However, regardless of what the uncertainty principle and theory of general relativity indicate, we don’t have a curled-up universe. Quite the contrary, at the time when Hawking was developing his wormhole theory, the value (the number) of the cosmological constant had been long thought, and observed, to be near zero. We find this out by observing the rate at which galaxies are moving away from one another, and from the fact of our own existence. ‘A large cosmological constant either positive or negative would make the universe unsuitable for the development of life,’ Hawking points out.13 The value of the cosmological constant is one of the examples of the ‘fine-tuning’ we saw in Chapter 9. As we shall see, Einstein was too quick to call it a ‘blunder’. But no one knew that in the early 1990s.
How can the cosmological constant possibly be so small, as we observe, when theory tells us it should be enormous? Recall once again the particle pairs in Hawking radiation. In supergravity, the theory Hawking spoke of in his Lucasian lecture, pairs of fermions (matter particles) in the vacuum give negative energy and balance the positive energy of pairs of bosons (messengers). This may indeed be the explanation, or at least part of it, but it’s a complicated matter. For one thing, these particles don’t only interact with gravity. However, even if we do have a lot of positives and negatives cancelling one another out, for all of these to cancel out to zero is a little too much to swallow. As Sidney Coleman, who shared Hawking’s enthusiasm for wormholes, puts it: ‘Zero is a suspicious number. Imagine that over a ten-year period you spend millions of dollars without looking at your salary, and when you finally compare what you spent with what you earned, they balance out to the penny.’14 For the cosmological constant to balance out to zero is even less likely.
Could wormholes solve the mystery? Hawking was thinking that wormholes branching off at every point make the cosmological constant, the energy density of the vacuum, a ‘quantum variable’ like the masses of particles. It can have any value. What’s the probability of its being near zero? Imagine the birth of a universe as a ‘baby’ branching off from an existing universe. Wormhole theory says there are plenty of universes – some more enormous than ours is today, others unimaginably smaller than an atom, and all sizes in between. The infant universe must copy its cosmological constant value from one of these other universes through a wormhole – ‘inherit’ it, you might say. It isn’t important to a human infant whether it inherits a talent for music; it becomes important only when the infant grows larger. It isn’t important to a baby universe whether it ‘inherits’ a cosmological constant value near zero. Its cosmological constant value won’t even be measurable until it’s quite a bit more grown-up. However, with all those assorted sizes of universes around, the infant is far more likely to inherit its cosmological constant value through wormhole attachments with large, cooler universes of the sort only possible when all those positives and negatives in the vacuum cancel out to zero. Coleman studied the probability of a universe (in wormhole theory) being a universe where the cosmological constant is near zero: our kind of universe. He found that any other sort of universe would be highly unlikely.
Wormholes and the Theory of Everything
Wormholes and baby universes fired the imaginations of many physicists. They began responding, disputing this and that, and offering alternative versions. That’s always a good sign. ‘The field of baby universes is in its infancy,’ quipped Hawking, ‘but growing fast.’15 Could wormholes and baby universes contribute to the search for a complete theory of the universe?
First of all, we’ve seen that the theory seemed to offer a new way of looking at the problem of the cosmological constant, the sticky question of the energy density in the vacuum, which ought to be shrinking the universe but isn’t. Did Hawking think wormholes are the theory that will solve this inconsistency between general relativity and quantum mechanics? ‘I would not go so far as that,’ Hawking said. ‘There is no fundamental inconsistency, but there are technical problems which wormholes don’t help.’16
Second, wormhole theory was a theory that didn’t break down if you followed it back to the ‘beginning’. With Einstein’s theories, if you follow things back to the Big Bang, you reach a singularity where the laws of physics as we know them break down. Hawking’s no-boundary proposal showed that in imaginary time there would be no singularity. Wormhole theory suggested that in imaginary time our universe may have begun as a baby universe branching off from another universe.
Third, wormhole theory linked quantum theory and relativity theory in a satisfying, geometric way, allowing us to think of quantum fluctuations, quantum wormholes and baby universes as not too different from the warping of spacetime and black holes on the astronomical level. The fundamental numbers in our universe, such as the masses and charges of particles and the cosmological constant, might be the result of the shape, the geometry of a labyrinth of interconnected universes.
Other theories can’t predict the masses and charges of particles. These are arbitrary elements in the theories. An alien who had never seen our universe couldn’t take these theories and use them to calculate what these fundamental quantities are, without peeking at the ‘real’ universe. We’ve seen that there is argument about whether wormholes might give us a way of understanding and calculating these fundamental numbers, or whether wormholes make their prediction less likely with any theory.
Theorists who work in the field of superstring theory, which says that the fundamental objects in the universe are not pointlike particles after all but tiny vibrating strings, were hoping their theory might eventually be able to predict particle masses and charges. Hawking was pessimistic. ‘If this picture of baby universes is correct, our ability to predict these quantities will be reduced.’17 If we knew how many universes there are out there and what their sizes are, it would be different, but we don’t know that. We can’t even see their joining on to or branching off our own. We can’t get an accurate picture of the shape of it all. We know only that if universes do join on or branch off, this changes the apparent values of such quantities as particle masses and charges. We end up with a small but definite amount of uncertainty in the predicted values.
