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The Ultimate Turtle

A chapter called “The Origin and Fate of the Universe” is the book’s centerpiece. About 1981 Hawking and Penrose became more and more impressed by the possibility that relativity ceases to apply on the quantum level. Just before the universe exploded there would be no singularity because quantum mechanics completely dominated the scene. Nor would there be a singularity if the universe contracted to the big crunch. These thoughts led Hawking to an elegant new model of the universe that he constructed with Jim Hartle, at the University of California, Santa Barbara.

It is hopeless to explain the new model in any detail here because it makes use of a special kind of time called “imaginary time,” which plays a role in calculating the most probable paths of particles. It is called imaginary because it is measured by complex numbers—numbers of the form a + b√-1, where a and b are real numbers and √-1 is imaginary.3 Like Einstein’s model, the new model is finite in volume but not unbounded. Unlike Einstein’s model, time is treated in exactly the same way as a space coordinate. Einstein’s three space coordinates were closed in a circle, but his time was open at both ends. In Hawking’s model, “real time” is replaced by imaginary time.

Hawking makes no attempt to explain his model except by a vague analogy. The universe is likened to a tiny region at the earth’s North Pole. Think of the earth’s axis as an imaginary time axis. The universe explodes and expands until it reaches its maximum size at the equator, then contracts to a tiny region at the South Pole. The two end spots are “singular” in the ordinary sense of being unique, but not in the technical sense of unextended points where the laws of science break down. Because the time axis is imaginary, it is not necessary to assume that the universe had a beginning or will have an end. The two spots are regions where disorder is total, the arrow of real time vanishes, and quantum events fluctuate aimlessly and forever in imaginary time.

From the standpoint of real time, the universe looks as if time began with the initial explosion and will cease after the big squeeze, but in imaginary time there are no singularities where time starts and stops. The universe emerged from a chaos that always was, and will go back to a chaos that will never cease. As Hawking puts it, the universe is eternal, “completely self-contained and not affected by anything outside itself. It would neither be created nor destroyed. It would just BE.”

It is not clear whether Hawking is a determinist who thinks history has to be the way it is, or whether chance and free will intervene, although early in his book he raises a curious paradox. If determinism reigns it would impose the outcome of our search for universal laws, but “why should it determine that we come to the right conclusions from the evidence? Might it not equally well determine that we draw the wrong conclusions? Or no conclusion at all?” Because the search has so far proved increasingly successful, Hawking sees no reason to abandon Einstein’s faith that the Old One may be subtle, but not malicious.

Space coordinates are symmetrical in the sense that they are the same in both directions and you can travel along them either way. But time is like a one-way street, with an arrow that points in only one direction. Hawking considers three foundations for the arrow: psychological, cosmological, and thermodynamic. The psychological basis is memory of the past. The cosmological basis is the expansion of the universe. The thermodynamic basis is the second law of thermodynamics, which says that events move in the direction of increasing entropy or disorder. Our psychological arrow points the same way as the thermodynamic arrow, Hawking reasons, because our minds are parts of the physical world. We remember events in the order in which disorder increases. “This makes the second law of thermodynamics almost trivial. Disorder increases with time because we measure time in the direction in which disorder increases. You can’t have a safer bet than that!”

Will the cosmological arrow ever reverse? That depends on the amount of mass in the universe. If it is below a certain ratio to the volume of the cosmos, the universe will expand forever and eventually die of the cold. If it is above the critical ratio, gravity will slow down the expansion and eventually reverse it. Early in his career Hawking defended the bizarre view that in a contracting universe time’s other two arrows would turn around and human beings (if any still existed) would live backward like a motion picture run in reverse. It is impossible to reconcile this with consciousness and free will, but in any case Hawking now admits that this was a youthful blunder. His new model allows disorder to continue increasing throughout the contracting phase, although disorder would be too extreme to permit life. Of his earlier view he writes:

What should you do when you find you have made a mistake like that? Some people never admit that they are wrong and continue to find new, and often mutually inconsistent, arguments to support their case—as Eddington did in opposing black hole theory. Others claim to have never really supported the incorrect view in the first place or, if they did, it was only to show that it was inconsistent. It seems to me much better and less confusing if you admit in print that you were wrong. A good example of this was Einstein, who called the cosmological constant, which he introduced when he was trying to make a static model of the universe, the biggest mistake of his life.

