The Perfect Theory (10 page)

As experimental techniques advanced at the turn of the twentieth century, nature began to appear chunky and discrete, not smooth and continuous. In other words, nature seemed to be quantized. In the early twentieth century, a makeshift model for nature at the smallest scales began to emerge, a motley set of new rules for how atoms behaved and how they interacted with light. While Einstein himself occasionally made a contribution to this new science, he mostly observed the developments with some disbelief. The new rules proposed for a quantized world were clunky and didn't fit the elegant mathematical picture that had emerged from his principles of relativity.

In 1927, the rules of quantum physics finally fell into place. Two physicists, Werner Heisenberg and Erwin Schrödinger, each independently came up with new theories that could consistently explain the quantum nature of atoms. And like Einstein when constructing his general theory of relativity, the two men had to couch their versions of quantum theory in new mathematics. Heisenberg used matrices, tables of numbers that have to be worked with very carefully. Unlike ordinary numbers, if you multiply two matrices A and B, you will normally get a different result than you would if you were to multiply B with A, which can lead to some quite startling results. Schrödinger opted to describe reality—the atoms, nuclei, and electrons that stuff is made of—as matter waves, exotic objects that, just as in Heisenberg's theory, would lead to some strange physical phenomena.

The most notorious result to come out of the new quantum physics was the uncertainty principle. In classical Newtonian physics, objects move in a predictable way in response to outside forces. Once you know the exact position and velocities of a system's constituents and any forces acting on the system, you can predict all of the system's future configurations. Prediction becomes particularly easy; all you need to know is each particle's position in space and the direction and magnitude of its velocity. But in the new quantum theory it was
impossible
to know both the position and the velocity of a particle with perfect accuracy. A particularly persistent and stubborn experimenter in a lab who tries to pin down the position of a particle with perfect precision will have
absolutely no idea
what its velocity is. You could imagine that it is like working with an angry caged animal: the more you try to confine it, the more furious it will get, pounding on the walls of its cage. If you put it in too small a box, the pressure from its pounding on the walls will be immense. Quantum physics brought uncertainty and randomness into the heart of physics. It was precisely this randomness that could be put to use in solving the problem of white dwarfs.

 

Subrahmanyan Chandrasekhar yearned to do great things, almost desperately. Born into an affluent Brahmin family in India, Chandra, as he became widely known, was an intense and committed student. He excelled at mathematics and was meticulous and fearless at calculating. While studying at the University of Madras, he was exposed to the new ideas coming over from Europe, starstruck by the great men who were building the new physics of the twentieth century. From a young age, and with a feverish passion, he set about trying to join the fray of modern physics. As he said, later in life,
“Certainly one of the earliest motives that I had was to show the world what an Indian could do.”

Chandra was entranced by the new quantum physics. He read all the new textbooks that came his way, among them Eddington's recently published book,
The
Internal Constitution of the Stars.
But what really won him over was a book on the quantum properties of matter by the German physicist Arnold Sommerfeld. Inspired by Sommerfeld's work, he set to work making a name for himself by writing papers on the statistical properties of quantum systems and how they interact. One of the first papers he wrote was published in the
Proceedings of the Royal Society
when Chandra was not yet eighteen years old. Clearly capable of taking part in the great discoveries of the new quantum physics in Europe, Chandra chose England to pursue his calling and set off on the long trip to Cambridge for his PhD.

It was during his long voyage on a ship of the Lloyd Triestino line that Chandra made the startling discovery that would transform his life. Obsessed with his work, he decided to spend his trip focusing on a paper written by Ralph Fowler, one of Eddington's colleagues at Cambridge, which seemed to solve the problem of white dwarfs. Fowler had invoked two quantum concepts and dragged them into astrophysics. The first was Heisenberg's uncertainty principle, the fact that you couldn't pin down a particle and at the same time determine its state of motion or velocity. The second concept was the exclusion principle, which states that two electrons (or protons) within an atom cannot be in exactly the same physical state—the exotic matter wave that Schrödinger had proposed as the fundamental quantum description of a particle—at the same time. Indeed, it is as if there is a fundamental, inexorable repulsion between them, preventing them from occupying that same state.

