4
Those who have lost the capacity for most physical pleasures value those that remain even more. A touch. A symphony. A scent. A taste. Meals were always important to Stephen. But they were also a time of connection. They were a hiatus from the world of mathematics in favor of engagement in the human realm. Still, even at mealtime, there was no hiatus in Stephen’s keen thought processes. If his approach to physics had the same mischievousness as his approach to humanity, his approach to humanity had the same sharpness of intellect that he employed in his physics.
Once at dinner when Stephen was still working on his Ph.D., he found himself at a table at Trinity College with a South African engineer. The engineer had just arrived in Cambridge. But if he marveled, as I had, at the university, and especially at Trinity—where Newton had studied—he kept that to himself. What he did do was proudly hold forth about how well South Africa was faring. According to the engineer, these were fabulous times in his homeland.
Stephen was never one to hold back on what he thought. On one occasion, after he’d become famous, he’d been invited as an honored guest to watch a modern production of the opera Madame Butterfly in Berlin. It turned out to be a mediocre performance. Afterward, the principal, delighted to host Stephen, said, “Professor Hawking, what did you think of the performance?” Stephen replied, “It wasn’t very good, was it?” His host was surprised at that answer. But then he said to Stephen, “Yes. I agree.”
The South African engineer’s disquisition couldn’t be described as either mediocre or not mediocre. It was just his opinion, expressed at too great a length. But it got Stephen’s attention. Stephen had ideas about it, and he wasn’t going to keep them to himself. He asked the engineer, “What about the black people?”
“They don’t really count,” the engineer said. In the early 1960s, that was not an unusual reply.
“Why don’t they count?” Stephen asked.
“They can’t take care of themselves,” he said. He talked about apartheid. It works, he said, and it’s necessary.
Although Stephen didn’t argue, he kept asking questions. He was challenging the man’s beliefs not by disagreeing with them, but in the Socratic style, by forcing him to see the implications, unadorned, of what he was saying.
The engineer had started the conversation, stating what he “knew” to be true. He had never before examined it very closely. But Stephen made their dinner conversation an exploration of the man’s beliefs, an exploration that the engineer himself had obviously never made. In the end, the man was flustered. Now that he’d been pushed to understand the foundation of his beliefs about apartheid and the nature of black people, he was questioning himself.
I once had a physics professor who advised me that “if you like asking questions and searching for answers, become a physicist. If you like learning the answers and applying them, become an engineer.” That’s a broad generalization, but it illustrates a difference in both the philosophy and psychology of those fields. Are you one who tends to learn and apply knowledge, or to question and create it? In leading the engineer to question, Stephen was just being Stephen, for it is by questioning your beliefs, and those of others, that important discoveries occur, not just in life but in physics.
The engineer had viewed his country as most people view the night sky, as constellations of white dots floating in a vast and unimportant sea of black. Through his questioning, Stephen led him to see more than just the dots. Stephen would do that to his fellow physicists, too. While they marveled at the stars and the galaxies, Stephen raised questions about the space in between them. Where did it come from? How did it all begin? In trying to understand the meaning of our existence, those seemed to him to be the most basic of questions. Yet, as Stephen began his Ph.D., few were asking them.
This was during the era in which general relativity and cosmology were in the doldrums. Physicists’ lack of interest in the birth of the universe seemed to make sense, because physics is an empirical science while the origin of the universe is not something we can observe directly. Because light takes time to get to us, by observing the light from distant galaxies we can essentially look back in time, but not that far back. Nor did anyone, in the early 1960s, know of any indirect way to test a theory of the universe’s origin. As a result of such issues, physicists tended to consider cosmology a pseudoscience, a mathematical playground outside the realm of experimental testing. That would begin to change after the accidental discovery in 1964 of the faint afterglow left over from the big bang, called the cosmic microwave background radiation. When Stephen was starting out at Cambridge, that was still a year or two away.
Another issue back then was the difficulty of understanding just what Einstein’s theory actually does predict. Like any theory in physics, Einstein’s is a scheme of mathematics and rules about what it represents and how to apply it. To extract what the theory has to say about a particular system, you have to use the scheme to set up equations tailored to that system and solve them, or at least approximate the solution. Einstein’s equations are in most cases extremely difficult to solve, so today we investigate their implications through the use of supercomputers, but the computer power available back then was feeble in comparison.
Due to difficulties of that sort, when Stephen moved to Cambridge the practitioners of general relativity and cosmology were mainly mathematicians whose work was detached from reality and whose models of the universe were unrealistic. That kept them occupied, but nobody paid much attention to their papers. The low quality of the work prompted Caltech physicist Richard Feynman to write his wife from a 1962 conference on gravity in Warsaw, “Because there are no experiments this field is not an active one…there are hosts of dopes here and it is not good for my blood pressure: such inane things are said and seriously discussed that I get into arguments…”
Most physicists concurred that questions of the origin of the universe were dead ends, but those were the questions that had won Stephen’s heart. And so, rather than being discouraged, he viewed the fact that the field was a backwater as an advantage. To him, the field wasn’t “dead,” it was “ripe”—and he was just the person to pluck it.
