5

Implosion Is Compulsory

in which even the nuclear force,

supposedly the strongest of all forces,

cannot resist the crush of gravity

Zwicky

I n the 1930s and 1940s, many of Fritz Zwicky’s colleagues regarded him as an irritating buffoon. Future generations of astronomers would look back on him as a creative genius.

“By the time I knew Fritz in 1933, he was thoroughly convinced that he had the inside track to ultimate knowledge, and that everyone else was wrong,” says William Fowler, then a student at Caltech (the California Institute of Technology) where Zwicky taught and did research. Jesse Greenstein, a Caltech colleague of Zwicky’s from the late 1940s onward, recalls Zwicky as “a self-proclaimed genius.¼ There’s no doubt that he had a mind which was quite extraordinary. But he was also, although he didn’t admit it, untutored and not self-controlled. ¼ He taught a course in physics for which admission was at his pleasure. If he thought that a person was sufficiently devoted to his ideas, that person could be admitted. ¼ He was very much alone [among the Caltech physics faculty, and was] not popular with the establishment. . . . His publications often included violent attacks on other people.”

Zwicky—a stocky, cocky man, always ready for a fight—did not hesitate to proclaim his inside track to ultimate knowledge, or to tout the revelations it brought. In lecture after lecture during the 1930s, and article after published article, he trumpeted the concept of a neutron star— a concept that he, Zwicky, had invented to explain the origins of the most energetic phenomena seen by astronomers: supernovae, and cosmic rays. He even went on the air in a nationally broadcast radio show to popularize his neutron stars. But under close scrutiny, his articles and lectures were unconvincing. They contained little substantiation for his ideas.

It was rumored that Robert Millikan (the man who had built Caltech into a powerhouse among science institutions), when asked in the midst of all this hoopla why he kept Zwicky at Caltech, replied that it just might turn out that some of Zwicky’s far-out ideas were right. Millikan, unlike some others in the science establishment, must have seen hints of Zwicky’s intuitive genius—a genius that became widely recognized only thirty-five years later, when observational astronomers discovered real neutron stars in the sky and verified some of Zwicky’s extravagant claims about them.

Fritz Zwicky among a gathering of scientists at Caltech in 1931. Also in the photograph are Richard Tolman (who will be an important figure later in this chapter), Robert Millikan, and Albert Einstein. [Courtesy of the Archives, California Institute of Technology.]

Among Zwicky’s claims, the most relevant to this book is the role of neutron stars as stellar corpses. As we shall see, a normal star that is too massive to die a white-dwarf death may die a neutron-star death instead. If all massive stars were to die that way, then the Universe would be saved from the most outrageous of hypothesized stellar corpses: black holes. With light stars becoming white dwarfs when they die, and heavy stars becoming neutron stars, there would be no way for nature to make a black hole. Einstein and Eddington, and most physicists and astronomers of their era, would heave a sigh of relief.

Z wicky had been lured to Caltech in 1925 by Millikan. Millikan expected him to do theoretical research on the quantum mechanical structures of atoms and crystals, but more and more during the late 1920s and early 1930s, Zwicky was drawn to astrophysics. It was hard not to be entranced by the astronomical Universe when one worked in Pasadena, the home not only of Caltech but also of the Mount Wilson Observatory, which had the world’s largest telescope, a reflector 2.5 meters (100 inches) in diameter.

In 1931 Zwicky latched on to Walter Baade, a new arrival at Mount Wilson from Hamburg and Göttingen and a superb observational astronomer. Baade and Zwicky shared a common cultural background: Baade was German, Zwicky was Swiss, and both spoke German as their native language. They also shared respect for each other’s brilliance. But there the commonality ended. Baade’s temperament was different from Zwicky’s. He was reserved, proud, hard to get to know, universally well informed—and tolerant of his colleagues’ peculiarities. Zwicky would test Baade’s tolerance during the coming years until finally, during World War II, he and Zwicky would split violently. “Zwicky called Baade a Nazi, which he wasn’t, and Baade said he was afraid that Zwicky would kill him. They became a dangerous pair to put in the same room,” recalls Jesse Greenstein.

During 1932 and 1933, Baade and Zwicky were often seen in Pasadena, animatedly conversing in German about stars called “novae,” which suddenly flare up and shine 10,000 times more brightly than before; and then, after about a month, slowly dim down to normalcy. Baade, with his encyclopedic knowledge of astronomy, was aware of tentative evidence that, in addition to these “ordinary” novae, there might also be unusual, rare, superluminous novae. Astronomers at first had not suspected that those novae were superluminous, since they appeared through telescopes to be roughly the same brightness as ordinary novae. However, they resided in peculiar nebulas (shining “clouds”); and in the 1920s, observations at Mount Wilson and elsewhere began to convince astronomers that those nebulas were not simply clouds of gas in our own Milky Way galaxy, as had been thought, but rather were galaxies in their own right-giant assemblages of nearly 10 ¹² (a trillion) stars, far outside our own galaxy. The rare novae seen in these galaxies, being so much farther away than our own galaxy’s ordinary novae, would have to be intrinsically far more luminous than ordinary novae in order to have a similar brightness as seen from Earth.

Baade collected from the published literature all the observational data he could find about each of the six superluminous novae that astronomers had seen since the turn of the century. These data he combined with all the observational information he could get about the distances to the galaxies in which they lay, and from this combination he computed how much light the superluminous novae put out. His conclusion was startling: During flare-up these superluminous novae were typically 10 ⁸ (100 million) times more luminous than our Sun! (Today we know, thanks largely to work in 1952 by Baade himself, that the distances were underestimated in the 1930s by nearly a factor of 10, and that correspondingly ¹ the superluminous novae are nearly 10 ¹⁰ —10 billion—times more luminous than our Sun.)

The galaxy NGC 4725 in the constellation Coma Berenices. .Left: As photographed on 10 May 1940, before a supernova outburst. Right: On 2 January 1941 during the supernova outburst. The white line points to the supernova, in the outer reaches of the galaxy. This galaxy is now known to be 30 million light-years from Earth and to contain 3 × 10 ¹¹ (a third of a trillion) stars. [Courtesy California Institute of Technology.]

Zwicky, a lover of extremes, was fascinated by these superluminous novae. He and Baade discussed them endlessly and coined for them the name supernovae. Each supernova, they presumed (correctly), was produced by the explosion of a normal star. And the explosion was so hot, they suspected (this time incorrectly), that it radiated far more energy as ultraviolet light and X-rays than as ordinary light. Since the ultraviolet light and X-rays could not penetrate the Earth’s atmosphere, it was impossible to measure just how much energy they contained. However, one could try to estimate their energy from the spectrum of the observed light and the laws of physics that govern the hot gas in the exploding supernova.

By combining Baade’s knowledge of the observations and of ordinary novae with Zwicky’s understanding of theoretical physics, Baade and Zwicky concluded (incorrectly) that the ultraviolet radiation and X-rays from a supernova must carry at least 10,000 and perhaps 10 million times more energy even than the visible light. Zwicky, with his love of extremes, quickly assumed that the larger factor, 10 million, was correct and quoted it with enthusiasm.

This (incorrect) factor of 10 million meant that during the several days that the supernova was at its brightest, it put out an enormous amount of energy: roughly a hundred times more energy than our Sun will radiate in heat and light during its entire 10-billion-year lifetime. This is about as much energy as one would obtain if one could convert a tenth of the mass of our Sun into pure, luminous energy!

(Thanks to decades of subsequent observational studies of supernovae—many of them by Zwicky himself—we now know that the Baade-Zwicky estimate of a supernova’s energy was not far off the mark. However, we also know that their calculation of this energy was badly flawed: Almost all the outpouring energy is carried by particles called neutrinos and not by X-ray and ultraviolet radiations as they thought. Baade and Zwicky got the right answer purely by luck.)

What could be the origin of this enormous supernova energy? To explain it, Zwicky invented the neutron star.

Z wicky was interested in all branches of physics and astronomy, and he fancied himself a philosopher. He tried to link together all phenomena he encountered in what he later called a “morphological fashion.” In 1932, the most popular of all topics in physics or astronomy was nuclear physics , the study of the nuclei of atoms. From there, Zwicky extracted the key ingredient for his neutron-star idea: the concept of a neutron.

Since the neutron will be so important in this chapter and the next, I shall digress briefly from Zwicky and his neutron stars to describe the discovery of the neutron and the relationship of neutrons to the structure of atoms.

After formulating the “new” laws of quantum mechanics in 1926 (Chapter 4 ), physicists spent the next five years using those quantum mechanical laws to explore the realm of the small. They unraveled the mysteries of atoms (Box 5.1) and of materials such as molecules, metals, crystals, and white-dwarf matter, which are made from atoms. Then, in 1931, physicists turned their attention inward to the cores of atoms and the atomic nuclei that reside there.

The nature of the atomic nucleus was a great mystery. Most physicists thought it was made from a handful of electrons and twice as many protons, bound together in some as yet ill-understood way. However, Ernest Rutherford in Cambridge, England, had a different hypothesis: protons and neutrons. Now, protons were already known to exist. They had been studied in physics experiments for decades, and were known to be about 2000 times heavier than electrons and to have positive electric charges. Neutrons were unknown. Rutherford had to postulate the neutron’s existence in order to get the laws of quantum mechanics to explain the nucleus successfully. A successful explanation required three things: (1) Each neutron must have about the same mass as a proton but have no electric charge, (2) each nucleus must contain about the same number of neutrons as protons, and (3) all the neutrons and protons must be held together tightly in their tiny nucleus by a new type of force, neither electrical nor gravitational-a force called, naturally, the nuclear force. (It is now also called the strong force.) The neutrons and protons would protest their confinement in the nucleus by claustrophobic, erratic, high-speed motions; these motions would produce degeneracy pressure; and that pressure would counterbalance the nuclear force, holding the nucleus steady at its size of about 10 ⁻¹³ centimeter.

Box 5.1

The Internal Structures of Atoms

An atom consists of a cloud of electrons surrounding a central, massive nucleus. The electron cloud is roughly 10 ⁻⁸ centimeter in size (about a millionth the diameter of a human hair), and the nucleus at its core is 100,000 times smaller, roughly 10 ⁻¹³ centimeter; see the diagram below. If the electron cloud were enlarged to the size of the Earth, then the nucleus would become the size of a football field. Despite its tiny size, the nucleus is several thousand times heavier than the tenuous electron cloud.

The negatively charged electrons are held in their cloud by the electrical pull of the positively charged nucleus, but they do not fall into the nucleus for the same reason as a white-dwarf star does not implode: A quantum mechanical law called the Pauli exclusion principle forbids more than two electrons to occupy the same region of space at the same time (two can do so if they have opposite “spins,” a subtlety ignored in Chapter 4 ). The cloud’s electrons therefore get paired together in cells called “orbitals.” Each pair of electrons, in protest against being confined to its small cell, undergoes erratic, high-speed “claustrophobic” motions, like those of electrons in a white-dwarf star (Chapter 4 ). These motions give rise to “electron degeneracy pressure,” which counteracts the electrical pull of the nucleus. Thus, one can think of the atom as a tiny white-dwarf star, with an electric force rather than a gravitational force pulling the electrons inward, and with electron degeneracy pressure pushing them outward.

The right-hand diagram below sketches the structure of the atomic nucleus, as discussed in the text; it is a tiny cluster of protons and neutrons, held together by the nuclear force.

In 1931 and early 1932, experimental physicists competed vigorously with each other to test this description of the nucleus. The method was to try to knock some of Rutherford’s postulated neutrons out of atomic nuclei by bombarding the nuclei with high-energy radiation. The competition was won in February 1932 by a member of Rutherford’s own experimental team, James Chadwick. Chadwick’s bombardment succeeded, neutrons emerged in profusion, and they had just the properties that Rutherford had postulated. The discovery was announced with fanfare by newspapers around the world, and naturally it caught Zwicky’s attention.

T he neutron arrived on the scene in the same year as Baade and Zwicky were struggling to understand supernovae. This neutron was just what they needed, it seemed to Zwicky. Perhaps, he reasoned, the core of a normal star, with densities of, say, 100 grams per cubic centimeter, could be made to implode until it reached a density like that of an atomic nucleus, 10 ¹⁴ (100 trillion) grams per cubic centimeter; and perhaps the matter in that shrunken stellar core would then transform itself into a “gas” of neutrons—a “neutron star” Zwicky called it. If so, Zwicky computed (correctly in this case), the shrunken core’s intense gravity would bind it together so tightly that not only would its circumference have been reduced, but so would its mass. The stellar core’s mass would now be 10 percent lower than before the implosion. Where would that 10 percent of the core’s mass have gone? Into explosive energy, Zwicky reasoned (correctly again; see Figure 5.1 and Box 5.2).

If, as Zwicky believed (correctly), the mass of the shrunken stellar core is about the same as the mass of the Sun, then the 10 percent of it that is converted to explosive energy, when the core becomes a neutron star, would produce 10 ⁴⁶ joules, which is close to the energy that Zwicky thought was needed to power a supernova. The explosive energy might heat the outer layers of the star to an enormous temperature and blast them off into interstellar space (Figure 5.1), and as the star exploded, its high temperature might make it shine brightly in just the manner of the supernovae that he and Baade had identified.

Zwicky did not know what might initiate the implosion of the star’s core and convert it into a neutron star, nor did he know how the core might behave as it imploded, and therefore he could not estimate how long the implosion would take (is it a slow contraction or a high-speed implosion?). (When the full details were ultimately worked out in the 1960s and later, the core turned out to implode violently; its own intense gravity drives it to implode from about the size of the Earth to 100 kilometers circumference in less than 10 seconds.) Zwicky also did not understand in detail how the energy from the core’s shrinkage might create a supernova explosion, or why the debris of the explosion would shine very brightly for a few days and remain quite bright for a few months, rather than a few seconds or hours or years. However, he knew-or he thought he knew-that the energy released by forming a neutron star was the right amount, and that was enough for him.

5.1 Fritz Zwicky’s hypothesis for triggering supernova explosions: The supernova’s explosive energy comes from the implosion of a star’s normal-density core to form a neutron star.

Box 5.2

The Equivalence of Mass and Energy

Mass, according to Einstein’s special relativity laws, is just a very compact form of energy. It is possible, though how is a nontrivial issue, to convert any mass, including that of a person, into explosive energy. The amount of energy that comes from such conversion is enormous. It is given by Einstein’s famous formula E =Mc ² , where E is the explosive energy, M is the mass that gets converted to energy, and c =2.99792 × 10 ⁸ meters per second is the speed of light. From the 75-kilogram mass of a typical person this formula predicts an explosive energy of 7 × 10 ¹⁸ joules, which is thirty times larger than the energy of the most powerful hydrogen bomb that has ever been exploded.

The conversion of mass into heat or into the kinetic energy of an explosion underlies Zwicky’s explanation for supernovae (Figure 5.1), the nuclear burning that keeps the Sun hot (later in this chapter), and nuclear explosions (next chapter).

