Coming of Age in the Milky Way - Timothy Ferris (2003)



Where wast thou when I laid the foundations of the earth? Declare if thou hast understanding!

—Yahweh, to Job

Who really knows?


           Speculation about the origin of the universe is an old and notorious human activity. Old, I suppose, because there is no birth certificate for the human species: We are obliged to investigate our origins on our own, and in doing so have found it necessary to ponder as well the derivation of the wider world of which we are a part. Notorious, because the cosmogonic speculations that resulted told us more about ourselves than about the universe they claimed to describe: All, to some extent, were psychological projections, patterns cast outward from the mind onto the sky, like dancing shadows from a jack-o’-lantern.

Prescientific creation myths depended for their survival less on their accordance with the data of observation (of which there was in any event very little) than on the extent to which they were satisfying or reassuring or poetically resonant. Cherished insofar as they were our own, these tales emphasized what mattered most to the societies that preserved them. The Sumerians, living at a confluence of rivers, envisioned creation as having resulted from what amounted to a mud-wrestling match among the gods. (From a clod thrown off, the earth congealed.) The Mayans, obsessed with ball playing, conjectured that their creator was transformed into a solar kickball each time the planet Venus disappeared behind the sun. Tahitian fisherman told of an angler god who tugged their islands from the ocean floor; the Japanese sword-wielders formed their islands from drops of blood dripping from a cosmic blade. To the logic-loving Greeks, creation was elemental: For Thales of Miletus, the universe originally was water; for Anaximenes (also of Miletus), air; for Heraclitus, fire. In the fecund Hawaiian Islands, genesis was managed by a team of spirits skilled in embryology and child development. African bushmen huddled around a fire watched the sparks fly upward into the night sky and recited these words:

The girl arose; she put her hands into the wood ashes; she threw up the wood ashes into the sky. She said, “The wood ashes must become the Milky Way. They must lie white along in the sky, that the stars may stand outside of the Milky Way, and the Milky Way be the Milky Way, while it used to be wood ashes.”1

The advent of science and technology has brought about an improvement in the sophistication of cosmogonic theorizing—relative at least to what preceded it, if not to the bald reality (if there be such) of the great yawning cosmos (if it be a cosmos). But science has by no means freed the creation question from its old entanglement in human presuppositions and desires. The question of how the universe began is at best elusive, and when we hunt after it, our quivers bristling with quarks and leptons and curved space tensors and quantum probabilities, we have an only marginally better justification for our audacity than was enjoyed by Tahitian visionaries who imagined that God might cast his fishing line and catch not a fish but an emerald isle. Many scientists understood this very well, and many, consequently, would have nothing to do with cosmogony, the study of the origin of the universe. Some left the matter alone simply because they could see no practical way of approaching it. Others, adhering to the doctrine of causation, banished the issue of a first cause to exile in realms beyond science. As the astronomer Allan Sandage said:

If there was a creation event, it had to have had a cause. This was Aquinas’s whole question, one of the five ways he established the existence of God. If you can find the first effect, you have at least come close to the first cause, and if you find the first cause, that to him was God. What do astronomers say? As astronomers you can’t say anything except that here is a miracle, what seems almost supernatural, an event which has come across the horizon into science, through the big bang. Can you go the other way, back outside the barrier and finally find the answer to the question of why is there something rather than nothing? No, you cannot, not within science. But it still remains an incredible mystery: Why is there something instead of nothing?2

Such reservations notwithstanding, a few scientists did attempt to investigate the question of how the universe might have originated, while admitting that their efforts were probably “premature,” as Weinberg mildly put it. At its best, if viewed with an encouraging squint, their work appeared to shine a lamp into the anterooms of genesis. What they illuminated there was very strange, but this was, if anything, encouraging: We should hardly expect to find the familiar at the wellsprings of creation.

Two of their hypotheses—one called vacuum genesis, the other quantum genesis—seemed best to hint at what the near future might promise for human knowledge of the origin of the universe.

