Throughout the 1950s and 1960s both the strong and weak forces were systematically unpeeled and studied in detail. As they became better understood, a mathematical similarity began to emerge between them and the electromagnetic force, suggesting there might be one unified force that manifests as one of the three different forces depending on the situation. By the late 1960s, Steven Weinberg of MIT, Sheldon Glashow of Harvard, and Abdus Salam of Imperial College in London had proposed a new way of packing at least two of the forces, the electromagnetic and weak forces, together into one electroweak force. The strong force couldn’t yet be brought into the mix but looked so similar to the other forces that there was a belief that it should be possible to come up with a “grand unified theory” of the electromagnetic, weak, and strong forces. In the 1970s, the electroweak theory and the theory of the strong force were shown to be renormalizable, just like QED. All the pesky infinities that arose in their calculations could be replaced by known values, making the theories eminently predictable. The combination of the electroweak and strong theories became known as the standard model and made accurate predictions that were confirmed in laboratories like the gigantic particle accelerator at CERN in Geneva, Switzerland. This almost completely unified, yet powerful and predictive quantum theory of the three forces—electromagnetic, weak, and strong—was universally accepted.
By all, that is, except Paul Dirac. Although he was impressed with the younger generation that had put together the standard model and marveled at some of the mathematics that had been used, he repeatedly railed against the infinities and what he considered to be the nefarious trick of renormalization. In the few public lectures he gave in which he deigned to mention the standard model, he chided his colleagues for not trying harder to find a better theory with no infinities. Toward the end of his career at Cambridge, Dirac became more and more isolated. He stubbornly rejected the developments in quantum physics. Despite his craving for privacy, he felt ignored by the rest of the physics world, which had embraced QED and saw him as a figure of the past. So he withdrew, keeping to his study at St. John’s College and avoiding the department where he held his professorship, paying no attention to the great discoveries in general relativity that were coming from Dennis Sciama, Stephen Hawking, Martin Rees, and their collaborators. As one of their contemporaries at Cambridge recalls, “Dirac was this ghost we rarely saw and never spoke to.” He retired from his position as the Lucasian Professor in 1969 and moved to Florida to take up a professorship there. In his final years he wouldn’t have been surprised to see general relativity refuse to bow to the techniques of renormalization.
Bryce DeWitt had no idea what a struggle his pursuit of a quantum theory of gravity would be. While working with Julian Schwinger at Harvard, he had witnessed the birth of QED firsthand. When he decided to tackle gravity, DeWitt chose to treat it just like electromagnetism and tried to reproduce the successes of QED. There were similarities between electromagnetism and gravity: both were long-range forces that could extend over large distances. In QED, the transmission of electromagnetic force could be described as being carried by a massless particle, the photon. You can view electromagnetism as a sea of photons zipping back and forth between charged particles, like electrons and protons, pushing them apart or pulling them together, depending on their relative charges. DeWitt approached a quantum theory of gravity in an analogous way, replacing the photon with another massless particle, the graviton. These gravitons would bounce back and forth between massive particles, pulling them together to create what we call the gravitational force. This approach abandoned all the beautiful ideas of geometry. While gravity was still described in terms of Einstein’s equations, DeWitt chose to think of it as just another force, bringing to bear all the techniques of QED.
For the next twenty years, DeWitt tried to figure out how to quantize the graviton, but he found it a gargantuan challenge. Once again Einstein’s field equations were simply too unwieldy and entangled to be dealt with easily. He watched as the theory of the other forces developed and saw the similarities in the difficulties. But while the problems with unifying the strong, weak, and electromagnetic forces seemed to fall away, general relativity was obstinate, unwilling to be shoehorned into the same set of quantum rules that seemed to apply to the other three forces. Through his battle, DeWitt was not alone: Matvei Bronstein, Paul Dirac, Richard Feynman, Wolfgang Pauli, and Werner Heisenberg had all had a go at quantizing the graviton at some point before him. Steven Weinberg and Abdus Salam, the architects of the successful model of the electroweak force, attempted to apply the techniques that they had developed for the standard model, but they too found that gravity was too difficult.
As DeWitt labored on, grappling with the graviton and trying to quantize it, isolated pockets of interest in his work developed. John Wheeler cheered him on and set his students working on it, as did the Pakistani physicist Abdus Salam, Dennis Sciama in Oxford, and Stanley Deser, based in Boston. But in general, reactions to work on quantum gravity were mixed and often cool. Michael Duff, a former student of Salam, recalls presenting his results on quantum gravity at a conference in Cargèse, Corsica, and being “greeted with hoots of derision.” A student of Dennis Sciama named Philip Candelas, who was working on quantum properties of fields living on spacetimes with different geometries, heard that members of the faculty of physics at Oxford were muttering that he “wasn’t doing physics.” Quantum gravity was still too unformed compared to the work on quantizing the other forces. To many, it was perceived as a waste of time.