Zwicky was not content with just explaining supernovae; he wanted to explain everything in the Universe. Among all the unexplained things, the one getting the most attention at Caltech in 1932–1933 was cosmic rays—high-speed particles that bombard the Earth from space. Caltech’s Robert Millikan was the world leader in the study of cosmic rays and had given them their name, and Caltech’s Carl Anderson had discovered that some of the cosmic-ray particles were made of antimatter . ² Zwicky, with his love of extremes, managed to convince himself (correctly it turns out) that most of the cosmic rays were coming from outside our solar system, and (incorrectly) that most were from outside our Milky Way galaxy—indeed, from the most distant reaches of the Universe—and he then convinced himself (roughly correctly) that the total energy carried by all the Universe’s cosmic rays was about the same as the total energy released by supernovae throughout the Universe. The conclusion was obvious to Zwicky (and perhaps correct ³ ): Cosmic rays are made in supernova explosions.

It was late 1933 by the time Zwicky had convinced himself of these connections between supernovae, neutrons, and cosmic rays. Since Baade’s encyclopedic knowledge of observational astronomy had been a crucial foundation for these connections, and since many of Zwicky’s calculations and much of his reasoning had been carried out in verbal give-and-take with Baade, Zwicky and Baade agreed to present their work together at a meeting of the American Physical Society at Stanford University, an easy day’s drive up the coast from Pasadena. The abstract of their talk, published in the 15 January 1934 issue of the Physical Review, is shown in Figure 5.2. It is one of the most prescient documents in the history of physics and astronomy.

It asserts unequivocally the existence of supernovae as a distinct class of astronomical objects—although adequate data to prove firmly that they are different from ordinary novae would be produced by Baade and Zwicky only four years later, in 1938. It introduces for the first time the name “supernovae” for these objects. It estimates, correctly, the total energy released in a supernova. It suggests that cosmic rays are produced by supernovae—a hypothesis still thought plausible in 1993, but not firmly established (see Footnote 3). It invents the concept of a star made out of neutrons—a concept that would not become widely accepted as theoretically viable until 1939 and would not be verified observationally until 1968. It coins the name neutron star for this concept. And it suggests “with all reserve” (a phrase presumably inserted by the cautious Baade) that supernovae are produced by the transformation of ordinary stars into neutron stars—a suggestion that would be shown theoretically viable only in the early 1960s and would be confirmed by observation only in the late 1960s with the discovery of pulsars (spinning, magnetized neutron stars) inside the exploding gas of ancient supernovae.

5.2 Abstract of the talk on supernovae, neutron stars, and cosmic rays given by Walter Baade and Fritz Zwicky at Stanford University in December 1933.

Astronomers in the 1930s responded enthusiastically to the Baade—Zwicky concept of a supernova, but treated Zwicky’s neutron-star and cosmic-ray ideas with some disdain. “Too speculative” was the general consensus. “Based on unreliable calculations,” one might add, quite correctly. Nothing in Zwicky’s writings or talks provided more than meager hints of substantiation for the ideas. In fact, it is clear to me from a detailed study of Zwicky’s writings of the era that he did not understand the laws of physics well enough to be able to substantiate his ideas. I shall return to this later in the chapter.

S ome concepts in science are so obvious in retrospect that it is amazing nobody noticed them sooner. Such was the case with the connection between neutron stars and black holes. Zwicky could have begun to make that connection in 1933, but he didn’t; it would get made in a tentative way six years later and definitively a quarter century later. The tortured route that finally rubbed physicists’ noses in the connection will occupy much of the rest of this chapter.

To appreciate the story of how physicists came to recognize the neutron-star/black-hole connection, it will help to know something about the connection in advance. Thus, the following digression:

What are the fates of stars when they die? Chapter 4 revealed a partial answer, an answer embodied in the right-hand portion of Figure 5.3 (which is the same as Figure 4.4). That answer depends on whether the star is less massive or more massive than 1.4 Suns (Chandrasekhar’s limiting mass).

If the star is less massive than the Chandrasekhar limit, for example if the star is the Sun itself, then at the end of its life it follows the path labeled “death of Sun” in Figure 5.3. As it radiates light into space, it gradually cools, losing its thermal (heat-induced) pressure. With its pressure reduced, it no longer can withstand the inward pull of its own gravity; its gravity forces it to shrink. As it shrinks, it moves leftward in Figure 5.3 toward smaller circumferences, while staying always at the same height in the figure because its mass is unchanging. (Notice that the figure plots mass up and circumference to the right.) And as it shrinks, the star squeezes the electrons in its interior into smaller and smaller cells, until finally the electrons protest with such strong degeneracy pressure that the star can shrink no more. The degeneracy pressure counteracts the inward pull of the star’s gravity, forcing the star to settle down into a white-dwarf grave on the boundary curve (white-dwarf curve) between the white region of Figure 5.3 and the shaded region. If the star were to shrink even more (that is, move leftward from the white-dwarf curve into the shaded region), its electron degeneracy pressure would grow stronger and make the star expand back to the white-dwarf curve. If the star were to expand into the white region, its electron degeneracy pressure would weaken, permitting gravity to shrink it back to the white-dwarf curve. Thus, the star has no choice but to remain forever on the white-dwarf curve, where gravity and pressure balance perfectly, gradually cooling and turning into a black dwarf—a cold, dark, solid body about the size of the Earth but with the mass of the Sun.

If the star is more massive than Chandrasekhar’s 1.4-solar-mass limit, for example if it is the star Sirius, then at the end of its life it will follow the path labeled “death of Sirius.” As it emits radiation and cools and shrinks, moving leftward on this path to a smaller and smaller circumference, its electrons get squeezed into smaller and smaller cells; they protest with a rising degeneracy pressure, but they protest in vain. Because of its large mass, the star’s gravity is strong enough to squelch all electron protest. The electrons can never produce enough degeneracy pressure to counterbalance the star’s gravity ⁴ ; the star must, in Arthur Eddington’s words, “go on radiating and radiating and contracting and contracting, until, I suppose, it gets down to a few kilometers radius, when gravity becomes strong enough to hold in the radiation, and the star can at last find peace.”

Or that would be its fate, if not for neutron stars. If Zwicky was right that neutron stars can exist, then they must be rather analogous to white-dwarf stars, but with their internal pressure produced by neutrons instead of electrons. This means that there must be a neutron-star curve in Figure 5.3, analogous to the white-dwarf curve, but at circumferences (marked on the horizontal axis) of roughly a hundred kilometers, instead of tens of thousands of kilometers. On this neutron-star curve neutron pressure would balance gravity perfectly, so neutron stars could reside there forever.

Suppose that the neutron-star curve extends upward in Figure 5.3 to large masses; that is, suppose it has the shape labeled B in the figure. Then Sirius, when it dies, cannot create a black hole. Rather, Sirius will shrink until it hits the neutron-star curve, and then it can shrink no more. If it tries to shrink farther (that is, move to the left of the neutron-star curve into the shaded region), the neutrons inside it will protest against being squeezed; they will produce a large pressure (partly due to degeneracy, that is, “claustrophobia,” and partly due to the nuclear force); and the pressure will be large enough to overwhelm gravity and drive the star back outward. If the star tries to reexpand into the white region, the neutrons’ pressure will decline enough for gravity to take over and squeeze it back inward. Thus, Sirius will have no choice but to settle down onto the neutron-star curve and remain there forever, gradually cooling and becoming a solid, cold, black neutron star.

5.3 The ultimate fate of a star more massive than the Chandrasekhar limit of 1.4 Suns depends on how massive neutron stars can be. If they can be arbitrarily massive (curve B ) , then a star such as Sirius, when it dies, can only implode to form a neutron star; it cannot form a black hole. If there is an upper mass limit for neutron stars (as on curve A ), then a massive dying star can become neither a white dwarf nor a neutron star; and unless there is some other graveyard available, it will die a black-hole death.

Suppose, instead, that the neutron-star curve does not extend upward in Figure 5.3 to large masses, but bends over in the manner of the hypothetical curve marked A. This will mean that there is a maximum mass that any neutron star can have, analogous to the Chandrasekhar limit of 1.4 Suns for white dwarfs. As for white dwarfs, so also for neutron stars, the existence of a maximum mass would herald a momentous fact: In a star more massive than the maximum, gravity will completely overwhelm the neutron pressure. Therefore, when so massive a star dies, it must either eject enough mass to bring it below the maximum, or else it will shrink inexorably, under gravity’s pull, right past the neutron-star curve, and then—if there are no other possible stellar graveyards, nothing but white dwarfs, neutron stars, and black holes-it will continue shrinking until it forms a black hole.

Thus, the central question, the question that holds the key to the ultimate fate of massive stars, is this: How massive can a neutron star be? If it can be very massive, more massive than any normal star, then black holes can never form in the real Universe. If there is a maximum possible mass for neutron stars, and that maximum is not too large, then black holes will form—unless there is yet another stellar graveyard, unsuspected in the 1930s.

This line of reasoning is so obvious in retrospect that it seems amazing that Zwicky did not pursue it, Chandrasekhar did not pursue it, Eddington did not pursue it. Had Zwicky tried to pursue it, however, he would not have got far; he understood too little nuclear physics and too little relativity to be able to discover whether the laws of physics place a mass limit on neutron stars or not. At Caltech there were, however, two others who did understand the physics well enough to deduce neutron-star masses: Richard Chace Tolman, a chemist turned physicist who had written a classic textbook called Relativity, Thermodynamics, and Cosmology; and J. Robert Oppenheimer, who would later lead the American effort to develop the atomic bomb.

Tolman and Oppenheimer, however, paid no attention at all to Zwicky’s neutron stars. They paid no attention, that is, until 1938, when the idea of a neutron star was published (under the slightly different name of neutron core ) by somebody else, somebody whom, unlike Zwicky, they respected: Lev Davidovich Landau, in Moscow.

Landau

L andau’s publication on neutron cores was actually a cry for help: Stalin’s purges were in full swing in the U.S.S.R., and Landau was in danger. Landau hoped that by making a big splash in the newspapers with his neutron-core idea, he might protect himself from arrest and death. But of this, Tolman and Oppenheimer knew nothing.

Landau was in danger because of his past contacts with Western scientists:

Soon after the Russian revolution, science had been targeted for special attention by the new Communist leadership. Lenin himself had pushed a resolution through the Eighth Congress of the Bolshevik party in 1919 exempting scientists from requirements for ideological purity: “The Problem of industrial and economic development demands the immediate and widespread use of experts in science and technology whom we have inherited from capitalism, despite the fact that they inevitably are contaminated with bourgeois ideas and customs.” Of special concern to the leaders of Soviet science was the sorry state of Soviet theoretical physics, so, with the blessing of the Communist party and the government, the most brilliant and promising young theorists in the U.S.S.R. were brought to Leningrad (Saint Petersburg) for a few years of graduate study, and then, after completing the equivalent of a Ph.D., were sent to Western Europe for one or two years of postdoctoral study.

Why postdoctoral study? Because by the 1920s physics had become so complex that Ph.D.-level training was not sufficient for its mastery. To promote additional training worldwide, a system of postdoctoral fellowships had been set up, funded largely by the Rockefeller Foundation (profits from capitalists’ oil ventures). Anyone, even ardent Russian Marxists, could compete for these fellowships. The winners were called “postdoctoral fellows” or simply “postdocs.”

Why Western Europe for postdoctoral study? Because in the 1920s Western Europe was the mecca of theoretical physics; it was the home of almost every outstanding theoretical physicist in the world. Soviet leaders, in their desperation to transfuse theoretical physics from Western Europe to the U.S.S.R., had no choice but to send their young theorists there for training, despite the dangers of ideological contamination.

Of all the young Soviet theorists who traveled the route to Leningrad, then to Western Europe, and then back to the U.S.S.R., Lev Davidovich Landau would have by far the greatest influence on physics. Born in 1908 into a well-to-do Jewish family (his father was a petroleum engineer in Baku on the Caspian Sea), he entered Leningrad University at age sixteen and finished his undergraduate studies by age nineteen. After just two years of graduate study at the Leningrad Physicotechnical Institute, he completed the equivalent of a Ph.D. and went off to Western Europe, where he spent eighteen months of 1929–30 making the rounds of the great theoretical physics centers in Switzerland, Germany, Denmark, England, Belgium, and Holland.

Left: Lev Landau, as a student in Leningrad in the mid-1920s. Right: Landau, with fellow physics students George Gamow and Yevgenia Kanegiesser, horsing around in the midst of their studies in Leningrad, ca. 1927. In reality, Landau never played any musical instrument. [Left: courtesy AlP Emilio Segre Visual Archives, Margarethe Bohr Collection; right: courtesy Library of Congress.]

A fellow postdoctoral student in Zurich, German-born Rudolph Peierls, later wrote, “I vividly remember the great impression Landau made on all of us when he appeared in Wolfgang Pauli’s department in Zurich in 1929.¼ It did not take long to discover the depth of his understanding of modern physics, and his skill in solving basic problems. He rarely read a paper on theoretical physics in detail, but looked at it long enough to see whether the problem was interesting, and if so, what was the author’s approach. He then set to work to do the calculation himself, and if the answer agreed with the author’s he approved of the paper.” Peierls and Landau became the best of friends.

Tall, skinny, intensely critical of others as well as himself, Landau despaired that he had been born a few years too late. The golden age of physics, he thought, had been 1925–27 when de Broglie, Schrödinger, Heisenberg, Bohr, and others were creating the new quantum mechanics; if born earlier, he, Landau, could have been a participant. “All the nice girls have been snapped up and married, and all the nice problems have been solved. I don’t really like any of those that are left,” he said in a moment of despair in Berlin in 1929. But, in fact, explorations of the consequences of the laws of quantum mechanics and relativity were only beginning, and those consequences would hold wonderful surprises: the structure of the atomic nucleus, nuclear energy, black holes and their evaporation, superfluidity, superconductivity, transistors, lasers, and magnetic resonance imaging, to name only a few. And Landau, despite his pessimism, would become a central figure in the quest to discover these consequences.

Upon his return to Leningrad in 1931, Landau, who was an ardent Marxist and patriot, resolved to focus his career on transfusing modern theoretical physics into the Soviet Union. He succeeded enormously, as we shall see in later chapters.

Soon after Landau’s return, Stalin’s iron curtain descended, making further travel to the West almost impossible. As George Gamow, a Leningrad classmate of Landau’s, later recalled: “Russian science now had become one of the weapons for fighting the capitalistic world. Just as Hitler was dividing science and the arts into Jewish and Aryan camps, Stalin created the notion of capitalistic and proletarian science. It [was becoming] ¼ a crime for Russian scientists to ‘fraternize’ with scientists of the capitalistic countries.”

The political climate went from bad to horrid. In 1936 Stalin, having already killed 6 or 7 million peasants and kulaks (landowners) in his forced collectivization of agriculture, embarked on a several-year-long purge of the country’s political and intellectual leadership, a purge now called the Great Terror. The purge included execution of almost all members of Lenin’s original Politburo, and execution or forced disappearance, never to be seen again, of the top commanders of the Soviet army, fifty out of seventy-one members of the Central Committee of the Communist party, most of the ambassadors to foreign countries, and the prime ministers and chief officials of the non-Russian Soviet Republics. At lower levels roughly 7 million people were arrested and imprisoned and 2.5 million died—half of them intellectuals, including a large number of scientists and some entire research teams. Soviet biology, genetics, and agricultural sciences were destroyed.

In late 1937 Landau, by now a leader of theoretical physics research in Moscow, felt the heat of the purge nearing himself. In panic he searched for protection. One possible protection might be the focus of public attention on him as an eminent scientist, so he searched among his scientific ideas for one that might make a big splash in West and East alike. His choice was an idea that he had been mulling over since the early 1930s: the idea that “normal” stars like the Sun might possess neutron stars at their centers—neutron cores Landau called them.