First, vacuum genesis. The central problem of cosmogony is to explain how something came from nothing. By “something” we mean the totality of matter and energy, space and time—the universe that we inhabit. The question of what is meant by “nothing,” however, is more subtle. In classical science, “nothing” was a vacuum, the empty space that intervenes between particles of matter. But this conception always posed problems, as witness the long inquiry into whether space was filled with an aether, and in any event it did not long survive the coming of quantum physics.

The quantum vacuum is never really empty, but instead roils with “virtual” particles. Virtual particles may be thought of as representing the possibility, delineated by the Heisenberg indeterminacy principle, that a “real” particle will arrive at a given time and place: Like the pop-up silhouettes on a police firing range, they represent not only what is but what might be. As quantum physics sees it, every “real” particle is surrounded by a corona of virtual particles and antiparticles that bubble up out of the vacuum, interact with one another, and then vanish, having lived on borrowed, Heisenberg time. (“Created and annihilated, created and annihilated—what a waste of time,” mused Richard Feynman.)3 A free proton, say, is not alone in its travels, but is surrounded by a corona of virtual protons, the existence of which influences its behavior in ways that are not only observable but are, indeed, fundamental to the interactions of the proton as we know it. One example of the reality of virtual particles resides in the fact that the stars shine: To revisit the Coulomb barrier one last time, it is the structure of the virtual particle clouds surrounding protons that makes it possible for protons at the centers of stars to tunnel through one another’s electrical fields often enough for nuclear fusion to be maintained.

The quantum vacuum, then, is a seething ocean, out of which virtual particles are constantly emerging and into which they constantly subside. And this is not merely an abstraction but a practical reality; as the American physicist Charles Misner notes:

There is a billion dollar industry—the TV industry—which does nothing except produce in empty space potentialities for electrons, were they to be inserted there, to perform some motion. A vacuum so rich in marketable potentialities cannot properly be called a void; it is really an ether.4

The rules governing the brief existence of the virtual particles are set by the uncertainty principle and by the law of conservation of matter and energy. They state that the probable frequency with which virtual particles of a given mass can be produced, and the amount of time each can cavort before falling back into nonexistence, is determined by the energy potential of the vacuum. In a low-energy environment, massive particles like the W and Z bosons cannot borrow enough energy to exist in any quantity for any discernible interval: That is why we do not normally encounter these bosons in nature today, and why it was necessary to spend millions of dollars souping up the CERN accelerator until it could inject enough energy into the vacuum to make a few Ws appear and survive long enough to trigger Carlo Rubbia’s detector. In the early universe, however, there would have been adequate ambient energy in the vacuum for the W and Z bosons to pop up all the time; this is the historical basis for the assertion of the electroweak theory that these bosons gamboled about in great numbers when the universe was young, managing the affairs of the unified electroweak force.

What has this to do with the origin of the universe? Perhaps little or nothing. Or perhaps, according to the vacuum genesis hypothesis, everything.

The protocols governing virtual particle production are tantalizingly open-ended, in that they place no absolute upper limit on the masses or lifetimes of the particles that can be created out of the vacuum. The known laws of science permit us to deduce the energy potential of the vacuum by observing the rate of particle production, but they set no ceiling on the energy that a given vacuum might contain. A vacuum that had looked quite unprepossessing might suddenly give birth to a particle as massive as a planet: Such an event is highly unlikely, but it is not impossible. Genesis, of course, can be quite unlikely—it need have happened but once—and it is through this keyhole that the vacuum genesis hypothesis entered the halls of science. Its thesis is that the entire universe originated as a single, extraordinarily massive virtual particle, one that sprang unbidden from a vacuum billions of years ago.

