Hawking expected his calculations to show that rotating black holes produce the radiation the Russians predicted. What he discovered was something far more dramatic: ‘I found, to my surprise and annoyance, that even nonrotating black holes should apparently create and emit particles at a steady rate.’14 At first he thought something had to be wrong with his calculations and he spent many hours trying to find his error. He was particularly eager that Jacob Bekenstein should not find out about his discovery and use it as an argument supporting his idea about event horizons and entropy. But the more Hawking thought about it, the more he had to admit that his own calculations were certainly not far off the mark. The clincher was that the spectrum of the emitted particles was precisely what you’d expect from any hot body.
Bekenstein was right: You cannot make entropy decrease and the universe get more orderly by throwing matter carrying entropy into black holes as though they were great rubbish bins. As matter carrying entropy goes into a black hole, the area of the event horizon gets larger: the entropy of the black hole increases. The total entropy of the universe both inside and outside black holes hasn’t become any less.
But Hawking was on to a bigger puzzle now. How can black holes possibly have a temperature and emit particles if nothing can escape past the event horizon? He found the answer in quantum mechanics.
When we think of space as a vacuum, we haven’t got it quite right. We’ve already seen that space is never a complete vacuum. Now we’ll find out why.
The uncertainty principle means we can never know both the position and the momentum of a particle at the same time with complete accuracy. It means something more than that: we can never know both the value of a field (a gravitational field or an electromagnetic field, for instance) and the rate at which the field is changing over time with complete accuracy. The more precisely we know the value of a field, the less precisely we know the rate of change, and vice versa: the seesaw again. The upshot is that a field can never measure zero. Zero would be a very precise measurement of both the value of the field and its rate of change, and the uncertainty principle won’t allow that. You don’t have empty space unless all fields are exactly zero: no zero – no empty space.
Instead of the empty space, the true vacuum, that most of us assume is out there, we have a minimum amount of uncertainty, a bit of fuzziness, as to just what the value of a field is in ‘empty’ space. One way to think of this fluctuation in the value of the field, this wobbling a bit towards the positive and negative sides of zero so as never to be zero, is as follows:
Pairs of particles – pairs of photons or gravitons, for instance – continually appear. The two particles in a pair start out together then move apart. After an interval of time too short to imagine they come together again and annihilate one another – a brief but eventful life. Quantum mechanics tells us this is happening all the time, everywhere in the ‘vacuum’ of space. These may not be ‘real’ particles that we can detect with a particle detector, but they are not imaginary. Even if they are only ‘virtual’ particles, we know they exist because we can measure their effects on other particles.
Some of the pairs will be pairs of matter particles, fermions. In this case, one of the pair is an antiparticle. ‘Antimatter’, familiar from fantasy games and science fiction (it drives the starship Enterprise), isn’t purely fictional.
You may have heard that the total amount of energy in the universe always stays the same. There cannot be any suddenly appearing from nowhere. How do we get around that rule with these newly created pairs? They’re created by a very temporary ‘borrowing’ of energy. Nothing permanent at all. One of the pair has positive energy. The other has negative energy. The two balance out. Nothing is added to the total energy of the universe.
Hawking reasoned that there will be many particle pairs popping up at the event horizon of a black hole. The way he pictures it, a pair of virtual particles appears. Before the pair meet again and annihilate, the one with negative energy crosses the event horizon into the black hole. Does that mean the positive energy partner must follow its unfortunate companion in order to meet and annihilate? No. The gravitational field at the event horizon of a black hole is strong enough to do an astounding thing to virtual particles, even those unfortunates with negative energy: it can change them from ‘virtual’ to ‘real’.
The transformation makes a remarkable difference to the pair. They are no longer obliged to find one another and annihilate. They can both live much longer, and separately. The particle with positive energy might fall into the black hole, too, of course, but it doesn’t have to. It’s free of the partnership. It can escape. To an observer at a distance it appears to come out of the black hole. In fact, it comes from just outside. Meanwhile, its partner has carried negative energy into the black hole (Figure 6.2).
The radiation that’s emitted by black holes in this manner is now called Hawking radiation. And with Hawking radiation, his second famous discovery about black holes, Hawking showed that his first famous discovery, the second law of black hole dynamics (that the area of the event horizon can never decrease), doesn’t always hold. Hawking radiation means that a black hole might get smaller and eventually evaporate entirely. It was a truly radical concept.
Figure 6.2. Hawking radiation
How does Hawking radiation make a black hole get smaller? As the black hole transforms virtual particles to real particles, it loses energy. How can this happen, if nothing escapes through the event horizon? How can it lose anything? It’s rather a trick answer: when the particle with negative energy carries this negative energy into the black hole, that makes less energy in the black hole. Negative means ‘minus’, which means less.
That’s how Hawking radiation robs the black hole of energy. When something has less energy, it automatically has less mass. Remember Albert Einstein’s equation, E = mc2. The E stands for energy, the m for mass, the c for the speed of light. When the energy (on one side of the equal sign) grows less (as it is doing in the black hole), something on the other side of the equal sign grows less too. The speed of light (c) can’t change. It must be the mass that grows less. So, when we say a black hole is robbed of energy, we’re also saying it’s robbed of mass.
