The name Schwarzschild was constantly popping up in scientific articles by astronomers and astrophysicists as the link between collapsed or frozen stars and quasars became more and more compelling. But, as Wheeler recalled years later, the name that he and his colleagues in the United States were using—“completely collapsed gravitational object”—was cumbersome, and “after you get around to saying that about ten times, you look desperately for something better.” At a conference in Baltimore, in 1967, a member of the audience helped him out and proposed the term black hole. Wheeler adopted it, and the name stuck.
In 1969 one of Dennis Sciama’s colleagues at Cambridge, Donald Lynden-Bell, stated in the introduction to one of his papers, “We would be wrong to conclude that such massive objects in spacetime should be unobservable, however. It is my thesis that we have been observing them indirectly for many years.” He argued that massive black holes at the center of galaxies would suck in the surrounding material just as Penrose had described it, like water falling down a drain, gurgling around and around. The rotating gas around the hole would form a flat disk, just like Saturn’s rings, and the whole system would be locked spinning on its axis. The nuclei of galaxies, fueled by these accretion disks, would then be veritable beacons of light, and Lynden-Bell could show how the energy was created and emitted. Martin Rees had also, with Dennis Sciama, set to work trying to build detailed models of quasars that could explain all the different strange properties—their size, their distances, how quickly they would flicker and pulsate, and what ranges of energy would be pumped out. Over the next few years, Rees, with Lynden-Bell and their students and postdocs at Cambridge, were able to come up with a beautiful, meticulous model of the fireworks surrounding quasars and radio sources. All the pieces were falling into place.
And then, finally, Zel’dovich and Novikov’s x-rays started trickling in. Starting in the 1960s, a team led by the Italian physicist Riccardo Giaccone sent rockets up out of Earth’s atmosphere where, for a few minutes, they would look for x-rays. They found them, bright spots of x-rays spread across the sky that outshone the planets in the solar system. In the early 1970s the Uhuru satellite was launched from a platform near Mombasa in Kenya with the sole goal of mapping out the x-ray sky. It was a resounding success, making exquisite measurements of over three hundred x-ray objects.
In the midst of the multiple sources that Uhuru measured was one object, Cygnus X-1, a particularly bright source lying in the constellation of Cygnus. It had first been seen in 1964 during one of the early rocket flights, but Uhuru found that its x-ray light flickered extraordinarily quickly, several times a second, a sure indication that it was an incredibly compact object. Uhuru’s measurements were rapidly followed by observations in radio frequency and optical frequencies that identified the smoking gun that Zel’dovich and Novikov had predicted—a star that is slowly being stripped of its envelope and gently wobbles as it is tugged about by an invisible, dense object with a mass of more than eight suns. There it was: the first evidence of a black hole; not certain, but highly probable. It was small, powerful, and invisible yet beaming out x-rays.
In the summer of 1972, Bryce and Cécile DeWitt organized a summer school at Les Houches in the French Alps. In attendance were the young relativists—trained by Sciama, Wheeler, and Zel’dovich—who had now become the world authorities: Brandon Carter and Stephen Hawking from Cambridge, Kip Thorne and his student James Bardeen along with Remo Ruffini from Caltech and Princeton, and Igor Novikov representing Moscow. They were the new prophets of black holes.
“The story of the phenomenal transformation of general relativity within little more than a decade, from a quiet backwater of research, harboring a handful of theorists, to a booming outpost attracting increasing numbers of highly talented young people . . . is by now familiar,” the DeWitts wrote in the preface to the proceedings of the Les Houches meeting. “No single object or concept epitomizes more completely the present stage of evolution than the black holes.” The meeting was the culmination of a decade of phenomenal discovery.
