The Grand Design

by Stephen Hawking

  Model-dependent realism can provide a framework to discuss questions such as: If the world was created a finite time ago, what happened before that? An early Christian philosopher, St. Augustine (354–430), said that the answer was not that God was preparing hell for people who ask such questions, but that time was a property of the world that God created and that time did not exist before the creation, which he believed had occurred not that long ago. That is one possible model, which is favored by those who maintain that the account given in Genesis is literally true even though the world contains fossil and other evidence that makes it look much older. (Were they put there to fool us?) One can also have a different model, in which time continues back 13.7 billion years to the big bang. The model that explains the most about our present observations, including the historical and geological evidence, is the best representation we have of the past. The second model can explain the fossil and radioactive records and the fact that we receive light from galaxies millions of light-years from us, and so this model—the big bang theory—is more useful than the first. Still, neither model can be said to be more real than the other.

  Some people support a model in which time goes back even further than the big bang. It is not yet clear whether a model in which time continued back beyond the big bang would be better at explaining present observations because it seems the laws of the evolution of the universe may break down at the big bang. If they do, it would make no sense to create a model that encompasses time before the big bang, because what existed then would have no observable consequences for the present, and so we might as well stick with the idea that the big bang was the creation of the world.

  A model is a good model if it:

  Is elegant

  Contains few arbitrary or adjustable elements

  Agrees with and explains all existing observations

  Makes detailed predictions about future observations that can disprove or falsify the model if they are not borne out.

  For example, Aristotle’s theory that the world was made of four elements, earth, air, fire, and water, and that objects acted to fulfill their purpose was elegant and didn’t contain adjustable elements. But in many cases it didn’t make definite predictions, and when it did, the predictions weren’t always in agreement with observation. One of these predictions was that heavier objects should fall faster because their purpose is to fall. Nobody seemed to have thought that it was important to test this until Galileo. There is a story that he tested it by dropping weights from the Leaning Tower of Pisa. This is probably apocryphal, but we do know he rolled different weights down an inclined plane and observed that they all gathered speed at the same rate, contrary to Aristotle’s prediction.

  The above criteria are obviously subjective. Elegance, for example, is not something easily measured, but it is highly prized among scientists because laws of nature are meant to economically compress a number of particular cases into one simple formula. Elegance refers to the form of a theory, but it is closely related to a lack of adjustable elements, since a theory jammed with fudge factors is not very elegant. To paraphrase Einstein, a theory should be as simple as possible, but not simpler. Ptolemy added epicycles to the circular orbits of the heavenly bodies in order that his model might accurately describe their motion. The model could have been made more accurate by adding epicycles to the epicycles, or even epicycles to those. Though added complexity could make the model more accurate, scientists view a model that is contorted to match a specific set of observations as unsatisfying, more of a catalog of data than a theory likely to embody any useful principle.

  We’ll see in Chapter 5 that many people view the “standard model,” which describes the interactions of the elementary particles of nature, as inelegant. That model is far more successful than Ptolemy’s epicycles. It predicted the existence of several new particles before they were observed, and described the outcome of numerous experiments over several decades to great precision. But it contains dozens of adjustable parameters whose values must be fixed to match observations, rather than being determined by the theory itself.

  As for the fourth point, scientists are always impressed when new and stunning predictions prove correct. On the other hand, when a model is found lacking, a common reaction is to say the experiment was wrong. If that doesn’t prove to be the case, people still often don’t abandon the model but instead attempt to save it through modifications. Although physicists are indeed tenacious in their attempts to rescue theories they admire, the tendency to modify a theory fades to the degree that the alterations become artificial or cumbersome, and therefore “inelegant.”

  If the modifications needed to accommodate new observations become too baroque, it signals the need for a new model. One example of an old model that gave way under the weight of new observations was the idea of a static universe. In the 1920s, most physicists believed that the universe was static, or unchanging in size. Then, in 1929, Edwin Hubble published his observations showing that the universe is expanding. But Hubble did not directly observe the universe expanding. He observed the light emitted by galaxies. That light carries a characteristic signature, or spectrum, based on each galaxy’s composition, which changes by a known amount if the galaxy is moving relative to us. Therefore, by analyzing the spectra of distant galaxies, Hubble was able to determine their velocities. He had expected to find as many galaxies moving away from us as moving toward us. Instead he found that nearly all galaxies were moving away from us, and the farther away they were, the faster they were moving. Hubble concluded that the universe is expanding, but others, trying to hold on to the earlier model, attempted to explain his observations within the context of the static universe. For example, Caltech physicist Fritz Zwicky suggested that for some yet unknown reason light might slowly lose energy as it travels great distances. This decrease in energy would correspond to a change in the light’s spectrum, which Zwicky suggested could mimic Hubble’s observations. For decades after Hubble, many scientists continued to hold on to the steady-state theory. But the most natural model was Hubble’s, that of an expanding universe, and it has come to be the accepted one.

