Soviet scientists were occasionally allowed to attend meetings in the West. The Third Meeting on General Relativity and Cosmology, the successor of the Chapel Hill meeting, was held in London in 1965, with over two hundred relativists in attendance. When Khalatnikov presented his results there, all those relativists paid close attention. While it was evident that Einstein’s theory had taken off in the Soviet Union, it was difficult for Western scientists to tell exactly what was going on. Translations of the main Soviet journal, Soviet Physics, were always delayed.
Penrose sat quietly and listened to Khalatnikov’s presentation. He knew they were wrong but thought it would be “undiplomatic” to speak out. “You couldn’t really prove anything doing it the way they did it,” he says. “There were simply too many assumptions. They couldn’t rule out singularities like that.” In fact, Penrose could prove that singularities always formed, contrary to Khalatnikov’s claim. Penrose’s results were completely general because he had used his own new methods of looking at spacetime.
Since his first encounter with Sciama at the Kingswood restaurant in Cambridge almost ten years before, Penrose had developed his diagrams into a set of rules for how to think of light, or anything for that matter, propagating through spacetime. He could take an arbitrary spacetime, and from looking at some of its most basic properties and what kind of stuff it contained, he could get a definitive sense of what would happen to it, whether it would collapse to a point or explode out to infinity. When he applied his rules to the problem of gravitational collapse, what Wheeler called “the issue of the final state,” the outcome was inevitable: singularities. Penrose wrote up his paper, “Gravitational Collapse and Spacetime Singularities,” and submitted it to Physical Review Letters. As he summarized in his paper, “Deviations from spherical symmetry cannot prevent spacetime singularities from arising.” Almost half a century later, it is still a masterpiece of concision, clarity, and rigor: a perfect paper in just under three pages, with a brief explanation of the problem, the mathematical toolkit and the proof in a small paragraph, all illustrated with one of Penrose’s signature diagrams.
When Khalatnikov gave his presentation, Penrose had already submitted his paper. It was about to be accepted and would be published in December of that year, but his techniques were unfamiliar to most of the relativists in the audience, especially the Russians. When Charles Misner, one of John Wheeler’s students, stood up and challenged Khalatnikov with Penrose’s result, it was a lost battle. Suspicious of Penrose’s result, the Russians refused to accept that there might be an error in their own approach. “I hid in the corner,” Penrose recalls. “It was too embarrassing.”
But Penrose was right. What became known as his singularity theorem had far-reaching consequences. It meant that if general relativity was correct, the Schwarzschild and Kerr solutions, those strange spacetimes with singularities at their centers, had to exist in the universe. They weren’t merely mathematical constructs. Einstein and Eddington were wrong. Four years later, Khalatnikhov and Lifshitz admitted defeat. In 1969 they looked at their calculations again, this time with one of their students, Vladimir Belinski. To their dismay, they found a mistake. While in 1961 they had thought that the collapse that leads to the formation of a singularity was too special and unnatural to occur in the real world, with Belinski they found quite the opposite. In their own way they confirmed Penrose’s theorem: singularities always formed. They humbly published their results in the West, publicly acknowledging their mistake.
Penrose had proved the inevitability of singularities in gravitational collapse and answered Wheeler’s question about the final state. Deeper confirmation would soon follow.
Martin Ryle may have failed in his first attempts to dismantle Cambridge’s steady-state orthodoxy through his initial radio source measurements, but his data was improving. In 1961, when he released the 4C Catalogue of radio sources, most of the radio astronomers agreed that many of the problems with the previous data had been fixed. But the end of the steady state would begin with the theory’s own adherents.
Dennis Sciama was a strong advocate of Hoyle’s steady-state theory. He was also fascinated by quasars and assigned one of his students, Martin Rees, the task of looking at Ryle’s new measurements in different ways. Rees took a simpler and much cleaner approach than Ryle’s technique of plotting the number of quasars as a function of flux. Instead, Rees took a subset of thirty-five quasars with measured redshifts and divided it up into three slices. One slice exhibited low redshift, corresponding to quasars close to Earth in time and distance. The second slice contained quasars with medium redshifts, and the final slice was made up of objects with high redshifts viewed in the distant past.