The first physicist to think of vacuum genesis was Edward Tryon. A modest messenger for so startling a hypothesis, Tryon had graduated Phi Beta Kappa from Cornell and had won his Ph.D. under Weinberg at Berkeley, but he was only an assistant professor at Columbia University, and his countenance did not seem destined to adorn any scientific Mount Rushmore. One afternoon during the fall 1969 academic semester, assistant professor Tryon was in the audience at a seminar being conducted by the luminary English cosmologist Dennis Sciama. As happens to everyone at times, Tryon drifted off into a reverie at one point during the talk. His thoughts wandered to the boiling quantum vacuum and the virtual particles that appear out of it. Suddenly he was seized by an idea, and was startled to hear himself interrupting Sciama’s talk. “Maybe,” he blurted out, “the universe is a vacuum fluctuation.”

Tryon’s colleagues laughed. They thought it was a joke. “It just cracked them up,” Tryon recalled more than a decade later, still looking pained at the memory. “I was deeply embarrassed…. I never told them I’d not been joking.”5

Humbled, Tryon put the idea out of his mind, but it came back to him in full force three years later, one evening while he was sitting quietly at home. “I had a revelation,” he recalled, blushing. “I visualized the universe erupting out of nothing as a quantum fluctuation and I realized that it was possible and that it explained the critical density of the universe. I understood all those things in an instant, and a chill ran through my body.”6

At the magnetic north of Tryon’s speculation stood the realization that the overall energy content of the universe might well be zero. True, when one adds up the energy released by the big bang and by starlight, plus the frozen energy that we call matter that is bound up in the stars and planets, the total is an enormous positive sum. But there is also gravitation, which, since it is purely attractive, belongs on the minus side of the ledger. (Gravity was Tryon’s specialty.) Interestingly, the gravitational potential of the earth or of any other object turns out to be approximately equal to its total energy content as calculated via E = mc2. If this were true for the universe as a whole, then the universe would have no net positive energy, and could have emerged from a vacuum without violating the law of conservation of energy.

But is it true that the universe has zero net energy? The answer, Tryon realized, could be found in the rate at which cosmic expansion might be slowing down. The universe is continuing to expand, owing to impetus generated by the big bang. The rate of expansion, however, was thought to be decreasing with time, owing to the mutual gravitational attraction exerted by the galaxies upon one another. Such a rate of slowing could reveal the overall mass density of the universe, a quantity the cosmologists symbolize by the Greek letter omega. If omega was equal to or less than 1, the mass density would be insufficient to stop expansion, and the universe would go on expanding forever. Geometrically, such a universe is described as “open,” meaning that the overall curvature of space is hyperbolic. If omega was more than 1, the expansion would be destined eventually to stop, after which the universe presumably would collapse into another fireball. If omega was exactly 1, then expansion would continue forever, forever slowing but never quite coming to a halt.

Tryon’s speculation required that omega be equal to or less than 1. Strangely, omega appears be exactly (or almost exactly) equal to 1. Indeed, the reason that observational cosmologists like Sandage and Tammann had been unable to determine conclusively whether the universe is open or closed was precisely because it is balanced at or close to an omega of value unity. Cosmic space, in other words, is neither dramatically open nor dramatically closed, but is perfectly—or almost perfectly—flat.

That it should be so is nothing short of astonishing. The gross features of the present-day universe are highly dependent upon tiny variations in the early universe—just as, say, a variation of millimeters in the angle at which a bat strikes a baseball can produce variations of hundreds of feet in where the ball lands in the outfield. In the standard big bang model, for the universe to be flat today it must have been incredibly flat at the beginning: At one second ABT, the cosmic matter density would have to have fallen within one trillionth of 1 percent of the critical value. At 10−35 second the permitted deviation would have been even smaller—less than one part in 1049. If this happened by pure chance, it was very lucky indeed; the odds against it are vanishingly small.