Einstein and Eddington had been profoundly mistaken. Even Wheeler had caved in and by 1967 had accepted that nature didn’t abhor the singularities in general relativity. Schwarzschild’s solution, discovered so long ago on the battlefields of the eastern front, and Kerr’s solution, discovered in the heat of the Texas summer, were real and must exist in nature. They were the true endpoints of gravitational collapse. They were predicted by general relativity, inevitable and simple, and they could do wonderful things in nature: power quasars and strip stars of their envelopes. The radio sky, again and again, threw up tantalizing glimpses, and the x-ray mayhem that was being uncovered seemed to point to small dense objects. No measurement was yet definitive, but the real existence of black holes was becoming unavoidable. Bets were being made on which of the various strange beasts being observed in the sky could actually be black holes. They were almost a reality.
The group gathered at Les Houches had also, in the previous few years, realized that if black holes were to be found in nature, they had to be as mathematically simple as Schwarzschild’s and Kerr’s solutions. While Ezra (“Ted”) Newman from Syracuse University had slightly extended Kerr’s solution to include black holes that were electrically charged, the full black hole solution to Einstein’s theory could be completely characterized in terms of just three numbers: its mass, how fast it was spinning, and how much charge it had. This was a startling result. Why couldn’t a black hole have a bit more mass on one side, like a mountain on the surface of the Earth, compensated by less mass on the other side, like a valley? Or why couldn’t it indent on one side while continuing to have the same mass? You could in fact imagine black holes with the same mass, spin, and charge all looking different, each having its own individual characteristics. But the math proved otherwise and showed resolutely that with general relativity such complications would quickly disappear. The hills would flatten out, the valleys would fill up, and the squashed areas would swell up. Black holes with the same mass, spin, and charge would all quickly settle down to look exactly the same as one another, completely indistinguishable. Wheeler described this uniform makeup by saying, “Black holes have no hair,” and the proof became known as the “no-hair” theorem.
The Les Houches meeting showed what could happen when great minds tackle great problems. As Martin Rees recalls of that period, “There were three groups trying to understand black holes: Moscow, Cambridge, and Princeton. And I always felt there was a congenial atmosphere among them all.” Indeed, during a time of tremendous isolation between the East and West, their collaborative meetings pushed the science forward. Kip Thorne and Stephen Hawking would visit Zel’dovich in Moscow and compare notes on accretion disks, gravitational collapse, and singularities. As important were the short and difficult trips to the West taken by the Soviet physicists. As Novikov recalls of his visit to one of the Texas Symposiums in 1967, this time in New York, “Despite our desperate efforts to gather maximum information and talk to as many colleagues as possible, we were physically unable to cover all that was of interest.” Years later, at the Les Houches meeting in 1972, Novikov and Thorne would coauthor one of the papers on accretion disks.
In ten years, Einstein’s theory of general relativity had been transformed. The Texas Symposium had become a regular gathering of many hundreds of astrophysicists, many of whom now considered themselves relativists. As Roger Penrose put it, “I saw black holes change from a piece of mathematics into something people actually believed in.” The generation that came out of the Golden Age of General Relativity would be rewarded with prestigious positions at some of the top universities. In the United Kingdom, Martin Rees and Stephen Hawking would be given prestigious chairs at Cambridge, as would Roger Penrose at Oxford. In the United States, Wheeler’s students found themselves on the faculties of Caltech, Maryland, and a number of other top universities, as did Zel’dovich’s offspring in the Soviet Union. All of this for their work on general
relativity. It seemed that Einstein’s theory had finally become part of mainstream physics in a truly spectacular way.
Chapter 9
Unification Woes
IN 1947, FRESH OUT OF graduate school, Bryce DeWitt met Wolfgang Pauli and told him he was working on quantizing the gravitational field. DeWitt couldn’t understand why the two great theories of the twentieth century—quantum physics and general relativity—were kept at arm’s length. “What is the gravitational field doing there, in such splendid isolation?” he wondered. “What if one simply dragged it forcibly into the mainstream of theoretical physics and quantized it?” Pauli hadn’t been entirely supportive of DeWitt’s plans. “That is a very important problem,” he told him, “but it will take someone really smart.” No one would deny DeWitt’s considerable intelligence, but for more than half a century, general relativity would prove remarkably resistant to his efforts.