T he reasoning behind Landau’s idea was this: The Sun and other normal stars support themselves against the crush of their own gravity by means of thermal (heat-induced) pressure. As the Sun radiates heat and light into space, it must cool, contract, and die in about 30 million years’ time—unless it has some way to replenish the heat that it loses. Since there was compelling geological evidence, in the 1920s and 1930s, that the Earth had been kept at roughly constant temperature for 1 billion years or longer, the Sun must be replenishing its heat somehow. Arthur Eddington and others had suggested (correctly) in the 1920s that the new heat might come from nuclear reactions, in which one kind of atomic nucleus is transmuted into another—what is now called nuclear burning or nuclear fusion; see Box 5.3. However, the details of this nuclear burning had not been worked out sufficiently, by 1937, for physicists to know whether it could do the job. Landau’s neutron core provided an attractive alternative.

Just as Zwicky could imagine powering a supernova by the energy released when a normal star implodes to form a neutron star, so Landau could imagine powering the Sun and other normal stars by the energy released when its atoms, one by one, get captured onto a neutron core (Figure 5.4).

5.4 Lev Landau’s speculation as to the origin of the energy that keeps a normal star hot.

Box 5.3

Nuclear Burning (Fusion) Contrasted with I Ordinary Burning

Ordinary burning is a chemical reaction. In chemical reactions, atoms get combined into molecules, where they share their electron clouds with each other; the electron clouds hold the molecules together. Nuclear burning is a nuclear reaction. In nuclear burning, atomic nuclei get fused together (nuclear fusion ) to form more massive atomic nuclei; the nuclear force holds the more massive nuclei together.

The following diagram shows an example of ordinary burning: the burning of hydrogen to produce water (an explosively powerful form of burning that is used to power some rockets that lift payloads into space). Two hydrogen atoms combine with an oxygen atom to form a water molecule. In the water molecule, the hydrogen and oxygen atoms share their electron clouds with each other, but do not share their atomic nuclei.

The following diagram shows an example of nuclear burning: the fusion of a deuterium (“heavy hydrogen”) nucleus and an ordinary hydrogen nucleus to form a helium-3 nucleus. This is one of the fusion reactions that is now known to power the Sun and other stars, and that powers hydrogen bombs ( Chapter 6 ). The deuterium nucleus contains one neutron and one proton, bound together by the nuclear force; the hydrogen nucleus consists of a single proton; the helium-3 nucleus created by the fusion contains one neutron and two protons.

Capturing an atom onto a neutron core was much like dropping a rock onto a cement slab from a great height: Gravity pulls the rock down, accelerating it to high speed, and when it hits the slab, its huge kinetic energy (energy of motion) can shatter it into a thousand pieces. Similarly, gravity above a neutron core should accelerate infalling atoms to very high speeds, Landau reasoned. When such an atom plummets into the core, its shattering stop converts its huge kinetic energy (an amount equivalent to 10 percent of its mass) into heat. In this scenario, the ultimate source of the Sun’s heat is the intense gravity of its neutron core; and, as for Zwicky’s supernovae, the core’s gravity is 10 percent efficient at converting the mass of infalling atoms into heat.

The burning of nuclear fuel (Box 5.3), in contrast to capturing atoms onto a neutron core (Figure 5.4), can convert only a few tenths of 1 percent of the fuel’s mass into heat. In other words, Eddington’s heat source (nuclear energy) was roughly 30 times less powerful than Landau’s heat source (gravitational energy). ⁵

Landau had actually developed a more primitive version of his neutron- core idea in 1931. However, the neutron had not yet been discovered then and atomic nuclei had been an enigma, so the capture of atoms onto the core in his 1931 model had released energy by a totally speculative process, one based on an (incorrect) suspicion that the laws of quantum mechanics might fail in atomic nuclei. Now that the neutron had been known for five years and the properties of atomic nuclei were beginning to be understood, Landau could make his idea much more precise and convincing. By presenting it to the world with a big splash of publicity, he might deflect the heat of Stalin’s purge.

I n late 1937, Landau wrote a manuscript describing his neutron-core idea; to make sure it got maximum public attention, he took a series of unusual steps: He submitted it for publication, in Russian, to Doklady Akademii Nauk (Reports of the Academy of Sciences of the U.S.S.R, published in Moscow), and in parallel he mailed an English version to the same famous Western physicist as Chandrasekhar had appealed to, when Eddington attacked him (Chapter 4 ), Niels Bohr in Copenhagen. (Bohr, as an honorary member of the Academy of Sciences of the D.S.S.R., was more or less acceptable to Soviet authorities even during the Great Terror.) With his manuscript, Landau sent Bohr the following letter:

5 November 1937, Moscow

Dear Mr. Bohr!

I enclose an article about stellar energy, which I have written. If it makes physical sense to you, I ask that you submit it to Nature. If it is not too much trouble for you, I would be very glad to learn your opinion of this work.

With deepest thanks.

Yours, L. Landau

(Nature is a British scientific magazine that publishes, quickly, announcements of discoveries in all fields of science and that has one of the highest worldwide circulations among serious scientific journals.)

Landau had friends in high places-high enough to arrange that, as soon as word was received back that Bohr had approved his article and had submitted it to Nature, a telegram would be sent to Bohr by the editorial staff of Izvestia. (Izvestia was one of the two most influential newspapers in the U.S.S.R., a newspaper run by and in behalf of the Soviet government.) The telegram went out on 16 November 1937 saying:

Inform us, please, of your opinion of the work of Professor Landau. Telegraph to us, please, your brief conclusion.

Editorial Staff, Izvestia

Bohr, evidently a bit puzzled and worried by the request, replied from Copenhagen that same day:

The new idea of Professor Landau about neutron cores of massive stars is of the highest level of excellence and promise. I will be happy to send a short evaluation of it and of various other researches by Landau. Inform me please, more exactly, for what purpose my opinion is needed.

Bohr

The Izvestia staff responded that they wanted to publish Bohr’s evaluation in their newspaper. They did just that on 23 November, in an article that described Landau’s idea and praised it highly:

This work of Professor Landau’s has aroused great interest among Soviet physicists, and his bold idea gives new life to one of the most important processes in astrophysics. There is every reason to think that Landau’s new hypothesis will turn out to be correct and will lead to solutions to a whole series of unsolved problems in astrophysics.... Niels Bohr has given an extremely complimentary evaluation of the work of this Soviet scientist [Landau], saying that “The new idea of L. Landau is excellent and very promising.”

This campaign was not enough to save Landau. Early in the morning of 28 April 1938, the knock came on the door of his apartment, and he was taken away in an official black limousine as his wife-to-be Cora watched in shock from the apartment door. The fate that had befallen so many others was now also Landau’s.

The limousine took Landau to one of Moscow’s most notorious political prisons, the Butyrskaya. There he was told that his activities as a German spy had been discovered, and he was to pay the price for them. That the charges were ludicrous (Landau, a Jew and an ardent Marxist spying for Nazi Germany?) was irrelevant. The charges almost always were ludicrous. In Stalin’s Russia one rarely knew the real reason one had been imprisoned-though in Landau’s case, there are indications in recently revealed KGB files: In conversations with colleagues, he had criticized the Communist party and the Soviet government for their manner of organizing scientific research, and for the massive arrests of 1936–37 that ushered in the Great Terror. Such criticism was regarded as an “anti-Soviet activity” and could easily land one in prison.

Landau was lucky. His imprisonment lasted but one year, and he survived it—just barely. He was released in April 1939 after Pyotr Kapitsa, the most famous Soviet experimental physicist of the 1930s, appealed directly to Molotov and Stalin to let him go on grounds that Landau and only Landau, of all Soviet theoretical physicists, had the ability to solve the mystery of how superfluidity comes about. ⁶ (Superfluidity had been discovered in Kapitsa’s laboratory, and independently by J. F. Allen and A. D. Misener in Cambridge, England, and if it could be explained by a Soviet scientist, this would demonstrate doubly to the world the power of Soviet science.)

Landau emerged from prison emaciated and extremely ill. In due course, he recovered physically and mentally, solved the mystery of superfluidity using the laws of quantum mechanics, and received the Nobel Prize for his solution. But his spirit was broken. Never again could he withstand even mild psychological pressure from the political authorities.

Oppenheimer

I n California, Robert Oppenheimer was in the habit of reading with care every scientific article published by Landau. Thus, Landau’s article on neutron cores in the 19 February 1938 issue of Nature caught his immediate attention. Coming from Fritz Zwicky, the idea of a neutron star as the energizer for supernovae was—in Oppenheimer’s view—a far-out, flaky speculation. Coming from Lev Landau, a neutron core as the energizer for a normal star was worthy of serious thought. Might the Sun actually possess such a core? Oppenheimer vowed to find out.

Oppenheimer’s style of research was completely different from any encountered thus far in this book. Whereas Baade and Zwicky worked together as co-equal colleagues whose talents and knowledge complemented each other, and Chandrasekhar and Einstein each worked very much alone, Oppenheimer worked enthusiastically amidst a large entourage of students. Whereas Einstein had suffered when required to teach, Oppenheimer thrived on teaching.

Like Landau, Oppenheimer had gone to the mecca of theoretical physics, Western Europe, to get educated; and like Landau, Oppenheimer, upon returning home, had launched a transfusion of theoretical physics from Europe to his native land.

By the time of his return to America, Oppenheimer had acquired so tremendous a reputation that he received offers of faculty jobs from ten American universities including Harvard and Caltech, and from two in Europe. Among the offers was one from the University of California at Berkeley, which had no theoretical physics at all. “I visited Berkeley,” Oppenheimer recalled later, “and I thought I’d like to go there because it was a desert.” At Berkeley he could create something entirely his own. However, fearing the consequences of intellectual isolation, Oppenheimer accepted both the Berkeley offer and the Caltech offer. He would spend the autumn and winter in Berkeley, and the spring at Caltech. “1 kept the connection with Caltech.¼ it was a place where 1 would be checked if 1 got too far off base and where 1 would learn of things that might not be adequately reflected in the published literature.”

At first Oppenheimer, as a teacher, was too fast, too impatient, too overbearing with his students. He didn’t realize how little they knew; he couldn’t bring himself down to their level. His first lecture at Caltech in the spring of 1930 was a tour de force—powerful, elegant, insightful. When the lecture was over and the room had emptied, Richard Tolman, the chemist-turned-physicist who by now was a close friend, remained behind to bring him down to earth: “Well, Robert,” he said; “that was beautiful but 1 didn’t understand a damned word.”

However, Oppenheimer learned quickly. Within a year, graduate students and postdocs began flocking to Berkeley from all over America to learn physics from him, and within several years he had made Berkeley a more attractive place even than Europe for American theoretical physics postdocs.

One of Oppenheimer’s postdocs, Robert Serber, later described what it was like to work with him: “Oppie (as he was known to his Berkeley students) was quick, impatient, and had a sharp tongue, and in the earliest days of his teaching he was reputed to have terrorized the students. But after five years of experience he had mellowed (if his earlier students were to be believed). His course [on quantum mechanics] was an inspirational as well as an educational achievement. He transmitted to his students a feeling of the beauty of the logical structure of physics and an excitement about the development of physics. Almost everyone listened to the course more than once, and Oppie occasionally had difficulty in dissuading students from coming a third or fourth time.¼

“Oppie’s way of working with his research students was also original. His group consisted of 8 or 10 graduate students and about a half dozen postdoctoral fellows. He met the group once a day in his office. A little before the appointed time, the members straggled in and disposed themselves on the tables and about the walls. Oppie came in and discussed with one after another the status of the student’s research problem while the others listened and offered comments. All were exposed to a broad range of topics. Oppenheimer was interested in everything; one subject after another was introduced and coexisted with all the others. In an afternoon they might discuss electrodynamics, cosmic rays, astrophysics and nuclear physics.”

Each spring Oppenheimer piled books and papers into his convertible and several students into the rumble seat, and drove down to Pasadena. “We thought nothing of giving up our houses or apartments in Berkeley,” said Serber, “confident that we could find a garden cottage in Pasadena for twenty-five dollars a month.”

For each problem that interested him, Oppenheimer would select a student or postdoc to work out the details. For Landau’s problem, the question of whether a neutron core could keep the Sun hot, he selected Serber.

Robert Serber (left) and Robert Oppenheimer (right) discussing physics, ca. 1942. [Courtesy D.S. Information Agency.]

Oppenheimer and Serber quickly realized that, if the Sun has a neutron core at its center, and if the core’s mass is a large fraction of the Sun’s mass, then the core’s intense gravity will hold the Sun’s outer layers in a tight grip, making the Sun’s circumference far smaller than it actually is. Thus, Landau’s neutron-core idea could work only if neutron cores can be far less massive than the Sun.

“How small can the mass of a neutron core be?” Oppenheimer and Serber were thus driven to ask themselves. “What is the minimum possible mass for a neutron core?” Notice that this is the opposite question to the one that is crucial for the existence of black holes; to learn whether black holes can form, one needs to know the maximum possible mass for a neutron star (Figure 5.3 above). Oppenheimer as yet had no inkling of the importance of the maximum-mass question, but he now knew that the minimum neutron-core mass was central to Landau’s idea.

In his article Landau, also aware of the importance of the minimum neutron-core mass, had used the laws of physics to estimate it. With care Oppenheimer and Serber scrutinized Landau’s estimate. Yes, they found, Landau had properly taken account of the attractive forces of gravity inside and near the core. And yes, he had properly taken account of the degeneracy pressure of the core’s neutrons (the pressure produced by the neutrons’ claustrophobic motions when they get squeezed into tiny cells). But no, he had not taken proper account of the nuclear force that neutrons exert on each other. That force was not yet fully understood. However, enough was understood for Oppenheimer and Serber to conclude that probably, not absolutely definitely, but probably, no neutron core can ever be lighter than of a solar mass. If nature ever succeeded in creating a neutron core lighter than this, its gravity would be too weak to hold it together; its pressure would make it explode.

At first sight this did not rule out the Sun’s possessing a neutron core; after all, a -solar-mass core, which was allowed by Oppenheimer and Serber’s estimates, might be small enough to hide inside the Sun without affecting its surface properties very much (without affecting the things we see). But further calculations, balancing the pull of the core’s gravity against the pressure of surrounding gas, showed that the core’s effects could not be hidden: Around the core there would be a shell of white-dwarf-type matter weighing nearly a full solar mass, and with only a tiny amount of normal gas outside that shell, the Sun could not look at all like we see it. Thus, the Sun could not possess a neutron core, and the energy to keep the Sun hot must come from somewhere else.

Where else? At the same time as Oppenheimer and Serber in Berkeley were doing these calculations, Hans Bethe at Cornell University in Ithaca, New York, and Charles Critchfield at George Washington University in Washington, D.C., were using the newly developed laws of nuclear physics to demonstrate in detail that nuclear burning (the fusion of atomic nuclei; Box 5.3) can keep the Sun and other stars hot. Eddington had been right and Landau had been wrong—at least for the Sun and most other stars. (As of the early 1990s, it appears that a few giant stars might, in fact, use Landau’s mechanism.)

Oppenheimer and Serber had no idea that Landau’s paper was a desperate attempt to avoid prison and possible death, so on 1 September 1938, as Landau languished in Butyrskaya Prison, they submitted their critique of him to the Physical Review. Since Landau was a great enough physicist to take the heat, they said quite frankly: “An estimate of Landau . . . led to the value 0.001 solar masses for the limiting [minimum] mass [of a neutron core]. This figure appears to be wrong. . . . [Nuclear forces] of the often assumed spin exchange type preclude the existence of a [neutron] core for stars with masses comparable to that of the Sun.”