One could of course make the equations come out right by inserting the required matter density as an “initial condition,” but this amounted to invoking the guiding hand of God, which in science is rather like playing tennis without a net.* Alternately, one could “explain” the flatness of the universe by identifying it as a prerequisite of human existence. This argument, called the anthropic principle, went as follows: Were the cosmic matter density only slightly higher, the universe would have stopped expanding and have collapsed before enough time had elapsed for stars and planets and life to form; were it only slightly lower, the universe would have expanded too rapidly for stars and planets to have congealed from the rapidly thinning primordial gas. Therefore, the argument goes, the fact that we are here constrains certain cosmological parameters, among them the value of omega. The anthropic principle “explains” the miracle of the flat universe if we imagine the creation of many universes, only a fraction of which chance to have the values requisite for life to appear in them. But the explanation cannot be tested unless the creation of other universes can be established, something that may well be impossible by definition. In that sense, the anthropic principle is a dead-end street. The English physicist Stephen Hawking, whose work is said to have contributed to the formulation of the principle, nonetheless called it “a counsel of despair.”7

But where there is enigma there is also the promise of discovery: A paradox may signal an inadequacy in the way we are looking at a question, thereby suggesting a new and more fruitful way of approaching it. This, I think, is what Bohr meant when he exclaimed, “How wonderful that we have met with paradox. Now we have some hope of making progress.”8 And it was in this spirit that the flatness conundrum was resolved, by the invention of a new cosmological hypothesis, the inflationary universe.

The inflation hypothesis was first proposed by a young American physicist named Alan Guth. He learned of the flatness problem one November afternoon in 1978 at Cornell, in a talk by Robert Dicke, a resourceful Princeton relativist whose thoughts on the cosmic background radiation recalled those of Gamow. Trained as a physicist, Guth at the time knew little of cosmology, and, with the fierce conservatism of the young, dismissed ideas about the early evolution of the universe as “too speculative.” Dicke’s point about the oddity of omega equaling 1 struck Guth as “amazing,” he recalled, but at the time he had no idea what to do about it.

The physics community, however, was at the time commencing its mating dance with cosmology, and Guth soon found himself working on the question of how magnetic monopoles might have been produced in the early universe. Guth found monopoles intriguing: First conceived in Dirac’s austere imagination in 1931, they were purported to be massive particles with a unipolar magnetic charge. The grand unified theories indicated that they would have been created out of knots in space-time, by the same symmetry-breaking event that split the electroweak and strong nuclear forces asunder. Anachronistically, each magnetic monopole would harbor trapped W and Z bosons, as well as a tiny region at its core where the unified, electronuclear force still functioned.

The problem that engaged the attention of Guth, and of his Cornell colleague Henry Tye, was that the grand unified theories predicted the production of far too many magnetic monopoles—roughly one hundred times more monopoles than there are atoms. Given that most of the matter in the universe is invisible—the “dark matter” question—cosmologists generally welcomed the suggestior that massive subatomic particles might make up the deficit, but this was an embarrassment of riches. Searches for monopoles had turned up null results: One event had been recorded, on Valentine’s Day, 1982, on a device built by Bias Cabrera in a basement laboratory at Stanford, but Cabrera’s result had never been repeated, at Stanford or anywhere else. This plus several other lines of inquiry suggested that the cosmic monopole population was either negligible or zero. The disagreement between theory, which predicted many monopoles, and observation, which permitted few, could be resolved, Guth and Tye found, if the fabric of space-time had been smoother than expected at the time of the grand unified phase transition. Smoother space-time meant fewer space-time knots, resulting in fewer monopoles. It also meant an omega equal or close to 1.

On the evening of December 6, 1979, Guth wrote the words EVOLUTION OF THE UNIVERSE atop a blank page that he then went on to fill with calculations. His hypothesis was that the universe initially had expanded much faster than at the linear rate it evinces today—that, as Guth would later put it, there had been an “inflationary epoch,” during which the universe expanded exponentially. This meant that space was flatter and smoother by the time of the grand unified phase transition, and that far fewer monopoles therefore were produced. Here, too, was the solution to the flatness problem Dicke had outlined: Since the universe would have been much larger at the end of an inflationary period than was envisioned in the old, linear-expansion model, space would be much flatter—just as, say, an acre of the surface of the earth is flatter than is an acre of a spherical asteroid only ten miles in diameter.

