The Grand Design

by Stephen Hawking

But how do we know we have the true, undistorted picture of reality? Might not we ourselves also be inside some big goldfish bowl and have our vision distorted by an enormous lens? The goldfish’s picture of reality is different from ours, but can we be sure it is less real?

us—the beings in the simulated world could not gaze into their universe from the outside, there would be no reason for them to doubt their own pictures of reality. This is a modern version of the idea that we are all figments of someone else’s dream.

There is no picture- or theory-independent concept of reality. Instead we will adopt a view that we will call model-dependent realism: the idea that a physical theory or world picture is a model (generally of a mathematical nature) and a set of rules that connect the elements of the model to observations. This provides a framework with which to interpret modern science.

In other words, if you see a herd of zebras fighting for a spot in the parking garage, it is because there really is a herd of zebras fighting for a spot in the parking garage. All other observers who look will measure the same properties, and the herd will have those properties whether anyone observes them or not. In philosophy that belief is called realism.

according to the principles of quantum physics, which is an accurate description of nature, a particle has neither a definite position nor a definite velocity unless and until those quantities are measured by an observer. It is therefore not correct to say that a measurement gives a certain result because the quantity being measured had that value at the time of the measurement.

Strict realists often argue that the proof that scientific theories represent reality lies in their success. But different theories can successfully describe the same phenomenon through disparate conceptual frameworks.

Anti-realists suppose a distinction between empirical knowledge and theoretical knowledge. They typically argue that observation and experiment are meaningful but that theories are no more than useful instruments that do not embody any deeper truths underlying the observed phenomena.

George Berkeley (1685–1753) even went as far as to say that nothing exists except the mind and its ideas. When a friend remarked to English author and lexicographer Dr. Samuel Johnson (1709–1784) that Berkeley’s claim could not possibly be refuted, Johnson is said to have responded by walking over to a large stone, kicking it, and proclaiming, “I refute it thus.” Of course the pain Dr. Johnson experienced in his foot was also an idea in his mind, so he wasn’t really refuting Berkeley’s ideas. But his act did illustrate the view of philosopher David Hume (1711–1776), who wrote that although we have no rational grounds for believing in an objective reality, we also have no choice but to act as if it is true.

According to model-dependent realism, it is pointless to ask whether a model is real, only whether it agrees with observation. If there are two models that both agree with observation, like the goldfish’s picture and ours, then one cannot say that one is more real than another.

Our perception—and hence the observations upon which our theories are based—is not direct, but rather is shaped by a kind of lens, the interpretive structure of our human brains.

How do I know that a table still exists if I go out of the room and can’t see it? What does it mean to say that things we can’t see, such as electrons or quarks—the particles that are said to make up the proton and neutron—exist? One could have a model in which the table disappears when I leave the room and reappears in the same position when I come back, but that would be awkward, and what if something happened when I was out, like the ceiling falling in? How, under the table-disappears-when-I-leave-the-room model, could I account for the fact that the next time I enter, the table reappears broken, under the debris of the ceiling? The model in which the table stays put is much simpler and agrees with observation. That is all one can ask.

Nevertheless, according to model-dependent realism, quarks exist in a model that agrees with our observations of how subnuclear particles behave.

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.

To paraphrase Einstein, a theory should be as simple as possible, but not simpler.

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.”

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.

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.

Another of the main tenets of quantum physics is the uncertainty principle, formulated by Werner Heisenberg in 1926. The uncertainty principle tells us that there are limits to our ability to simultaneously measure certain data, such as the position and velocity of a particle. According to the uncertainty principle, for example, if you multiply the uncertainty in the position of a particle by the uncertainty in its momentum (its mass times its velocity) the result can never be smaller than a certain fixed quantity, called Planck’s constant. That’s a tongue-twister, but its gist can be stated simply: The more precisely you measure speed, the less precisely you can measure position, and vice versa.

According to quantum physics, no matter how much information we obtain or how powerful our computing abilities, the outcomes of physical processes cannot be predicted with certainty because they are not determined with certainty. Instead, given the initial state of a system, nature determines its future state through a process that is fundamentally uncertain. In other words, nature does not dictate the outcome of any process or experiment, even in the simplest of situations. Rather, it allows a number of different eventualities, each with a certain likelihood of being realized. It is, to paraphrase Einstein, as if God throws the dice before deciding the result of every physical process. That idea bothered Einstein, and so even though he was one of the fathers of quantum physics, he later became critical of it.