To nonscientists it may seem that theoretical physicists mainly solve problems. But what is more important than solving problems is posing them, because the questions you ask govern the answers you find. Questions are both a reflection of, and a determinant of, the way you look at the world. Stephen had a knack for dismissing what would later turn out to be unimportant and for quickly identifying what was really the heart of a matter. He intuitively asked the right questions and questioned the dubious assumptions of others. Because of that, Stephen was viewed as a rebel. That role came naturally to him—he ignored conventional wisdom just as he ignored the speed limits and the advice of his doctors. He drove his car wildly and recklessly, and his physics was also wild and unrestrained. But it wasn’t reckless. In physics, Stephen always knew, even as a graduate student, where he wanted to go, and why.
Physics is supposed to be a field of reason and logic. That is an important part of it, but in order to reason logically, you must first have a framework of thought that defines the assumptions you are making, the concepts you will use, and the questions you seek to answer. People often accept the frameworks they inherit from others, from history, or from their past, and never question or sufficiently examine them.
With regard to Stephen’s burning How did it all begin? question, for two millennia everyone had assumed that the universe had either always been in existence and was unchanging, or else that it was created at some moment—for example, as described in the Bible—and had been relatively unchanging since then.*1 Philosophers from Aristotle to Kant, as well as scientists, including even Isaac Newton, believed this.
Newton should have known better. How could a collection of galaxies and stars maintain a stationary configuration when each, through the force of gravity, pulls all the others toward it? Shouldn’t the objects coalesce over time? And, since forever is a long time, shouldn’t all matter, by now, be clumped together in a big dense ball? Newton was aware of this issue but talked himself out of it by convincing himself that if the universe were infinitely large, the clumping wouldn’t happen. That is wrong. Others, after Newton, tried to modify his theory to make gravity repulsive at long distances, employing a mathematical alteration small enough that it wouldn’t noticeably affect the orbit of the planets but large enough that it keeps the universe from collapsing upon itself. They were unsuccessful. Even Einstein joined the game. He added an extra “anti-gravity” term, called the cosmological constant, to the equations of general relativity to supply the repulsive force needed to keep the cosmos from contracting.*2
The realization that all these eminent philosophers and scientists were misguided—that the universe is changing, expanding, evolving—is one of the most extraordinary discoveries of the twentieth century. It is due to American astronomer Edwin Hubble, who had taught Spanish and coached basketball in a high school in New Albany, Indiana, before deciding to pursue a Ph.D. at the University of Chicago.
After graduating, Hubble had the good fortune to arrive at the Mount Wilson Observatory near Caltech in 1919, just as a new telescope was being installed. At the time, the prevailing view was that the universe consisted only of the Milky Way galaxy. Then, in 1924, Hubble discovered that the specks astronomers see when they examine nebulae—whitish clouds that stretch between the stars—were made of other, distant galaxies. Those clouds of galaxies seemed to extend as far as the Mount Wilson telescope would allow him to see. We now know that they extend even farther.
Because stars are hot, the atoms in their atmosphere are in a state of high energy. Some of that is energy of motion, but some is stored internally, in the electrons within the atom. Quantum theory tells us that the energy of those orbiting electrons can only take on certain values. When an electron leaps from one such energy level to a lower one, the atom emits light with a frequency that reflects the energy difference between the level the electron came from and the one it landed in. But each element has a unique set of energy levels. As a result, atoms of hydrogen, helium, and other elements each emit light that consists of a unique set of frequencies. That light provides a fingerprint that can be used to identify the element it came from. Astronomers use that fingerprint to identify the composition of comets, nebulae, and various types of stars.
In his years at Mount Wilson, Hubble noticed that compared to the light we observe coming from atoms here on earth, the light emanating from other galaxies was shifted toward the lower frequencies, the red end of the spectrum. He also noted that the farther away the galaxy, the greater that “redshift.”
The frequency shifts that captured Hubble’s imagination are due to a phenomenon first studied by Austrian physicist Christian Doppler in 1842. Doppler found that the color of light you observe from any given source depends on its motion with respect to you. The light will be redder if its source is moving away from you, and bluer if it moves toward you. Taking Doppler’s theory into account, Hubble’s work showed that the galaxies were moving away from us—and the more distant they were, the faster they were moving. This led to the dizzying conclusion that the universe is not only far vaster than anyone had thought, but that it is also expanding.