Fowler took the uncertainty and exclusion principles and set out to apply them to Sirius B. He reasoned that the material in a white dwarf such as Sirius B was so dense that he could think of it as a gas of electrons and protons being squeezed together. The electrons are so much lighter that they are allowed to roam more freely and jiggle about much more vigorously. The exclusion principle means that electrons have to be careful not to encroach on one another's space, and as the density builds up, each electron has less and less space to move in. As each electron is pinned down more and more, the uncertainty principle kicks in and the velocities and motions get higher and higher, forcing the electrons against each other. These fast-moving, jiggling electrons lead to an outward push, a
quantum
pressure inside the white dwarf, that can counteract the pull of gravity. In a certain state, the gravity exactly balances the quantum pressure and the white dwarf can sit placidly, hardly glowing but resisting a catastrophic fate. Fowler's explanation cleared up Eddington's problem. It seemed that stars could end up as white dwarfs. It closed the narrative of stellar evolution and solved the cliffhanger in
The Internal Constitution of the Stars
—or so it seemed.

Chandra took another look at Fowler's result and did something very simple. He put in the numbers he expected for the density of the electron gas in the white dwarfs. The number he came out with was immense but unsurprising, exactly as Fowler had claimed in his paper. What Fowler had failed to do was work out how large the velocities of the electrons would actually be. When Chandra did this simple calculation, he was shocked: the electrons would have to be zipping around close to the speed of light. And this is where Fowler's argument fell apart, for he had completely ignored the rules of special relativity that are so important when things start moving at the speed of light. Fowler made the mistake of assuming that the electrons inside the white dwarf could move as fast as they wanted, even if that meant they were zipping around
faster
than the speed of light.

Chandra set out to fix Fowler's mistake. He followed Fowler's reasoning all the way up until the electrons were moving close to the speed of light. If the white dwarf was too dense, and the particles were indeed moving close to or at the speed of light, he used Einstein's special theory of relativity, which posited that they couldn't move any faster. The result he obtained was intriguing. He found that if the white dwarf became too heavy, it would also become too dense and the electrons would be unable to sustain the gravitational pull. In other words, there was a maximum mass for a white dwarf. In his calculation, Chandra found that it couldn't be larger than about 90 percent of the mass of the sun. (Years later it would be shown that the correct value is more like 140 percent of the mass of the sun.) If a star ended its life as a white dwarf heavier than this maximum mass, it would be unable to support itself. Gravity would win out and inexorable collapse would ensue.

When he arrived in Cambridge, Chandra gave Eddington and Fowler a draft of his calculation, but they ignored it. There was something deeply unsettling about the instability, which would wreck the edifice Eddington had so promisingly put forward and to which Fowler had added, and so the Cambridge men kept their distance. Over a period of four years, Chandra perfected his argument, and his confidence in his result grew. In 1933 Chandra finished his PhD and, at age twenty-two, was made a fellow of Trinity College. By 1935 Chandra had finessed his calculation still further and was prepared to present his results at one of the monthly meetings of the Royal Astronomical Society.

On January 11, 1935, Chandra stood up in front of a crowd of distinguished astronomers at the Royal Astronomical Society, at Burlington House in London. Carefully and meticulously Chandra worked through his results, presenting the details of his nineteen-page paper, which was about to be published by the
Monthly Notices
of the society. He finished by saying,
“A star of large mass cannot pass into the white dwarf stage, and one is left speculating on other possibilities.” This strange result was there in the mathematics and physics that they all believed and had to be taken seriously. When Chandra finished, there was polite applause and a smattering of questions. It was done.

