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The Ultimate Turtle

A Brief History of Time: From the Big Bang to Black Holes

by Stephen W. Hawking, introduction by Carl Sagan
Bantam, 198 pp., $18.95

My goal is simple. It is complete understanding of the universe, why it is as it is and why it exists at all.”

—Stephen Hawking, 1981

Stephen Hawking opens his new book with a marvelous old anecdote. A famous astronomer, after a lecture, was told by an elderly lady, who was perhaps under the influence of Hinduism, that his cosmology was all wrong. The world, she said, rests on the back of a giant tortoise. When the astronomer asked what the tortoise stands on, she replied: “You’re very clever, young man, very clever. But it’s turtles all the way down.”

Most people, Hawking writes, would find this cosmology ridiculous, but if we take the turtles as symbols of more and more fundamental laws, the tower is not so absurd. There are two ways to view it. Either a single turtle is at the bottom, standing on nothing, or it’s turtles all the way down. Both views are held by leading physicists. David Bohm and Freeman Dyson, to mention two, favor the infinite regress—wheels within wheels, boxes inside boxes, but never a final box.1 Hawking is on the other side. He believes that physics is finally closing in on the ultimate turtle. But before discussing his stimulating book, which climaxes with this amazing prediction, I shall say something about the book’s even more extraordinary author.

Hawking, age forty-four, is the Lucasian Professor of Mathematics at Cambridge University, a chair held by Isaac Newton and Paul Dirac. Few living physicists could occupy this chair more deservedly, even though, as many by now know, Hawking has for two decades been confined to a wheelchair. He is already a legend, not just because of his brilliant contributions to theoretical physics, but also for his courage, optimism, and humor in the face of a crippling illness. Lou Gehrig’s disease may be gnawing away at his body, but it has left his mind intact. Hawking actually sees himself as fortunate. He has chosen a profession in which he can work entirely inside his head, and his disability has freed him from numerous academic chores.

A tracheostomy made necessary by a pneumonia attack in 1985 has silenced his voice. He speaks by way of a computer and speech synthesizer attached to his wheelchair. Because the synthesizer was made in California, he apologizes to strangers for his American accent. He has a devoted wife and three children. He has visited the United States some thirty times, Moscow seven times, and flown around the world. At a Chicago discotheque he once wheeled onto the floor and spun his chair in time to the music.

A Brief History of Time is Hawking’s first popularly written book. Warned that every equation would cut sales in half, he has left out all formulas except Einstein’s famous E = mc2, which he hopes will not frighten half his readers. Hawking’s prose is as informal and clear as his topics are profound. Work that he accomplished during what he calls his early “classical” phase—by “classical” he means work in relativity theory—is summed up in The Large Scale Structure of Spacetime, a book written with South African cosmologist George Ellis. Avoid it, Hawking advises; it is so technical as to be “quite unreadable.” His “quantum phase,” begun in 1974, supplies the subject matter for his thoroughly readable Brief History of Time.

The book’s first chapter is a quick survey of changing models of the universe, starting with Aristotle’s concentric spheres that rotated about a round earth. Its elaboration by Ptolemy held sway in the Western world until Copernicus moved the sun to the center in one of the greatest paradigm shifts in the history of science. Medieval thinkers continually debated two big questions: Did time begin with creation? Did God create matter out of nothing or out of pre-existing primal matter? Hawking does not mention Aquinas, who argued that God could easily have made a universe with an eternal past, but we know better because Genesis says so. Hawking does mention Augustine’s earlier argument that time had no meaning until God, who is outside of time, created the heavens and the earth. What was God doing before then? Here is how Augustine replies in his Confessions:

I answer not, as a certain person is reported to have done facetiously (avoiding the pressure of the question), “He was preparing hell,” saith he, “for those who pry into mysteries.” It is one thing to perceive, another to laugh,—these things I answer not. For more willingly would I have answered, “I know not what I know not,” than that I should make him a laughing-stock who asketh deep things, and gain praise as one who answereth false things. But I say that Thou, our God, art the Creator of every creature; and if by the term “heaven and earth” every creature is understood, I boldly say, “That before God made heaven and earth, He made not anything. For if He did, what did He make unless the creature?”

An even more familiar passage occurs a few paragraphs later:

At no time, therefore, hadst Thou not made anything, because Thou hadst made time itself. And no times are co-eternal with Thee, because Thou remainest for ever; but should these continue, they would not be times. For what is time? Who can easily and briefly explain it? Who even in thought can comprehend it, even to the pronouncing of a word concerning it? But what in speaking do we refer to more familiarly and knowingly than time? And certainly we understand when we speak of it; we understand also when we hear it spoken of by another. What, then, is time? If no one ask of me, I know; if I wish to explain to him who asks, I know not.

Einstein’s model of the universe, the first to be based on relativity theory, is best understood as a three-dimensional analogue of the surface of a sphere. The sphere’s surface is finite but unbounded. A plane flying in the straightest possible line across the earth’s surface never reaches an edge, but eventually returns to where it started. In Einstein’s model, space is the curved hypersurface of a four-dimensional sphere. The cosmos is finite in volume but unbounded. A spaceship traveling the straightest possible path would eventually circle the cosmos. To prevent gravity from collapsing his model, Einstein imagined a repulsive force that would keep the universe stable, but it was soon shown that stability would be impossible. His universe would have to be either expanding or contracting.