Rees’s idea was simple but remarkably clever. In the steady-state model, in which the universe does not evolve over time, each slice should have approximately the same number of quasars. Instead, Rees found almost no quasars in the most recent slice. Almost all of them were in the farthest slice. In other words, the number of quasars seemed to have changed with time—there were more in the past—and so the universe couldn’t be in a steady state. The plot told it all—the steady-state universe didn’t work. “It was really that plot that converted Dennis,” Rees recalls. From then on Sciama believed in Lemaître’s theory, or the Big Bang as Hoyle had called it in his lectures, and whatever that entailed.
The final nail in the coffin of the steady-state theory came from across the pond in New Jersey. Arno Penzias and Robert Wilson had been working on an antenna at Holmdel, one of the telecommunications sites belonging to Bell Labs. They wanted to retrofit the antenna, a huge horn that captured radio waves, and use it to measure the galaxy. To accurately map out the structure of the Milky Way, they first needed to determine the precision of their instrument. So they used the antenna to stare at nothingness and check how well they could see it.
But what they saw wasn’t nothing. Penzias and Wilson were definitely seeing or, to be more precise, hearing something: a low, soft hiss streaming out of empty space. No matter how they adjusted their instrument, they couldn’t get rid of it. These two men had inadvertently stumbled upon a relic from the early universe, a fossil of the Big Bang.
In the late 1940s a Russian physicist working in the United States, George Gamow, predicted the existence of a very cold bath of light permeating the universe. He started from the Abbé Lemaître’s idea that the universe started in a hot, dense soup from which all the elements eventually emerged. The argument goes as follows: Imagine a universe in its simplest state, just full of hydrogen atoms. The hydrogen atom is the elementary building block of chemistry, a proton and an electron held together by electromagnetic force. If you bombard a hydrogen atom with enough energy, you can rip the electron away from its nucleus, leaving a lone proton floating in space.
Now imagine a gas of hydrogen atoms pushed together in a hot bath. They will collide, move around, and be bombarded by energetic photons, beams of light whizzing around. And the hotter they are, the more likely it is that the electrons will rip away from the protons. If the environment is very hot, very few hydrogen atoms will remain intact. Instead of a gas of hydrogen, the universe will be full of free protons and electrons. Early in the life of the universe, when the universe’s temperature was greater than a few thousand degrees, you would find very few atoms and mostly free protons and electrons. As time passes and the universe cools, electrons stick to nuclei, leaving mostly hydrogen and helium atoms, an almost insignificant smattering of heavier elements, and a faint, almost invisible background of light. This is what Arno Penzias and Robert Wilson saw—clear evidence for a hot, dense state at early times. It was as close as one could get to proving the existence of a Big Bang, as Hoyle had disparagingly called it, and it would be another of Dennis Sciama’s students, Stephen Hawking, who would take that final step.
There was something of Einstein in the young Hawking, and indeed his childhood friends would often call him that. He hadn’t shone at school, and if an
ything he had been relaxed, playful, and naughty, a slight, untidy boy who delighted in entertaining his colleagues. Hawking had become increasingly interested in science and, on applying to Oxford, had aced the entrance exam and interview. He found Oxford ridiculously easy and had done well enough to impress his tutors and lecturers. It was at Cambridge as a PhD student, under Sciama’s tutelage, that Hawking would be steered toward the cosmos and, finding his scientific voice, would spell out one significant consequence of Penzias and Wilson’s discovery.
