space dimensions, and so even though other numbers of large space dimensions may have a greater probability amplitude, we are interested only in histories with three.

  What about the curled-up dimensions? Recall that in M-theory the precise shape of the remaining curled-up dimensions, the internal space, determines both the values of physical quantities such as the charge on the electron and the nature of the interactions between elementary particles, that is, the forces of nature. Things would have worked out neatly if M-theory had allowed just one shape for the curled dimensions, or perhaps a few, all but one of which might have been ruled out by some means, leaving us with just one possibility for the apparent laws of nature. Instead, there are probability amplitudes for perhaps as many as 10500 different internal spaces, each leading to different laws and values fo
r the physical constants.

  If one builds the history of the universe from the bottom up, there is no reason the universe should end up with the internal space for the particle interactions that we actually observe, the standard model (of elementary particle interactions). But in the top-down approach we accept that universes exist with all possible internal spaces. In some universes electrons have the weight of golf balls and the force of gravity is stronger than that of magnetism. In ours, the standard model, with all its parameters, applies. One can calculate the probability amplitude for the internal space that leads to the standard model on the basis of the no-boundary condition. As with the probability of there being a universe with three large space dimensions, it doesn’t matter how small this amplitude is relative to other possibilities because we already observed that the standard model describes our universe.

  The theory we describe in this chapter is testable. In the prior examples we emphasized that the relative probability amplitudes for radically different universes, such as those with a different number of large space dimensions, don’t matter. The relative probability amplitudes for neighboring (i.e., similar) universes, however, are important. The no-boundary condition implies that the probability amplitude is highest for histories in which the universe starts out completely smooth. The amplitude is reduced for universes that are more irregular. This means that the early universe would have been almost smooth, but with small irregularities. As we’ve noted, we can observe these irregularities as small variations in the microwaves coming from different directions in the sky. They have been found to agree exactly with the general demands of inflation theory; however, more precise measurements are needed to fully differentiate the top-down theory from others, and to either support or refute it. These may well be carried out by satellites in the future.

  Hundreds of years ago people thought the earth was unique, and situated at the center of the universe. Today we know there are hundreds of billions of stars in our galaxy, a large percentage of them with planetary systems, and hundreds of billions of galaxies. The results described in this chapter indicate that our universe itself is also one of many, and that its apparent laws are not uniquely determined. This must be disappointing for those who hoped that an ultimate theory, a theory of everything, would predict the nature of everyday physics. We cannot predict discrete features such as the number of large space dimensions or the internal space that determines the physical quantities we observe (e.g., the mass and charge of the electron and other elementary particles). Rather, we use those numbers to select which histories contribute to the Feynman sum.

  We seem to be at a critical point in the history of science, in which we must alter our conception of goals and of what makes a physical theory acceptable. It appears that the fundamental numbers, and even the form, of the apparent laws of nature are not demanded by logic or physical principle. The parameters are free to take on many values and the laws to take on any form that leads to a self-consistent mathematical theory, and they do take on different values and different forms in different universes. That may not satisfy our human desire to be special or to discover a neat package to contain all the laws of physics, but it does seem to be the way of nature.

  There seems to be a vast landscape of possible universes. However, as we’ll see in the next chapter, universes in which life like us can exist are rare. We live in one in which life is possible, but if the universe were only slightly different, beings like us could not exist. What are we to make of this fine-tuning? Is it evidence that the universe, after all, was designed by a benevolent creator? Or does science offer another explanation?

  HE CHINESE TELL OF A TIME during the Hsia dynasty (ca. 2205—ca. 1782 BC) when our cosmic environment suddenly changed. Ten suns appeared in the sky. The people on earth suffered greatly from the heat, so the emperor ordered a famous archer to shoot down the extra suns. The archer was rewarded with a pill that had the power to make him immortal, but his wife stole it. For that offense she was banished to the moon.

