The first Texas Symposium on Relativistic Astrophysics was almost canceled. President John F. Kennedy had just been assassinated in Dallas, and conference goers were simply too scared to come to Dallas and run the risk of being shot. The Dallas relativists asked the mayor to reach out to potential attendees individually and assure them of the city’s safety. It worked. Over three hundred people turned up in Dallas to hear the latest about radio stars and what could be made of them. Among the crowd was Robert Oppenheimer, who had discouraged work on general relativity at the institute in Princeton. He was intrigued by these new radio stars, for they were, as he described them, “incredibly beautiful . . . spectacular events of unprecedented grandeur.” He commented on how the meeting resembled those in quantum physics almost two decades before “when all one had was confusion and lots of data.” For him, it was an exciting time.
The meeting went on for three days, with astronomers and relativists alike debating the import of the strange “quasi stellar radio sources” in Ryle’s 3C Catalogue. One of the meeting’s attendees starting calling them “quasars,” which was quicker and easier to pronounce. For the relativists, these quasars seemed so massive and so concentrated that Schwarzschild’s weird solution, and Oppenheimer and Snyder’s calculation, had to be taken into account if any sense was to be made of the data. The astronomers and astrophysicists found the quasars so bizarre and mysterious that they started paying attention to what the relativists were saying. Maybe, just maybe, general relativity had to be brought into the picture to make any sense of these new discoveries.
At Dallas, more than ten years after he had started working on general relativity, John Wheeler was present and ready to say his piece. The big unanswered question on his mind was what he called “the issue of the final state.” He wanted to find out what happens at the endpoint of gravitational collapse. He still found it impossible to believe Oppenheimer and Snyder’s prediction that singularities formed, and he was convinced general relativity would play an integral role in explaining why they wouldn’t. Despite his prejudice, he felt duty-bound to explain all the possibilities and enlist his audience in his pursuit of the final state. Before his talk, Wheeler picked up a piece of chalk and meticulously filled a blackboard with his elaborate pictures and equations illustrating what he had been thinking about for almost a decade. On the board were plots showing how he thought a star would collapse under its own weight and how general relativity predicted the star’s inexorable movement toward its final fate. Scattered around were equations, bits of Einstein’s field equations, summaries of quantum physics, a hodgepodge of brilliance that helped him lay out his results of the past ten years. More than anything, Wheeler’s talk was an apologia of general relativity arguing that it should be taken seriously by any right-minded astrophysicist.
For many of the astronomers the results were too fanciful, and one of the attendees recalled “utter disbelief” on the face of “a distinguished participant.” Yet others marveled that the universe had finally caught up with Wheeler. It seemed the general theory of relativity that he had been thinking about for so long now actually had relevance and might be of use to understand the new radio observations.
In a description of the meeting, Life magazine said, “The scientists, having stretched their imagination to a point that once would have embarrassed science fiction writers, were hardly less mystified than they were before they began their talks . . . so fantastic is the nature of radio sources that no bets were ruled out.” During the after-dinner speech, Thomas Gold summed up the extraordinary turn of events that they were witnessing at the symposium: “Here we have a case that allowed one to suggest that the relativists with their sophisticated work were not only magnificent cultural ornaments but might actually be useful to science! Everyone is pleased: the relativists who feel they are . . . suddenly experts in a field they hardly knew existed; the astrophysicists for having enlarged . . . their empire by the annexation of another subject—general relativity.” He ended on a cautious note, saying, “Let us all hope that it is right. What a shame it would be if we had to go and dismiss all the relativists again.”
With his incredible vision and persistence, John Wheeler had overseen the resurrection of Einstein’s moribund theory. By devoting his fearsome intellect and creativity to training a new generation of brilliant young relativists, and supporting the new centers that were scattered throughout the country, he had nurtured a new and vibrant community that could think deeply about gravity. Finally, the data had been obliging, and with astronomers, physicists, and mathematicians ready to tackle the big questions, the Texas Symposium heralded a new era. General relativity was back.
