The Perfect Theory

by Pedro G. Ferreira

  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

  Seeing Gravity

  JOSEPH 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.

  Hermann Bondi made the most compelling case for gravitational waves at the Chapel Hill meeting in 1957. Bondi, then leading a relativity group at King’s College London, presented a simple thought experiment: Take a rod and thread it through two rings a small distance apart f
rom each other. Tighten the rings ever so slightly so that they can still move but rub against the rod. If a gravitational wave passes through, it will barely affect the rod itself. The rod will be too stiff to sense anything much. But the rings will be dragged up and down on the rod, like buoys in the sea being tossed about by the waves. They will move back and forth, coming close and moving apart as the wave flies through, and in doing so they will rub against the rod and heat it up, giving it energy. Given that the only place the energy could come from is the gravitational waves, the waves must carry energy. Bondi’s argument was simple and effective. Richard Feynman, who was also attending the meeting, presented a similar line of reasoning, and the majority of the participants were convinced. Gravitational waves were out there, ready to be discovered. Joe Weber had been at Chapel Hill, mesmerized by the discussions. Bondi, Feynman, and all the other participants could sit around discussing the reality of gravitational waves, but he would actually go out and look for them.

  Weber was just the sort of person who would attempt the impossible. An obsessive tinkerer, he had learned to fix radios to make money as teenager. An artistic visionary, constantly pushing technology beyond what was thought feasible, he would design and build experiments with the barest resources and then use them to probe the outer edges of the physical world. His drive infected all aspects of his life; he ran three miles every morning and worked a full day until he was in his late seventies.

  Weber had trained at the United States Naval Academy as an electrical engineer and commanded a ship during the Second World War. Because of his expertise in electronics and radio he was asked to lead the navy’s electronic countermeasures program. When he came out of the war, he became a professor of electrical engineering at the University of Maryland, where he decided to switch fields, studying for a PhD in physics.

  In the mid-1950s, Weber became interested in gravity. John Wheeler had stepped in and encouraged Weber to take the plunge, bringing him to Europe for a year to think about the new frontier of general relativity. When Weber returned, he was ready to start designing and building an instrument. As he gradually immersed himself in the task of recording gravitational waves, he sketched out various possibilities, filling up notebooks with designs for contraptions. One method particularly took his fancy. The idea was simple: Build big, heavy cylinders of aluminum and suspend them from the ceiling. Strapped around the belly of each cylinder would be a set of incredibly sensitive detectors that would send an electrical pulse to a recorder if the cylinder vibrated. Anything could set it off—a phone ringing, a car trundling by, a slamming door. So Weber had to isolate the cylinders as much as possible, eliminating all possible sources of tremors and jerks.

  When Weber finally turned on his cylinders, or Weber bars as they became known, he immediately began to pick up tremors. The bars vibrated, and once all the known disturbances had been eliminated, a few were left over: little blips of what just might be gravitational radiation. There was something odd about the blips, though. If they were truly gravitational radiation, they must have come from such an explosive event that it would have been observed through telescopes. The signal was too strong to be gravitational radiation. Weber had to improve his kit.

  To be absolutely sure that any tremor in the cylinders came from a gravitational wave passing through, Weber placed one of his four bars at the Argonne National Laboratory, almost a thousand kilometers away from his laboratory at the University of Maryland. If cylinders at both places trembled at the same time, it would be a strong sign that they were being sprayed by gravitational waves coming from outer space. Weber would compare the readings of the detectors on each one of his bars. If a reading shot up on more than one bar at the same time, it would be more likely that the source of the disturbance was the same external thing—a gravitational wave—that had shaken both of the bars, and not just some randomly coordinated jiggle in each of the bars themselves. He would look for these “coincidences,” as he called them. Once again, Weber turned on his machine and waited.

  By 1969, after working on his experiment for over a decade, Weber had something to show the world: a handful of coincident tremors not only between the ANL and the University of Maryland cylinders but between all four of his cylinders. It was too much of a coincidence to be random. They must have been sensing something in unison. There were no earthquakes, nor was there any strange electromagnetic storm to which he could attribute the phenomenon. Weber appeared to have discovered gravitational waves.

