Leaping the Abyss
Stephen Hawking on black holes, unified field theory, and Marilyn Monroe.
Stephen Hawking on black holes, unified field theory, and Marilyn Monroe.
Stephen Hawking seemed slightly worse, as always. It is a miracle that he has clung to life for over 20 years with Lou Gehrig's disease. Each time I see him I feel that this will be the last, that he cannot hold on to such a thin thread for much longer.
Hawking turned 60 in January. Over the course of his brilliant career, he has worked out many of the basics of black hole physics, including, most strikingly, his prediction that black holes aren't entirely black. Instead, if they have masses equivalent to a mountain's, they radiate particles of all kinds. Smaller holes would disappear in a fizz of radiation—a signature that astronomers have searched for but so far not found.
The enormous success of Hawking's 1988 book, A Brief History of Time, has made him a curious kind of cultural icon. He wonders how many of the starlets and rock stars who mentioned the book on talk shows actually read it.
With his latest book, The Universe in a Nutshell (Bantam), he aims to remedy the situation with a plethora of friendly illustrations to help readers decipher such complex topics as superstring theory and the nature of time. The trick is translating equations into sentences, no mean feat. The pictures help enormously, though purists deplore them as oversimplified. I feel that any device is justified to span such an abyss of incomprehension.
When I entered Stephen's office at the University of Cambridge, his staff was wary of me, plainly suspecting I was a "civilian" harboring a crank theory of the universe. But I'd called beforehand, and then his secretary recognized me from years past. (I am an astrophysicist and have known Stephen since the 1970s.) When I entered the familiar office his shrunken form lolled in his motorized chair as he stared out, rendered goggle-eyed by his thick glasses—but a strong spirit animated all he said.
Hawking lost his vocal cords years ago, to an emergency tracheotomy. His gnarled, feeble hands could not hold a pen. For a while after the operation he was completely cut off from the world, an unsettling parallel to those mathematical observers who plunge into black holes, their signals to the outside red-shifted and slowed by gravity's grip to dim, whispering oblivion.
A Silicon Valley firm came to the rescue. Engineers devised tailored, user friendly software and a special keyboard for Hawking. Now his frail hand moved across it with crablike speed. The software is deft, and he could build sentences quickly. I watched him flit through the menu of often-used words on his liquid crystal display, which hung before him in his wheelchair. The invention has been such a success that the Silicon Valley folk now supply units to similarly afflicted people worldwide.
"Please excuse my American accent," the speaker mounted behind the wheelchair said with a California inflection. He coded this entire remark with two keystrokes.
Although I had been here before, I was again struck that a man who had suffered such an agonizing physical decline had on his walls several large posters of a person very nearly his opposite: Marilyn Monroe. I mentioned her, and Stephen responded instantly, tapping one-handed on his keyboard, so that soon his transduced voice replied, "Yes, she's wonderful. Cosmological. I wanted to put a picture of her in my latest book, as a celestial object." I remarked that to me the book was like a French Impressionist painting of a cow, meant to give a glancing essence, not the real, smelly animal. Few would care to savor the details. Stephen took off from this to discuss some ideas currently booting around the physics community about the origin of the universe, the moment just after the Big Bang.
Stephen's great politeness paradoxically made me ill at ease; I was acutely aware of the many demands on his time, and, after all, I had just stopped by to talk shop.
"For years my early work with Roger Penrose seemed to be a disaster for science," Stephen said. "It showed that the universe must have begun with a singularity, if Einstein's general theory of relativity is correct. That appeared to indicate that science could not predict how the universe would begin. The laws would break down at the point of singularity, of infinite density." Mathematics cannot handle physical quantities like density that literally go to infinity. Indeed, the history of 20th century physics was in large measure about how to avoid the infinities that crop up in particle theory and cosmology. The idea of point particles is convenient but leads to profound, puzzling troubles.
I recalled that I had spoken to Stephen about mathematical methods of getting around this problem one evening at a party in King's College. There were analogies to methods in elementary quantum mechanics, methods he was trying to carry over into this surrealistic terrain.
"It now appears that the way the universe began can indeed be determined, using imaginary time," Stephen said. We discussed this a bit. Stephen had been using a mathematical device in which time is replaced, as a notational convenience, by something called imaginary time. This changes the nature of the equations, so he could use some ideas from the tiny quantum world. In the new equations, a kind of tunneling occurs in which the universe, before the Big Bang, has many different ways to pass through the singularity. With imaginary time, one can calculate the chances for a given tunneling path into our early universe after the beginning of time as we know it.