  In our quest to find the laws that govern the universe we have formulated a number of theories or models, such as the four-element theory, the Ptolemaic model, the phlogiston theory, the big bang theory, and so on. With each theory or model, our concepts of reality and of the fundamental constituents of the universe have changed. For example, consider the theory of light. Newton thought that light was made up of little particles or corpuscles. This would explain why light travels in straight lines, and Newton also used it to explain why light is bent or refracted when it passes from one medium to another, such as from air to glass or air to water.

  The corpuscle theory could not, however, be used to explain a phenomenon that Newton himself observed, which is known as Newton’s rings. Place a lens on a flat reflecting plate and illuminate it with light of a single color, such as a sodium light. Looking down from above, one will see a series of light and dark rings centered on where the lens touches the surface. This would be difficult to explain with the particle theory of light, but it can be accounted for in the wave theory.

  According to the wave theory of light, the light and dark rings are caused by a phenomenon called interference. A wave, such as a water wave, consists of a series of crests and troughs. When waves collide, if those crests and troughs happen to correspond, they reinforce each other, yielding a larger wave. That is called constructive interference. In that case the waves are said to be “in phase.” At the other extreme, when the waves meet, the crests of one wave might coincide with the troughs of the other. In that case the waves cancel each other and are said to be “out of phase.” That situation is called destructive interference.

  In Newton’s rings the bright rings are located at distances from the center where the separation between the lens and the reflecting plate is such that the wave reflected from the lens differs from the wave reflected from the
plate by an integral (1, 2, 3,…) number of wavelengths, creating constructive interference. (A wavelength is the distance between one crest or trough of a wave and the next.) The dark rings, on the other hand, are located at distances from the center where the separation between the two reflected waves is a half-integral (½, 1½, 2½,…) number of wavelengths, causing destructive interference—the wave reflected from the lens cancels the wave reflected from the plate.

  In the nineteenth century, this was taken as confirming the wave theory of light and showing that the particle theory was wrong. However, early in the twentieth century Einstein showed that the photoelectric effect (now used in television and digital cameras) could be explained by a particle or quantum of light striking an atom and knocking out an electron. Thus light behaves as both particle and wave.

  The concept of waves probably entered human thought because people watched the ocean, or a puddle after a pebble fell into it. In fact, if you have ever dropped two pebbles into a puddle, you have probably seen interference at work, as in the picture above. Other liquids were observed to behave in a similar fashion, except perhaps wine if you’ve had too much. The idea of particles was familiar from rocks, pebbles, and sand. But this wave/particle duality—the idea that an object could be described as either a particle or a wave—is as foreign to everyday experience as is the idea that you can drink a chunk of sandstone.

  Dualities like this—situations in which two very different theories accurately describe the same phenomenon—are consistent with model-dependent realism. Each theory can describe and explain certain properties, and neither theory can be said to be better or more real than the other. Regarding the laws that govern the universe, what we can say is this: There seems to be no single mathematical model or theory that can describe every aspect of the universe. Instead, as mentioned in the opening chapter, there seems to be the network of theories called M-theory. Each theory in the M-theory network is good at describing phenomena within a certain range. Wherever their ranges overlap, the various theories in the network agree, so they can all be said to be parts of the same theory. But no single theory within the network can describe every aspect of the universe—all the forces of nature, the particles that feel those forces, and the framework of space and time in which it all plays out. Though this situation does not fulfill the traditional physicists’ dream of a single unified theory, it is acceptable within the framework of model-dependent realism.

  We will discuss duality and M-theory further in Chapter 5, but before that we turn to a fundamental principle upon which our modern view of nature is based: quantum theory, and in particular, the approach to quantum theory called alternative histories. In that view, the universe does not have just a single existence or history, but rather every possible version of the universe exists simultaneously in what is called a quantum superposition. That may sound as outrageous as the theory in which the table disappears whenever we leave the room, but in this case the theory has passed every experimental test to which it has ever been subjected.