SPECTACULAR REALIZATION, the young Guth wrote in his notebook the following day, drawing a box around the words. The hypothesis was not unprecedented; its revised picture of phase transitions had been arrived at independently by Katsuhiko Sato in Japan and Martin Einhorn in the United States, and the “pumping” of the expansion rate up to an exponential rate by a symmetry-breaking mechanism had been proposed by Demosthenes Kazanas of NASA. Nor did it work very well in its original form; it had to be refined, by A. D. Linde in Moscow and by Andreas Albrecht and Paul Steinhardt at the University of Pennsylvania. But Guth came up with the idea on his own, and in its finished form it enlightened and illuminated the study of the very early universe.

The inflationary model hypothesizes that the universe underwent a brief period of very rapid expansion, after which it settled into the linear expansion rate that has characterized it ever since.

According to the inflationary scenario, the radius of the universe increased by some 1050 times, from smaller than a proton to larger than a softball, during the first 10−30 second of time. During this brief but critical period the universe was a vacuum. Its potential mass and energy could not yet manifest itself as particles, because space was expanding too fast for the particles to congeal out of the vacuum. Technically, one described this condition by saying that the vacuum was hung up in a symmetrical state during a phase transition. A simile may be drawn from water. Liquid water is more symmetrical than ice, and the change in water when it cools from a liquid to a solid state marks a phase transition that breaks the symmetry. If liquid water is cooled very rapidly to below its freezing point it will not congeal into ice at once, but instead will linger in a liquid state for a while. Similarly, in the inflationary universe account, the cosmic vacuum remains empty even after falling below the temperature at which particle production ordinarily would take place. Indeed, it is this hang-up that drives the expansion: The latent energy is tied up in what is called a zero-value Higgs field, and the field acts as an engine that inflates the dimensions of cosmic space, driving the expansion so that the empty universe balloons in perfect, Platonic sphericity.*

Eventually (meaning after about 10−30 second) the quantum instability of the situation catches up with it, and the expansion abruptly slows to a linear rate. When that happens the energy latent in the vacuum precipitates out as particles and antiparticles. (Thus was new life lent to the much ridiculed steady-state picture of atoms congealing out of a vacuum.) The particles mutually annihilate, and the resulting flood of energy inaugurates the big bang. The grand unified theories, the composition of which requires attention to Higgs fields, even demonstrated how symmetry-breaking at the end of the inflationary epoch could have delivered up a small imbalance of matter over antimatter, leaving a residue, after the fireworks were over, from which to build the material universe.

Inflation resolved not only the flatness problem, revealing why omega is equal to or nearly unity, but also another major cosmological mystery, the horizon problem. The observable universe, taken as a whole, is remarkably homogeneous. In every star, in every direction, we find identical atoms functioning in accord with the same physical laws, and the cosmic background radiation, too, is everywhere the same. This, strange to say, had never been explained by the standard big bang model. The trouble was that the linearly expanding universe of the old model expanded too rapidly for all the quanta of the very early universe to have ever been in causal contact with one another: 90 percent of the universe in the old model lay beyond the causal horizon of any one observer, meaning that there was insufficient time for information, even if traveling at the speed of light, to permeate the universe.

This omission mocked the universality of natural law. How could atoms and photons on one side of the universe behave exactly like atoms and photons on the other side, if they had never communicated with one another? To visualize the problem, imagine a marching band gathered on a greensward, ready to start playing as soon as the drummer standing at the center delivers a downbeat. At the moment that time begins, the band members march rapidly away from the drummer in all directions, at nearly the speed of sound. The result will be chaos. Only a few musicians will hear the downbeat; most will go hurrying away, unable to hear it, and so will not know when to start playing or what to play. In cosmological terms, the speed of sound is replaced by the speed of light, the fastest velocity at which information can be exchanged. The standard model required that the particles of the early universe depart before they could get their marching orders: Without hearing the drumbeat, then, how did the first quarks “know” how to be quarks, and all the photons learn the rules that govern photons? Had such been the true tale of genesis, nearly every cluster of galaxies would be made of different stuff and would obey different laws. Instead, the observable universe is a lawful unity. How so?