"Sure, the equations can be interpreted that way," I argued, "but it's really a trick, isn't it?"
Stephen said, "Yes, but perhaps an insightful trick."
"We don't have a truly deep understanding of time," I replied, "so replacing real time with imaginary time doesn't mean much to us."
"Imaginary time is a new dimension, at right angles to ordinary, real time," Stephen explained. "Along this axis, if the universe satisfies the 'no boundary' condition, we can do our calculations. This condition says that the universe has no singularities or boundaries in the imaginary direction of time. With the 'no boundary' condition, there will be no beginning or end to imaginary time, just as there is no beginning or end to a path on the surface of the Earth."
"If the path goes all the way around the Earth," I said. "But of course, we don't know that in imaginary time there won't be a boundary."
"My intuition says there will be no blocking in that special coordinate, so our calculations make sense."
"Sense is just the problem, isn't it? Imaginary time is just a mathematical convenience." I shrugged in exasperation at the span between cool mathematical spaces and the immediacy of the raw world; this is a common tension in doing physics. "It's unrelated to how we feel time. The seconds sliding by. Birth and death."
"True. Our minds work in real time, which begins at the Big Bang and will end, if there is a Big Crunch—which seems unlikely, now, from the latest data showing accelerating expansion. Consciousness would come to an end at a singularity."
"Not a great consolation," I said.
He grinned. "No, but I like the 'no boundary' condition. It seems to imply that the universe will be in a state of high order at one end of real time but will be disordered at the other end of time, so that disorder increases in one direction of time. We define this to be the direction of increasing time. When we record something in our memory, the disorder of the universe will increase. This explains why we remember events only in what we call the past, and not in the future."
"Remember what you predicted in 1980 about final theories like this?" I chided him.
"I suggested we might find a complete unified theory by the end of the century." Stephen made the transponder laugh dryly. "OK, I was wrong. At that time, the best candidate seemed to be N=8 supergravity. Now it appears that this theory may be an approximation to a more fundamental theory, of superstrings. I was a bit optimistic to hope that we would have solved the problem by the end of the century. But I still think there's a 50-50 chance that we will find a complete unified theory in the next 20 years."
"I've always suspected that the structure never ends as we look to smaller and smaller scales—and neither will the theories," I offered.
"It is possible that there is no ultimate theory of physics at all. Instead, we will keep on discovering new layers of structure. But it seems that physics gets simpler, and more unified, the smaller the scale on which we look. There is an ultimate length scale, the Planck length, below which space-time may just not be defined. So I think there will be a limit to the number of layers of structure, and there will be some ultimate theory, which we will discover if we are smart enough."
"Does it seem likely that we are smart enough?" I asked.
Another grin. "You will have to get your faith elsewhere."
"I can't keep up with the torrent of work on superstrings." Mathematical physics is like music, which a young and zesty spirit can best seize and use, as did Mozart.
"I try," he said modestly.
We began discussing recent work on "baby universes"—bubbles in space-time. To us large creatures, space-time is like the sea seen from an ocean liner, smooth and serene. Up close, though, on tiny scales, it's waves and bubbles. At extremely fine scales, pockets and bubbles of space-time can form at random, sputtering into being, then dissolving. Arcane details of particle physics suggest that sometimes—rarely, but inevitably—these bubbles could grow into a full-fledged universe.
This might have happened a lot at the instant just immediately after the Big Bang. Indeed, some properties of our universe may have been created by the space-time foam that roiled through those infinitesimally split seconds. Studying this possibility uses the "wormhole calculus," which samples the myriad possible frothing bubbles (and their connections, called wormholes).
Averaging over this foam in a mathematical sense, smoothing its properties a bit, Hawking and others have tried to find out whether a final, rather benign universe like ours was an inevitable outcome of that early turbulence. The jury isn't in on this point, and it may be out forever—the calculations are tough, guided by intuition rather than facts. Deciding whether they meaningfully predict anything is a matter of taste. This recalls Oscar Wilde's aphorism that in matters of great import, style is always more important than substance.
If this picture of the first split second is remotely right, much depends on the energy content of the foam. The energy to blow up these bubbles would be countered by an opposite, negative energy, which comes from the gravitational attraction of all the matter in the bubble. If the outward pressure just balances the inward attraction (a pressure, really) of the mass, then you could get a universe much like ours: rather mild, with space-time not suffering any severe curvature—what astronomers call "flat." This seems to be so on such relatively tiny scales as our solar system, and flatness prevails even on the size range of our galaxy. Indeed, flatness holds on immense scales, as far as we can yet see.