L andau’s neutron cores and Zwicky’s neutron stars are really the same thing. A neutron core is nothing but a neutron star that happens, somehow, to find itself inside a normal star. To Oppenheimer this must have been clear, and now that he had begun to think about neutron stars, he was drawn inexorably to the issue that Zwicky should have tackled but could not: What, precisely, is the fate of massive stars when they exhaust the nuclear fuel that, according to Bethe and Critchfield, keeps them hot? Which corpses will they create: white dwarfs? neutron stars? black holes? others?

Chandrasekhar’s calculations had shown unequivocally that stars less massive than 1.4 Suns must become white dwarfs. Zwicky was speculating loudly that at least some stars more massive than 1.4 Suns will implode to form neutron stars, and in the process generate supernovae. Might Zwicky be right? And will all massive stars die this way, thus saving the Universe from black holes?

One of Oppenheimer’s great strengths as a theorist was an unerring ability to look at a complicated problem and strip away the complications until he found the central issue that controlled it. Several years later, this talent would contribute to Oppenheimer’s brilliance as the leader of the American atomic bomb project. Now, in his struggle to understand stellar death, it told him to ignore all the complications that Zwicky was trumpeting about—the details of the stellar implosion, the transformation of normal matter into neutron matter, the release of enormous energy and its possible powering of supernovae and cosmic rays. All this was irrelevant to the issue of the star’s final fate. The only relevant thing was the maximum mass that a neutron star can have. If neutron stars can be arbitrarily massive (curve B in Figure 5.3 above), then black holes can never form. If there is a maximum possible neutron-star mass (curve A in Figure 5.3), then a star heavier than that maximum, when it dies, might form a black hole.

Having posed this maximum-mass question with stark clarity, Oppenheimer went about solving it, methodically and unequivocally—and, as was his standard practice, in collaboration with a student, in this case a young man named George Volkoff. The tale of Oppenheimer and Volkoff’s quest to learn the masses of neutron stars, and the central contributions of Oppenheimer’s Caltech friend Richard Tolman, is told in Box 5.4. It is a tale that illustrates Oppenheimer’s mode of research and several of the strategies by which physicists operate, when they understand clearly some of the laws that govern the phenomenon they are studying, but not all: In this case Oppenheimer understood the laws of quantum mechanics and general relativity, but neither he nor anyone else understood the nuclear force very well.

Despite their poor knowledge of the nuclear force, Oppenheimer and Volkoff were able to show unequivocally (Box 5.4) that there is a maximum mass for neutron stars, and it lies between about half a solar mass and several solar masses.

In the 1990s, after fifty years of additional study, we know that Oppenheimer and Volkoff were correct; neutron stars do, indeed, have a maximum allowed mass, and it is now known to lie between 1.5 and 3 solar masses, roughly the same ballpark as their estimate. Moreover, since 1967 hundreds of neutron stars have been observed by astronomers, and the masses of several have been measured with high accuracy. The measured masses are all close to 1.4 Suns; why, we do not know.

Box 5.4

The Tale of Oppenheimer, Volkoff, and Tolman: AQuest for Neutron-Star Masses

When embarking on a complicated analysis, it is helpful to get one’s bearings by beginning with a rough, “order-of-magnitude” calculation, a calculation accurate only to within a factor of, say, 10. In keeping with this rule of thumb, Oppenheimer began his assault on the issue of whether neutron stars can have a maximum mass by a crude calculation, just a few pages long. The result was intriguing: He found a maximum mass of 6 Suns for any neutron star. If a detailed calculation gave the same result, then Oppenheimer could conclude that black holes might form when stars heavier than 6 Suns die.

A “detailed calculation” meant selecting a mass for a hypothetical neutron star, then asking whether, for that mass, neutron pressure inside the star can balance gravity. If the balance can be achieved, then neutron stars can have that mass. It would be necessary to choose one mass after another, and for each ask about the balance between pressure and gravity. This enterprise is harder than it might sound, because pressure and gravity must balance each other everywhere inside the star. However, it was an enterprise that had been pursued once before, by Chandrasekhar, in his analysis of white dwarfs (the analysis performed using Arthur Eddington’s Braunschweiger calculator, with Eddington looking over Chandrasekhar’s shoulder; Chapter 4 ).

Oppenheimer could pattern his neutron-star calculations after Chandrasekhar’s white-dwarf calculations, but only after making two crucial changes: First, in a white dwarf the pressure is produced by electrons, and in a neutron star by neutrons, so the equation of state (the relation between pressure and density) will be different. Second, in a white dwarf, gravity is weak enough that it can be described equally well by Newton’s laws or by Einstein’s general relativity; the two descriptions will give almost precisely the same predictions, so Chandrasekhar chose the simpler description, Newton’s. By contrast, in a neutron star, with its much smaller circumference, gravity is so strong that using Newton’s laws might cause serious errors, so Oppenheimer would have to describe gravity by Einstein’s general relativistic laws. ^* Aside from these two changes—a new equation of state (neutron pressure instead of electron) and a new description of gravity (Einstein’s instead of Newton’s)—Oppenheimer’s calculation would be the same as Chandrasekhar’s.

Having gotten this far, Oppenheimer was ready to turn the details of the calculation over to a student. He chose George Volkoff, a young man from Vancouver, who had emigrated from Russia in 1924.

Oppenheimer explained the problem to Volkoff and told him that the mathematical description of gravity that he would need was in a textbook that Richard Tolman had written, Relativity, Thermodynamics, and Cosmology. The equation of state for the neutron pressure, however, was a more difficult issue, since the pressure would be influenced by the nuclear force (with which neutrons push and pull on each other). Although the nuclear force was becoming well understood at the densities inside atomic nuclei, it was very poorly understood at the ten times higher higher densities that neutrons would face deep inside a massive neutron star. Physicists did not even know whether the nuclear force was attractive at these densities or repulsive (whether neutrons pulled on each other or pushed), and thus there was no way to know whether the nuclear force reduced the neutrons’ pressure or increased it. But Oppenheimer had a strategy to deal with these unknowns.

Pretend, at first, that the nuclear force doesn’t exist, Oppenheimer suggested to Volkoff. Then all the pressure will be of a sort that is well understood; it will be neutron degeneracy pressure (pressure produced by the neutrons’ “claustrophobic” motions). Balance this neutron degeneracy pressure against gravity, and from the balance, calculate the structures and masses that neutron stars would have in a universe without any nuclear force. Then, afterward, try to estimate how the stars’ structures and masses will change if, in our real Universe, the nuclear force behaves in this, that, or some other way.

With such well-posed instructions it was hard to miss. It took only a few days for Volkoff, guided by daily discussions with Oppenheimer and by Tolman’s book, to derive the general relativistic description of gravity inside a neutron star. And it took only a few days for him to translate the well-known equation of state for degenerate electron pressure into one for degenerate neutron pressure. By balancing the pressure against the gravity, Volkoff obtained a complicated differential equation whose solution would tell him the star’s internal structure. Then he was stymied. Try as he might, Volkoff could not solve his differential equation to get a formula for the star’s structure; so, like Chandrasekhar with white dwarfs, he was forced to solve his equation numerically. Just as Chandrasekhar had spent many days in 1934 punching the buttons of Eddington’s Braunschweiger calculator to compute the analogous white-dwarf structure, so Volkoff labored through much of November and December 1938, punching the buttons of a Marchant calculator.

While Volkoff punched buttons in Berkeley, Richard Tolman in Pasadena was taking a different tack: He strongly preferred to express the stellar structure in terms of formulas instead of just numbers off a calculator. A single formula can embody all the information contained in many many tables of numbers. If he could get the right formula, it would contain simultaneously the structures of stars of 1 solar mass, 2 solar masses, 5 solar masses—any mass at all. But even with his brilliant mathematical skills, Tolman was unable to solve Volkoff’s equation in terms of formulas.

“On the other hand,” Tolman presumably argued to himself, “we know that the correct equation of state is not really the one Volkoff is using. Volkoff has ignored the nuclear force; and since we don’t know the details of that force at high densities, we don’t know the correct equation of state. So let me ask a different question from Volkoff. Let me ask how the masses of neutron stars depend on the equation of state. Let me pretend that the equation of state is very ‘stiff,’ that is, that it gives exceptionally high pressures, and let me ask what the neutron-star masses would be in that case. And then let me pretend the equation of state is very ‘soft,’ that is, that it gives exceptionally low pressures, and ask what then would be the neutron-star masses. In each case, I will adjust the hypothetical equation of state into a form for which I can solve Volkoff’s differential equation in formulas. Though the equation of state I use will almost certainly not be the right one, my calculation will still give me a general idea of what the neutron-star masses might be if nature happens to choose a stiff equation of state, and what they might be if nature chooses a soft one.”

On 19 October, Tolman sent a long letter to Oppenheimer describing some of the stellar-structure formulas and neutron-star masses he had derived for several hypothetical equations of state. A week or so later, Oppenheimer drove down to Pasadena to spend a few days talking with Tolman about the project. On 9 November, Tolman wrote Oppenheimer another long letter, with more formulas. In the meantime, Volkoff was punching away on his Marchant buttons. In early December, Volkoff finished. He had numerical models for neutron stars with masses 0.3, 0.6, and 0.7 solar mass; and he had found that, if there were no nuclear force in our Universe, then neutron stars would always be less massive than 0.7 solar mass.

What a surprise! Oppenheimer’s crude estimate, before Volkoff started computing, had been a maximum mass of 6 solar masses. To protect massive stars against forming black holes, the careful calculation would have had to push that maximum mass up to a hundred Suns or more. Instead, it pushed the mass down—way down, to 0.7 solar mass.

Tolman came up to Berkeley to learn more of the details. Fifty years later Volkoff recalled the scene with pleasure: “I remember being greatly overawed by having to explain to Oppenheimer and Tolman what I had done. We were sitting out on the lawn of the old faculty club at Berkeley. Amidst the nice green grass and tall trees, here were these two venerated gentlemen and here was I, a graduate student just completing my Ph.D., explaining my calculations.”

Now that they knew the masses of neutron stars in an idealized universe with no nuclear force, Oppenheimer and Volkoff were ready to estimate the influence of the nuclear force. Here the formulas that Tolman had worked out so carefully for various hypothetical equations of state were helpful. From Tolman’s formulas one could see roughly how the star’s structure would change if the nuclear force was repulsive and thereby made the equation of state more “stiff” than the one Volkoff had used, and the change if it was attractive and thereby made the equation of state more “soft.” Within the range of believable nuclear forces, those changes were not great. There must still be a maximum mass for neutron stars, Tolman, Oppenheimer, and Volkoff concluded, and it must lie somewhere between about a half solar mass and several solar masses.

* See the discussion in the last section of Chapter 1 (“The Nature of Physical Law”) of the relationship between different descriptions of the laws of physics and their domains of validity.

O ppenheimer and Volkoffs conclusion cannot have been pleasing to people like Eddington and Einstein, who found black holes anathema. If Chandrasekhar was to be believed (as, in 1938, most astronomers were coming to understand he should), and if Oppenheimer and Volkoff were to be believed (and it was hard to refute them), then neither the white-dwarf graveyard nor the neutron-star graveyard could inter massive stars. Was there any conceivable way at all, then, for massive stars to avoid a black-hole death? Yes; two ways.

First, all massive stars might eject so much matter as they age (for example, by blowing strong winds off their surfaces or by nuclear explosions) that they reduce themselves below 1.4 solar masses and enter the white-dwarf graveyard, or (if one believed Zwicky’s mechanism for supernovae, which few people did) they might eject so much matter in supernova explosions that they reduce themselves below about 1 solar mass during the explosion and wind up in the neutron-star graveyard. Most astronomers, through the 1940s and 1950s, and into the early 1960s–if they thought at all about the issue–espoused this view.

Second, besides the white-dwarf, neutron-star, and black-hole graveyards, there might be a fourth graveyard for massive stars, a graveyard unknown in the 1930s. For example, one could imagine a graveyard in Figure 5.3 at circumferences intermediate between neutron stars and white dwarfs—a few hundred or a thousand kilometers. The shrinkage of a massive star might be halted in such a graveyard before the star ever gets small enough to form either a neutron star or a black hole.

If World War II and then the cold war had not intervened, Oppenheimer and his students, or others, would likely have explored such a possibility in the 1940s and would have showed firmly that there is no such fourth graveyard.

However, World War II did intervene, and it absorbed the energies of almost all the world’s theoretical physicists; then after the war, crash programs to develop hydrogen bombs delayed further the return of physicists to normalcy (see the next chapter).

Finally, in the mid-1950s, two physicists emerged from their respective hydrogen bomb efforts and took up where Oppenheimer and his students had left off. They were John Archibald Wheeler at Princeton University in the United States and Yakov Borisovich Zel’dovich at the Institute of Applied Mathematics in Moscow—two superb physicists, who will be major figures in the rest of this book.

Wheeler

I n March 1956, Wheeler devoted several days to studying the articles by Chandrasekhar, Landau, and Oppenheimer and Volkoff. Here, he recognized, was a mystery worth probing. Could it really be true that stars more massive than about 1.4 Suns have no choice, when they die, but to form black holes? “Of all the implications of general relativity for the structure and evolution of the Universe, this question of the fate of great masses of matter is one of the most challenging,” Wheeler wrote soon thereafter; and he set out to complete the exploration of stellar graveyards that Chandrasekhar and Oppenheimer and Volkoff had begun.

To make his task very precise, Wheeler formulated a careful characterization of the kind of matter from which cold, dead stars should be made: He called it matter at the endpoint of thermonuclear evolution, since the word thermonuclear had become popular for the fusion reactions that power nuclear burning in stars and also power the hydrogen bomb. Such matter would be absolutely cold, and it would have burned its nuclear fuel completely; there would be no way, by any kind of nuclear reaction, to extract any more energy from the matter’s nuclei. For this reason, the nickname cold, dead matter will be used in this book instead of “matter at the endpoint of thermonuclear evolution.”

Wheeler set himself the goal to understand all objects that can be made from cold, dead matter. These would include small objects like balls of iron, heavier objects such as cold, dead planets made of iron, and still heavier objects: white dwarfs, neutron stars, and whatever other kinds of cold, dead objects the laws of physics allow. Wheeler wanted a comprehensive catalog of cold, dead things.

John Archibald Wheeler, ca. 1954. [Photo by Blackstone-Shelburne, New York City; courtesy J. A. Wheeler.]

Wheeler worked in much the same mode as had Oppenheimer, with an entourage of students and postdocs. From among them he selected B. Kent Harrison, a serious-minded Mormon from Utah, to work out the details of the equation of state for cold, dead matter. This equation of state would describe the details of how the pressure of such matter rises as one gradually compresses it to higher and higher density—or, equivalently, how its resistance to compression changes as its density Increases.

Wheeler was superbly prepared to give Harrison guidance in computing the equation of state for cold, dead matter, since he was among the world’s greatest experts on the laws of physics that govern the structure of matter: the laws of quantum mechanics and nuclear physics. During the preceding twenty years, he had developed powerful mathematical models to describe how atomic nuclei behave; with Niels Bohr he had developed the laws of nuclear fission (the splitting apart of heavy atomic nuclei such as uranium and plutonium, the principle underlying the atomic bomb); and he had been the leader of a team that designed the American hydrogen bomb (Chapter 6 ). Drawing on this expertise, Wheeler guided Harrison through the intricacies of the analysis.