General relativity stood alone in its incompatibility with quantum physics. The ascent of the quantum after the Second World War led to a completely new and powerful theory that brought together all the forces with the fundamental constituents of matter as a simple, coherent whole—all the forces, that is, except gravity. Albert Einstein and Arthur Eddington had tried and failed for decades to come up with their own unified theories. Quantum theory was different. It was tested with staggering precision in gigantic collider experiments in Europe and the United States, a success story marrying beautiful mathematics and conceptual brilliance with real, down-to-earth measurements.
Despite its successes, there was one man who refused to cheer on the new postwar quantum physics. Paul Dirac thought the quantum theory of particles and forces was a sham and a piece of messy thinking. It performed a sleight of hand, sidestepping fundamental problems by making some infinite numbers magically disappear. Dirac was convinced this trickery was what prevented general relativity from joining in the full glory of the unification of all the forces.
There was something impenetrable about Paul Dirac, a tall, slim man who hardly said anything in polite company. When he did speak, his words were almost too precise and to the point. He would often come across as painfully shy and preferred to work on his own, obsessed with the mathematical beauty that he believed underpinned reality. His papers were mathematical gems with far-reaching real-world consequences. He originally trained as an engineer in Bristol but quickly established himself as one of the prophets of the new quantum when he came to Cambridge in his early twenties. He was rapidly made a fellow of St. John’s College in Cambridge and soon afterward became the Lucasian Professor of Mathematics, a chair that had been filled by Isaac Newton in the seventeenth century. Cambridge gave him a sheltered existence where he could hide away yet also influence generations of physicists, among them some of the astrophysicists and relativists who came to reenergize general relativity in the 1960s. Both Fred Hoyle and Dennis Sciama had been his PhD students, and Roger Penrose had sat in on his lectures, marveling at their clarity and precision.
Ironically, it was Paul Dirac’s own fundamental equation for the electron—the Dirac equation, as it became known—that took the first step on the path toward unification, bringing together Einstein’s principle of special relativity and the foundations of quantum physics. The equations for quantum physics tell us how the quantum state of a system, such as an electron bound to a proton in a hydrogen atom, evolves with time. It makes a very clear distinction between space and time. Einstein’s special relativity brings space and time together into one indivisible thing—spacetime. It also combines the laws of mechanics and the laws of light into a coherent framework. Paul Dirac was able to bring the laws of quantum physics into this same framework. With Dirac’s equation, all of physics, including quantum physics, could obey the special principle of relativity.
Particles in the universe can be divided into two types—fermions and bosons. As a rule of thumb, the particles that make up stuff are mostly fermions, and the particles that carry the forces of nature are mostly bosons. Fermions include the building blocks of atoms, such as electrons, protons, and neutrons. As we have seen when looking at white dwarfs and neutrons stars, these particles have a bizarre quantum property that arises from the Pauli exclusion principle: No two fermions can occupy the same physical state. When squeezed into the same space, they push each other apart through quantum pressure. Fowler, Chandra, and Landau used this pressure to explain how white dwarfs and neutron stars sustained themselves below their critical mass. Unlike fermions, bosons do not satisfy the Pauli exclusion principle and can be compressed together at will. An example of a boson is the photon, the carrier of the electromagnetic force.
The equation that Dirac found describes the quantum physical behavior of an electron, a fermion, while also satisfying Einstein’s special theory of relativity. It is an equation that describes the probabilities for finding an electron in any given position in space or with any given speed. Instead of singling out space, Dirac’s equation is defined in all of spacetime in one coherent way, as special relativity demands. Dirac’s equation contains a wealth of insights and information about the natural world and its fundamental particles. To his surprise, his equation also predicted the existence of antiparticles. An antiparticle has the same mass but the opposite charge of its corresponding particle. The antiparticle of an electron is called a positron. It looks exactly like an electron, but its charge is positive instead of negative. According to Dirac’s equation, both electrons and positrons have to exist in nature. The equation also predicts that pairs of electrons and positrons can pop out of the vacuum, effectively created out of nothing. This was bizarre and difficult to understand, especially given that when Dirac first wrote down his equation no one had ever seen a positron. Dirac held back from claiming that positrons actually existed until, in 1932, they were detected in cosmic rays. Dirac won the Nobel Prize the following year.