At first blush, inflation would seem only to make matters worse, since it postulates an even speedier cosmic expansion rate. But actually it resolves the dilemma, by permitting the material of the very early universe to remain together, in causal contact, for a relatively long period before inflation began. The band members now have time to listen for the downbeat before leaving; then they board the inflationary express, which goes so fast that they soon catch up with the linear expansion rate. Now they all have their marching orders when they go, and all, consequently, can play the same tune. Inflation thus explained why the cosmic background radiation is isotropic, and why the quarks and electrons of the earth are identical to those of the Coma cluster of galaxies.*

All of which was cheering to Ed Tryon and his little cadre of vacuum genesis enthusiasts. The inflationary hypothesis made vacuum genesis appear more plausible, by admitting the possibility that the universe could have started as a relatively modest, cold particle, with the heat of the big bang coming later, in the blast of fire released by latent vacuum energy when the inflationary epoch ended. And inflation painted the vacuum in new and more vibrant colors. Once one entertained the idea that all the matter and energy in the universe erupted from a vacuum at a brief but finite interval after the beginning of time, it no longer seemed quite so preposterous to imagine that the whole affair might have begun as a vacuum.

Guth, for his part, became an aficionado of the vacuum, regarding it less as emptiness than as a cornucopia. He calculated that only a small amount of vacuum flux might, if sufficiently concentrated, have been enough to set off inflation. If, then, our universe began as a quantum flux—a sort of bubble—in a primordial vacuum, other universes might reasonably be imagined to have formed from other bubbles. Moreover, Guth conjectured, creation need not necessarily be relegated solely to the past, but might happen again: If a vacuum instability in our universe were to blister in such a way as to form another universe, we would never know it. From our perspective, the only trace of the new creation event would be a pinpoint of infinite spatial curvature. As it happens, there appear to be such places here and there, in the infinitely curved regions of space surrounding black holes. Conceivably, every time a giant star goes supernova and its remnant collapses to form a black hole it might give birth to a new universe, on another side of spacetime.

If so, Guth speculated, the artificial creation of a black hole through application of an advanced technology could create another universe. Nor would such a custom-made black hole have to be terribly massive. “You might even be able to start a new universe using energy equivalent to just a few pounds of matter,” Guth suggested, in a 1987 interview. “Provided you could find some way to compress it to a density of about 1075 grams per cubic centimeter, and provided you could trigger the thing, inflation would do the rest.” And if we could do it, so, perhaps, could someone else have done it long ago. “For all we know,” said Guth, who had a gift for the laconic statement of radical ideas, “our own universe may have started in someone’s basement.”9

If only to get our feet back on the ground, let it be noted that there were problems with both the inflationary universe and vacuum genesis. Inflation smoothed out the early universe, all right, but did so with such a vengeance that theorists had trouble coaxing enough lumpiness out of the equations to allow for the formation of galaxies and of the superclusters (and, evidently, meta-superclusters) in which they are gathered. Vacuum genesis suffered from a lingering suspicion that, if anything, it was just not crazy enough. The quantum vacuum is a characteristic of the universe we live in—virtual particles today boil in the space between real particles —but who was to say that the same was true of the “vacuum” that allegedly preceded the beginning of the expansion of the universe? That vacuum, after all, ought to have been very different from the one we encounter in the present-day universe: Presumably its relativistic curvature was infinite and its matter content zero, and neither is true of cosmic space today.