The result of their analysis, the equation of state for cold, dead matter, is depicted and discussed in Box 5.5. At the densities of white dwarfs, it was the same equation of state as Chandrasekhar had used in his white-dwarf studies (Chapter 4 ); at neutron-star densities, it was the same as Oppenheimer and Volkoff had used (Box 5.4); at densities below white dwarfs and between white dwarfs and neutron stars, it was completely new.

W ith this equation of state for cold, dead matter in hand, John Wheeler asked Masami Wakano, a postdoc from Japan, to do with it what Volkoff had done for neutron stars and Chandrasekhar for white dwarfs: Combine the equation of state with the general relativistic equation describing the balance of gravity and pressure inside a star, and from that combination deduce a differential equation describing the star’s structure; then solve the differential equation numerically. The numerical calculations would produce the details of the internal structures of all cold, dead stars and, most important, the stars’ masses.

The calculations for the structure of a single star (the distribution of density, pressure, and gravity inside the star) had required Chandrasekhar and Volkoff many days of effort as they punched the buttons of their calculators in Cambridge and Berkeley in the 1930s. Wakano in Princeton in the 1950s, by contrast, had at his disposal one of the world’s first digital computers, the MANIAC—a room full of vacuum tubes and wires that had been constructed at the Princeton Institute for Advanced Study for use in the design of the hydrogen bomb. With the MANIAC, Wakano could crunch out the structure of each star in less than an hour.

Box 5.5

The Harrison–Wheeler Equation of State for Cold, Dead Matter

The drawing above depicts the Harrison–Wheeler equation of state. Plotted horizontally is the matter’s density. Plotted vertically is its resistance to compression (or adiabatic index, as physicists like to call it)—the percentage increase in pressure that accompanies a 1 percent increase in density. The boxes attached to the curve show what is happening to the matter, microscopically, as it is compressed from low densities to high. The size of each box, in centimeters, is written along the box’s top.

At normal densities (left edge of the figure), cold, dead matter is composed of iron. If the matter’s atomic nuclei were heavier than iron, energy could be released by splitting them apart to make iron (nuclear fission, as in an atomic bomb). If its nuclei were lighter than iron, energy could be released by joining them together to make iron (nuclear fusion, as in a hydrogen bomb). Once in the form of iron, the matter can release no more nuclear energy by any means whatsoever. The nuclear force holds neutrons and protons together more tightly when they form iron nuclei than when they form any other kind of atomic nucleus.

As the iron is squeezed from its normal density of 7.6 grams per cubic centimeter up toward 100, then 1000 grams per cubic centimeter, the iron resists by the same means as a rock resists compression: The electrons of each atom protest with “claustrophobic” (degeneracy-like) motions against being squeezed by the electrons of adjacent atoms. The resistance at first is huge not because the repulsive forces are especially strong, but rather because the starting pressure, at low density, is very low. (Recall that the resistance is the percentage increase in pressure that accompanies a 1 percent increase in density. When the pressure is low, a strong increase in pressure represents a huge percentage increase and thus a huge “resistance.” Later, at higher densities where the pressure has grown large, a strong pressure increase represents a much more modest percentage increase and thus a more modest resistance.)

At first, as the cold matter is compressed, the electrons congregate tightly around their iron nuclei, forming electron clouds made of electron orbitals. (There are actually two electrons, not one, in each orbital—a subtlety overlooked in Chapter 4 but discussed briefly in Box 5.1.) As the compression proceeds, each orbital and its two electrons are gradually confined into a smaller and smaller cell of space; the claustrophobic electrons protest this confinement by becoming more wave-like and developing higher-speed, erratic, claustrophobic motions (“degeneracy motions”; see Chapter 4 ). When the density has reached 10 ⁵ (100,000) grams per cubic centimeter, the electrons’ degeneracy motions and the degeneracy pressure they produce have become so large that they completely overwhelm the electric forces with which the nuclei pull on the electrons. The electrons no longer congregate around the iron nuclei; they completely ignore the nuclei. The cold, dead matter, which began as a lump of iron, has now become the kind of stuff of which white dwarfs are made, and the equation of state has become the one that Chandrasekhar, Anderson, and Stoner computed in the early 1930s (Figure 4.3): a resistance of , and then a smooth switch to at a density of about 10 ⁷ grams per cubic centimeter when the erratic speeds of the electrons near the speed of light.

The transition from white-dwarf matter to neutron-star matter begins at a density of 4 × 10 ¹¹ grams per cubic centimeter, according to the Harrison–Wheeler calculations. The calculations show several phases to the transition: In the first phase, the electrons begin to be squeezed into the atomic nuclei, and the nuclei’s protons swallow them to form neutrons. The matter, having thereby lost some of its pressure-sustaining electrons, suddenly becomes much less resistant to compression; this causes the sharp cliff in the equation of state (see diagram above). As this first phase proceeds and the resistance plunges, the atomic nuclei become more and more bloated with neutrons, thereby triggering the second phase: Neutrons begin to drip out of (get squeezed out of) the nuclei and into the space between them, alongside the few remaining electrons. These dripped-out neutrons, like the electrons, protest the continuing squeeze with a degeneracy pressure of their own. This neutron degeneracy pressure terminates the over-the-cliff plunge in the equation of state; the resistance to compression recovers and starts rising. In the third phase, at densities between about 10 ¹² and 4 × 10 ¹² grams per cubic centimeter, each neutron-bloated nucleus completely disintegrates, that is, breaks up into individual neutrons, forming the neutron gas studied by Oppenheimer and Volkoff, plus a tiny smattering of electrons and protons. From there on upward in density, the equation of state takes on the Oppenheimer–Volkoff neutron-star form (dashed curve in the diagram when nuclear forces are ignored; solid curve using the best 1990s understanding of the influence of nuclear forces).

The results of Wakano’s calculations are shown in Figure 5.5. This figure is the firm and final catalog of cold, dead objects; it answers all the questions we raised, early in this chapter, in our discussion of Figure 5.3.

In Figure 5.5, the circumference of a star is plotted rightward and its mass upward. Any star with circumference and mass in the white region of the figure has a stronger internal gravity than its pressure, so its gravity makes the star shrink leftward in the diagram. Any star in the shaded region has a stronger pressure than gravity, so its pressure makes the star expand rightward in the diagram. Only along the boundary of white and shaded do gravity and pressure balance each other perfectly; thus, the boundary curve is the curve of cold, dead stars that are in pressure/gravity equilibrium.

5.5 The circumferences (plotted horizontally), masses (plotted vertically), and central densities (labeled on curve) for cold, dead stars, as computed by Masami Wakano under the direction of John Wheeler, using the equation of state of Box 5.5. At central densities above those of an atomic nucleus (above 2 x 1014 grams per cubic centimeter), the solid curve is a modern, 1990s, one that takes proper account of the nuclear force, and the dashed curve is that of Oppenheimer and Volkoff without nuclear forces.

As one moves along this equilibrium curve, one is tracing out dead “stars” of higher and higher densities. At the lowest densities (along the bottom edge of the figure and largely hidden from view), these “stars” are not stars at all; rather, they are cold planets made of iron. (When Jupiter ultimately exhausts its internal supply of radioactive heat and cools off, although it is made mostly of hydrogen rather than iron, it will nevertheless lie near the rightmost point on the equilibrium curve.) At higher densities than the planets are Chandrasekhar’s white dwarfs.

When one reaches the topmost point on the white-dwarf part of the curve (the white dwarf with Chandrasekhar’s maximum mass of 1.4 Suns ⁷ ) and then moves on to still higher densities, one meets cold, dead stars that cannot exist in nature because they are unstable against implosion or explosion (Box 5.6). As one moves from white-dwarf densities toward neutron-star densities, the masses of these unstable equilibrium stars decrease until they reach a minimum of about 0.1 solar mass at a circumference of 1000 kilometers and a central density of 3 × 10 ¹³ grams per cubic centimeter. This is the first of the neutron stars; it is the “neutron core” that Oppenheimer and Serber studied and showed cannot possibly be as light as the 0.001 solar mass that Landau wanted for a core inside the Sun.

Box 5.6

Unstable Inhabitants of the Gap between White Dwarfs and Neutron Stars

Along the equilibrium curve in Figure 5.5, all the stars between the white dwarfs and the neutron stars are unstable. An example is the star with central density 10 ¹³ grams per cubic centimeter, whose mass and circumference are those of the point in Figure 5.5 marked 10 ¹³ . At the 10 ¹³ point this star is in equilibrium; its gravity and pressure balance each other perfectly. However, the star is as unstable as a pencil standing on its tip.

If some tiny random force (for example, the fall of interstellar gas onto the star) squeezes the star ever so slightly, that is, reduces its circumference so it moves leftward a bit in Figure 5.5 into the white region, then the star’s gravity will begin to overwhelm its pressure and will pull the star into an implosion; as the star implodes, it will move strongly leftward through Figure 5.5 until it crosses the neutron-star curve into the shaded region; there its neutron pressure will skyrocket, halt the implosion, and push the star’s surface back outward until the star settles down into a neutron-star grave, on the neutron-star curve.

By contrast, if, when the star is at the 10 ¹³ point, instead of being squeezed inward by a tiny random force, its surface gets pushed outward a bit (for example, by a random increase in the erratic motions of some of its neutrons), then it will enter the shaded region where pressure overwhelms gravity; the star’s pressure will then make its surface explode on outward across the white-dwarf curve and into the white region of the figure; and there its gravity will take over and pull it back inward to the white-dwarf curve and a white-dwarf grave.

This instability (squeeze the 10 ¹³ star a tiny bit and it will implode to become a neutron star; expand it a tiny bit and it will explode to become a white dwarf) means that no real star can ever live for long at the 10 ¹³ point—or at any other point along the portion of the equilibrium curve marked “unstable.”

Moving on along the equilibrium curve, we meet the entire family of neutron stars, with masses ranging from 0.1 to about 2 Suns. The maximum neutron-star mass of about 2 Suns is somewhat uncertain even in the 1990s because the behavior of the nuclear force at very high densities is still not well understood. The maximum could be as low as 1.5 Suns but not much lower, or as high as 3 Suns but not much higher.

At the (approximately) 2-solar-mass peak of the equilibrium curve, the neutron stars end. As one moves further along the curve to still higher densities, the equilibrium stars become unstable in the same manner as those between white dwarfs. and neutron stars (Box 5.6). Because of this instability, these “stars,” like those between white dwarfs and neutron stars, cannot exist in nature. Were they to form, they would immediately implode to become black holes or explode to become neutron stars.

Figure 5.5 is absolutely firm and unequivocal: There is no third family of stable, massive, cold, dead objects between the white dwarfs and the neutron stars. Therefore, when stars such as Sirius, which are more massive than about 2 Suns, exhaust their nuclear fuel, either they must eject all of their excess mass or they will implode inward past white-dwarf densities, past neutron-star densities, and into the critical circumference—where today, in the 1990s, we are completely certain they must form black holes. Implosion is compulsory. For stars of sufficiently large mass, neither the degeneracy pressure of electrons nor the nuclear force between neutrons can stop the implosion. Gravity overwhelms even the nuclear force.

There remains, however, a way out, a way to save all stars, even the most massive, from the black-hole fate: Perhaps all massive stars eject enough mass late in their lives (in winds or explosions), or during their deaths, to bring them below about 2 Suns so they can end up in the neutron-star or white-dwarf graveyard. During the 1940s, 1950s, and early 1960s, astronomers tended to espouse this view, when they thought at all about the issue of the final fates of stars. (By and large, however, they didn’t think about the issue. There were no observational data pushing them to think about it; and the observational data that they were gathering on other kinds of objects—normal stars, nebulas, galaxies—were so rich, challenging, and rewarding as to absorb the astronomers’ full attention.)

Today, in the 1990s, we know that heavy stars do eject enormous amounts of mass as they age and die; they eject so much, in fact, that most stars born with masses as large as 8 Suns lose enough to wind up in the white-dwarf graveyard, and most born between about 8 and 20 Suns lose enough to wind up in the neutron-star graveyard. Thus, nature seems almost to protect herself against black holes. But not quite: The preponderance of the observational data suggest (but do not yet firmly prove) that most stars born heavier than about 20 Suns remain so heavy when they die that their pressure provides no protection against gravity. When they exhaust their nuclear fuel and begin to cool, gravity overwhelms their pressure and they implode to form black holes. We shall meet some of the observational data suggesting this in Chapter 8 .

T here is much to be learned about the nature of science and scientists from the neutron-star and neutron-core studies of the 1930s.

The objects that Oppenheimer and Volkoff studied were Zwicky’s neutron stars and not Landau’s neutron cores, since they had no surrounding envelope of stellar matter. Nevertheless, Oppenheimer had so little respect for Zwicky that he declined to use Zwicky’s name for them, and insisted on using Landau’s instead. Thus, his article with Volkoff describing their results, which was published in the 15 February 1939 issue of the Physical Review, carries the title “On Massive Neutron Cores.” And to make sure that nobody would mistake the origin of his ideas about these stars, Oppenheimer sprinkled the article with references to Landau. Not once did he cite Zwicky’s plethora of prior neutron-star publications.

Zwicky, for his part, watched with growing consternation in 1938 as Tolman, Oppenheimer, and Volkoff pursued their studies of neutronstar structure. How could they do this? he fumed. Neutron stars were his babies, not theirs; they had no business working on neutron star—sand, besides, although Tolman would talk to him occasionally, Oppenheimer was not consulting him at all!

In the plethora of papers that Zwicky had written about neutron stars, however, there was only talk and speculation, no real details. He had been so busy getting under way a major (and highly successful) observational search for supernovae and giving lectures and writing papers about the idea of a neutron star and its role in supernovae that he had never gotten around to trying to fill in the details. But now his competitive spirit demanded action. Early in 1938 he did his best to develop a detailed mathematical theory of neutron stars and tie it to his supernova observations. His best effort was published in the 15 April 1939 issue of the Physical Review under the title “On the Theory and Observation of Highly Collapsed Stars.” His paper is two and a half times longer than that of Oppenheimer and Volkoff; it contains not a single reference to the two-months-earlier Oppenheimer–Volkoff article, though it does refer to a subsidiary and minor article by Volkoff alone; and it contains nothing memorable. Indeed, much of it is simply wrong. By contrast, the Oppenheimer–Volkoff paper is a tour de force, elegant, rich in insights, correct in all details.

Despite this, Zwicky is venerated today, more than half a century later, for inventing the concept of a neutron star, for recognizing, correctly, that neutron stars are created in supernova explosions and energize them, for proving observationally, with Baade, that supernovae are indeed a unique class of astronomical objects, for initiating and carrying through a definitive, decades-long observational study of supernovae—and for a variety of other insights unrelated to neutron stars or supernovae.

How is it that a man with so meager an understanding of the laws of physics could have been so prescient? My own opinion is that he embodied a remarkable combination of character traits: enough understanding of theoretical physics to get things right qualitatively, if not quantitatively; so intense a curiosity as to keep up with everything happening in all of physics and astronomy; an ability to discern, intuitively, in a way that few others could, connections between disparate phenomena; and, of not least importance, such great faith in his own inside track to truth that he had no fear whatsoever of making a fool of himself by his speculations. He knew he was right (though he often was not), and no mountain of evidence could convince him to the contrary.

