The Perfect Theory (24 page)

Bekenstein wanted to address the paradox of what would happen if you threw a box of stuff into a black hole. The box could contain anything: encyclopedias, hydrogen gas, a lump of iron. To keep it simple, let's consider our box of gas. The box will disappear into the hole and very rapidly the no-hair theorem will kick in. After the event, there will be no way of knowing what originally fell in. All information about the box will be lost. But if this is so, all the disorder of the gas in the box—all that entropy—has also disappeared, and the total entropy of the universe has gone down. Black holes appear to violate the second law of thermodynamics.

The way that Bekenstein found to salvage the second law of thermodynamics was to use Hawking's result. If you throw stuff into a black hole, the area of the event horizon never decreases—it either stays the same or increases. And so Bekenstein concluded that if the second law of thermodynamics is to be satisfied in the universe, black holes
must
have entropy, directly related to the surface area of the event horizon. The increase in the area of the black hole would more than compensate for the loss of disorder, sucked in behind the event horizon, and the entropy of the universe could never decrease. Yet, if Bekenstein pushed his solution of the paradox to its ultimate consequences, he came up with a bizarre result. If a black hole has entropy, then, just like the box of gas molecules, it should also have a temperature. Even Bekenstein felt he was going too far and wrote in his paper,
“We emphasize that one should not regard T as the temperature of the black hole; such an identification can easily lead to all sort of paradoxes, and is thus not useful.”

Despite Bekenstein's reservations, Hawking found his claim galling. According to the laws of thermodynamics, there is no way to increase the entropy of a black hole without causing it to radiate heat in some way. For Hawking, this was going too far. To him, it was obvious that black holes were black: things could fall into black holes, but they definitely couldn't come out. The fact that the overall area of black holes couldn't decrease, as he himself had shown, might look like entropy, but it wasn't
really
entropy—entropy was just a useful analogy for explaining the behavior.

But there were hints that Bekenstein might be right and Hawking wrong. For a start, in 1969 Roger Penrose found that a spinning black hole, described by Kerr's solution, could emit energy. Imagine a fast-moving particle traveling at close to the speed of light as it falls into the orbit of a Kerr black hole. If it decays into two particles, one of which is sucked into the event horizon, the remaining particle can be sped up and thrown out with more energy than went in, conserving the total energy of the system, and the universe. With this odd process, known as Penrose superradiance, black holes are effectively emitting energy as if they are shining in some bizarre way. But there were more ideas floating around. In 1973 Stephen Hawking visited Yakov Zel'dovich and his young colleague Alexei Starobinsky and learned that they had worked out what would happen to a Kerr black hole: it would strip away the quantum vacuum that surrounded it, using its energy to emit energy and indeed radiate.

Hawking decided to use quantum physics to think about particles close to the event horizon of a black hole, where strange things could happen. What he found there was strange indeed. Quantum physics allows pairs of particles and antiparticles to form out of the vacuum. In ordinary circumstances these particles are created and then, just as quickly, collide with each other and are annihilated, completely disappearing. But, as Hawking found, the situation is very different near the event horizon: some of the antiparticles will be sucked into the black hole while the particles remain. This process will happen again and again, and as the antiparticles are sucked in, the black hole will, slowly and surely, emit a stream of energetic particles. Hawking worked out the details of what would happen if the particles were massless, like photons. And he found that, observed from afar, the black hole would shine with an incredibly low brightness, very similar to a dim star. And just like a star, our sun, for example, it would be possible to assign it a temperature. By looking at the light our sun emits, we can measure its surface temperature to be about 6,000 degrees Kelvin. In other words,
because
of quantum physics, Hawking had found that the black holes predicted by general relativity emitted light and had a temperature.