Given the state of a system at some time, the laws of nature determine the probabilities of various futures and pasts rather than determining the future and past with certainty.

Quantum physics tells us that nothing is ever located at a definite point because if it were, the uncertainty in momentum would have to be infinite. In fact, according to quantum physics, each particle has some probability of being found anywhere in the universe.

It could mean instead that particles take every possible path connecting those points. This, Feynman asserted, is what makes quantum physics different from Newtonian physics. The situation at both slits matters because, rather than following a single definite path, particles take every path, and they take them all simultaneously!

Feynman showed that, for a general system, the probability of any observation is constructed from all the possible histories that could have led to that observation. Because of that his method is called the “sum over histories” or “alternative histories” formulation of quantum physics.

the principle that observing a system must alter its course. Can’t we, as we do when our supervisor has a spot of mustard on her chin, discreetly watch but not interfere? No. According to quantum physics, you cannot “just” observe something. That is, quantum physics recognizes that to make an observation, you must interact with the object you are observing. For instance, to see an object in the traditional sense, we shine a light on it. Shining a light on a pumpkin will of course have little effect on it. But shining even a dim light on a tiny quantum particle—that is, shooting photons at it—does have an appreciable effect, and experiments show that it changes the results of an experiment in just the way that quantum physics describes.

if you turn on a light to determine which slit the particles pass through, thereby eliminating the other option, you will make the interference pattern disappear. And indeed, when the experiment is performed, turning on a light changes the results from the interference pattern, to a pattern like that! Moreover, we can vary the experiment by employing very faint light so that not all of the particles interact with the light.

how thorough our observation of the present, the (unobserved) past, like the future, is indefinite and exists only as a spectrum of possibilities. The universe, according to quantum physics, has no single past, or history. The fact that the past takes no definite form means that observations you make on a system in the present affect its past.

Newton’s law of gravity, published in 1687, said that every object in the universe attracts every other object with a force proportional to its mass. It made a great impression on the intellectual life of its era because it showed for the first time that at least one aspect of the universe could be accurately modeled, and it established the mathematical machinery to do so. The idea that there are laws of nature brings up issues similar to that for which Galileo had been convicted of heresy about fifty years earlier. For instance, the Bible tells the story of Joshua praying for the sun and moon to stop in their trajectories so he would have extra daylight to finish fighting the Amorites in Canaan. According to the book of Joshua, the sun stood still for about a day. Today we know that that would have meant that the earth stopped rotating. If the earth stopped, according to Newton’s laws anything not tied down would have remained in motion at the earth’s original speed (1,100 miles per hour at the equator)—a high price to pay for a delayed sunset. None of this bothered Newton himself, for as we’ve said, Newton believed that God could and did intervene in the workings of the universe.

The result was a set of equations describing both electric and magnetic forces as manifestations of the same physical entity, the electromagnetic field. Maxwell had unified electricity and magnetism into one force. Moreover, he showed that electromagnetic fields could propagate through space as a wave. The speed of that wave is governed by a number that appeared in his equations, which he calculated from experimental data that had been measured a few years earlier. To his astonishment the speed he calculated equaled the speed of light, which was then known experimentally to an accuracy of 1 percent. He had discovered that light itself is an electromagnetic wave!

It’s probably no accident that the wavelengths we are able to see with the naked eye are those in which the sun radiates most strongly: It’s likely that our eyes evolved with the ability to detect electromagnetic radiation in that range precisely because that is the range of radiation most available to them. If we ever run into beings from other planets, they will probably have the ability to “see” radiation at whatever wavelengths their own sun emits most strongly, modulated by factors such as the light-blocking characteristics of the dust and gases in their planet’s atmosphere. So aliens who evolved in the presence of X-rays might have a nice career in airport security.

it is not possible to assign to every event a time with which every observer will agree. Instead, all observers have their own measures of time, and the times measured by two observers who are moving relative to each other will not agree.

curvature. In Einstein’s theory, objects move on geodesics, which are the nearest things to straight lines in a curved space. Lines are geodesics on the flat plane, and great circles are geodesics on the surface of the earth. In the absence of matter, the geodesics in four-dimensional space-time correspond to lines in three-dimensional space. But when matter is present, distorting space-time, the paths of bodies in the corresponding three-dimensional space curve in a manner that in Newtonian theory was explained by the attraction of gravity. When space-time is not flat, objects’ paths appear to be bent, giving the impression that a force is acting on them.