Hawking meanwhile wasn’t worrying overly much about whether work like this was leading him to the Theory of Everything. His strategy is to concentrate on areas he understands, chipping away at the problem of what happens and how things work when relativity and quantum mechanics are taken together. What he discovers about the universe in this way should hold true, he thinks, regardless of what the theory of everything turns out to be and who finds it. His picture should fit in as part of the larger, or more basic, picture.
Saving History
Science fiction buffs will be disappointed if we don’t discuss the possibility that something larger than a particle can travel through a wormhole into another universe or into another part of our universe. There has been a lot of science fiction utilizing the idea. On the face of it this form of travel seems as though it ought to be feasible.
Science fiction and scientific speculation joined hands when Kip Thorne and his graduate students studied the possibility at the request in 1985 of Carl Sagan. Sagan needed a way to get the heroine of his novel Contact to a very distant location in space in no time at all. The problem is that a wormhole large enough for you or me or Sagan’s heroine to get through would be dangerously unstable. Even so small a disturbance as our presence would destroy the wormhole, and us with it. Thorne eventually thought he had found the answer, a way to hold the throat of a wormhole open using exotic material with a negative energy density – possible perhaps for a civilization much more advanced than our own. Hawking’s reaction to Thorne’s suggestion was characteristically succinct: ‘You’re wrong.’ ‘There is little politeness in our community when one of us believes the other is wrong,’ commented Thorne.18
Hawking set out to back up his opinion, and the result was something that he called the ‘chronology protection conjecture’. His objection was speci
fically to a wormhole that was a time machine. The ‘conjecture’ was that nature prevents the trajectory in spacetime that would allow one to travel back in time (a ‘closed, time-like curve’). The time-machine wormhole would always explode when you tried to activate it, and that explosion, Hawking declared, would ‘keep the universe safe for historians’. No one could travel back in time and change history. Thorne, in a paper written for Hawking’s sixtieth birthday in 2002, reminded his readers and listeners that the chronology protection conjecture was just that, a ‘conjecture’, ‘because both he and I were working with the laws of physics in a domain where we are uneasy about whether they really are correct’.19 Hawking had also argued that ‘the best evidence we have that time travel is not possible, and never will be, is that we have not been invaded by hordes of tourists from the future’,20 but he also wryly speculated that it could be that our time in history has become such a notoriously unpleasant tourist destination that visitors from the future always avoid it.
Kip Thorne called Hawking’s paper about the ‘chronology protection conjecture’ a ‘tour de force’, which didn’t of course necessarily mean he agreed with it. For Thorne’s sixtieth birthday, Hawking gave him a calculation of the quantum mechanical probability of success for a wormhole time machine. Hawking had not become any more optimistic. He came up with 1 part in 1060.21
What about a smaller black hole? When primordial black holes evaporate, what happens to things that fell into them earlier? Wormhole theory suggested that they may not necessarily return to our universe as particles. The particles instead may slip off into a baby universe. The information paradox rears its ugly head! Of course, this baby universe might join on again to our region of space-time. Then it would look like another black hole, which formed and evaporated. Things falling into one black hole would emerge as particles from the other black hole, and vice versa. That’s space travel of a sort – if you happen to be a particle – and no information would be lost.
Could wormholes and baby universes offer a solution to the ‘information paradox’? If anyone was raising his or her head hopefully, thinking that perhaps the universe also had a way of keeping itself safe from information loss, those hopes were not going to be encouraged by Hawking any time soon.
PART III
1990–2000
13
‘Is the end in sight for theoretical physics?’
THE BUILDING THAT housed the University of Cambridge Department of Applied Mathematics and Theoretical Physics from the middle of the twentieth century until 2000 was a grimy behemoth of no architectural distinction whatsoever. One had to conclude that those who worked there happily had to be pretty much oblivious to their surroundings or just loved the old place for other than aesthetic reasons.
The entrance was off Silver Street through a narrow alleyway, an asphalt car park and a red door. The interior of the building was institutional; the floor plan pieced together illogically. A corridor beyond a small reception area made an abrupt right turn past an ancient black metal lift, continued straight for a while, then bent and widened past letterboxes and overstuffed bulletin boards with lecture and seminar notices and some lewd graffiti, narrowed again abruptly, and ended at the door of a large common room.
For decades, it was in this common room that the DAMTP gathered for tea every afternoon at four. For most of the day the room was deserted and dimly lighted. The colour scheme showed a preference for lime green – in vinyl armchairs grouped around low tables, woodwork and the lower halves of the pillars supporting the high ceiling. There was a table with stacks of scientific publications, a rogues’ gallery of small photos of present students and faculty on one wall, and formal portraits of former Lucasian professors on another. At the far end of the room enormous windows provided a view of a blank wall across the alley and admitted little light.