It was a remarkably clean and unambiguous mathematical result with far-reaching consequences. Hawking's calculation was able to show that the temperature with which a black hole shines is inversely proportional to its mass. So, for example, a black hole with the mass of the sun would have a temperature of a billionth of a Kelvin, and a black hole with the mass of the moon would have a temperature of about 6 degrees Kelvin. As the black hole shines, it sheds some of its mass. This process happens incredibly slowly. A black hole with the mass of the sun would take an inordinately long time to shed all its mass, or “evaporate,” as Hawking described it. But much smaller black holes could evaporate much more quickly. So, for example, a black hole with a mass of about a trillion kilograms (a small black hole from an astrophysical point of view) would evaporate within the lifetime of the universe, releasing a burst of energy in the last tenth of a second. As Hawking described it, it would be “a fairly small explosion by astronomical standards but it is equivalent to about 1 million 1-Mton hydrogen bombs.” Hawking called his paper, which he would end up publishing in
Nature,
“Black Hole Explosions?”

 

When Stephen Hawking presented his talk at the Oxford symposium, he sat awkwardly in a wheelchair at the front of the auditorium. He had something groundbreaking to say, and he spoke clearly and purposefully, explaining his calculations to the gathered audience. When he finished, he was met by near silence. As Philip Candelas, a student of Dennis Sciama at the time, recalls,
“People treated Hawking with great respect but no one really understood what he was saying.” As Hawking himself later recalled,
“I was greeted with general incredulity. . . . The chairman of the session . . . claimed it was all nonsense.” In the review of the Oxford symposium in
Nature,
it was acknowledged that “the main attraction of the conference was a presentation by the indefatigable S. Hawking,” yet the author of the review was skeptical about his prediction of exploding black holes, writing, “Exciting though this prospect may be, no plausible physical mechanism could be discerned which might lead to such a dramatic effect.”

It would take some time for Hawking's discovery to sink in, but a few people immediately realized the significance of what he had done. Dennis Sciama referred to Hawking's paper as “one of the most beautiful in the history of physics” and immediately set some of his students to work on pushing it further. John Wheeler described Hawking's result as “like candy rolling on the tongue.” Bryce DeWitt set about rederiving Hawking's result his own way and wrote a review of black hole radiation that would convince a whole new group of people.

Hawking's calculation of black hole radiation wasn't quantum gravity. It didn't involve quantizing the gravitational field by working out the rules and processes that gravitons would be subjected to, as DeWitt and so many had been trying and failing to do. But it did successfully mix the quantum and general relativity to give an interesting hard result, something that quantum gravity, if it ever came to fruition, might refer to and explain in more detail. And so, over the next few years, black hole radiation brought new hope to the impossible challenge of quantizing gravity. Hawking firmly trained his sights on quantizing not only objects within spacetime but spacetime itself. Training a new set of students to work on his program, Hawking would remain intensely focused on quantum gravity for the next forty years. It was fitting, then, that ten years after Paul Dirac retired from the Lucasian Professorship at DAMTP, Stephen Hawking was appointed to it, a position he ended up holding for over twenty-five years.

When John Wheeler was asked by a young student how he could best be prepared for working on quantum gravity—would it be better to be an expert in general relativity or in quantum physics?—he replied that it would probably be better if the student worked on something else altogether. It was wise advice. Stubborn infinities continued to thwart every attempt at quantizing general relativity, and it seemed that any endeavor in the quest for quantum gravity was destined for failure.

Yet it was also true, as Hawking had shown with his spectacular result, that when general relativity and quantum physics did meet, unexpected things happened. Black holes had entropy and emitted heat, which went against the idea relativists had of black holes being, well, black. But Bekenstein's and Hawking's calculations also seemed to shed new light on the quantum, to which general relativity seemed to do odd things. In a usual, run-of-the-mill physical system, like a box of gas, the entropy is related to volume. The more volume there is, the more possible ways there are to randomize things and create disorder, the hallmark of entropy. All that randomness, that disorder, is stored away
in
the box. The direct relation between entropy and volume is part and parcel of textbook thermodynamics. But what Bekenstein and Hawking found, as we saw, is that the entropy of the black hole is related to the
area
of its surface and not to the volume it takes up in space. That's like our box full of gas particles somehow storing its entropy in the walls of the box instead of in the random movements of the gas particles within. How do we store entropy on a black hole's surface, which, as we know, should be simple and hairless, just uniformly emitting light through Hawking radiation?