Some theorists proposed, instead, a set of even stranger but at least equally promising hypotheses. Together, these ideas went by the name of “quantum genesis.” Their approach involved taking the random nature of quantum flux to heart and enshrining it as the ruling law of the extremely early universe. Here a pioneer was Stephen Hawking, holder of Newton’s old chair as Lucasian Professor of Mathematics at Cambridge University. Described by colleagues as “the nearest thing we have to a living Einstein,” Hawking carried on a productive career in physics despite suffering from ALS, a disease that attacks the central nervous system. He worked from a wheelchair, writing and communicating by means of a computer controlled by a toggle that he manipulated with one finger. He expressed impatience less with his affliction than with people who worshiped him as a hero, pitied him as a sick man, or otherwise treated him as if he were any different from any other genius. In his postdoctoral days Hawking and his colleague Roger Penrose demonstrated that general relativity implies that the universe began in a “singularity,” a state of infinitely curved space in which the laws of relativity break down; this proved, as Hawking put it, that “relativity predicts its own downfall.”10

But quantum theory might function where relativity did not, and in later years Hawking began to explore the prospect of understanding the origin of the universe in terms of quantum probabilities. His tools included “imaginary time”—a kind of time measured in terms of imaginary numbers—and Richard Feynman’s “sum over histories” method of doing quantum mechanics.

Imaginary numbers make no sense when handled by customary mathematical rules. An example is the square root of —1, which will produce an “error” message if demanded of an electronic calculator. They work quite well, however, according to their own rules; imaginary numbers have been employed to excellent effect, for instance, in hydrodynamics. Feynman’s “sum over histories” strategy consists of calculating all the possible past trajectories of a particle, and arriving, via quantum probabilities, at the most likely path by which the particle reached its observed state. Hawking, working with the American cosmologist James Hartle at the University of California at Santa Barbara, applied this method to the universe as a whole. Speaking via an interpreter, in a vaulted hardwood hall at Padua where Galileo used to lecture, Hawking announced that he had been able to derive the quantum wave function of the universe as a whole. “The universe today is accurately described by classical general relativity,” he said.

However, classical relativity predicts that there will be a singularity in the past, and near that singularity, the curvature [of space] will be very high, classical relativity will break down, and quantum effects will have to be taken into account. In order to understand the initial conditions of the universe, we have to turn to quantum mechanics, and the quantum state of the universe will determine the initial conditions for the classical universe. So today I want to make a proposal for the quantum state of the universe.11

What emerged was a tale of cosmic evolution possessed of a strangely alien beauty. All world lines diverge from the singularity of genesis, Hawking noted, like longitude lines proceeding from the north pole on a globe of the earth. As we travel along our world line we see the other lines moving away from us, as would an explorer sailing south along a given longitude; this is the expansion of the universe. Billions of years hence the expansion will halt and the universe will collapse, eventually to meld into another fireball at the end of time. There is, however, no meaning to the question of when time began, or when it will end: “If the suggestion that spacetime is finite but unbounded is correct,” said Hawking on another occasion, “the big bang is rather like the North Pole of the earth. To ask what happens before the big bang is a bit like asking what happens on the surface of the earth one mile north of the North Pole. It’s a meaningless question.”12

Imaginary time in Hawking’s view was the once and future time, and time as we know it but the broken-symmetry shadow of that original time. When a hand calculator cries “error” upon being asked the value of the square root of —1, it is telling us, in its way, that it belongs to this universe, and knows not how to inquire into the universe as it was prior to the moment of genesis. And that is the state of all science, until we have the tools in hand to explore the very different regime that pertained when time began.

Another quantum approach to genesis, championed by John Wheeler, emphasized the quantization of space itself. Just as matter and energy are made of quanta, went this line of reasoning, so space itself ought to be quantized at its foundations. Wheeler liked to compare quantum space to the sea: Viewed from orbit, the surface of the ocean looks smooth, but if we set out in a rowboat on the surface, “we see foam and froth and breaking waves. And that foam and froth is how we picture the structure of space down at the very smallest scales.”13

In the present-day universe, the foamy structure of space manifests itself in the constant blooming forth of virtual particles. In the extremely early universe—meaning prior to the Planck time—space would have been a very rough sea indeed, and its storm-tossed quantum flux might have dominated all particle interactions. How, here, do we find our bearings?