After overwhelming evidence was found that the universe is expanding, two influential models were proposed. The physicist George Gamow claimed that the universe started with what the astronomer Fred Hoyle derisively called the “big bang.” Hoyle and his friends countered with a “steady state” universe, infinite in both space and time, that has always looked the same as it does now, and is destined to look the same forever. To maintain the overall structure, it is necessary to assume that hydrogen atoms are continually forming in space to provide the matter that keeps coalescing into stars.

The steady-state model was shot down by the discovery of background radiation that could only be explained as a remnant of a primeval fireball. Gamow’s big bang became the standard model. For a while, cosmologists toyed with the notion of “oscillating” models in which the universe expands, reaches a limit, contracts to a small size, then starts over again with another explosion. Recent theoretical work, Hawking writes, makes such “bouncing” models extremely unlikely.

Before describing his new model of the universe, Hawking provides an artfully condensed overview of relativity theory and quantum mechanics. In Newton’s cosmology, motion is “absolute” in the sense that it can be measured relative to a fixed, motionless space that nineteenth-century physicists called the “stagnant ether.” Newton’s time is also absolute in the sense that one unvarying time pervades the universe. Einstein abandoned both notions. Space and time were fused into a single structure. Light became the only nonrelative motion, its velocity impossible to exceed, and never changing regardless of an observer’s motion. Gravity and inertia became a single phenomenon, not a “force” but merely the tendency of objects to take the simplest possible paths through a space-time distorted by the presence of large masses of matter such as stars and planets.

There is a curious mistake in Hawking’s discussion of Newton’s cosmology. We are told that Newton believed in absolute time but not in absolute space, and for this was sharply criticized by Bishop Berkeley. It was the other way around. Newton defended absolute space against the “relational” view of his archrival Leibniz, who argued that space is no more than the relative positions of objects. Inertial phenomena, such as the centrifugal force that turns the surface of water concave in a bucket rotating rapidly around its vertical axis, makes it necessary, Newton insisted, to view motion as relative to a fixed space. Berkeley argued that no body could move or rotate except in relation to other bodies—a striking anticipation of relativity theory.

Hawking also misleadingly attributes to Berkeley the belief that “all material objects…are an illusion.” The Irish bishop did not think objects were illusions in any ordinary sense of the word. No one argued more cogently than he that the outside world is not dependent on human observations. For Berkeley, the structure of a tree or stone is maintained by the mind of God. He would have been delighted by quantum mechanics in which “matter” dissolves into mathematics. All material objects are made of molecules, but molecules are made of atoms, and atoms in turn are made of electrons, protons, and neutrons. And what are subatomic particles made of? They are quantized aspects of fields that are pure mathematical structures, made of nothing else. Applied to a field or its particle, the word “matter” loses all meaning. Nevertheless, for both Berkeley and a particle physicist, rocks are as nonillusory as they were for Samuel Johnson, who naively supposed he refuted Berkeley by kicking a large stone.

Hawking’s chapter on the expanding universe centers on a famous paper he wrote with Roger Penrose, now at Oxford University. Penrose had been the first to show that if a massive star collapses into a black hole, a region of space-time from which light cannot escape, it must (if the laws of relativity hold “all the way down”) produce a space-time singularity—a geometrical point of zero extension. At that point gravity would produce an infinite density and an infinite spatial curvature. When the variables of a law acquire infinite values, the law becomes meaningless. In plain language, physicists have no idea what happens at black hole singularities, if indeed they exist.

Hawking devotes two chapters to black holes. Although there is yet no decisive evidence that black holes exist, most cosmologists now are convinced that they do. (The best candidate for a black hole is the invisible part of a binary star system in the constellation of Cygnus, the swan.) Hawking’s major contribution to black hole theory was showing that as a star’s matter falls into a black hole, quantum interactions must occur and particles escape in what is known as “Hawking radiation.” As the title of a chapter indicates, “black holes ain’t so black.” Mini–black holes are tiny structures that may have formed in great numbers after the big bang. Hawking showed that if they exist, radiation will cause them to evaporate and ultimately explode. When Hawking delivered his classic paper on this in 1974, the conference chairman, John Taylor, called the paper rubbish. 2 Dennis Sciama, a British cosmologist, had an opposite reaction. He called the paper one of “the most beautiful in the history of physics.”

  1. 1

    Dyson’s new book, Infinite in All Directions (Harper and Row, 1988), is, as the title suggests, a hymn to the inexhaustible diversity of nature toward both the large and small. He writes: “I hope that the notion of a final statement of the laws of physics will prove as illusory as the notion of a formal decision process for all of mathematics. If it should turn out that the whole of physical reality can be described by a finite set of equations, I would be disappointed. I would feel that the Creator had been uncharacteristically lacking in imagination.”

  2. 2

    John Taylor, a British mathematical physicist, is noted for having written one of the most worthless of all books about black holes. It is exceeded in rubbishness only by his later book Superminds (since repudiated), which extols the spoonbending powers of psychic children.

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