The Universes We Still Don’t Know

The Grand Design

by Stephen Hawking and Leonard Mlodinow
Bantam, 198 pp., $28.00



Sara Krulwich/The New York Times/Redux





One of Hawking’s themes in this book does have an impact on religion. This is his adoption of an idea, increasingly popular among physicists, that the expanding cloud of galaxies that we call the universe, extending at least tens of billions of light years in all directions, may be only part of a much grander “multiverse.” The multiverse is supposed to contain a vast number of other parts that might be called universes, in which even what are usually called the laws of nature are very different from what we observe.

If the multiverse idea is correct, it will remove what some have conceived to be evidence for a benevolent creator: the fact that the laws of nature seem to favor the appearance of life. For instance, if one of the two types of quarks that make up atomic nuclei were much heavier or much lighter than the other, there would be only a few stable elements, not the rich menu of actual elements that appears to be necessary for life. Hawking makes more of such examples than I would; no very great fine-tuning of the quark masses is needed to make the chemical elements needed for life sufficiently abundant.

But there is one example cited by Hawking of a really remarkable fine-tuning of physical constants, without which life could never have appeared. It has to do with dark energy, the energy of empty space. In 1998 astronomers discovered that the expansion of the universe is speeding up, an acceleration that is generally attributed to dark energy. The dark energy turned out to be about three times larger than the energy contained in the masses of all types of matter in the universe. But there is something strange about how much of this dark energy there is. We can calculate the contributions of quantum mechanical effects to dark energy—in fact, these calculations were done by several theorists before 1998. But these contributions to the dark energy turn out to be so large that, if they were not almost entirely canceled out by other contributions, the universe would be expanding much more rapidly than is observed—so rapidly that gravitationally bound systems like galaxies and stars and planets could never have formed.

Such a cancellation is possible because there are other contributions to the dark energy that we haven’t been able to calculate, in part because these contributions depend on things we don’t know, and they could cancel out the contributions to the dark energy that we can calculate. (One of the things we don’t know that affects the dark energy is the value of the so-called cosmological constant posited by Einstein in 1917, in a modification of the equations governing the gravitational field in the General Theory of Relativity.) But in order for these so-far incalculable contributions to give a total dark energy small enough to allow for the formation of gravitationally bound systems (and as small as is inferred from measurements of the expansion of the universe), constants of nature like the cosmological constant would have to be fine-tuned to make the cancellation complete to about fifty-six decimal places.

On the other hand, a multiverse would have so many parts that quantities like the quark masses and Einstein’s cosmological constant and other constants of nature would have a wide range of possible values. It is likely that in the great majority of these parts of the multiverse, constants like the quark masses and the cosmological constant and even perhaps the dimensionality of space would take values unsuitable for life. But with a wide enough range of these constants in different parts of the multiverse, there would be some parts where life could appear. Obviously, it should be no surprise and no sign of cosmic benevolence that we are in one of these favored parts of the multiverse, just as it is no sign of a benevolent creator that in a galaxy with billions of planets, we evolved on one of the minority of planets that are suitable for life. Where else could we be, except on a planet that can sustain life?

Hawking quotes a notorious 2003 statement by the cardinal archbishop of Vienna, which attacked the multiverse idea as something “invented to avoid the overwhelming evidence for purpose and design found in modern science.” Not so. As Hawking says, the multiverse idea is not a notion invented to account for the miracle of fine- tuning. He discusses two different lines of thought that led physicists to the idea of a multiverse, neither having anything to do with the conditions necessary for life.


One such line of thought arose in the theory of chaotic inflation, developed by Andrei Linde. Inflation is an early period of exponentially rapid cosmic growth, like the growth of a bank account that pays 100 percent interest every tiny fraction of a second.2 This exponential expansion is now believed to have preceded the present, more stately phase of cosmic expansion. As originally conceived by Alan Guth (and still assumed in most calculations), inflation was supposed to have occurred uniformly everywhere in space. But no theory accounts for such uniformity. It seems more natural to suppose that the universe, on very large scales, is chaotic, pervaded by wildly fluctuating fields, and that purely by chance now and then conditions in a patch of space allow that patch to begin an exponential inflation. In a small minority of cases these patches would grow into something like our present universe, in which life is possible.