Landau, like Zwicky, had great self-confidence and little fear of appearing a fool. For example, he did not hesitate to publish his 1931 idea that stars are energized by superdense stellar cores in which the laws of quantum mechanics fail. In mastery of theoretical physics, Landau totally outclassed Zwicky; he was among the top ten theorists of the twentieth century. Yet his speculations were wrong and Zwicky’s were right. The Sun is not energized by neutron cores; supernovae are energized by neutron stars. Was Landau, by contrast with Zwicky, simply unlucky? Perhaps partly. But there is another factor: Zwicky was immersed in the atmosphere of Mount Wilson, then the world’s greatest center for astronomical observations. And he collaborated with one of the world’s greatest observational astronomers, Walter Baade, who was a master of the observational data. And at Caltech he could and ‘did talk almost daily with the world’s greatest cosmic-ray observers. By contrast, Landau had almost no direct contact with observational astronomy, and his articles show it. Without such contact, he could not develop an acute sense for what things are like out there, far beyond the Earth. Landau’s greatest triumph was his masterful use of the laws of quantum mechanics to explain the phenomenon of superfluidity, and in this research, he interacted extensively with the experimenter, Pyotr Kapitsa, who was probing superfluidity’s details.

For Einstein, by contrast with Zwicky and Landau, close contact between observation and theory was of little importance; he discovered his general relativistic laws of gravity with almost no observational input. But that was a rare exception. A rich interplay between observation and theory is essential to progress in most branches of physics and astronomy.

And what of Oppenheimer, a man whose mastery of physics was comparable to Landau’s? His article, with Volkoff, on the structure of neutron stars is one of the great astrophysics articles of all time. But, as great and beautiful as it is, it “merely” filled in the details of the neutron-star concept. The concept was, indeed, Zwicky’s baby—as were supernovae and the powering of supernovae by the implosion of a stellar core to form a neutron star. Why was Oppenheimer, with so much going for him, far less innovative than Zwicky? Primarily, I think, because he declined—perhaps even feared—to speculate. Isidore I. Rabi, a close friend and admirer of Oppenheimer, has described this in a much deeper way:

“[I]t seems to me that in some respects Oppenheimer was overeducated in those fields which lie outside the scientific tradition, such as his interest in religion, in the Hindu religion in particular, which resulted in a feeling for the mystery of the Universe that surrounded him almost like a fog. He saw physics clearly, looking toward what had already been done, but at the border he tended to feel that there was much more of the mysterious and novel ‘than there actually was. He was insufficiently confident of the power of the intellectual tools he already possessed and did not drive his thought to the very end because he felt instinctively that new ideas and new methods were necessary to go further than he and his students had already gone.”

1. The amount of light received at Earth is inversely proportional to the square of the distance to the supernova, so a factor 10 error in distance meant a factor 100 error in Baade’s estimate of the total light output.

2. Antimatter gets its name from the fact that when a particle of matter meets a particle of antimatter, they annihilate each other.

3. It turns out that cosmic rays are made in many different ways. It is not yet known which way produces the most cosmic rays, but a strong possibility is the acceleration of particles to high speeds by shock waves in gas-cloud remnants of supernova explosions, long after the explosions are finished. If this is the case, then in an indirect sense Zwicky was correct.

4. The reason was explained in Box 4.2.

5. This may seem surprising to people who think of the nuclear force as far more powerful than the gravitational force. The nuclear force is, indeed, far more powerful when one has only a few atoms or atomic nuclei at one’s disposal. However, when one has several solar masses’ worth of atoms (10 ⁵⁷ atoms) or more, then the gravitational force of all the atoms put together can become overwhelmingly more powerful than their nuclear force. This simple fact in the end guarantees, as we shall see later in this chapter, that when a massive star dies its huge gravity will overwhelm the repulsion of its atomic nuclei and will crunch them to form a black hole.

6. Superfluidity is a complete absence of viscosity (internal friction) that occurs in some fluids when they are cooled to a few degrees above absolute zero temperature—that is, cooled to about minus 270 degrees Celsius.

7. Actually, the maximum white-dwarf mass in Figure 5.5 (Wakano’s calculation) is 1.2 Suns, which is slightly less than the 1.4 Suns that Chandrasekhar calculated. The difference is due to a different chemical composition: Wakano’s stars were made of “cold, dead matter” (mostly iron), which has 46 percent as many electrons as nucleons (neutrons and protons). Chandrasekhar’s stars were made of elements such as helium, carbon, nitrogen, and oxygen, which have 50 percent as many electrons as nucleons. In fact, most white dwarfs in our Universe are more nearly like Chandrasekhar’s than like Wakano’s. That is why, in this book, I consistently quote Chandrasekhar’s value for the maximum mass: 1.4 Suns.

6

Implosion to What?

in which all the armaments

of theoretical physics

cannot ward off the conclusion:

implosion produces black holes

T he confrontation was inevitable. These two intellectual giants, J. Robert Oppenheimer and John Archibald Wheeler, had such different views of the Universe and of the human condition that time after time they found themselves on opposite sides of deep issues: national security, nuclear weapons policy—and now black holes.

The scene was a lecture hall at the University of Brussels in Belgium. Oppenheimer and Wheeler, neighbors in Princeton, New Jersey, had journeyed there along with thirty-one other leading physicists and astronomers from around the world for a full week of discussions on the structure and evolution of the Universe.

It was Tuesday, 10 June 1958. Wheeler had just finished presenting, to the assembled savants, the results of his recent calculations with Kent Harrison and Masami Wakano—the calculations that had identified, unequivocally, the masses and circumferences of all possible cold, dead stars (Chapter 5 ). He had filled in the missing gaps in the Chandrasekhar and Oppenheimer–Volkoff calculations, and had confirmed their conclusions: Implosion is compulsory when a star more massive than about 2 Suns dies, and the implosion cannot produce a white dwarf, or a neutron star, or any other kind of cold, dead star, unless the dying star ejects enough mass to pull itself below the maximum-mass limit of about 2 Suns.

“Of all the implications of general relativity for the structure and evolution of the Universe, this question of the fate of great masses of matter is one of the most challenging,” Wheeler asserted. On this his audience could agree. Wheeler then, in a near replay of Arthur Eddington’s attack on Chandrasekhar twenty-four years earlier (Chapter 4 ), described Oppenheimer’s view that massive stars must die by imploding to form black holes, and then he opposed it: Such implosion “does not give an acceptable answer,” Wheeler asserted. Why not? For essentially the same reason as Eddington had rejected it; in Eddington’s words, “there should be a law of Nature to prevent a star from behaving in this absurd way.” But there was a deep difference between Eddington and Wheeler: Whereas Eddington’s 1935 speculative mechanism to save the Universe from black holes was immediately branded as wrong by such experts as Niels Bohr, Wheeler’s 1958 speculative mechanism could not at the time be proved or disproved—and fifteen years later it would turn out to be partially right (Chapter 12 ).

Wheeler’s speculation was this. Since (in his view) implosion to a black hole must be rejected as physically implausible, “there seems no escape from the conclusion that the nucleons [neutrons and protons] at the center of an imploding star must necessarily dissolve away into radiation, and that this radiation must escape from the star fast enough to reduce its mass [below about 2 Suns]” and permit it to wind up in the neutron-star graveyard. Wheeler readily acknowledged that such a conversion of nucleons into escaping radiation was outside the bounds of the known laws of physics. However, such conversion might result from the as yet ill-understood “marriage” of the laws of general relativity with the laws of quantum mechanics (Chapters 12–14). This, to Wheeler, was the most enticing aspect of “the problem of great masses”: The absurdity of implosion to form a black hole forced him to contemplate an entirely new physical process. (See Figure 6.1.)

Oppenheimer was not impressed. When Wheeler finished speaking, he was the first to take the floor. Maintaining a politeness that he had not displayed as a younger man, he affirmed his own view: “I do not know whether non-rotating masses much heavier than the sun really occur in the course of stellar evolution; but if they do, I believe their implosion can be described in the framework of general relativity [without asserting new laws of physics]. Would not the simplest assumption be that such masses undergo continued gravitational contraction and ultimately cut themselves off more and more from the rest of the Universe [that is, form black holes]?” (See Figure 6.1.)

6.1 Contrast of Oppenheimer’s view of the fates of large masses ( upper sequence ) with Wheeler’s 1958 view ( lower sequence ).

Wheeler was equally polite, but held his ground. “It is very difficult to believe ‘gravitational cutoff is a satisfactory answer,” he asserted.

Oppenheimer’s confidence in black holes grew out of detailed calculations he had done nineteen years earlier:

Black-Hole Birth: A First Glimpse

I n the winter of 1938–39, having just completed his computation with George Volkoff of the masses and circumferences of neutron stars (Chapter 5 ), Oppenheimer was firmly convinced that massive stars, when they die, must implode. The next challenge was obvious: use the laws of physics to compute the details of the implosion. What would the implosion look like as seen by people in orbit around the star? What would it look like as seen by people riding on the star’s surface? What would be the final state of the imploded star, thousands of years after the implosion?

This computation would not be easy. Its mathematical manipulations would be the most challenging that Oppenheimer and his students had yet tackled: The imploding star would change its properties rapidly as time passes, whereas the Oppenheimer-Volkoff neutron stars had been static, unchanging. Spacetime curvature would become enormous inside the imploding star, whereas it had been much more modest in neutron stars. To deal with these complexities would require a very special student. The choice was obvious: Hartland Snyder.

Snyder was different from Oppenheimer’s other students. The others came from middle-class families; Snyder gave the impression of working class, though his father was actually an engineer. It was rumored (incorrectly) that he was a truck driver in Utah before turning physicist. As Robert Serber recalls, “Hartland pooh-poohed a lot of things that were standard for Oppie’s students, like appreciating Bach and Mozart and going to string quartets and liking fine food and liberal politics.”

The Caltech nuclear physicists were a more rowdy bunch than Oppenheimer’s entourage; on Oppenheimer’s annual spring trek to Pasadena, Hartland fit right in. Says Caltech’s William Fowler, “Oppie was extremely cultured; knew literature, art, music, Sanskrit. But Hartland—he was like the rest of us bums. He loved the Kellogg Lab parties, where Tommy Lauritsen played the piano and Charlie Lauritsen [leader of the lab] played the fiddle and we sang college songs and drinking songs. Of all of Oppie’s students, Hartland was the most independent.”

Hartland was also different mentally. “Hartland had more talent for difficult mathematics than the rest of us,” recalls Serber. “He was very good at improving the cruder calculations that the rest of us did.” It was this talent that made him a natural for the implosion calculation.

Before embarking on the full, complicated calculation, Oppenheimer insisted (as always) on making a first, quick survey of the problem. How much could be learned with only a little effort? The key to this first survey was Schwarzschild’s geometry for the curved space-time outside a star (Chapter 3 ).

Schwarzschild had discovered his spacetime geometry as a solution to Einstein’s general relativistic field equation. It was the solution for the exterior of a static star, one that neither implodes nor explodes nor pulsates. However, in 1923 George Birkhoff, a mathematician at Harvard, had proved a remarkable mathematical theorem: Schwarzschild’s geometry describes the exterior of any star that is spherical, including not only static stars but also imploding, exploding, and pulsating ones.

For their quick calculation, then, Oppenheimer and Snyder simply assumed that a spherical star, upon exhausting its nuclear fuel, would implode indefinitely, and without probing what happens inside the star, they computed what the imploding star would look like to somebody far away. With ease they inferred that, since the spacetime geometry outside the imploding star is the same as outside any static star, the imploding star would look very much like a sequence of static stars, each one more compact than the previous one.

Now, the external appearance of such static stars had been studied two decades earlier, around 1920. Figure 6.2 reproduces the embedding diagrams that we used in Chapter 3 to discuss that appearance. Recall that each embedding diagram depicts the curvature of space inside and near a star. To make the depiction comprehensible, the diagram displays the curvature of only two of the three dimensions of space: the two dimensions on a sheet that lies precisely in the star’s equatorial “plane” (left half of the figure). The curvature of space on this sheet is visualized by imagining that we pull the sheet out of the star and out of the physical space in which we and the star live, and move it into a flat (uncurved), fictitious hyperspace. In the uncurved hyperspace, the sheet can maintain its curved geometry only by bending downward like a bowl (right half of the figure).

6.2 (Same as Figure 3.4.) General relativity’s predictions for the curvature of space and the redshift of light from a sequence of three highly compact, static (non-imploding) stars that all have the same mass but have different circumferences.

The figure shows a sequence of three static stars that mimic the implosion that Oppenheimer and Snyder were preparing to analyze. Each star has the same mass, but they have different circumferences. The first is four times bigger around than the critical circumference (four times bigger than the circumference at which the star’s gravity would become so strong that it forms a black hole). The second is twice the critical circumference, and the third is precisely at the critical circumference. The embedding diagrams show that the closer the star is to its critical circumference, the more extreme is the curvature of space around the star. However, the curvature does not become infinitely extreme. The bowl-like geometry is smooth everywhere with no sharp cusps or points or creases, even when the star is at its critical circumference; that is, the spacetime curvature is not infinite, and, correspondingly, since tidal gravitational forces (the kinds of forces that stretch one from head to foot and produce the tides on the Earth) are the physical manifestation of spacetime curvature, tidal gravity is not infinite at the critical circumference.

In Chapter 3 we also discussed the fate of light emitted from the surfaces of static stars. We learned that because time flows more slowly at the stellar surface than far away (gravitational time dilation), light waves emitted from the star’s surface and received far away will have a lengthened period of oscillation and correspondingly a lengthened wavelength and a redder color. The light’s wavelength gets shifted toward the red end of the spectrum as the light climbs out of the star’s intense gravitational field (gravitational redshift). When the static star is four times larger than its critical circumference, the light’s wavelength is lengthened by 15 percent (see the photon of light in the upper right part of the figure); when the star is at twice its critical circumference, the redshift is 41 percent (middle right); and when the star is precisely at its critical circumference, the light’s wavelength is infinitely redshifted, which means that the light has no energy left at all and therefore has ceased to exist.

Oppenheimer and Snyder, in their quick calculation, inferred two things from this sequence of static stars: First, an imploding star, like these static stars, would probably develop strong spacetime curvature as it nears its critical circumference, but not infinite curvature and therefore not infinite tidal gravitational forces. Second, as the star implodes, light from its surface should get more and more redshifted, and when it reaches the critical circumference, the redshift should become infinite, making the star become completely invisible. In Oppenheimer’s words, the star should “cut itself off’ visually from our external Universe.

Was there any way, Oppenheimer and Snyder asked themselves, that the star’s internal properties—ignored in this quick calculation—could save the star from this cutoff fate? For example, might the implosion be forced to go so slowly that never, even after an infinite time, would the critical circumference actually be reached?

Oppenheimer and Snyder would have liked to answer these questions by calculating the details of a realistic stellar implosion, as depicted in the left half of Figure 6.3. Any real star will spin, as does the Earth, at least a little bit. Centrifugal forces due to that spin will force the star’s equator to bulge out at least a little bit, as does Earth’s equator. Thus, the star cannot be precisely spherical. As it implodes, the star must spin faster and faster like a figure skater pulling in his arms; and its faster spin will cause centrifugal forces inside the star to grow, making the equatorial bulge more pronounced—sufficiently pronounced, perhaps, that it even halts the implosion, with the outward centrifugal forces then fully balancing gravity’s pull. Any real star has high density and pressure in its center, and lower density and pressure in its outer layers; as it implodes, high-density lumps will develop here and there like blueberries in a blueberry muffin. Moreover, the star’s gaseous matter, as it implodes, will form shock waves—analogues of breaking ocean waves—and these shocks may eject matter and mass from some parts of the star’s surface just as an ocean wave can eject droplets of water into the air. Finally, radiation (electromagnetic waves, gravitational waves, neutrinos) will pour out of the star, carrying away mass.