Intractable and inscrutable, with all of the new mind-boggling results in black holes, quantum gravity had become the ultimate challenge for clever young physicists. Yet, while quantum gravity became a veritable battleground of ideas that would play out over the following decades, another battle was taking place in general relativity. Instead of thought experiments and clever mathematics, it involved instruments and detectors trying to measure elusive waves in the fabric of spacetime emanating from colliding black holes.

Chapter 10

J
OSEPH WEBER WAS
once heralded as the first observer of gravitational waves. He created the field of gravitational wave experiments almost single-handedly. In the late 1960s and early 1970s, Weber's results were celebrated as major accomplishments for relativity. But by 1991, he had been brought low. As he told his local newspaper that year,
“We're number one in the field, but I haven't gotten any funding since 1987.”

On the face of it, Joe Weber's situation seemed bizarrely unfair. At the height of his career, his results were discussed at all the major conferences of general relativity alongside neutron stars, quasars, the hot Big Bang, and radiating black holes. They were the subject of countless papers trying to explain them. Weber was a shoo-in for a Nobel Prize. And then, just as quickly as he had risen to prominence, Weber was cast out into the hinterland of academia. Shunned by his colleagues, rejected by the funding agencies, unable to publish in any of the mainstream journals, Weber was condemned to a long and lonely scientific death, an odd and uncomfortable footnote in the history of general relativity. Some would even say that it was only after Weber's fall that the real quest for gravitational waves began.

 

Gravitational waves are to gravity what electromagnetic waves are to electricity and magnetism. When James Clerk Maxwell showed that electricity and magnetism could be unified into one overarching theory, electromagnetism, he set the foundations for Heinrich Hertz to show that there would be electromagnetic waves that would oscillate at a range of frequencies. At visible frequencies, these waves would be the light that our eyes are so attuned to picking up and interpreting. At longer frequencies, these would be the radio waves that bombard our radio receivers, transmit the wireless information to and from our laptops, and allow us to see the immensely energetic quasars out in the far recesses of the universe.

Within months of coming up with general relativity, Albert Einstein had shown that, just like electromagnetism, in his new theory, spacetime should contain waves. The waves would be ripples in space and time themselves. Spacetime acts sort of like a pond; when you throw in a pebble, it sends out ripples that propagate from one end to the other. Just like electromagnetic waves and the ripples of water in a pond, gravitational waves can carry energy from one place to another.

Unlike electromagnetic waves, gravitational waves have proved incredibly difficult to find. They are very inefficient at carrying energy out of a gravitating system. As the Earth orbits around the sun at a distance of 150 million kilometers, it slowly loses energy through gravitational waves and drifts closer to the sun, but the distance between the Earth and the sun shrinks at a minuscule rate, about the width of a proton per day. This means that during its whole lifetime, the Earth will drift closer to the sun by a mere
millimeter.
Even if something is large enough to generate a copious amount of gravitational waves, those waves become the faintest whispers when they travel through spacetime. Spacetime is actually less like a pond of water and more like an incredibly dense sheet of steel that barely trembles at the hardest of kicks.

Gravitational waves were hard for other physicists to stomach. For almost half a century after Einstein argued that they existed, many refused to believe they were real. They were seen as yet another mathematical oddity that could be explained away with a deeper understanding of Einstein's general theory of relativity. Arthur Eddington, for one, staunchly rejected the existence of gravitational waves. Having repeated Einstein's calculation in which he worked out how gravitational waves would appear in general relativity, he went on to argue that they were an artifact of how you chose to describe space and time. They arose because of a mistake, an ambiguity in labeling positions in space and time, and could be done away with completely. These waves weren't real waves, and unlike electromagnetic waves that traveled at the speed of light, Eddington dismissed gravitational waves for traveling at the
“speed of thought.” In a surprising turn of events, Einstein himself decided that he had been mistaken in his original calculation, and in 1936 he submitted a paper along with one of his young assistants, Nathan Rosen, to the
Physical Review
in which they argued that gravitational waves simply couldn't exist.