The other suggestion of a multiverse comes from quantum mechanics, the mathematical framework for all physics. The weirdest thing about quantum mechanics is what is called the superposition of states. It is possible (even common) for a particle to be in a quantum state in which it cannot be said to be at any single one of its possible positions. Instead, it is in a combination of all its possible positions—a superposition—so that any single observation of its position can give any of a number of possible results, with different probabilities depending on the nature of the superposition. In principle, as Erwin Schrödinger famously pointed out, even a cat can be in a superposition of states, in some of which it is alive and in others dead. Similarly the whole universe can be in a superposition of many different states, in which the constants of nature like quark masses take different values, with a small minority of these states favorable for life.

All this is highly speculative, but not idiosyncratic. These ideas are widely discussed by physicists. Hawking does take a somewhat unusual position in his suggestion that the multiverse came into being as a quantum mechanical superposition of states because in the very early universe all four dimensions behaved like space, with no time. I won’t try to explain how this works, because I don’t find it convincing. True, Hawking has shown that it is useful to carry out calculations of processes in the early universe by mathematically distorting the dimension of time so that it becomes effectively one of space. But this does not mean that time actually was space in the early universe. After all, other theorists, going back to Julian Schwinger in the 1950s, have calculated subtle effects in atomic and particle physics by just such a distortion of the time dimension into one of space, but the usefulness of this mathematical trick does not change the fact that today we live in three spatial dimensions and one temporal dimension.


The idea of a multiverse received a big boost in recent years from developments in what used to be called string theory. It is now thought that the various known versions of string theory and a vast number of other theories all represent approximate solutions to an unknown fundamental theory, which Hawking calls M-theory. These different approximate solutions describe different sets of particles or strings or membranes in spacetimes of various different dimensionalities, with different values of physical constants. Supposedly, these various solutions of the fundamental theory that Hawking calls M-theory are realized in different parts of the multiverse.

Hawking manages to make this fundamental theory seem a little better understood than it actually is, when he says that it is a theory in eleven spacetime dimensions. The term M-theory was introduced in 1995 by Edward Witten. (Witten has never explained what the “M” stands for.) Witten’s M-theory was indeed an eleven-dimensional theory of particles and membranes, but this theory was proposed as just one of the many approximate solutions of an unknown fundamental theory, not as the fundamental theory itself. We have no idea about the spacetime dimensionality of this underlying theory. Many physicists think that it is not a theory about any sort of spacetime, and that space and time emerge only in approximate solutions of the fundamental theory.

So if we know so little about the fundamental theory, why do we think that there is one? Hawking cites the fact that, in circumstances in which two string theories or other supposed approximate solutions of the fundamental theory ought both to be valid, calculations show that the two solutions agree with each other. (This was Witten’s point in a celebrated lecture at the University of Southern California in 1995.) Hawking uses a very helpful analogy, with maps of regions on the earth’s surface. It is impossible to make a map of any large part of the earth on a flat sheet of paper without terrible distortions. But we can divide the whole area of the earth’s surface into overlapping regions, each region not more than a few hundred miles in diameter, small enough that distances and directions on a map of the region give a good approximate representation of actual distances and directions on the earth itself. Even if we didn’t know in advance that these maps all represent parts of the same surface, we could discover this by noting that the maps of any two overlapping regions agree in the area where they overlap. The earth’s surface in this analogy corresponds to the fundamental theory that Hawking calls M-theory, and the individual maps correspond to the various approximate solutions to this theory.

Hawking raises a striking and disturbing possibility that perhaps there is no underlying theory, that all we will ever have is a number of approximate theories, each valid under different circumstances, and agreeing with each other where the circumstances overlap. Here the nice analogy with maps of the earth breaks down. It is true that one cannot make a reliable map of the whole earth’s spherical surface on a flat sheet of paper, but after all there is an earth, not just a bunch of overlapping approximate maps.


More than this, Hawking expresses a radically skeptical view of reality in general. One sees this in his statement that in quantum mechanics “the universe doesn’t have just a single history, but every possible history.” This is true if by history one means what was meant in classical physics, a smooth progression of particles from one position to another at each succeeding instant. I prefer a different way of looking at quantum mechanics. The universe or any other system does have a definite history, but what is changing smoothly at every instant is not the positions of particles or the values of fields, but something called the state vector. In general, a vector is any quantity that has magnitude and direction, like the velocity of a bird, but the state vector is a vector in a space known as Hilbert space, that has not three but an infinite number of dimensions. The directions of the state vector at any instant encodes everything about the state of the system at that instant.