All these effects Oppenheimer and Snyder would have liked to include in their calculations, but to do so was a formidable task, far beyond the capabilities of any physicist or computing machine in 1939. It would not become feasible until the advent of supercomputers in the 1980s. Thus, to make any progress at all, it was necessary to build an idealized model of the imploding star and then compute the predictions of the laws of physics for that model.

Such idealizations were Oppenheimer’s forte: When confronted with a horrendously complex situation such as this one, he could discern almost unerringly which phenomena were of crucial importance and which were peripheral.

For the imploding star, one feature was crucial above all others, Oppenheimer believed: gravity as described by Einstein’s general relativistic laws. It, and only it, must not be compromised when formulating a calculation that could be done. By contrast, the star’s spin and its nonspherical shape could be ignored; they might be crucially important for some imploding stars, but for stars that spin slowly, they probably would have no strong effect. Oppenheimer could not really prove this mathematically, but intuitively it seemed clear, and indeed it has turned out to be true. Similarly, his intuition said, the outpouring of radiation was an unimportant detail, as were shock waves and density lumps. Moreover, since (as Oppenheimer and Volkoff had shown) gravity could overwhelm all pressure in massive, dead stars, it seemed safe to pretend (incorrectly, of course) that the imploding star has no internal pressure whatsoever—neither thermal pressure, nor pressure arising from the electrons’ or neutrons’ claustrophobic degeneracy motions, nor pressure arising from the nuclear force. A real star, with its real pressure, might implode in a different manner from an idealized, pressureless star; but the differences of implosion should be only modest, not great, Oppenheimer’s intuition insisted.

Thus it was that Oppenheimer suggested to Snyder an idealized computational problem: Study, using the precise laws of general relativity, the implosion of a star that is idealized as precisely spherical, nonspinning, and nonradiating, a star with uniform density (the same near its surface as at its center) and with no internal pressure whatsoever; see Figure 6.3.

Even with all these idealizations—idealizations that would generate skepticism in other physicists for thirty years to come—the calculation was exceedingly difficult. Fortunately, Richard Tolman was available in Pasadena for help. Leaning heavily on Tolman and Oppenheimer for advice, Snyder worked out the equations governing the entire implosion—and in a tour de force, he managed to solve them. He now had the full details of the implosion, expressed in formulas! By scrutinizing those formulas, first from one direction and then another, physicists could read off whatever aspect of the implosion they wished—how it looks from outside the star, how it looks from inside, how it looks on the star’s surface, and so forth.

6.3 Left: Physical phenomena in a realistic, imploding star. Right: The idealizations that Oppenheimer and Snyder made in order to compute stellar implosion.

E specially intriguing is the appearance of the imploding star as observed from a static, external reference frame, that is, as seen by observers outside the star who remain always at the same fixed circumference instead of riding inward with the star’s imploding matter. The star, as seen in a static, external frame, begins its implosion in just the way one would expect. Like a rock dropped from a rooftop, the star’s surface falls downward (shrinks inward) slowly at first, then more and more rapidly. Had Newton’s laws of gravity been correct, this acceleration of the implosion would continue inexorably until the star, lacking any internal pressure, is crushed to a point at high speed. Not so according to Oppenheimer and Snyder’s relativistic formulas. Instead, as the star nears its critical circumference, its shrinkage slows to a crawl. The smaller the star gets, the more slowly it implodes, until it becomes frozen precisely at the critical circumference. No matter how long a time one waits, if one is at rest outside the star (that is, at rest in the static, external reference frame), one will never be able to see the star implode through the critical circumference. That is the unequivocal message of Oppenheimer and Snyder’s formulas.

Is this freezing of the implosion caused by some unexpected, general relativistic force inside the star? No, not at all, Oppenheimer and Snyder realized. Rather, it is caused by gravitational time dilation (the slowing of the flow of time) near the critical circumference. Time on the imploding star’s surface, as seen by static external observers, must flow more and more slowly when the star approaches the critical circumference, and correspondingly everything occurring on or inside the star including its implosion must appear to go into slow motion and then gradually freeze.

As peculiar as this might seem, even more peculiar was another prediction made by Oppenheimer and Snyder’s formulas: Although, as seen by static external observers, the implosion freezes at the critical circumference, it does not freeze at all as viewed by observers riding inward on the star’s surface. If the star weighs a few solar masses and begins about the size of the Sun, then as observed from its own surface, it implodes to the critical circumference in about an hour’s time, and then keeps right on imploding past criticality and on in to smaller circumferences.

By 1939, when Oppenheimer and Snyder discovered these things, physicists had become accustomed to the fact that time is relative; the flow of time is different as measured in different reference frames that move in different ways through the Universe. But never before had anyone encountered such an extreme difference between reference frames. That the implosion freezes forever as measured in the static, external frame but continues rapidly on past the freezing point as measured in the frame of the star’s surface was extremely hard to comprehend. Nobody who studied Oppenheimer and Snyder’s mathematics felt comfortable with such an extreme warpage of time. Yet there it was in their formulas. One might wave one’s arms with heuristic explanations, but no explanation seemed very satisfying. It would not be fully understood until the late 1950s (near the end of this chapter).

By looking at Oppenheimer and Snyder’s formulas from the viewpoint of an observer on the star’s surface, one can deduce the details of the implosion even after the star sinks within its critical circumference; that is, one can discover that the star gets crunched to infinite density and zero volume, and one can deduce the details of the spacetime curvature at the crunch. However, in their article describing their calculations, Oppenheimer and Snyder avoided any discussion of the crunch whatsoever. Presumably Oppenheimer was prevented from discussing it by his own innate scientific conservatism, his unwillingness to speculate (see the last two paragraphs of Chapter 5 ).

If reading the star’s final crunch off their formulas was too much for Oppenheimer and Snyder to face, even the details outside and at the critical circumference were too bizarre for most physicists in 1939. At Caltech, for example, Tolman was a believer; after all, the predictions were unequivocal consequences of general relativity. But nobody else at Caltech was very convinced. General relativity had been tested experimentally only in the solar system, where gravity is so weak that Newton’s laws give almost the same predictions as general relativity. By contrast, the bizarre Oppenheimer–Snyder predictions relied on ultra-strong gravity. General relativity might well fail before gravity ever became so strong, most physicists thought; and even if it did not fail, Oppenheimer and Snyder might be misinterpreting what their mathematics was trying to say; and even if they were not misinterpreting their mathematics, their calculation was so idealized, so devoid of spin, lumps, shocks, and radiation, that it should not be taken seriously.

Such skepticism held sway throughout the United States and Western Europe, but not in the U.S.S.R. There Lev Landau, still recuperating from his year in prison, kept a “Golden List” of the most important physics research articles published anywhere in the world. Upon reading the Oppenheimer–Snyder paper, Landau entered it in his List, and he proclaimed to his friends and associates that these latest Oppenheimer revelations had to be right, even though they were extremely difficult for the human mind to comprehend. So great was Landau’s influence that his view took hold among leading Soviet theoretical physicists from that day forward.

Nuclear Interlude

W ere Oppenheimer and Snyder right, or were they wrong? The answer would likely have been learned definitively during the 1940s had World War 11 and then crash programs to develop the hydrogen bomb not intervened. But the war and the bomb did intervene, and research on impractical, esoteric issues like black holes became frozen in time as physicists turned their full energies to weapons design.

Only in the late 1950s did the weapons efforts wind down enough to bring stellar implosion back into physicists’ consciousness. Only then did the skeptics launch their first serious attack on the Oppenheimer–Snyder predictions. Carrying the banner of the skeptics at first, but not for long, was John Archibald Wheeler. From the outset, a leader of the believers was Wheeler’s Soviet counterpart, Yakov Borisovich Zel’-dovich.

The characters of Wheeler and Zel’dovich were shaped in the fire of nuclear weapons projects during the nearly two decades that black-hole research was frozen in time, the decades of the 1940s and 1950s. From their weapons work, Wheeler and Zel’dovich emerged with crucial tools for analyzing black holes: powerful computational techniques, a deep understanding of the laws of physics, and interactive research styles in which they would continually stimulate younger colleagues. They also emerged carrying difficult baggage—a set of complex relationships with some of their key colleagues: Wheeler with Oppenheimer; Zel’dovich with Landau and with Andrei Sakharov.

J ohn Wheeler, fresh out of graduate school in 1933, and the winner of a Rockefeller-financed National Research Council postdoctoral fellowship, had a choice of where and with whom to do his postdoctoral study. He could have chosen Berkeley and Oppenheimer, as did most NRC theoretical physics postdocs in those days; instead he chose New York University and Gregory Breit. “In personality they [Oppenheimer and Breit] were utterly different,” Wheeler says. “Oppenheimer saw things in black and white and was a quick decider. Breit worked in shades of grey. Attracted to issues that require long reflection, I chose Breit.”

From New York University in 1933, Wheeler moved on to Copenhagen to study with Niels Bohr, then to an assistant professorship at the University of North Carolina, followed by one at Princeton University, in New Jersey. In 1939, while Oppenheimer and students in California were probing neutron stars and black holes, Wheeler and Bohr at Princeton (where Bohr was visiting) were developing the theory of nuclear fission: the breakup of heavy atomic nuclei such as uranium into smaller pieces, when the nuclei are bombarded by neutrons (Box 6.1). Fission had just been discovered quite unexpectedly by Otto Hahn and Fritz Strassman in Germany, and its implications were ominous: By a chain reaction of fissions a weapon of unprecedented power might be made. But Bohr and Wheeler did not concern themselves with chain reactions or weapons; they just wanted to understand how fission comes about. What is the underlying mechanism? How do the laws of physics produce it?

Box 6.1

Fusion, Fission, and Chain Reactions

The fusion of very light nuclei to form medium-sized nuclei releases huge amounts of energy. A simple example from Box 5.3 is the fusion of a deuterium nucleus (“heavy hydrogen,” with one proton and one neutron) and an ordinary hydrogen nucleus (a single proton) to form a helium-3 nucleus (two protons and one neutron): Such fusion reactions keep the Sun hot and power the hydrogen bomb (the “superbomb” as it was called in the 1940s and 1950s).

The fission (splitting apart) of a very heavy nucleus to form two medium-sized nuclei releases a large amount of energy—far more than comes from chemical reactions (since the nuclear force which governs nuclei is far stronger than the electromagnetic force which governs chemically reacting atoms), but much less energy than comes from the fusion of light nuclei. A few very heavy nuclei undergo fission naturally, without any outside help. More interesting for this chapter are fission reactions in which a neutron hits a very heavy nucleus such as uranium-235 (a uranium nucleus with 235 protons and neutrons) and splits it roughly in half:

There are two special, heavy nuclei, uranium-235 and plutonium-239, with the property that their fission produces not only two medium-sized nuclei, but also a handful of neutrons (as in the drawing above). These neutrons make possible a chain reaction: If one concentrates enough uranium-235 or plutonium-239 into a small enough package, then the neutrons released from one fission will hit other uranium or plutonium nuclei and fission them, producing more neutrons that fission more nuclei, producing still more neutrons that fission still more nuclei, and so on. The result of this chain reaction, if uncontrolled, is a huge explosion (an atomic bomb blast); if controlled in a reactor, the result can be highly efficient electric power.

Bohr and Wheeler were remarkably successful. They discovered how the laws of physics produce fission, and they predicted which nuclei would be the most effective at sustaining chain reactions: uranium-235 (which would become the fuel for the bomb to destroy Hiroshima) and plutonium-239 (a type of nucleus that does not exist in nature but that the American physicists would soon learn how to make in nuclear reactors and would use to fuel the bomb to destroy Nagasaki). However, Bohr and Wheeler were not thinking of bombs in 1939; they only wanted to understand.

The Bohr–Wheeler article explaining nuclear fission was published in the same issue of the Physical Review as the Oppenheimer–Snyder article describing the implosion of a star. The publication date was 1 September 1939, the very day that Hitler’s troops invaded Poland, triggering World War 11.

Y akov Borisovich Zel’dovich was bom into a Jewish family in Minsk in 1914; later that year his family moved to Saint Petersburg (renamed Leningrad in the 1920s, then restored to Saint Petersburg in the 1990s). Zel’-dovich completed high school at age fifteen and then, instead of entering university, went to work as a laboratory assistant at the Physicotechnical Institute in Leningrad. There he taught himself so much physics and chemistry and did such impressive research that, without any formal university training, he was awarded a Ph.D. in 1934, at age twenty.

In 1939, while Wheeler and Bohr were developing the theory of nuclear fission, Zel’dovich and a close friend, Yuli Borisovich Khariton, were developing the theory of chain reactions produced by nuclear fission: Their research was triggered by an intriguing (incorrect) suggestion from French physicist Francis Perrin that volcanic eruptions might be powered by natural, underground nuclear explosions, which result from a chain reaction of fissions of atomic nuclei. However, nobody including Perrin had worked out the details of such a chain reaction. Zel’dovich and Khariton—already among the world’s best experts on chemical explosions—leaped on the problem. Within a few months they had shown (as, in parallel, did others in the West) that such an explosion cannot occur in nature, because naturally occurring uranium consists mostly of uranium-238 and not enough uranium-235. However, they concluded, if one were to artificially separate out uranium-235 and concentrate it, then one could make a chain-reaction explosion. (The Americans would soon embark on such separation to make the fuel for their Hiroshima bomb.) The curtain of secrecy had not yet descended around nuclear research, so Zel’dovich and Khariton published their calculations in the most prestigious of Soviet physics journals, the Journal of Experimental and Theoretical Physics, for all the world to see.

D uring the six years of World War II, physicists of the warring nations developed sonar, mine sweepers, rockets, radar, and, most fatefully, the atomic bomb. Oppenheimer led the “Manhattan Project” at Los Alamos, New Mexico, to design and build the American bombs. Wheeler was the lead scientist in the design and construction of the world’s first production-scale nuclear reactors, in Hanford, Washington, which made the plutonium-239 for the Nagasaki bomb.

After the bombs’ decimation of Hiroshima and Nagasaki and the deaths of several hundred thousand people, Oppenheimer was in anguish: “If atomic bombs are to be added to the arsenals of a warring world, or to the arsenals of nations preparing for war, then the time will come when mankind will curse the name of Los Alamos and Hiroshima.” “In some sort of crude sense which no vulgarity, no humor, no overstatement can quite extinguish, the physicists have known sin; and this is a knowledge which they cannot lose.”

But Wheeler had the opposite kind of regret: “As I look back on [1939 and my fission theory work with Bohr], I feel a great sadness. How did it come about that I looked on fission first as a physicist [simply curious to know how fission works], and only secondarily as a citizen [intent on defending my country]? Why did I not look at it first as a citizen and only secondarily as a physicist? A simple survey of the records shows that between twenty and twenty-five million people perished in World War 11 and more of them in the later years than in the earlier years. Every month by which the war was shortened would have meant a saving of the order of half a million to a million lives. Among those granted life would have been my brother Joe, killed in October 1944 in the Battle for Italy. What a difference it would have made if the critical date [of the atomic bomb’s first use in the war] had been not August 6, 1945, but August 6, 1943.”