Chapter 8
Singularities
WHILE MOST OF the audience listened to John Wheeler’s presentation at the 1963 Texas Symposium with incomprehension, one young mathematician watched enthralled as Wheeler lectured in front of his carefully prepared blackboard of equations and plots. “Wheeler’s talk made a real impression on me,” Roger Penrose recalls. And even though Wheeler stubbornly refused to accept the existence of singularities, he was, in Penrose’s mind, asking the right question: Could these singularities be an essential ingredient of general relativity? Wheeler’s talk at the Texas Symposium heralded the start of a decade that would be dubbed the “Golden Age of General Relativity” (by one of Wheeler’s own students, Kip Thorne), and Roger Penrose would be one of the brilliant thinkers to see it through.
Penrose has spent his life playing with spacetime: cutting it up, gluing it back together, pushing it to its limits. He sees things differently, possessing a mathematician’s gaze enhanced by a more visceral understanding of space and time. His drawings, known as Penrose diagrams, unwrap spacetime and reveal its oddest properties. They visualize what happens to light as it zooms past the Schwarzschild surface, how light behaves as you follow it back to the Big Bang, and even how space and time can be stretched to look like the frothy surface of the sea.
Penrose was still an undergraduate, studying mathematics in London, when he first felt the pull of general relativity. He taught himself the basics using a book by Erwin Schrödinger aptly called Space-Time Structure. But what really set him thinking about the details were Fred Hoyle’s lectures proselytizing about his steady-state theory. There was something fascinating but also odd about the universe that Hoyle was describing—it didn’t fit with Penrose’s understanding of relativity. He decided to pay a visit to his brother Oliver, also a mathematician, who was studying for a PhD in Cambridge. He thought Oliver could help him understand this strange theory that so appealed to him.
Cambridge in the 1950s, despite the staid atmosphere of centuries-old cloisters and the stifling rituals of the colleges and university, was becoming an exciting place. Paul Dirac, an English physicist who had played a crucial role in showing that the quantum theories of Heisenberg and Schrödinger were one and the same, gave brilliant, exquisitely crafted lectures on quantum mechanics. Hermann Bondi lectured on general relativity and cosmology and, with Fred Hoyle, actively promoted their steady-state universe. And then there was Dennis Sciama.
Penrose and his brother met at the Kingswood restaurant in Cambridge to discuss Fred Hoyle’s radio lectures. Penrose simply couldn’t understand Hoyle’s claim that in the steady-state model, galaxies would speed up and away so quickly that at some point they would disappear over a cosmic horizon. He recalls thinking that something else ought to happen, something he could show with his diagrams. Oliver pointed over to another table and said, “Well, you can ask Dennis. He knows all about it.” He walked Roger Penrose over to Dennis Sciama and introduced them. They hit it off immediately.
Sciama was only four years older than Penrose but was already embroiled in Einstein’s theory with a passion that he would pass along to a string of students and collaborators over almost fifty years. He had done a stint at the Institute for Advanced Study in the year before Einstein died. In one of his few conversations with Einstein, Sciama had boldl
y, and somewhat rashly, declared that he was there to “support the ‘old Einstein’ against the new.” Einstein had laughed at his impudence. Sciama had studied with Paul Dirac, to the extent that such a thing was possible, and had become seduced by the work of Hoyle, Bondi, and Gold. Yet while he was a staunch believer in the steady-state universe, he paid attention to what the radio astronomers were finding. The results coming out of Ryle’s group down the road intrigued him. He could see how they might sink Hoyle’s model.
That evening in the Kingswood, Penrose explained to Sciama why galaxies wouldn’t disappear from sight. They would get dimmer and, from a distance, would appear to freeze in time, just as Oppenheimer and Snyder had shown would happen with an imploding star as its surface passes through the Schwarzschild horizon. Sciama saw the spark in Penrose’s eyes and loved his fresh approach to looking at spacetime. They would be friends for the next fifty years.