Keep this in mind and recall what Newton discovered about gravity: any change in the mass of a body changes the amount of gravitational pull it exerts on another body. If the Earth becomes less massive (not smaller this time, less massive), its gravitational pull feels weaker out where the moon is orbiting. If a black hole loses mass, its gravitational pull becomes weaker out where the event horizon (the radius-of-no-return) has been. Escape velocity at that radius becomes less than the speed of light. There is now a smaller radius where escape velocity is the speed of light. A new event horizon forms closer in. The event horizon has shrunk. This is the only way we know that a black hole can get smaller.
If we measure Hawking radiation from a large black hole, one resulting from the collapse of a star, we’ll be disappointed. A black hole this size has a surface temperature of less than a millionth of a degree above absolute zero. The larger the black hole the lower the temperature. Hawking says, ‘Our 10-solar-mass black hole might emit a few thousand photons a second, but they would have a wavelength the size of the black hole and so little energy we would not be able to detect them.’15 The way it works is that the greater the mass, the greater the area of the event horizon. The greater the area of the event horizon, the greater the entropy. The greater the entropy, the lower the surface temperature and the rate of emission.
Exploding Black Holes?
However, as early as 1971 Hawking had suggested that there was a second type of black hole: tiny ones, the most interesting ones about the size of the nucleus of an atom. These would positively crackle with radiation. The smaller a black hole is, the hotter its surface temperature. Referring to these tiny black holes, Hawking declares: ‘Such holes hardly deserve [to be called] black: they really are white hot.’16
‘Pri
mordial black holes’, as Hawking called them, would not have formed from the collapse of stars. They would be relics of the very early universe when there were pressures that could press matter together extremely tightly. A primordial black hole would by now be much smaller even than when it started out. It’s been losing mass for a long time.
Hawking radiation would have drastic consequences for a primordial black hole. As the mass grows less and the black hole gets smaller, the temperature and rate of emission of particles at the event horizon increase. The hole loses mass more and more quickly. The lower the mass, the higher the temperature – a vicious circle!
How would the story end? Hawking guessed that the little black hole disappears in a huge final puff of particle emission, like millions of hydrogen bombs exploding. Will a large black hole ever explode? Some models have it that the universe will come to an end long before it reaches that stage.
The idea that a black hole could get smaller and finally explode was so much the reverse of everything anybody thought about black holes in 1973 that Hawking had grave doubts about his discovery. For weeks he kept it under wraps, reviewing the calculations in his head. If he found it so hard to believe, it was fearful to predict what the rest of the scientific world would make of it. No scientist enjoys the prospect of ridicule. On the other hand, Hawking knew that if he was right, his findings would revolutionize astrophysics. At one point he locked himself in the bathroom to think about the problem. ‘I worried about this all over Christmas, but I couldn’t find any convincing way to get rid of [these findings].’17
Hawking tested his idea on his close associates. The reception was mixed. Martin Rees, a friend since their days as graduate students at Cambridge, approached their old thesis supervisor, Denis Sciama, with the exclamation, ‘Have you heard? Stephen’s changed everything!’ Sciama rallied to Hawking’s support, urging him to release his findings. Hawking complained that Penrose phoned him, full of enthusiasm, just as he was sitting down to his 1974 birthday dinner, ready to tuck into his goose. He appreciated Penrose’s excitement, Hawking said, but, once into the subject, they talked too long. His dinner got cold.18
Hawking agreed to present his bizarre discovery in February in a paper at the Rutherford–Appleton Laboratory south of Oxford. Sciama was the organizer of the meeting, the Second Quantum Gravity Conference. Hawking had hedged his bets a little by putting a question mark in the title of his paper, ‘Black Hole Explosions?’, but, travelling to Oxford, he still agonized over his decision to announce his discovery.
The short presentation, including slides of equations, was greeted with silence that became embarrassing, and few questions. Hawking’s arguments had gone over the heads of many in the audience, experts in other fields. But it was more or less obvious to everyone that he was proposing something completely contrary to accepted theory. Those who did understand were shocked and unprepared to argue with him. The lights were snapped back on. The moderator, John G. Taylor, a respected professor from the University of London, rose and declared: ‘Sorry, Stephen, but this is absolute rubbish.’19
Hawking published this ‘rubbish’ the next month in the prestigious science magazine Nature.20 Taylor and Paul C. W. Davies disagreed with Hawking in a paper in the same issue.21 Within a few days physicists all over the world were discussing Hawking’s shocking idea. Zel’dovich had reservations at first, but when Kip Thorne was next in Moscow he had an urgent summons to visit the Soviet physicist. When Thorne arrived, Zel’dovich and Starobinsky greeted him with hands in the air, as though they were in the old American West and Thorne had them at gunpoint: ‘We give in. Hawking was right. We were wrong.’22
Some were calling Hawking’s discovery the most significant in theoretical physics in years. Sciama said the paper was ‘one of the most beautiful in the history of physics’.23 John Wheeler, always a master with words, said that talking about Hawking’s beautiful discovery was like ‘rolling candy on the tongue’.24 Kip Thorne commented that as Stephen had lost the use of his hands he had developed ‘geometrical arguments that he could do pictorially in his head … a very powerful set of tools that nobody else really had. And if you are the only master in the world of these new tools, that means there are certain kinds of problems you can solve and nobody else can.’25 Things were certainly looking up.