Astrophysicists sometimes use a “raisin bread” analogy to explain this thinking. Before I describe that, it is important to understand that the expansion of the universe is not like the explosion of a bomb. A bomb blows hot gases and shrapnel out into space that is already there. But there is no “outside” of the universe. When physicists say the universe is expanding, we mean that space itself is growing, from within: if you pick any two points the distance between them increases over time.
The raisin bread analogy works like this: Imagine you are inside a ball of dough riddled with raisins that are roughly evenly distributed. The ball of dough represents three-dimensional space. The raisins represent the galaxy clusters. This model has a flaw, in that space therefore has an edge, the outer surface of the dough ball. Space has no such edge, but for the purpose of this analogy that’s not an important distinction. Now let the dough rise until its radius has doubled. A raisin an inch away from you will then be two inches away—an inch farther than when we started. In such a scenario a raisin that started three inches away will now be six inches away. It will have moved three inches in the same amount of time, so the speed at which it is moving away from you will be three times that of the first. Similarly, a raisin that started five inches away will now be at a distance of ten inches, having moved five inches in that time. As the dough keeps expanding all the raisins will move away from you, and the farther away a raisin, the faster it will recede.
In 1929, almost a century after Darwin started to formulate his theory of biological evolution, Hubble had discovered that the universe, too, was evolving. But the idea of an unchanging universe did not die easily. Physicists, who are good at such things, concocted theories to save their precious preconception. One of the most famous came from Fred Hoyle’s work on the steady state theory. Adherents of that theory didn’t dispute that the distant galaxies were moving away from us, but the theory postulated that new matter is constantly being created, so that the density of matter remains unchanged as the universe expands, with the new matter filling in the new space. In that way, the universe could remain, on the cosmic scale, unchanged.
The steady state theory’s main competitor at the time was the big bang theory. Hoyle wanted nothing to do with that latter theory, but he was responsible for its name. It came from a comment he made on a BBC radio broadcast in 1949, when he called it “the hypothesis that all the matter in the universe was created in one big bang at a particular time in the remote past.” Some say he’d used the term sarcastically. He denied that. Either way, the term stuck.
If a theory draws a lot of interest, one of the first things physicists will do is name it. A measure of the lack of interest in the big bang theory was that it didn’t get its name until about twenty years after it was conceived. The theory had been invented by a brilliant Belgian priest and physics professor named Georges Lemaître. He began by analyzing Einstein’s equations, which in 1927 led him to argue that the universe must be expanding—two years before Hubble’s work showed that this was indeed the case. He then noted that if the universe is growing larger, it must have been smaller in the past, and that the farther back you go, the smaller the universe. He concluded in 1931 that at some time in the past the size of the universe must have been zero—in other words, that all the mass of the universe must have been concentrated into a single point. He called that the “primeval atom.”
The big bang theory seemed to imply that there was a moment of creation, but again, clever physicists found a way to avoid that conclusion. They created a version of the big bang theory in which, going back in time, matter didn’t all contract to a single point but rather to a small volume, so that, as time moves backward, particles of matter could skate past each other. As a result, instead of crashing into a single point, particles would come close, fly by one another, and again move farther apart. In that way, the universe would be eternal, but it would exist in alternate cycles of expansion and contraction. Belief in the steady state and the various forms of the big bang was divided when Stephen entered Cambridge—at least among those few physicists who gave it any thought at all.
Stephen told me once when I brought up the topic of religion that he did not “engage in metaphysics.” Like the philosophers, Stephen wanted to answer the great questions, but he wanted to do it using science, which he knew was much harder. In science, reason is not enough. In philosophy you are free to theorize. In science, experiment can prove that you are wrong. Stephen felt that scientists from Newton to Einstein had been let down by their philosophical and religious beliefs, seduced into ideas about physics that were not backed up by theory or experiment. And so he questioned the belief that the universe is unchanging and that it is eternal. Just as important, he questioned the even more widespread belief that the issue is not one of great importance.
In the repository at Cambridge, stamped with the date 1 FEB 1966, is Stephen Hawking’s Ph.D. dissertation: Properties of Expanding Universes. He was twenty-four then. The dissertation opens, “Some implications and consequences of the expanding universe are examined…” Typed by Jane—because Stephen was incapable of doing it—what follows are four chapters that include cross-outs and handwritten equations. The last chapter, about twenty pages long, is the one that made Stephen famous among his peers.
Stephen had arrived in Cambridge in October 1962. He spent his first two years of graduate school making lifelong friends and settling into married life, but in his physics he was drifting. He was studying general relativity, attacking various problems that he and his advisor, Sciama, thought promising, but not discovering anything much of note.