Wheeler—an elder statesman who learned his science from Einstein and Bohr and in turn educated a whole generation of physicists—thought the answer lay in spacetime geometry: “What else is there out of which to build a particle except geometry itself?”14 he asked. Wheeler compared the quantum flux of the early universe to a complicated sailor’s knot of a kind that looks impossibly tangled, yet will fall apart if one can find the end of the rope and give it a tug in the right way. The knot in his simile is the hyperdimensional geometry of the original universe, the untangled rope the universe we inhabit today. Penrose had said, “I do not believe that a real understanding of the nature of elementary partides can ever be achieved without a simultaneous deeper understanding of the nature of spacetime itself.”15 For Wheeler, this was true of the universe as a whole:

“Space is a continuum.” So bygone decades supposed from the start when they asked, “Why does space have three dimensions?” We, today, ask instead, “How does the world manage to give the impression it has three dimensions?” How can there be any such thing as a spacetime continuum except in books? How else can we look at “space” and “dimensionality” except as approximate words for an underpinning, a substrate, a “pre-geometry,” that has no such property as dimension?16

To answer such questions, Wheeler argued, science would somehow have to bootstrap itself into a new realm, a world of “law without law,” in which, as taught by the quantum indeterminacy principle, the answer depends upon the question asked. Wheeler recalled being the subject in a game of twenty questions. He left the room for a period during which the answer was to be decided upon by the other players, then returned and started asking questions. The answers were progressively slower in coming, until Wheeler finally guessed, “Cloud,” and was told, to general amusement, that he was right. When his friends stopped laughing they explained that they had been playing a trick on Wheeler: There had originally been no right answer; his friends had agreed to formulate their answers so that each would be consistent with the answers given to his previous questions. “What is the symbolism of the story?” asked Wheeler.

The world, we once believed, exists “out there” independent of any act of observation. The electron in the atom we once considered to have at each moment a definite position and a definite momentum. I, entering, thought the room contained a definite word. In actuality the word was developed step by step through the questions I raised, as the information about the electron is brought into being by experiment that the observer chooses to make; that is, by the kind of registering equipment that he puts into place. Had I asked different questions or the same questions in a different order I would have ended up with a different word as the experimenter would have ended up with a different story for the doings of the electron. … In the game no word is a word until that word is promoted to reality by the choice of questions asked and answers given. In the real world of quantum physics, no elementary phenomenon is a phenomenon until it is a recorded phenomenon.17

We are left, then, with an image of genesis as a soundless and insubstantial castle, where our eyes cast innovative, Homeric beams and the only voices are our own. Having ushered ourselves in and having reverently and diligently done our scientific homework, we ask, as best we can frame the question, how creation came to be. The answer comes back, resounding through vaulted chambers where mind and cosmos meet. It is an echo.

*“Initial” conditions in cosmology are seldom absolutely initial, since nobody yet knows how to calculate the state of matter and space-time prior to the Planck time, which culminated at about 10−43 second ABT. One instead designates as “initial” some point subsequent to the Planck epoch. For most purposes this is regarded as quite initial enough.

*The sphere can be in many dimensions; that is another question, addressed by the supersymmetry theories, which did not as yet prescribe a timetable describing when the young universe allegedly collapsed its ten or so dimensions into three of space and one of time.

*Inflation theory indicates that the universe is many billions of times greater in volume than had been estimated in the old big bang model. The observable universe, however, is thought to constitute but a fraction of the universe as a whole: Its limits are determined less by space than by time, in that we can see only those events the light from which has had time to reach Earth. If, for instance, the first stars began to shine thirteen billion years ago, then no observer will see stars any farther than thirteen billion light-years away, regardless of how large the universe as a whole may be.