Penrose eventually moved to Cambridge to pursue a PhD in mathematics, but he remained beguiled by the mathematical oddities he’d found in the geometry of spacetime. He desperately wanted to understand them better. When he finished his PhD, he took the plunge and decided to work on general relativity. He spent the next few years roaming the world, working with Wheeler in Princeton, Hermann Bondi in London, and Peter Bergmann in Syracuse. He finally joined Schild’s Austin, Texas, group in the autumn of 1963.
Texas was the hot spot for general relativity, and researchers there were flush with funding. “We didn’t really ask where the money was coming from or why anyone thought it was worthwhile to spend all that money on relativity,” Penrose says. “I always felt there must be some mistake.” One of Penrose’s colleagues was a young New Zealander named Roy Kerr. Kerr had spent long days in the Texas heat and humidity grappling with Einstein’s field equations, trying to find more complex, more realistic solutions. He had come up with an elegant set of equations that corresponded to a simple geometry for spacetime. Kerr’s solution could be seen as a more general form of Schwarzschild’s geometry. While Schwarzschild described a spacetime that was perfectly symmetric around a point, the point where the infamous singularity would lie, Kerr’s solution was symmetric around a line that cut through the whole of spacetime. It was as if he had set Schwarzschild’s solution spinning on an axis, twisting and tugging spacetime around it. If he wanted to retrieve Schwarzschild’s original solution, all he had to do was stop his solution from spinning.
Penrose immediately took to Kerr’s result. He spent hours discussing the discovery with his new colleagues at Austin, rephrasing the new spacetime in his own way. Like Sciama, Schild was taken by Penrose’s way of seeing things. Penrose’s mathematical insight and diagrams shed a completely new light on Kerr’s solution. Kerr submitted his remarkably simple and powerful result to the Physical Review Letters, the American journal that only a few years before had considered banning the publication of anything related to relativity. It was instantly accepted and published in September 1963, just a few months before the Texas Symposium was to take place in Dallas. There he could present his result to the astrophysicists.
Afraid that Kerr’s presentation might be too dry and mathematical, Schild tried to convince Penrose to present the new solution instead of Kerr. Penrose would have none of it; it was Kerr’s baby. Schild’s concerns were not entirely unfounded. When Kerr went to the podium to make his presentation, half of the participants left the hall. Kerr was young and unknown, a relativist among a gang of astrophysicists who had better things to do at that moment. Kerr spoke to the remaining, desultory crowd, and, as Penrose recalls, “They didn’t pay much attention to him.” Very few people understood the point of Kerr’s result, the first big step in making Schwarzschild’s solution more general, more real, and more useful to astrophysicists. Kerr wrote a short note for the conference proceedings, but the person charged with summing up the main results of the symposium left him out entirely. It was still too much general relativity for the astrophysicists to accept.
There wasn’t a single Soviet physicist at the first Texas Symposium. Much of the precious intellectual power of Soviet physics had been taken up with the Soviet nuclear project, leaving little time or attention for general relativity. However, just as a new generation of relativists emerged from the Manhattan Project in the United States and radar in the United Kingdom, many of the Soviet nuclear scientists would eventually lead a revival of general relativity in the Soviet Union in the 1960s.
The Soviet nuclear project was late getting started. During the Second World War, precious resources had been drained from the Soviet machine on the Soviet German front, which prevented Joseph Stalin from putting his men to work on the bomb. Starting in 1939, following John Wheeler and Niels Bohr’s paper that discussed the copious release of energy from the nuclear fission of heavy elements, scientific papers on nuclear fission in the West seemed to have dried up. To the Soviets, it was as if Western research into nuclear fission had ground to a halt. In 1942, when a Soviet physicist, Georgii Flerov, wrote to Stalin and alerted him to this strange state of affairs, Stalin became suspicious. He guessed that the Americans were working on a bomb, and he realized he had to get in the game. Once the war ended, Stalin plundered his own scientific elite to set up a bomb project. The team included Lev Landau and Yakov Zel’dovich.