It turns out that such bubbles could even form right now. An entirely separate space-time could pop into existence in your living room, say. It would start unimaginably small, then balloon to the size of a cantaloupe—but not before your very eyes, because, for quite fundamental reasons, you couldn't see it.
"They don't form in space, of course," Stephen said. "It doesn't mean anything to ask where in space these things occur." They don't take up room in our universe but rather are their own universes, expanding into spaces that did not exist before.
"They're cut off from us after we make them," I said. "No relics, no fossil?"
"I do not think there could be."
"Like an ungrateful child who doesn't write home." When talking about immensities, I sometimes grasp for something human.
"It would not form in our space, but rather as another space-time."
We discussed for a while some speculations about this that I had put into two novels, Cosm and Timescape. I had used Cambridge and the British scientific style in Timescape, published in 1980, before these ideas became current. I had arrived at them in part from some wide-ranging talks I had enjoyed with Stephen—all suitably disguised in the books, of course. Such enclosed space-times I had termed "onion universes," since in principle they could have further locked-away space-times inside them, and so on. It is an odd sensation when a guess turns out to have some substance—as much as anything as gossamer as these ideas can be said to be substantial.
"So they form and go," I mused. "Vanish. Between us and these other universes lies absolute nothingness, in the exact sense—no space or time, no matter, no energy."
"There can be no way to reach them," his flat voice said. "The gulf between us and them is unbridgeable. It is beyond physics because it is truly nothing, not physical at all."
The mechanical laugh resounded. Stephen likes the tug of the philosophical, and he seemed amused by the notion that universes are simply one of those things that happen from time to time.
His nurse appeared for a bit of physical cleanup, and I left him. Inert confinement to a wheelchair exacts a demeaning toll on one's dignity, but he showed no reaction to the daily round of being cared for by another in the most intimate way. Perhaps for him, it even helps the mind to slip free of the world's rub.
I sat in the common room outside his office, having tea and talking to some of his post-doctoral students. They were working on similarly wild ideas and were quick, witty, and keenly observant as they sipped their strong, dark Ceylonese tea. A sharp crew, perhaps a bit jealous of Stephen's time. They were no doubt wondering who this guy was, nobody they had ever heard of, a Californian with an accent tainted by Southern nuances, somebody who worked in astrophysics and plasma physics—which, in our age of remorseless specialization, is a province quite remote from theirs. I didn't explain; after all, I really had no formal reason to be there, except that Stephen and I were friends.
Stephen's secretary quietly came out and asked if I would join Stephen for dinner at Caius College. I had intended to eat in my favorite Indian restaurant, where the chicken vindaloo is a purging experience, and then simply rove the walks of Cambridge alone, because I love the atmosphere—but I instantly assented. Dinner at college high table is one of the legendary experiences of England. I could remember keenly each one I had attended; the repartee is sharper than the cutlery.
We made our way through the cool, atmospheric turns of the colleges, the worn wood and gray stones reflecting the piping of voices and squeaks of rusty bicycles. In misty twilight, student shouts echoing, Stephen's wheelchair jouncing over cobbled streets. He insisted on steering it himself, though his nurse hovered rather nervously. It had never occurred to me just how much of a strain on everyone there can be in round-the-clock care. A few people drifted along behind us, just watching him. "Take no notice," his mechanical voice said. "Many of them come here just to stare at me."
We wound among the ancient stone and manicured gardens, into Caius College. Students entering the dining hall made an eager rumpus. Stephen took the elevator, and I ascended the creaking stairs. The faculty entered after the students, me following with the nurse.
The high table is literally so. They carefully placed Stephen with his back to the long, broad tables of undergraduates. I soon realized that this is because watching him eat, with virtually no lip control, is not appetizing. He follows a set diet that requires no chewing. His nurse must chop up his food and spoon-feed him.
The dinner was noisy, with the year's new undergraduates staring at the famous Hawking's back. Stephen carried on a matter-of-fact, steady flow of conversation through his keyboard.
He had concerns about the physicists' Holy Grail, a unified theory of everything. Even if we could thrash our way through a thicket of mathematics to glimpse its outlines, it might not be specific enough—that is, we would still have a range of choices. Physics could end up dithering over arcane points, undecided, perhaps far from our particular primate experience. Here is where aesthetics might enter.
"If such a theory is not unique," he said, "one would have to appeal to some outside principle, which one might call God."