Stephen Hawking was a year older than Martin Rees and became fascinated by the mathematics of general relativity. Early on during his PhD studies, he had been diagnosed with Lou Gehrig’s disease and given just a couple of years to live. The initial news had been profoundly demoralizing, yet two years into his PhD he was still alive and well. His continued health galvanized him to focus on his work and try to understand what actually happened at the beginning of the universe’s expansion—at the Big Bang itself. Could it be that the singularities were inevitable at the beginning of time as well as in Wheeler’s final state?
As he raced against the possible onset of his illness, Hawking was able to show that, indeed, an expanding universe under normal conditions should have inevitably started off with a singularity. Over the years, he proved, with a South African physicist and fellow talented Sciama student named George Ellis, that a universe with relic radiation like that found by Penzias and Wilson must have started in a singular state. Finally, with Roger Penrose, he constructed a complete set of theorems that covered almost any possible model of an expanding universe that could be cooked up at the time. Singularities were inevitable, or so Penrose and Hawking’s math seemed to say, both in the future as well as in the past.
At the first Texas Symposium, there had been speculation that the distant, copious sources of radio waves in Ryle’s catalogue might somehow be related to the general relativistic collapse of supermassive stars. Chandra had once pointed out that superheavy white dwarfs would be unstable and might implode, and Oppenheimer and Snyder had shown that if stars were even heavier, the next stage in the inexorable collapse would be via neutron stars. While there was pretty convincing evidence for white dwarfs, there was no sign of neutron stars. That changed in 1965, when Jocelyn Bell arrived in Cambridge to start her PhD in Martin Ryle’s group.
Bell didn’t work with Ryle himself but with one of his more junior colleagues, Antony Hewish. Hewish had her build a radio telescope out of an assortment of wooden posts and chicken wire that she could use to pinpoint and study the position of quasars at 81.5 megahertz. As she puts it, her “first couple of years involved a lot of very heavy work in the field, or in a very cold shed.” But the job had its perks: “When I left I could swing a sledge hammer.” By 1967, Bell was taking data on a chart recorder, analyzing over 30 meters of chart paper a day, looking for the telltale signals of quasars. About 120 meters of paper would cover the whole sky.
There was something odd in the recording she was making. For each 120 meters of paper, there was a quarter-inch spike of data that Bell couldn’t understand. She couldn’t figure out what the signal was or where it was coming from. It was undoubtedly there, a set of chirps in a very specific direction of the sky. “We had begun nicknaming it ‘little green men,’” Bell recalls. “I went home feeling very fed up.” The team decided to go ahead and publish their mysterious finding.
In February 1968, a paper appeared in Nature titled “Observation of a Rapidly Pulsating Radio Source.” In it, Bell, Hewish, and their coauthors announced their discovery, declaring, “Unusual signals from pulsating radio sources have been recorded at the Mullard Radio Astronomy Observatory,” and then went on to make a bold claim: “The radiation seems to come from local objects within the galaxy, and may be associated with oscillations of white dwarf or neutron stars.” They speculated that the spikes in the chart paper were the oscillations or pulsations in these dense, compact radio sources.
The press took to the discovery, interviewing Hewish about its importance. But, as Bell recalls, “journalists were asking relevant questions like was I taller than or not quite as tall as Princess Margaret.” She says, “They’d turn to me and ask me what my vital statistics were or about how many boyfriends I had . . . that was all women were for.” The Sun headlined the news piece with “The Girl Who Spotted the Little Green Men.” It was the Daily Telegraph that came up with a name for the outlandish objects; a journalist suggested calling the objects “pulsars,” short for “pulsating radio stars.”
Yet again, radio astronomy had delivered in spades, and yet again, it was by chance. The discovery was momentous, and in 1974 the Nobel Prize was awarded to Bell’s supervisors, Tony Hewish and Martin Ryle. Bell was left out entirely, in what is seen by many as one of the greatest injustices in the history of the prize. Almost twenty years later, Bell attended the prize ceremony as the guest of another astronomer, Joseph Taylor Jr., when he won the Nobel Prize in 1993. “I did get to go in the end,” she recalls without any bitterness.