  Over the next few years, Joseph Weber perfected his experiment, making sure that he was not simply finding what he wanted to find. The tremors in the bars were few and far between and were buried in the noise of the experiment. The bars would jiggle simply because of their own heat, as the atoms and molecules within them vibrated back and forth, and if you weren’t careful, your eyes would pick up patterns where there were none. To get around this, Weber developed a computer program that would pick out the tremors and identify the coincidences automatically. He also decided to introduce a slight delay in recording the signal of one of the cylinders and then compare it with the other cylinders. If the coincidence were indeed true, the signal from one cylinder would arrive at the other time-delayed cylinder after the coincidence had actually happened—the number of coincidences would have to go down when comparing the records of the two cylinders. And, indeed, the number of coincidences fell.

  By 1970, Weber had been running his experiment long enough that he was able to pinpoint the direction of the gravitational radiation that his instrument was picking up. It seemed to be emanating from the center of the galaxy, which he saw as a good thing. As he wrote in his paper, “A good feature is the fact that [10 billion] solar masses are there and it is reasonable to find the source to be the region of the sky containing most of the mass of the galaxy.”

  As Weber became more convinced that he was actually detecting gravitational waves with his experiment, the rest of the world began paying attention. His discovery had caught everyone by surprise. Such a straightforward detection of gravitational waves was unexpected, yet there was no reason, a priori, to doubt his findings. Weber’s results were being brought up repeatedly by the relativists as they tried to figure out what they meant. Roger Penrose calculated what would happen if two gravitational waves collided with each other—could the final result be so explosive that it would trigger Weber’s machine? Stephen Hawking worked out his own thought experiment of throwing black holes at each other, hoping that they would send out a burst of gravitational radiation that could explain Weber’s detection. And throughout those early years, Weber’s fame continued to spread. He was interviewed for Time magazine, and his work was featured in the New York Times and countless other newspapers in the United States and Europe. The results kept on pouring in.

  Weber’s results were amazing, and they seemed almost too good to be true. Weber appeared to have found an unbelievable source of gravitational radiation, far bigger than anyone had ever thought possible. For however sophisticated Weber’s bars were and however refined the detectors he had glued to them, they weren’t that sensitive. To actually get a detectable tremble, Weber’s bars would have to be shaken by incredibly powerful gravitational waves, real behemoths traveling toward the Earth.

  That was a problem, for even though the presumed gravitational waves came from the center of the galaxy, where there was a lot of stuff ready to implode, collide, and stir up spacetime, that was over twenty thousand light-years away from Earth. If indeed there was a beacon of gravitational waves lurking at the heart of the Milky Way, the waves it emitted would have been diluted in the intervening space into almost nothing by the time they reached the Earth. In fact, as Weber pointed out, the amount of energy in the gravitational waves he was detecting was equivalent to a thousand stars the size of the sun being destroyed at the center of the galaxy each year, a truly colossal amount.

  Martin Rees at Cambridge was skeptical of Weber’s results from the beginning. With his former
PhD adviser, Dennis Sciama, and George Field from Harvard University, Rees worked out how much energy could be flooding out of the center of the galaxy in the form of gravitational waves. Rees and his collaborators found that, at most, two hundred stars the size of the sun could be destroyed each year to give rise to the gravitational waves. Any more than that, and the galaxy would have to be inflating, which they could verify was not the case by looking at the motion of nearby stars. Their calculation was approximate, so they were careful about their conclusions. In their paper they claimed, “Since the high rate of mass loss indicated by Weber’s experiments is not ruled out by direct astronomical considerations discussed here, it would be clearly desirable for these experiments to be repeated by other workers.” Weber was undaunted, for it was a theoretical argument that Rees, Field, and Sciama were putting forward. Maybe the theory was wrong, but his experiments were definitely right.

  Following Weber’s lead, in Moscow, Glasgow, Munich, Bell Labs, Stanford, and Tokyo new sets of experiments were being built. Some were exact copies of Weber’s, and all of them were in one way or another inspired by Weber’s original raft of designs. As they were gradually switched on, results started to trickle in, and a common pattern began to emerge; apart from a few events in the detector at Munich, none of them seemed to find the copious amounts of coincidences that Weber was finding with his apparatus. They simply weren’t there. Weber was unfazed. He had a ten-year head start thinking about these experiments, and it was clear to him that all the other experiments were much less sensitive than his, so there was no surprise that there was no signal. If they wanted to criticize his results, they should build a detector exactly like the one he had built, a “carbon copy.” Then they could talk. Several of the experimenters, including those in Glasgow and at Bell Labs in Holmdel, rebutted that the experiments they had built were carbon copies, and they still weren’t seeing anything like what Weber was finding. Again Weber had an excuse: their copies simply weren’t good enough.