  N 1999 A TEAM OF PHYSICISTS in Austria fired a series of soccer-ball-shaped molecules toward a barrier. Those molecules, each made of sixty carbon atoms, are sometimes called buckyballs because the architect Buckminster Fuller built buildings of that shape. Fuller’s geodesic domes were probably the largest soccer-ball-shaped objects in existence. The buckyballs were the smallest. The barrier toward which the scientists took their aim had, in effect, two slits through which the buckyballs could pass. Beyond the wall, the physicists situated the equivalent of a screen to detect and count the emergent molecules.

  If we were to set up an analogous experiment with real soccer balls, we would need a player with somewhat shaky aim but with the ability to launch the balls consistently at a speed of our choosing. We would position this player before a wall in which there are two gaps. On the far side of the wall, and parallel to it, we would place a very long net. Most of the player’s shots would hit the wall and bounce back, but some would go through one gap or the other, and into the net. If the gaps were only slightly larger than the balls, two highly collimated streams would emerge on the other side. If the gaps were a bit wider than that, each stream would fan out a little, as shown in the figure below.

  Notice that if we closed off one of the gaps, the corresponding stream of balls would no longer get through, but this would have no effect on the other stream. If we reopened the second gap, that would only increase the number of balls that land at any given point on the other side, for we would then get all the balls that passed through the gap that had remained open, plus other balls coming from the newly opened gap. What we observe with both gaps open, in other words, is the sum of what we observe with each gap in the wall separately opened. That is the reality we are accustomed to in everyday life. But that’s not what the Austrian researchers found when they fired their molecules.

  In the Austrian experiment, opening the second gap did indeed increase the number of molecules arriving at some points on the screen—but it decreased the number at others, as in the figure below. In fact, there were spots where no buckyballs landed when both slits were open but where balls did land when only one or the other gap was open. That seems very odd. How can opening a second gap cause fewer molecules to arrive at certain points?

  We can get a clue to the answer by examining the details. In the experiment, many of the molecular soccer balls landed at a spot centered halfway between where you would expect them to land if the balls went through either one gap or the other. A little farther out from that central position very few molecules arrived, but a bit farther away from the center than that, molecules were again observed to arrive. This pattern is not the sum of the patterns formed when each gap is opened separately, but you may recognize it from Chapter 3 as the pattern characteristic of interfering waves. The areas where no molecules arrive correspond to regions in which waves emitted from the two gaps arrive out of phase, and create destructive interference; the areas where many molecules arrive correspond to regions where the waves arrive in phase, and create constructive interference.

  In the first two thousand or so years of scientific thought, ordinary experience and intuition were the basis for theoretical explanation. As we improved our technology and expanded the range of phenomena that we could observe, we began to find nature behaving in ways that were less and less in line with our everyday experience and hence with our intuition, as evidenced by the experiment with buckyballs. That experiment is typical of the type of phenomena that cannot be encompassed by classical science but are described by what is called quantum physics. In fact, Richard Feynman wrote that the double-slit experiment like the one we described above “contains all the mystery of quantum mechanics.”

  The principles of quantum physics were developed in the first few decades of the twentieth century after Newtonian theory was found to be inadequate for the description of nature on the atomic—or subatomic—level. The fundamental theories of physics describe the forces of nature and how objects react to them. Classical theories such as Newton’s are built upon a framework reflecting everyday experience, in which material objects have an individual existence, can be located at definite locations, follow definite paths, and so on. Quantum physics provides a framework for understanding how nature operates on atomic and subatomic scales, but as we’ll see in more detail later, it dictates a completely different conceptual schema, one in which an object’s position, path, and even its past and future are not precisely determined. Quantum theories of forces such as gravity or the electromagnetic force are built within that framework.

  Can theories built upon a framework so foreign to everyday experience also explain the events of ordinary experience that were modeled so accurately by classical physics? They can, for we and our surroundings are composite structures, made of an unimaginably large number of atoms, more atoms than there are stars in the observable universe. And though the component atoms obey the principles of quantum physics, one can show that the large
assemblages that form soccer balls, turnips, and jumbo jets—and us—will indeed manage to avoid diffracting through slits. So though the components of everyday objects obey quantum physics, Newton’s laws form an effective theory that describes very accurately how the composite structures that form our everyday world behave.

  That might sound strange, but there are many instances in science in which a large assemblage appears to behave in a manner that is different from the behavior of its individual components. The responses of a single neuron hardly portend those of the human brain, nor does knowing about a water molecule tell you much about the behavior of a lake. In the case of quantum physics, physicists are still working to figure out the details of how Newton’s laws emerge from the quantum domain. What we do know is that the components of all objects obey the laws of quantum physics, and the Newtonian laws are a good approximation for describing the way macroscopic objects made of those quantum components behave.