Pulsars were the first tangible evidence for neutron stars. They don’t actually pulsate—they rotate, which causes them to emit a periodic signal. But they were the fabled missing link in gravitational collapse, posited by Landau, studied by Oppenheimer, and explored in meticulous detail by Wheeler and his disciples. They were the final step before the formation of Penrose’s inevitable singularities.
When Yakov Zel’dovich switched fields, he did so fearlessly. One of his students recalls Zel’dovich’s advice: “It is difficult, but interesting to master ten percent of . . . any field. . . . The path from ten to ninety percent is pure pleasure and genuine creativity. . . . To go through the next nine percent is infinitely difficult, and far from everyone’s ability. . . . The last percent is hopeless,” from which Zel’dovich concluded, “It is more reasonable to switch to a new problem before it is too late.”
Like Wheeler, Zel’dovich turned from nuclear research to relativity in his forties, and he went on to set up one of the most focused research groups in the world. The papers that Zel’dovich wrote with his students were almost impressionistic, often with quirky openings such as “The Godfather of psychoanalysis Professor Sigmund Freud taught us that the behavior of adults depends on their early childhood experiences. In the same spirit, the problem is to derive the . . . present . . . structure of the universe . . . from . . . its early behavior.” They read like condensed essays, with a smattering of equations, just enough to flesh out his point. When translated into English, they could be difficult to decipher. But over time they were appreciated for what they were: veritable gems of relativistic astrophysics.
When Zel’dovich switched fields, he went looking for frozen stars, as Schwarzschild and Kerr’s collapsing stars were called in the East. These frozen stars are invisible, emit no light, and have no surface that can reflect or shine. Yet Zel’dovich couldn’t accept that these strange objects would be hidden from view, for they were dramatic, distorting space and time about them. In fact, as he began to discuss with his students, they should exert an inexorable pull on anything that gets near them. And so, he surmised, by looking at the effect of the frozen stars on other things, it just might be possible to see them, not directly but indirectly. For example, if the sun got too close to a frozen star, it would be forced to orbit around it, much like the moon around the Earth. The frozen star would be invisible, so the sun would look as if it were dancing around on its own, wobbling about in a strange orbit with no center. Look for wobbling stars, Zel’dovich and his team proposed: stars that appear to be on their own but behave like half of a binary system.
But, Zel’dovich conjectured, frozen stars shouldn’t just nudge their partners around; they should positively rip them apart. He made a very simple assumption: as stuff falls into the gravitational field of a frozen star, it should approach the speed of light, condensing and heating up in the process. As the material mixes and collides, heating up as it falls onto the frozen star in a process
that has been dubbed accretion, it radiates energy. The accretion near the Schwarzschild horizon is so efficient it can emit up to 10 percent of its rest mass energy, an astounding amount of energy that makes it the most efficient energy-generating process in the universe. And so, in a short paper published in Doklady Akademii Nauk in 1964, Zel’dovich went on to speculate that the production of energy around a frozen star would be overwhelming, enough to explain the intensely bright quasars that were being found by radio astronomers. At exactly the same time, an American astronomer at Cornell University, Edwin Salpeter, was coming to the same conclusion, that copious radio emissions could come from a massive object that weighed more than a million solar masses or, as he put it, “extremely massive objects of relatively small size.”
Zel’dovich didn’t stop there. With his young colleague Igor Novikov he applied his argument to binary systems such as a normal star circling a frozen star. They speculated that the immense gravitational pull of the frozen star would strip the outer layers of the normal star of all its gas and fuel. It is like, as Roger Penrose once put it, “having to drain . . . a bath the size of Loch Lomond through a normal size plughole.” The forces that the gas would experience would be so tremendous that copious amounts of light at very high energy, known as x-rays, would be emitted. Look for the x-rays, Zel’dovich and his pupils told the world.
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