Chapter ten sketches some of the grand unification theories (GUTs) now being proposed to explain all the known forces in nature in relation to one another, including the latest theory of superstrings. In superstring theory, pointlike particles (electrons, for example) are replaced by inconceivably tiny strings, closed like rubber bands. Their vibrations in different modes determine the properties of all the particles. The strings vibrate in a space-time of ten dimensions; one is time, three are the spatial ones we know, and the other six are curled into tiny little hyperspheres as much smaller than an atom as the atom is smaller than the universe.

Superstrings solve so many problems about why the different particles have the properties they have that some physicists are euphoric over the possibility that they are about to discover a TOE—a theory of everything. Hawking is aware of similar overconfidence in the past. He quotes a notorious 1928 prediction by the physicist Max Born: “Physics, as we know it, will be over in six months.” Only two particles were then known: the electron and the proton. In spite of such failed prophecies, Hawking actually believes that physicists are nearing the end of their quest for all the fundamental laws of the universe.

One of the big mysteries that remain is why after the big bang all but three space dimensions “compacted” into the tiny hyperspheres. On this question Hawking invokes familiar arguments that we could not exist in a universe with fewer or more than three dimensions. He includes a drawing of a two-dimensional dog showing how food digestion would be impossible because a tube from mouth to anus would split the flat dog in half. Evidently Hawking has not looked into A.K. Dewdney’s fantastic book The Planiverse (Poseidon, 1984), in which methods of digestion in flatland are carefully worked out. As for dimensions above three, Hawking is quite right in saying that solar systems and atoms would be impossible, but the catch is that they are impossible only if based on laws we know. In my opinion Dewdney’s book provides strong grounds for not ruling out the notion that universes could operate efficiently with laws we don’t know.

Even if there is only one possible unified theory,” Hawking writes in his last chapter,

it is just a set of rules and equations. What is it that breathes fire into the equations and makes a universe for them to describe? The usual approach of science of constructing a mathematical model cannot answer the questions of why there should be a universe for the model to describe. Why does the universe go to all the bother of existing? Is the unified theory so compelling that it brings about its own existence? Or does it need a creator, and, if so, does he have any other effect on the universe? And who created him?

Hawking wisely does not try to answer these questions. He does, however, say that if the ultimate theory exists it should eventually be understandable by everybody. We will then be able to get on with the superultimate question of why we and the universe bother to exist. “If we find the answer to that,” writes Hawking in his book’s final sentence (except for three idiosyncratic appendixes that capsule the lives of Galileo, Newton, and Einstein), “it would be the ultimate triumph of human reason—for then we would know the mind of God.”

To me, a philosophical theist, there is not a chance of such a triumph. Even entertaining such a possibility strikes me as total folly. I firmly believe that it is not possible for science to discover any fact, or confirm any theory, that has the slightest bearing on why the universe bothers existing. As for time, I am among those who, like Augustine and Miguel de Unamuno, consider it the most terrible of mysteries. It is something given. You cannot even define it without smuggling time into your definition. The physicist John Wheeler is fond of saying that time is what keeps everything from happening at once. True, but this throws not a glimmer of light into the darkness. I have written elsewhere about why I believe time is bound up with other impenetrable mysteries such as free will and the foresight of God. I can imagine a possible world without time—just think of the universe as frozen to a halt—but I cannot conceive of you and me “existing” in such a world.

As Carl Sagan recognizes in his perceptive introduction, Hawking’s book is almost as much about God as it is about time and the universe,

…or perhaps about the absence of God. The word God fills these pages. Hawking embarks on a quest to answer Einstein’s famous question about whether God had any choice in creating the universe. Hawking is attempting, as he explicitly states, to understand the mind of God. And this makes all the more unexpected the conclusion of the effort, at least so far: a universe with no edge in space, no beginning or end in time, and nothing for a Creator to do.

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    The clearest explanation of imaginary time I know of for nonspecialists is to be found in the late Richard Feynman’s book Q.E.D., which stands for quantum electrodynamics (Princeton University Press, 1985).

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