Hawking took more time and care putting together a second paper about his discovery. Communications in Mathematical Physics, the journal to which he submitted it in March 1974, lost his paper and didn’t publish it until April 1975,26 after he resubmitted it. In the meantime, Hawking and his colleagues went on studying ‘Hawking radiation’ from many different angles. By the time the next four years had passed – and after a joint paper written by Hawking and Jim Hartle appeared in 197627 – Hawking radiation had been generally accepted throughout the theoretical physics world. Most agreed that Hawking had made a significant breakthrough. He had used the activity of virtual particles to explain about something that had arisen from the theory of relativity – black holes. He’d taken a step towards linking relativity and quantum physics.
PART II
1970–1990
7
‘These people must think we are used to an astronomical standard of living’
WHEN LUCY WAS born on 2 november 1970, the Hawkings had recently purchased the house they had been renting in Little St Mary’s Lane. Stephen’s parents had given them money to fix it up and qualify for a mortgage. The work had finally been completed when Jane was eight months pregnant.
Stephen was still insisting on pulling himself up and down the stairs and dressing himself in the morning and undressing at night. His comment that he had plenty of time to think about photons at the event horizons of black holes while getting ready for bed is one of very few admissions he has made that any of this was extremely slow and arduous. His walking, however, finally became so perilous that he consented to a wheelchair. He’d lost the battle to stay on his feet. Friends watched with sadness, but Hawking’s humour and strength of purpose didn’t fail him.
Hawking’s loss of the use of his hands, meaning he could no longer write and draw equations and diagrams, did not happen overnight. Over the years of gradual loss, he had time to adapt and train ‘his mind to think in a manner different from the minds of other physicists. He thinks in new types of intuitive mental pictures and mental equations that, for him, have replaced paper-and pen drawings and written equations,’ said Kip Thorne.1 Listening to Hawking himself, you get the impression that he believes he might have chosen this way of working even if he had full use of his hands: ‘Equations are just the boring part of mathematics. I prefer to see things in terms of geometry.’2 The calculations involved in the discovery of Hawking radiation were done almost entirely in his head.
After Lucy’s birth, Jane was juggling an all but impossible schedule, trying to finish her Ph.D. thesis while caring for Stephen, her toddler Robert and now her new baby girl. Her mother and a neighbour’s nanny helped with the children whenever they could. The cottage in Little St Mary’s Lane was a delight. As the children grew and Lucy became a proficient toddler, she joined her brother to play among the flowering plants and ancient stone markers in the Little St Mary’s churchyard across the lane. Jane remembers summers with the windows open and the happy voices of her children ‘piping in the churchyard’.
When Hawking’s January 1971 entry in the yearly Gravity Research Foundation Award, titled ‘Black Holes’, won top prize, the prize money allowed the Hawkings to buy a new car. Hawking had a salary from Caius and research assistantships from the DAMTP and the Institute of Astronomy. However, the family budget was still tight and not adequate to pay for a private school for Robert when he reached school age. He began instead at the fine local school, Newnham Croft Primary School, which my own daughter would attend fifteen years later. Robert seemed to be following in his father’s footsteps, excelling in maths and slow learning to read, but it was a new era, when ‘slow learning to read’ was not
to be accepted without taking proactive steps. Together with Stephen’s parents, Jane and Stephen bought half shares in a small terraced house. The rent from it would provide money for Robert’s fees at a private school where his mathematical prowess could be particularly respected and encouraged, as well as a retirement income for his grandparents.3 Robert transferred to the Perse School in Cambridge when he was seven.
The Hawkings continued to try to keep Stephen’s illness in the background of their lives and not allow it to become the most important thing about him or about them. They made a habit of not looking to the future. As far as the rest of the world could see, they succeeded so well that it came as a surprise when Jane Hawking mentioned how terrible the difficulties sometimes were. Discussing honours that had come her husband’s way, she told an interviewer: ‘I wouldn’t say [this overwhelming success makes] all the blackness worthwhile. I don’t think I am ever going to reconcile in my mind the swings of the pendulum we have experienced from the depths of a black hole to the heights of all the glittering prizes.’4 To judge from everything Stephen Hawking has written, he barely noticed the depths. Talking about them in any but the most offhand manner, which is the most he allows himself, would be for him a form of giving in, of defeat, and could undermine his resolute disregard of his problems. Most of the time, he continued to refuse to discuss his illness even with Jane, but that didn’t, for her, make it any less the gorilla in the room.
Stephen Hawking, His Life and Work Page 10