In February 1974, the United Kingdom was at a standstill. The price of oil had shot up, a succession of ineffectual governments had been trying to stem the rise of inflation, and the country was hamstrung by industrial strife. Every now and then the working week was shortened to three days to save energy, and rolling power cuts meant that evening meals were often eaten by candlelight. It was during these dark days that a meeting was convened to take stock of the progress in quantizing gravity, almost twenty-five years after DeWitt first set to work. Despite the somber economic climate, euphoria reigned at the start of the Oxford Symposium on Quantum Gravity. The predictions of the standard model of particle physics developed by Glashow, Weinberg, and Salam were being spectacularly confirmed at the massive particle accelerator at CERN. Surely quantum gravity would have to follow close behind.
Yet, as the speakers stood up and presented hints of solutions and ideas, again and again, the same problem seemed to scupper the most promising and popular route for quantizing gravity. DeWitt’s approach of forgetting about geometry and thinking of gravity simply as a force was not working. The organizers, paraphrasing Wolfgang Pauli, fretted, “What God hath torn asunder, let no man join.” The problem was that general relativity was not like QED and the standard model. With QED and the standard model it was always possible to renormalize all the masses and charges of the fundamental particles and get rid of the infinities that cropped up to get sensible results. But if the same tricks and techniques were applied to general relativity, the whole thing fell apart. Infinities kept on cropping up that refused to be renormalized. Tuck them away in one part of the theory and they would stick out in another part, and renormalizing the whole theory in one fell swoop proved impossible. Gravity, as described by general relativity, seemed far too entangled and different to be repackaged and fixed like the other forces. At the symposium, Mike Duff said ominously in the conclusion to his talk, “It appears that the odds are stacked against us, and only a miracle could save us from non-renormalizability.”
Quantum gravity had hit a dead end, and general relativity refused to join the other forces in one, unified picture. As a Nature article on the symposium glumly noted, “The presentation of technical results by M. Duff only served to confirm the extraordinary lengths which are necessary to make even minor progress.” This failure was all the more galling given that there had been such tremendous progress in relativistic astrophysics, black holes, and cosmology in the previou
s years, not to mention the spectacular success in the standard model of particle physics.
The Oxford symposium seemed like an admission of defeat, except for one surprising talk by the Cambridge physicist Stephen Hawking on black holes and quantum physics. In his talk, Hawking showed that there was a sweet spot where quantum physics and general relativity could be brought together. Furthermore, he claimed he could prove that black holes weren’t in fact black but shone with an incredibly dim light. It was an outlandish claim that would transform quantum gravity for the next four decades.
By the early 1970s, Stephen Hawking was already a fixture on the Cambridge scene, working at the Department of Applied Mathematics and Theoretical Physics, or DAMTP for short. At only thirty, he had already made a name for himself in general relativity. Coming out of Dennis Sciama’s stable of students, Hawking had worked with Roger Penrose to show that singularities had to exist in the very beginning of time. In the early 1970s he had turned his attention from cosmology to black holes and, with Brandon Carter and Werner Israel, had proved definitively that black holes have no hair: they lose any memory of how they were formed, and black holes with the same mass, spin, and charge all look exactly alike. He had also obtained an intriguing result about the sizes of black holes. If you took two black holes and merged them together, he found, the area of the Schwarzschild surface, or event horizon, of the final black hole had to be greater than or equal to the sum of the area of the original black holes. In practice, this meant that if you summed up the total area of black holes before and after any physical event, it always increased.
Hawking did all this work as Lou Gehrig’s disease claimed his body. Throughout the late sixties, he walked through the corridors at DAMTP with a cane, leaning against the wall for support, but he slowly and steadily became unable to move unaided. As his ability to write and draw, essential tools in the arsenal of a theoretical physicist, dwindled away, he developed a formidable capacity to think things through at length, allowing him to tackle deep issues in general relativity and quantum theory.
One might say Hawking’s great discovery was driven by his annoyance at a result put forward by a young Israeli PhD student of John Wheeler named Jacob Bekenstein. Bekenstein wanted to reconcile black holes with the second law of thermodynamics. To do so, he used one of Hawking’s results to come up with a completely ludicrous claim about black holes. To Hawking, the claim was entirely too speculative and simply wrong.
To understand Bekenstein’s claim, we need to take a quick detour into thermodynamics, the branch of physics that studies heat, work, and energy. The second law of thermodynamics (there are four in total) states that the entropy, or level of disorder, of a system always increases. Consider the classic example of a simple thermodynamic system: a box containing gas molecules. If the molecules are all at rest, neatly packed away in one corner, the system has low entropy—there is very little disorder. There is also no way the stationary particles will collide with the sides of the box and heat it up, so the system has a low temperature. Now imagine that the molecules begin to move. They roam freely throughout the box and spread out randomly, shifting the system to a high-entropy state. That is, the distribution of molecules inside the box becomes more disordered. As they move around, they collide with the walls of the box and transfer some of their energy to it, heating it up and increasing its temperature. The faster the molecules move, the quicker they randomize, and the quicker the entropy goes up until it reaches its maximum. Indeed, the quicker the molecules move around, the less likely it is that they will all coalesce into a peaceful, ordered state of low entropy. But not only that, faster molecules also transfer more heat to the walls of the box, increasing the temperature of the system even more. This shows us two things: the box tends toward a high-entropy state, as the second law of thermodynamics states, and with entropy comes temperature.
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 phy
sics, 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.”
The Perfect Theory Page 18