This vector does not have to point in a direction for which a particle is in one of the states of definite position, but it can point in intermediate directions, corresponding to superpositions of such states. This is why quantum mechanics seems so weird. But in this language there is nothing weird about the histories of physical systems. The direction of the state vector swings around as time passes in a way that is both definite and deterministic—the state of any system is always either one in which particles have definite positions, or one in which there is a definite superposition of such states. It is only if one insists on describing nature in the language of classical physics that we can say that it has no definite history.

Hawking gives a good description of how scientists come to the conclusion that something is real. We construct intellectual models that, within some range of phenomena, and to some degree of approximation, agree with observation. But he calls this “model-dependent reality,” and suggests that this is all there is to reality.

Questions about the nature of reality have puzzled scientists and philosophers for millenia. Like most people, I think that there is something real out there, entirely independent of us and our models, as the earth is independent of our maps. But this is because I can’t help believing in an objective reality, not because I have good arguments for it. I am in no position to argue that Hawking’s antirealism is wrong. But I do insist that neither quantum mechanics nor anything else in physics settles the question.


There are other points in this book where Hawking overestimates the ability of science to answer deep philosophical questions. From general ideas about determinism and experiments that show how our behavior is affected by physical influences, he concludes that we have no free will. He attributes the illusion of free will to the fact that a human being contains about a thousand trillion trillion particles, so that as a practical matter it is impossible to predict what people will do. I would say that free will is nothing but our conscious experience of deciding what to do, which I know I am experiencing as I write this review, and this experience is not invalidated by the reflection that physical laws made it inevitable that I would want to make these decisions. Thunderstorms also contain many trillion trillion particles, and it is difficult to predict what they will do, but we do not attribute free will to them, because we don’t think that they have the conscious experience of making decisions.

On his first page, Hawking says that “philosophy has not kept up with modern developments in science, particularly physics.” I would say instead that although philosophers have not done much to solve the ancient problems of philosophy, neither have physicists.

Don’t get me wrong. The Grand Design is well worth reading. It introduces the reader to topics at the frontier of theoretical physics, and it explains some scientific ideas (such as Feynman’s approach to quantum mechanics) more clearly for general readers than I have seen before. Where I do have serious disagreements with Hawking, it is about issues on which physicists and philosophers are divided, not matters that can be easily settled.


That said, because now and then I give a course at Texas on the history of science, I feel compelled to point out some historical errors in this book:

1) Perhaps motivated by his anti- realism, Hawking says that the advantage of the Copernican description of the solar system over that of Ptolemy was that “the equations of motion are much simpler in the frame of reference in which the sun is at rest.” No, the first clear indication of the superiority of the Copernican view did not come from the equations of motion published by Newton in 1687, but from Galileo’s 1610 observations of the phases of Venus, which clearly supported Copernicus over Ptolemy.3

2) Hawking says that only one of the calculations of Aristarchus survives, an analysis of the size of the earth’s shadow on the moon during a lunar eclipse, from which he inferred that the sun is much larger than the earth. But Aristarchus could never have reached that conclusion solely from observations of a lunar eclipse. In fact, his surviving work shows that Aristarchus also used observations of the apparent sizes (in fractions of a right angle) of the sun and moon, and the observation that the angle between the lines of sight to the sun and moon when the moon is half full is slightly less than a right angle.

3) Hawking credits Archimedes with the discovery that the angle at which a light ray is reflected from a mirror equals the angle at which it strikes the mirror. There is nothing about the law of reflection in the extant works of Archimedes, though he may have written about it in a book that is lost. The discovery of this law used to be credited to Euclid, who worked about a century before Archimedes, but historians today are not sure who discovered the law of reflection. If anyone should be credited with the law of reflection, I would vote for Hero of Alexandria (admittedly later than Euclid and Archimedes), who not only stated it but also proved it, on the assumption that the path of the reflected ray between the object and the observer should be as short as possible.

These are minor points that can easily be corrected in future editions, and that do not detract from the value of Hawking’s absorbing book.


The Atom at 3 PM March 10, 2011

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  2. 2

    To be specific, on the basis of observations of microwave radiation left over from the early universe, the time in which the universe doubled in size during inflation is estimated as having been roughly ten to the minus thirty-seven seconds. (Ten to the minus thirty-seven is a decimal point followed by thirty-six zeroes and a one.) 

  3. 3

    What Hawking says about the system of Ptolemy is more nearly true of the system of the sixteenth-century Danish astronomer Tycho Brahe, according to which the sun goes around the earth but the other planets go around the sun. Brahe’s theory gives the same predictions for the phases of the planets as that of Copernicus.