Lev Landau had suffered under the wave of persecutions during the great terror of the late 1930s. His stint in prison had left him a deeply bitter man, profoundly disillusioned by the regime, yet at its mercy. Landau had already become legendary, with a raft of discoveries to his name spanning from quantum mechanics to astrophysics. He had created a school of physics and a following of brilliant disciples who would be tried to the limit of their intellectual abilities just to be allowed to work with him. In fact, to be accepted as one of Landau’s protégés, aspirants had to pass a series of eleven punishing exams, known as “Landau’s Theoretical Minimum,” set and overseen by Landau himself, a process that could take up to two years. Only a few made it through the barrier and were able to work with the great man himself.
Yakov Zel’dovich, a Belorussian Jew just a few years younger than Landau, had been a precocious student. He became a lab assistant at seventeen, gained a doctorate at twenty-four, and rapidly became one of the Soviet authorities on combustion and ignition. It was inevitable that he would be roped into developing the bomb, and he did so with flair. From 1945 until 1963, Zel’dovich took part in the construction of the first Soviet atomic bomb, dubbed “Joe-1” by the Americans when they detected its explosion in August of 1949, and then worked on its successor, the “superbomb.” The Soviet Union had caught up with the Americans and become a nuclear power.
While Zel’dovich was passionate about the nuclear project, Landau, still smarting from his ordeal in the Lubyanka and nursing a profound hatred for Stalin, had been coerced into taking part. And while Zel’dovich greatly admired Landau, Landau was less charitable toward his colleague and the nuclear project as a whole. When Zel’dovich attempted to enlarge the Soviet nuclear bomb project, Landau called him “that bitch.” When Stalin died, he said to a colleague, “That’s it. He’s gone. I’m no longer afraid of him, and I won’t work on [nuclear weapons] anymore.” Nevertheless, for their contribution to the Soviet bomb project, both men were awarded the Stalin Prize and the Hero of Socialist Labour medal a number of times. Landau went on to win the Nobel Prize in 1962.
In the mid-1960s, Zel’dovich’s star was still rising, but Landau was incapacitated, laid low by a car crash that left him a shell of the man he once was, unable to do physics. Landau’s protégés carried on in his stead; they were the first Soviets to go after singularities in spacetime. The two young men, Isaak Khalatnikov and Evgeny Lifshitz, who had both undergone the rigors of an education with Landau, were well prepared to tackle the intricacies of Einstein’s theory to look at what happens when matter collapses under its own gravity.
Oppenheimer and Snyder had built their solution around a simple approximation,
a perfectly symmetric sphere of stuff collapsing inward. The perfect symmetry had initially bothered people like Wheeler, who saw it as too much of an idealization. The surface of the Earth is covered with irregularities: huge mountains and deep oceans and valleys. What if a collapsing star was similarly uneven? Could the irregularities and imperfections distort the collapse so much that parts of the surface would fall in far more quickly than others, rebound, and make their way out again? If that was so, singularities might never form.
The Russians addressed this question by loosening the symmetries Oppenheimer and Snyder had enforced. In Khalatnikov and Lifshitz’s calculation, spacetime could twist and churn in each direction in a different way. Imagine looking face-on at the seething mass of stuff, a massive star, for example, as it implodes, collapsing inward toward its center. In general, you would expect it to appear lopsided. The top and the bottom bits of the blob might collapse more quickly than the sides, so quickly that they might bounce right back out before the sides of the blob had time to collapse. Instead of everything falling inward, inexorably forming the singularity, there would always be some part moving outward, holding spacetime up. Only if the collapse was set up just so, perfectly symmetric around the center, would everything fall in at exactly the same time, allowing the singularity to form. Khalatnikov and Lifshitz’s paper, published in the Soviet journal Soviet Physics, came to the striking conclusion that in realistic situations singularities never formed. Schwarzschild’s and Kerr’s solutions were abstractions that should never form in nature. Einstein and Eddington, it appeared, had been right all along.
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