1. Gravity. This is the weakest of the four, but it is a long-range force and acts on everything in the universe as an attraction. This means that for large bodies the gravitational forces all add up and can dominate over all other forces.

2. Electromagnetism. This is also long-range and is much stronger than gravity, but it acts only on particles with an electric charge, being repulsive between charges of the same sign and attractive between charges of the opposite sign. This means the electric forces between large bodies cancel each other out, but on the scales of atoms and molecules they dominate. Electromagnetic forces are responsible for all of chemistry and biology. 3. Weak nuclear force. This causes radioactivity and plays a vital role in the formation of the elements in stars and the early universe. We don’t, however, come into contact with this force in our everyday lives. 4. Strong nuclear force. This force holds together the protons and neutrons inside the nucleus of an atom. It also holds together the protons and neutrons themselves, which is necessary because they are made of still tinier particles, the quarks we mentioned in Chapter 3. The strong force is the energy source for the sun and nuclear power, but, as with the weak force, we don’t have direct contact with it.

The quantum theory of the electromagnetic field, called quantum electrodynamics, or QED for short, was developed in the 1940s by Richard Feynman and others, and has become a model for all quantum field theories. As we’ve said, according to classical theories, forces are transmitted by fields. But in quantum field theories the force fields are pictured as being made of various elementary particles called bosons, which are force-carrying particles that fly back and forth between matter particles, transmitting the forces. The matter particles are called fermions. Electrons and quarks are examples of fermions. The photon, or particle of light, is an example of a boson.

According to QCD, the proton, the neutron, and many other elementary particles of matter are made of quarks, which have a remarkable property that physicists have come to call color (hence the term “chromodynamics,” although quark colors are just helpful labels—there is no connection with visible color). Quarks come in three so-called colors, red, green, and blue. In addition, each quark has an anti-particle partner, and the colors of those particles are called anti-red, anti-green, and anti-blue. The idea is that only combinations with no net color can exist as free particles. There are two ways to achieve such neutral quark combinations. A color and its anti-color cancel, so a quark and an anti-quark form a colorless pair, an unstable particle called a meson. Also, when all the three colors (or anti-colors) are mixed, the result has no net color. Three quarks, one of each color, form stable particles called baryons, of which protons and neutrons are examples (and three anti-quarks form the anti-particles of the baryons). Protons and neutrons are the baryons that make up the nucleus of atoms and are the basis for all normal matter in the universe.

In physics a system is said to have a symmetry if its properties are unaffected by a certain transformation such as rotating it in space or taking its mirror image.

Supersymmetry is a more subtle kind of symmetry that cannot be associated with a transformation of ordinary space.

Practically speaking, that means that each matter particle, such as a quark, ought to have a partner particle that is a force particle, and each force particle, such as the photon, ought to have a partner particle that is a matter particle. This has the potential to solve the problem of infinities because it turns out that the infinities from closed loops of force particles are positive while the infinities from closed loops of matter particles are negative, so the infinities in the theory arising from the force particles and their partner matter particles tend to cancel out.

string theory. According to string theory, particles are not points, but patterns of vibration that have length but no height or width—like infinitely thin pieces of string.

According to string theory, they are curved up into a space of very small size. To picture this, imagine a two-dimensional plane. We call the plane two-dimensional because you need two numbers (for instance, horizontal and vertical coordinates) to locate any point on it. Another two-dimensional space is the surface of a straw. To locate a point on that space, you need to know where along the straw’s length the point is, and also where along its circular dimension. But if the straw is very thin, you would get a very good approximate position employing only the coordinate that runs along the straw’s length, so you might ignore the circular dimension. And if the straw were a million-million-million-million-millionth of an inch in diameter, you wouldn’t notice the circular dimension at all. That is the picture string theorists have of the extra dimensions—they are highly curved, or curled, on a scale so small that we don’t see them. In string theory the extra dimensions are curled up into what is called the internal space, as opposed to the three-dimensional space that we experience in everyday life. As we’ll see, these internal states are not just hidden dimensions swept under the rug—they have important physical significance.