  The Chinese were right to think that a solar system with ten suns is not friendly to human life. Today we know that, while perhaps offering great tanning opportunities, any solar system with multiple suns would probably never allow life to develop. The reasons are not quite as simple as the searing heat imagined in the Chinese legend. In fact, a planet could experience a pleasant temperature while orbiting multiple stars, at least for a while. But uniform heating over long periods of time, a situation that seems necessary for life, would be unlikely. To understand why, let’s look at what happens in the simplest type of multiple-star system, one with two suns, which is called a binary system. About half of all stars in the sky are members of such systems. But even simple binary systems can maintain only certain kinds of stable orbits, of the type shown below. In each of these orbits there would likely be a time in which the planet would be either too hot or too cold to sustain life. The situation is even worse for clusters having many stars.

  Our solar system has other “lucky” properties without which sophisticated life-forms might never have evolved. For example, Newton’s laws allow for planetary orbits to be either circles or ellipses (ellipses are squashed circles, wider along one axis and narrower along another). The degree to which an ellipse is squashed is described by what is called its eccentricity, a number between zero and one. An eccentricity near zero means the figure resembles a circle, whereas an eccentricity near one means it is very flattened. Kepler was upset by the idea that planets don’t move in perfect circles, but the earth’s orbit has an eccentricity of only about 2 percent, which means it is nearly circular. As it turns out, that is a stroke of very good fortune.

  Seasonal weather patterns on earth are determined mainly by the tilt of the earth’s axis of rotation relative to the plane of its orbit around the sun. During winter in the Northern Hemisphere, for example, the North Pole is tilted away from the sun. The fact that the earth is closest to the sun at that time—only 91.5 million miles away, as opposed to around 94.5 million miles away from the sun in early July—has a negligible effect on the temperature compared with the effect of its tilt. But on planets with a large orbital eccentricity, the varying distance from the sun plays a much larger role. On Mercury, for example, with a 20 percent eccentricity, the temperature is over 200 degrees Fahrenheit warmer at the planet’s closest approach to the sun (perihelion) than when it is at its farthest from the sun (aphelion). In fact, if the eccentricity of the earth’s orbit were near one, our oceans would boil when we reached our nearest point to the sun, and freeze over when we reached our farthest, making neither winter nor summer vacations very pleasant. Large orbital eccentricities are not conducive to life, so we are fortunate to have a planet for which orbital eccentricity is near zero.

  We are also lucky in the relationship of our sun’s mass to our distance from it. That is because a star’s mass determines the amount of energy it gives off. The largest stars have a mass about a hundred times that of our sun, while the smallest are about a hundred times less massive. And yet, assuming the earth-sun distance as a given, if our sun were just 20 percent less or more massive, the earth would be colder than present-day Mars or hotter than present-day Venus.

  Traditionally, given any star, scientists define the habitable zone as the narrow region around the star in which temperatures are such that liquid water can exist. The habitable zone is sometimes called the “Goldilocks zone,” because the requirement that liquid water exist means that, like Goldilocks, the development of intelligent life requires that planetary temperatures be “just right.” The habitable zone in our solar system, pictured above, is tiny. Fortunately for those of us who are intelligent life-forms, the earth fell within it!

  Newton believed that our strangely habitable solar system did not “arise out of chaos by the mere laws of nature.” Instead, he maintained, the order in the universe was “created by God at first and conserved by him to this Day in the same state and condition.” It is easy to understand wh
y one might think that. The many improbable occurrences that conspired to enable our existence, and our world’s human-friendly design, would indeed be puzzling if ours were the only solar system in the universe. But in 1992 came the first confirmed observation of a planet orbiting a star other than our sun. We now know of hundreds of such planets, and few doubt that there exist countless others among the many billions of stars in our universe. That makes the coincidences of our planetary conditions—the single sun, the lucky combination of earth-sun distance and solar mass—far less remarkable, and far less compelling as evidence that the earth was carefully designed just to please us human beings. Planets of all sorts exist. Some—or at least one—support life. Obviously, when the beings on a planet that supports life examine the world around them, they are bound to find that their environment satisfies the conditions they require to exist.

  It is possible to turn that last statement into a scientific principle: Our very existence imposes rules determining from where and at what time it is possible for us to observe the universe. That is, the fact of our being restricts the characteristics of the kind of environment in which we find ourselves. That principle is called the weak anthropic principle. (We’ll see shortly why the adjective “weak” is attached.) A better term than “anthropic principle” would have been “selection principle,” because the principle refers to how our own knowledge of our existence imposes rules that select, out of all the possible environments, only those environments with the characteristics that allow life.