When Dirac first proposed his equation, he started a revolution in the understanding of particles and forces in nature. If the quantum physics of the electron could be described in the same framework as the electromagnetic field—that is, obeying Einstein’s special principle of relativity—why couldn’t the electromagnetic field itself be quantized like the electron? Instead of just describing light waves, it should naturally describe photons as well, the quanta of light that Einstein had posited existed in 1905. A quantum theory of electrons and light, known as quantum electrodynamics, or QED for short, was the next step on the path to the unification of particles and forces. Developed by Richard Feynman, Julian Schwinger, and Sin-Itiro Tomonaga after the Second World War, it signaled a new way of studying quantum physics: quantizing particles (electrons) and forces (the electromagnetic field) in one coherent whole. QED was a phenomenal success and allowed its creators to predict the properties of electrons and electromagnetic fields with unprecedented precision, winning them the Nobel Prize as well.
While QED worked spectacularly well, Paul Dirac viewed it with tremendous disgust. For at the core of its success was a method of calculating that affronted his deep belief in mathematical simplicity and elegance. It went by the name of renormalization. To understand what renormalization means, we need to look at how physicists use QED to calculate the mass of an electron. The mass of an electron has been beautifully measured in laboratories and equals 9.1 tenths of a billionth of a billionth of a billionth of a gram—a very small number. However, applying the equations of QED gives you an infinite value for the electron’s mass. This is because QED allows the creation and destruction of photons and short-lived pairs of electrons and positrons—the particles and antiparticles from Dirac’s equation—effectively out of nothing. All these virtual particles popping out of the vacuum boost the self-energy and mass of the electron, ultimately making it infinite. And so QED, if applied injudiciously, leads to infinities all over the place and gives the wrong answer. But Feynman, Schwinger, and Tomonaga argued that since we know that the final mass of the electron from our observations is finite, we
can simply take the calculated infinite result and “renormalize” it by replacing it with the known, measured value.
To the uncharitable observer it sounds like all renormalization does is throw away the infinities and arbitrarily replace them with finite values. Paul Dirac declared himself “very dissatisfied with the situation.” As he argued, “This is just not sensible mathematics. Sensible mathematics involves neglecting a quantity when it is small—not neglecting it just because it is infinitely great and you do not want it!” It seemed like a messy piece of slightly magical thinking, but there was no denying that it worked spectacularly well.
QED was one step on the long path to unification, but from the 1930s to the 1960s it had become clear that there were two other forces, apart from the electromagnetic and gravitational forces, that also needed to be included in the ultimate framework. One was the weak force, proposed in the 1930s by the Italian physicist Enrico Fermi to explain a particular type of radioactivity known as beta decay. In beta decay a neutron transforms itself into a proton and spits out an electron in the process. Such a process is impossible to understand using electromagnetism, so Fermi conjured up a new force that would allow that transformation to happen. This new force acts only at very short distances, at internuclear separations, and is much weaker than electromagnetism; hence its name. The other force, the strong force, is what glues protons and neutrons together to form nuclei. It also binds the more fundamental particles, called quarks, that make up protons, neutrons, and a plethora of other particles. While it also has a very short range, it is much stronger than the weak force (hence the creative name). The challenge, just as James Clerk Maxwell had unified the electric and magnetic forces into a single electromagnetic force in the mid-nineteenth century, was to come up with a common way of dealing with all four fundamental forces: gravitational, electromagnetic, weak, and strong.
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