Whether M-theory exists as a single formulation or only as a network, we do know some of its properties. First, M-theory has eleven space-time dimensions, not ten. String theorists had long suspected that the prediction of ten dimensions might have to be adjusted, and recent work showed that one dimension had indeed been overlooked. Also, M-theory can contain not just vibrating strings but also point particles, two-dimensional membranes, three-dimensional blobs, and other objects that are more difficult to picture and occupy even more dimensions of space, up to nine. These objects are called p-branes (where p runs from zero to nine).

The laws of M-theory therefore allow for different universes with different apparent laws, depending on how the internal space is curled. M-theory has solutions that allow for many different internal spaces, perhaps as many as 10500, which means it allows for 10500 different universes, each with its own laws. To get an idea how many that is, think about this: If some being could analyze the laws predicted for each of those universes in just one millisecond and had started working on it at the big bang, at present that being would have studied just 1020 of them. And that’s without coffee breaks.

The original hope of physicists to produce a single theory explaining the apparent laws of our universe as the unique possible consequence of a few simple assumptions may have to be abandoned. Where does that leave us? If M-theory allows for 10500 sets of apparent laws, how did we end up in this universe, with the laws that are apparent to us? And what about those other possible worlds?

universe is expanding involves a bit of subtlety. For example, we don’t mean the universe is expanding in the manner that, say, one might expand one’s house, by knocking out a wall and positioning a new bathroom where once there stood a majestic oak. Rather than space extending itself, it is the distance between any two points within the universe that is growing. That idea emerged in the 1930s amid much controversy, but one of the best ways to visualize it is still a metaphor enunciated in 1931 by Cambridge University astronomer Arthur Eddington. Eddington visualized the universe as the surface of an expanding balloon, and all the galaxies as points on that surface.

In 1922, Russian physicist and mathematician Alexander Friedmann investigated what would happen in a model universe based upon two assumptions that greatly simplified the mathematics: that the universe looks identical in every direction, and that it looks that way from every observation point. We know that Friedmann’s first assumption is not exactly true—the universe fortunately is not uniform everywhere! If we gaze upward in one direction, we might see the sun; in another, the moon or a colony of migrating vampire bats. But the universe does appear to be roughly the same in every direction when viewed on a scale that is far larger—larger even than the distance between galaxies. It is something like looking down at a forest. If you are close enough, you can make out individual leaves, or at least trees, and the spaces between them. But if you are so high up that if you hold out your thumb it covers a square mile of trees, the forest will appear to be a uniform shade of green. We would say that, on that scale, the forest is uniform.

So although we can employ the equations of general relativity and our observations of the heavens to learn about the universe at a very young age, it is not correct to carry the big bang picture all the way back to the beginning.

Ironically, though tiny variations in the CMBR are evidence for inflation, one reason inflation is an important concept is the nearly perfect uniformity of the temperature of the CMBR. If you make one part of an object hotter than its surroundings and then wait, the hot spot will grow cooler and its surroundings warmer until the temperature of the object is uniform. Similarly, one would expect the universe to eventually have a uniform temperature. But this process takes time, and if inflation hadn’t occurred, there wouldn’t have been enough time in the history of the universe for heat at widely separated regions to equalize, assuming that the speed of such heat transfer is limited by the speed of light. A period of very rapid expansion (much faster than light speed) remedies that because there would have been enough time for the equalization to happen in the extremely tiny preinflationary early universe.

To see how this works, we need to understand the principle that gravity warps space and time. Warpage of space is easier to visualize than warpage of time. Imagine that the universe is the surface of a flat billiard table. The table’s surface is a flat space, at least in two dimensions. If you roll a ball on the table it will travel in a straight line. But if the table becomes warped or dented in places, as in the illustration below, then the ball will curve.