Those studies, which would form the first three chapters of his Ph.D. dissertation, were unremarkable. They were independent mathematical analyses of various topics, and they made interesting points, mainly mathematical criticisms of Hoyle’s steady state theory. But the work had holes and left unanswered questions. Alone, those chapters might not have been sufficient to earn Stephen a Ph.D., and they certainly would not have made him famous. But thanks to Stephen’s becoming familiar with the work of a thirty-three-year-old mathematician named Roger Penrose, he added a fourth chapter, more or less independent of the others, and this was the chapter that would launch his career. Stephen learned of Penrose’s work in January 1965, after Penrose gave a seminar on it at King’s College, in London. Ten years younger than Penrose, Stephen had been attending that series of seminars. As it happens, he didn’t attend this one, but he heard about it from Brandon Carter, his office mate in Cambridge.
If, in the story of the universe, it is important to take into account the pull of all matter toward all other matter, it is equally important when telling the tale of a star. One might wonder, for example, why the sum of all those attractions doesn’t cause the star to collapse upon itself. The answer comes from the nuclear reactions within the star. They lend the stars heat, imparting to the gases a tendency to expand, thus balancing the compression effect of gravity. The work Penrose described in his talk concerned what happens after that, after a massive star burns out its nuclear fuel and begins to cool down. When that happens, the dying star begins to collapse under the force of its own gravity.
Penrose recognized that the collapse is a complex and chaotic process, and doesn’t necessarily maintain the original star’s neat spherical symmetry. As a result, the collapse can proceed according to two possible scenarios. One is reminiscent of the version of the big bang theory in which the particles skate past each other: as the star collapses, its constituents could all fall toward the star’s center but not toward precisely the same point. They might then race past one another, resulting in an expansion phase. In the other scenario, despite the chaos of the collapse the stuff of the star is all drawn to its precise center, where it is crushed into a single point in which the density of matter is infinite.
That second possibility, Penrose eventually proved, is the one that Einstein’s equations demand. In 1969, physicist John Wheeler would call dead stars of that sort—those with a point of infinite density at their center—black holes, but in 1965 there hadn’t yet been enough interest in them to produce an agreed-upon name.
Physicists call a point at which physical quantities become infinite a singularity. Physicists shun singularities because we shun infinities. We shun infinities because, though they may occur in mathematics, they don’t occur in the real world. Nothing we measure is infinite, so any theory that predicts that a singularity occurs must be wrong.
As a workaround, physicists tried to find a way to render the presence of the singularity moot. They thought of a few options. One is to point out that Einstein’s theory is not a quantum theory, and therefore at some point during the star’s collapse—when it reached a certain minute size—his theory would no longer apply without some (yet to be invented) modification. Will that modification eliminate the singularity? We don’t know. Another is to say that since we cannot look inside a black hole, the singularity is forever hidden—unobservable—and hence does not matter. That sounds reasonable, but it’s not that simple. Black holes can rotate, and some rather esoteric calculations suggest that that rotation might expose the singularity. So the jury on this is still out.
The famous chapter that Stephen added to his dissertation didn’t have to do with any of that. While Penrose’s work had stimulated many theorists to start pondering black holes, Stephen, as usual, took off in his own direction. He saw the story of the star collapsing under the force of gravity as being reminiscent of the big bang, only in reverse. What if the universe was like a giant black hole that, if you run time backward, collapses just like one of Penrose’s stars? Could he adapt Penrose’s mathematical methods to gain insight that escaped even Einstein? Could he prove that Einstein’s equations dictate that the big bang—and not the version that includes repeated cycles of expansion and contraction—must have occurred?
Like Galileo, who had taken a primitive spyglass, improved its optics, and directed it toward the heavens, Stephen appropriated Penrose’s mathematics and employed it to study the cosmos. With chapter four of his Ph.D. dissertation—and follow-up work done together with Penrose himself in the years to come—Stephen soon surpassed his advisor Dennis Sciama in reputation and eventually even his once-desired advisor, Fred Hoyle: he showed that, singularity and all, the big bang is an unavoidable consequence of general relativity. There were no cycles of expansion and contraction, there was a beginning, and at that moment, though physicists didn’t like it, the universe was packed into a space of zero volume. At least, those conclusions were the inevitable result of Einstein’s equations.
Around the time Stephen was doing his theoretical work, observational astrophysicists started to find experimental evidence of the big bang. Nuclear physics had shown that, in the first minutes after that event, the extremes of temperature and pressure would cause some hydrogen nuclei (protons) to fuse together, forming helium. Detailed calculations had indicated that we ought to find about one helium nucleus for every ten hydrogen nuclei, and astronomical observation confirmed this. The big bang theory also predicted that some radiation from that event should persist to this day—the cosmic microwave background radiation. That, too, had been discovered, two years before Stephen’s dissertation. But the mathematics proving that the big bang is a necessity of Einstein’s equations—that came from Stephen, in his first major foray into the world of physics.