Hawking’s office and a number of others opened off this common room. On his door there was a small placard: ‘QUIET PLEASE, THE BOSS IS ASLEEP’. Probably not true. Hawking spent long hours, over the years, working in that pleasant, high-ceilinged office with his computers, photos of his children, a few plants, a life-size picture of Marilyn Monroe on the door and always, after 1985, one of his nurses in attendance. His one oversized window overlooked the car park.
Hawking’s day there usually began at 11 a.m. His secretary reviewed his schedule with him. In the late 1980s, that became something of a joke. They seldom managed to follow it, and anyone who had an appointment with Hawking had to remain flexible.
The day continued with the soft clicking of his hand-held pressure switch. Propped in his chair, Hawking watched the computer screen impassively and selected words to communicate with visitors and interviewers, consult colleagues, advise students, converse over the telephone, write lectures or answer correspondence. Sometimes you heard the soft hum of his wheelchair motor as he guided it by means of a joystick through the common room and corridors to other rooms in the building for meetings and seminars. A nurse went with him. At intervals the well-modulated computer voice requested his nurse to adjust his position in the chair or suction fluid that accumulates in his breathing passage.
Hawking’s nursing staff in the late 1980s was large and competent and varied as to age and sex. They seemed indulgently fond of Hawking and devoted to the task of making him look nice, keeping his hair brushed, his glasses clean, his chin wiped of the saliva that runs from his mouth, and, as they put it, to ‘getting him sorted out’ many times a day. Hawking had no choice but to be totally dependent on others, but there was never any air of helplessness about him. On the contrary he was vigorous and decisive, unquestionably in charge of his life. His staff said that the strength of his personality made working for him and with him both rewarding and demanding. I was never aware of the unpleasant competition among the nurses that Jane Hawking would later write about.
In the late eighties the mail had become an impossible burden for Hawking’s research assistant, his personal assistant Sue Masey and one of his nurses who now helped them. They were struggling valiantly to write thoughtful answers to letters, poems, videotapes from all over the world, many of which told moving stories and deserved a personal response. It was sad to have to resort increasingly to polite preprinted postcards, but it would have taken all Hawking’s waking hours to handle even a fraction of his mail.
At 1 p.m., rain or shine, Hawking would propel his wheelchair with portable computer attached out into the narrow Cambridge streets, sometimes accompanied only by a nurse, sometimes by students, who trotted to keep up with him. It was a short journey through the heart of Cambridge, past the up-market shops in King’s Parade, King’s College Chapel and the Senate House, to Gonville and Caius, to lunch with other Fellows of his college. There a nurse arranged a bib around his shoulders and spooned food into his mouth. Eating was no deterrent to conversation for Hawking, whose finger moved continually on his hand-held device, choosing words to talk with those near him.
After lunch there was the return journey to the DAMTP. By then Hawking was notorious on at least two continents for his hair-raising wheelchair driving. Students would bound ahead into traffic on King’s Parade and Silver Street to stop cars, lorries and bicycles as he recklessly barrelled ahead assuming the right of way. Acquaintances feared he was more likely to be crushed by a lorry than die from ALS.
At 4 p.m. Hawking would emerge again from behind his lime green door. Teatime was a ritual in the department, and the empty, cavernous room would become suddenly deafeningly noisy with voices and the clatter of teacups. Most of the assembled physicists and mathematicians dressed as though they were on a construction site. Someone has commented that Hawking’s ‘relativity group’ looked like a rock group on a bad day. Their talk wasn’t small talk. It ranged among wormholes, Euclidean regions, scalar fields and black holes. Equations were scrawled on the low tables. Hawking’s wry wit set the tone in his corner of the room, but former students claim that a few remarks from him during tea were often mo
re valuable than an hour’s lecture by somebody else. Hawking had mastered the art of packing a lot into a few words. Reading over notes later, you realized how precisely he had chosen his words to say exactly what he meant.
At four thirty the common room would empty as rapidly as it had filled, and all but one of the long, fluorescent lighting fixtures were switched off. Hawking would glide back into his office to work until seven. In the late afternoon his students found him more available to help them.
On some evenings Hawking dined in college, or, in a specially equipped van bought with award money from the 1988 Israeli Wolf Prize in physics, he would be driven to a concert or the theatre. When there was a concert at Tim’s school, he would go to hear Tim play the cello with the orchestra. Tim was a good cellist, following in the footsteps of his sister Lucy. On other evenings Hawking would work late in his office.
It was on one of those late evenings, in December 1989, that I went in to talk with him about plans for writing my first book about him. We discussed black holes and I read him a paragraph I’d written to make sure I had it right. When I paused to complain that my writing sounded dull because my editor was opposed to any fun or humour in a book about science, Hawking said, ‘It should be fun. Tell him I said so.’ I was certain this would win the argument with my editor. After all, Hawking’s own book was flying off the shelves and had sold millions of copies. At one point, as I watched the words flit across the screen, I was startled that the message was ‘Would you please pull me up a little higher in my chair?’ Realizing after a moment of confusion that this wasn’t meant for me, I glanced over at the young male nurse sitting near us. He came to life, picked up Hawking and set him down in a better position.
Stephen Hawking, His Life and Work Page 21