I frowned. "Not as the Creator, but as a referee?"
"He would decide which theory was more than just a set of equations, but described a universe that actually exists."
"Or maybe all possible theories describe universes that exist!" he said with glee. "It is unclear what it means to say that something exists. In questions like, 'Does there exist a man with two left feet in Cambridge?,' one can answer this by examining every man in Cambridge. But there is no way that one can decide if a universe exists, if one is not inside it."
"The space-time Catch-22."
"So it is not easy to see what meaning can be given to the question, 'Why does the universe exist?' But it is a question that one can't help asking."
As usual, the ability to pose a question simply and clearly in no way implied a similar answer—or that an answer even existed.
After the dining hall, high table moved to the senior common room upstairs. We relaxed along a long, polished table in comfortable padded chairs, enjoying the traditional crisp walnuts and ancient aromatic port, Cuban cigars, and arch conversation, occasionally skewered by a witty interjection from Stephen.
Someone mentioned American physicist Stephen Weinberg's statement, in The First Three Minutes, that the more we comprehend the universe, the more meaningless it seems. Stephen doesn't agree, and neither do I, but he has a better reason. "I think it is not meaningful in the first place to say that the universe is pointless, or that it is designed for some purpose."
I asked, "No meaning, then, to the pursuit of meaning?"
"To do that would require one to stand outside the universe, which is not possible."
Again the image of the gulf between the observer and the object of study. "Still," I persisted, "there is amazing structure we can see from inside."
"The overwhelming impression is of order. The more we discover about the universe, the more we find that it is governed by rational laws. If one liked, one could say that this order was the work of God. Einstein thought so."
One of the college fellows asked, "Rational faith?"
Stephen tapped quickly. "We shouldn't be surprised that conditions in the universe are suitable for life, but this is not evidence that the universe was designed to allow for life. We could call order by the name of God, but it would be an impersonal God. There's not much personal about the laws of physics."
Walnuts eaten, port drunk, cigars smoked, it was time to go. When we left, Stephen guided his wheelchair through the shadowy reaches of the college, indulging my curiosity about a time-honored undergraduate sport: climbing Cambridge.
At night, young men sometimes scramble among the upper reaches of the steepled old buildings, scaling the most difficult points. They risk their necks for the glory of it. Quite out of bounds, of course. Part of the thrill is eluding the proctors who scan the rooftops late at night, listening for the scrape of heels. There is even a booklet about roof climbing, describing its triumphs and centuries-long history.
Stephen took me to a passageway I had been through many times, a shortcut to the Cam River between high, peaked buildings of undergraduate rooms. He said that it was one of the tough events, jumping across that and then scaling a steep, often slick roof beyond.
The passage looked to be about three meters across. I couldn't imagine leaping that gap from the slate-dark roofs. And at night, too. "All that distance?" I asked. My voice echoed in the fog.
"Yes," he said.
"Anybody ever miss?"
His eyes twinkled and he gave us a broad smile. "Yes." These Cambridge sorts have the real stuff, all right.
In the cool night Stephen recalled some of his favorite science fiction stories. He rarely read any fiction other than science fiction past the age of 12, he said. "It's really the only fiction that is realistic about our true position in the universe as a whole."
And how much stranger the universe was turning out than even those writers had imagined. Even when they discussed the next billion years, they could not guess the odd theories that would spring up within the next generation of physicists. Now there are speculations that our universe might have 11 dimensions, all told, all but three of space and one of time rolled up to tiny sizes. Will this change cosmology? So far, nobody knows. But the ideas are fun in and of themselves.
A week after my evening at Cambridge, I got from Stephen's secretary a transcript of all his remarks. I have used it here to reproduce his style of conversation. Printed out on his wheelchair computer, his sole link with us, the lines seem to come from a great distance. Across an abyss.
Portraying the flinty faces of science—daunting complexity twinned with numbing wonder—demands both craft and art. Some of us paint with fiction. Stephen paints with his impressionistic views of vast, cool mathematical landscapes. To knit together our fraying times, to span the cultural abyss, demands all these approaches—and more, if we can but invent them.
Stephen has faced daunting physical constrictions with a renewed attack on the large issues, on great sweeps of space and time. Daily he struggles without much fuss against the narrowing that is perhaps the worst element of infirmity. I recalled him rapt with Marilyn, still deeply engaged with life, holding firmly against tides of entropy.
I had learned a good deal from those few days, I realized, and most of it was not at all about cosmology.