The president of the RAS then turned to Eddington and invited him to step up to the podium to talk on his own paper, “Relativistic Degeneracy.” Eddington stood up to give his brief, fifteen-minute talk. He carefully went over Chandra's claim that his calculation scuppered Fowler's solution to the problem of white dwarfs. And then he summarily dismissed Chandra's watertight argument. To Eddington, Chandra's result was “a reductio ad absurdum of the relativistic degeneracy formula.” In fact, he firmly believed that “various accidents may intervene to save the star,” and furthermore, “I think there should be a law of nature to prevent a star from behaving in this absurd way!” Eddington's authority was such that Chandra's talk was immediately dismissed by most of the audience. If Eddington thought it was wrong, it
must
be wrong.

Chandra had come up against the mighty Eddington and lost. He was sabotaging Eddington's beautiful story of how stars lived and died, and Eddington didn't like it. If gravitational collapse overcame everything, Schwarzschild's strange solution would have to be faced head-on, with all its bizarre consequences. As Chandra himself said, many years later, “Now, that clearly shows that . . . Eddington realized that the existence of a limiting mass implies that black holes must occur in nature. But he did not accept that conclusion. . . . If he had accepted that, he would have been 40 years ahead of anybody else. In a way it is too bad.”

Chandra returned to Cambridge devastated. His run-in with Eddington was to mark him for the rest of his life. A few years later he was invited to take up a post in the Yerkes Observatory in Chicago. He stopped working on white dwarfs and shied away from thinking of what would happen if indeed their masses were too large. Would they lead to the inexorable formation of Schwarzschild's solution, or would something prevent that from happening along the way? Robert Oppenheimer would be the one to answer those questions.

 

J. Robert Oppenheimer was a child of the quantum. Brought up in an affluent New York family with van Goghs hanging on their walls, Oppenheimer had a gilded education, first studying at Harvard and then, in 1925, moving to Cambridge. Oppenheimer's Harvard mentor wrote in his letter of recommendation to Cambridge that Oppenheimer
“was evidently much handicapped by his lack of familiarity with ordinary physical manipulations,” although he added, “You will seldom find a more interesting betting proposition.” Oppenheimer's sojourn in Cambridge was a disaster and short-lived. After a nervous breakdown during which he assaulted one of his colleagues and confessed to trying to poison another, Oppenheimer decided to leave and try his luck in Göttingen.

Göttingen, the land of David Hilbert, had embraced quantum physics, and Oppenheimer couldn't have been at a better place to take part in the new revolution. Over the next two years he wrote a series of papers with his supervisor, Max Born, that would indelibly imprint his name in the history of quantum physics. Indeed, the Born-Oppenheimer approximation is still taught in universities today and is part of the paraphernalia used to calculate the quantum behavior of molecules. Oppenheimer finished his PhD in 1927 and a few years later returned to the United States to take up a position at the University of California at Berkeley.

At Berkeley, Oppenheimer set up one of the beacons of theoretical physics in 1930s America. Oppie, as he was fondly called, seemed to be able to hold forth on any topic, from art and poetry to physics and sailing. Sharp and incredibly quick at picking up on difficult concepts, he hopped from project to project, intellectually raiding new fields and making quick contributions that, while not necessarily profound, were undoubtedly timely and clever. He was impatient and sometimes cruel if he didn't agree with or understand an argument, but Oppenheimer's sheer magnetism and energy made him a natural leader, and he excelled at supporting and inspiring his group. He slowly and surely recruited a coterie of brilliant and enthusiastic students and researchers with whom he would tackle many of the new problems that were being discussed in Europe. Wolfgang Pauli, noting that Oppenheimer in his enthusiasm had a habit of muttering, dubbed his group the
“nim nim boys.” Berkeley was Oppenheimer's Göttingen, his Copenhagen.

And then, after nearly ten years of focusing almost exclusively on the quantum, in 1938, Oppenheimer became intrigued by Einstein's general theory of relativity. Like Chandra, he approached the theory from the quantum end, looking at how the quantum effects of matter might play off against the gravitational implosion of space and time.