I n the U.S.S.R., physicists abandoned all nuclear research in June 1941, when Germany attacked Russia, since other physics would produce quicker payoffs for national defense. As the German army marched on and surrounded Leningrad, Zel’dovich and his friend Khariton were evacuated to Kazan, where they worked intensely on the theory of the explosion of ordinary types of bombs, trying to improve the bombs’ explosive power. Then, in 1943, they were summoned to Moscow. It had become clear, they were told, that both the Americans and the Germans were mounting efforts to construct an atomic bomb. They were to be part of a small, elite, Soviet bomb development effort under the leadership of Igor V. Kurchatov.

By two years later, when the Americans bombed Hiroshima and Nagasaki, Kurchatov’s team had developed a thorough theoretical understanding of nuclear reactors for making plutonium-239, and had developed several possible bomb designs—and Khariton and Zel’-dovich had become the lead theorists on the project.

When Stalin learned of the American atomic bomb explosions, he angrily berated Kurchatov for the Soviet team’s slowness. Kurchatov defended his team: Amidst the war’s devastation, and with its limited resources, the team could not move more rapidly. Stalin told him angrily that if a child doesn’t cry, its mother can’t know what it needs. Ask for anything you need, he commanded, nothing will be refused; and he then demanded a no-holds-barred, crash project to construct the bomb, a project under the ultimate authority of Lavrenty Pavlovich Beria, the fearsome head of the secret police.

The magnitude of the effort that Beria mounted is hard to imagine. He commandeered the forced labor of millions of Soviet citizens from Stalin’s prison camps. These zeks, as they were colloquially called, constructed uranium mines, uranium purification factories, nuclear reactors, theoretical research centers, weapons test centers, and self-contained, small cities to support these facilities. The facilities, scattered across the face of the nation, were surrounded by levels of security unheard of in the Americans’ Manhattan Project. Zel’dovich and Khariton were moved to one of these facilities, in “a far away place” whose location, though almost certainly well known to Western authorities by the late 1950s, was forbidden to be revealed by Soviet citizens until 1990. ¹ The facility was known simply as Obyekt (“the Installation”); Khariton became its director, and Zel’dovich the leader of one of its key bomb design teams. Under Beria’s authority, Kurchatov set up several teams of physicists to pursue, in parallel and completely independently, each aspect of the bomb project; redundancy brings security. The teams at the Installation fed design problems to the other teams, including a small one led by Lev Landau at the Institute of Physical Problems in Moscow.

While this massive effort was rolling inexorably forward, Soviet spies were acquiring, through Klaus Fuchs (a British physicist who had worked on the American bomb project), the design of the Americans’ plutonium-based bomb. It differed somewhat from the design that Zel’dovich and his colleagues had produced, so Kurchatov, Khariton, and company faced a tough decision: They were under excruciating pressure from Stalin and Beria for results, and they feared the consequences of an unsuccessful bomb test in an era when failure often meant execution; they knew that the American design had worked at Alamogordo and Nagasaki, but they could not be completely sure of their own design; and they possessed enough plutonium for only one bomb. The decision was clear but painful: They put their own design on hold ² and converted their crash program over to the American design.

At last, on 29 August 1949—after four years of crash effort, untold misery, untold deaths of slave-labor zeks, and the beginning of an accumulation of waste from nuclear reactors near Cheliabinsk that would explode ten years later, contaminating hundreds of square miles of countryside—the crash program reached fruition. The first Soviet atomic bomb was exploded near Semipalatinsk in Soviet Asia, in a test witnessed by the Supreme Command of the Soviet army and government leaders.

O n 3 September 1949 an American WB-29 weather reconnaissance plane, on a routine flight from Japan to Alaska, discovered products of nuclear fission from the Soviet test. The data were given to a committee of experts, including Oppenheimer, for evaluation. The verdict was unequivocal. The Russians had tested an atomic bomb!

Amidst the panic that ensued (backyard bomb shelters; atomic bomb drills for schoolchildren; McCarthy’s “witch hunts” to root out spies, Communists, and their fellow travelers from government, army, media, and universities), a profound debate occurred amongst physicists and politicians. Edward Teller, one of the most innovative of the American atomic bomb design physicists, advocated a crash program to design and build the “superbomb” (or “hydrogen bomb”)—a weapon based on the fusion of hydrogen nuclei to form helium. The hydrogen bomb, if it could be built, would be awesome. There seemed no limit to its power. Did one want a bomb ten times more powerful than Hiroshima? a hundred times more powerful? a thousand? a million? If the bomb could be made to work at all, it could be made as powerful as one wished.

John Wheeler backed Teller: A crash program for the “super” was essential to counter the Soviet threat, he believed. Robert Oppenheimer and his General Advisory Committee to the D.S. Atomic Energy Commission were opposed. It was not at all obvious whether a superbomb as then conceived could ever be made to work, Oppenheimer and his committee argued. Moreover, even if it did work, any super that was vastly more powerful than an ordinary atomic bomb would likely be too heavy for delivery by airplane or rocket. And then there were the moral issues, which Oppenheimer and his committee addressed as follows. “We base our recommendations [against a crash program] on our belief that the extreme dangers to mankind inherent in the proposal wholly outweigh any military advantage that could come from this development. Let it be clearly realized that this is a super weapon; it is in a totally different category from an atomic bomb. The reason for developing such super bombs would be to have the capacity to devastate a vast area with a single bomb. Its use would involve a decision to slaughter a vast number of civilians. We are alarmed as to the possible global effects of the radioactivity generated by the explosion of a few super bombs of conceivable magnitude. If super bombs will work at all, there is no inherent limit in the destructive power that may be attained with them. Therefore, a super bomb might become a weapon of genocide.”

To Edward Teller and John Wheeler these arguments made no sense at all. The Russians surely would push forward with the hydrogen bomb; if America did not push forward as well, the free world could be put in enormous danger, they believed.

The Teller–Wheeler view prevailed. On 10 March 1950, President Truman ordered a crash program to develop the super.

The Americans’ 1949 design for the super appears in retrospect to have been a prescription for failure, just as Oppenheimer’s committee had suspected. However, since it was not certain to fail, and since nothing better was known, it was pursued intensely until March 1951, when Teller and Stanislaw Ulam invented a radically new design, one that showed bright promise.

The Teller–Ulam invention at first was just an idea for a design. As Hans Bethe has said, “Nine out of ten of Teller’s ideas are useless. He needs men with more judgement, even if they be less gifted, to select the tenth idea, which often is a stroke of genius.” To test whether this idea was a stroke of genius or a deceptive dud required turning it into a concrete and detailed bomb design, then carrying out extensive computations on the biggest available computers to see whether the design might work, and then, if the calculations predicted success, constructing and testing an actual bomb.

Two teams were set up to carry out the calculations: One at Los Alamos, the other at Princeton University. John Wheeler led the Princeton team. Wheeler’s team worked night and day for several months to develop a full bomb design based on the Teller–Ulam idea, and to test by computer calculations whether it would work. As Wheeler recalls, “We did an immense amount of calculation. We were using the computer facilities of New York, Philadelphia, and Washington—in fact, a very large fraction of the computer capacity of the United States. Larry Wilets, John Toll, Ken Ford, Louis Henyey, Carl Hausman, Dick l’Olivier, and others worked three six-hour stretches each day to get things out.”

When the calculations made it clear that the Teller–Ulam idea probably would work, a meeting was called, at the Institute for Advanced Study in Princeton (where Oppenheimer was the director), to present the idea to Oppenheimer’s General Advisory Committee and its parent U.S. Atomic Energy Commission. Teller described the idea, and then Wheeler described his team’s specific design and its predicted explosion. Wheeler recalls, “While I was starting to give my talk, Ken Ford rushed up to the window from outside, lifted it up, and passed in this big chart. I unrolled it and put it on the wall; it showed the progress of the thermonuclear combustion [as we had computed it.] ... The Committee had no option but to conclude that this thing made sense. . . . Our calculation turned Oppie around on the project.”

A portion of John Wheeler’s hydrogen bomb design team at Princeton University in 1952. Front row, left to right: Margaret Fellows, Margaret Murray, Dorothea Reiffel, Audrey Ojala, Christene Shack, Roberta Casey. Second row: Walter Aron, William Clendenin, Solomon Bochner, John Toll, John Wheeler, Kenneth Ford. Third and fourth rows: David Layzer, Lawrence Wilets, David Carter, Edward Frieman, Jay Berger, John Mclntosh, Ralph Pennington, unidentified, Robert Goerss. [Photo by Howard Schrader; courtesy Lawrence Wilets and John A Wheeler.]

Oppenheimer has described his own reaction: “The program we had in 1949 [the ‘prescription for failure’] was a tortured thing that you could well argue did not make a great deal of technical sense. It was therefore possible to argue also that you did not want it even if you could have it. The program in 1952 [the new design based on the Teller –Ulam idea] was technically so sweet that you could not argue about that. The issues became purely the military, the political and the humane problems of what you were going to do about it once you had it.” Suppressing his deep misgivings about the ethical issues, Oppenheimer, together with the other members of his committee, closed ranks with Teller, Wheeler, and the super’s proponents, and the project moved forward at an accelerated pace to construct and test the bomb. It worked as predicted by the combined calculations of Wheeler’s team and a cooperating team at Los Alamos.

Wheeler’s team’s extensive design calculations were ultimately written up as the secret Project Matterhorn Division B Report 31 or PMB-31. “I’m told,” says Wheeler, “that for at least ten years PMB-31 was the bible for design of thermonuclear devices” (hydrogen bombs).

I n 1949–50, while America was in a state of panic, and Oppenheimer, Teller, and others were debating whether America should mount a crash program to develop the super, the Soviet Union was already in the midst of a crash superbomb project of its own.

In spring 1948, fifteen months before the first Soviet atomic bomb test, Zel’dovich and his team at the Installation had carried out theoretical calculations on a superbomb design similar to the Americans’ “prescription for failure.” ³ In June 1948, a second superbomb team was established in Moscow under the leadership of Igor Tamm, one of the most eminent of Soviet theoretical physicists. Its members were Vitaly Ginzburg (of whom we shall hear much in Chapters 8 and 10 ), Andrei Sakharov (who would become a dissident in the 1970s, and then a hero and Soviet saint in the late 1980s and 1990s), Semyon Belen’ky, and Yuri Romanov. Tamm’s team was charged with the task of checking and refining the Zel’dovich team’s design calculations.

The Tamm team’s attitude toward this task is epitomized by a statement of Belen’ky’s at the time: “Our job is to lick Zel’dovich’s anus.” Zel’dovich, with his paradoxical combination of a forceful, demanding personality and extreme political timidity, was not among the most popular of Soviet physicists. But he was among the most brilliant. Landau, who as a leader of a small subsidiary design team occasionally received orders from Zel’dovich’s team to analyze this, that, or another facet of the bomb design, sometimes referred to him behind his back as “that bitch, Zel’dovich.” Zel’dovich, by contrast, revered Landau as a great judge of the correctness of physics ideas, and as his greatest teacher—though Zel’dovich had never taken a formal course from him.

It required only a few months for Sakharov and Ginzburg, in Tamm’s team, to come up with a far better design for a superbomb than the “prescription for failure” that Zel’dovich and the Americans were pursuing. Sakharov proposed constructing the bomb as a layered cake of alternating shells of a heavy fission fuel (uranium) and light fusion fuel, and Ginzburg proposed for the fusion fuel lithium deuteride (LiD). In the bomb’s intense blast, the LiD’s lithium nuclei would fission into tritium and helium nuclei, and the tritium would then fuse with the LiD’s deuterium to form helium nuclei, releasing enormous amounts of energy. The heavy uranium would strengthen the explosion by preventing its energy from leaking out too quickly, by helping compress the fusion fuel, and by adding fission energy to the fusion. When Sakharov presented these ideas, Zel’dovich grasped their promise immediately. Sakharov’s layered cake and Ginzburg’s LiD quickly became the focus of the Soviet superbomb effort.

To push the superbomb forward more rapidly, Sakharov, Tamm, Belen’ky, and Romanov were ordered transferred from Moscow to the Installation. But not Ginzburg. The reason seems obvious: Three years earlier, Ginzburg had married Nina Ivanovna, a vivacious, brilliant woman, who in the early 1940s had been thrown into prison on a trumped-up charge of plotting to kill Stalin. She and her fellow plotters supposedly were planning to shoot Stalin from a window in the room where she lived, as he passed by on Arbat Street below. When a troika of judges met to decide her fate, it was pointed out that her room did not have any windows at all looking out on Arbat Street, so in an unusual exhibition of mercy, her life was spared; she was merely sentenced to prison and then to exile, not death. Her imprisonment and exile presumably were enough to taint Ginzburg, the inventor of the LiD fuel for the bomb, and lock him out of the Installation. Ginzburg, preferring basic physics research over bomb design, was pleased, and the world of science reaped the rewards: While Zel’dovich, Sakharov, and Wheeler concentrated on bombs, Ginzburg solved the mystery of how cosmic rays propagate through our galaxy, and with Landau he used the laws of quantum mechanics to explain the origin of superconductivity.

I n 1949, as the Soviet atomic bomb project reached fruition, Stalin ordered that the full resources of the Soviet state be switched over, without pause, to a superbomb effort. The slave labor of zeks, the theoretical research facilities, the manufacturing facilities, the test facilities, the multiple teams of physicists on each aspect of the design and construction, all must be focused on trying to beat the Americans to the hydrogen bomb. Of this the Americans, in the midst of their debate over whether to mount a crash effort on the super, knew nothing. However, the Americans had superior technology and a large head start.

On 1 November 1952, the Americans exploded a hydrogen bomb–type device code-named Mike. Mike was designed to test the 1951 Teller–Ulam invention and was based on the design computations of Wheeler’s team and tile cooperating team at Los Alamos. It used liquid deuterium as its principal fuel. To liquify the deuterium and pipe it into the explosion region required an enormous, factory-like apparatus. Thus, this was not the kind of bomb that one could deliver on any airplane or rocket. Nevertheless, it totally destroyed the island of Elugelab in the Eniwetok Atoll in the Pacific Ocean; it was 800 times more powerful than the bomb that killed over 100,000 people in Hiroshima.

On 5 March 1953, amidst somber music, Radio Moscow announced that Joseph Stalin had died. There was rejoicing in America, and grief in the U.S.S.R. Andrei Sakharov wrote to his wife, Klava, “I am under the influence of a great man’s death. I am thinking of his humanity.”

On 12 August 1953, at Semipalatinsk, the Soviets exploded their first hydrogen bomb. Dubbed Joe-4 by the Americans, it used Sakharov’s layered-cake design and Ginzburg’s LiD fusion fuel, and it was small enough to deliver in an airplane. However, the fuel in Joe-4 was not ignited by the Teller–Ulam method, and as a result Joe-4 was rather less powerful than the Americans’ Mike: “only” about 30 Hiroshimas, compared to Mike’s 800.

In fact, in the language of the American bomb design physicists, Joe-4 was not a hydrogen bomb at all; it was a boosted atomic bomb, that is, an atomic bomb whose power is boosted by the inclusion of some fusion fuel. Such boosted atomic bombs were already part of the American arsenal, and the Americans refused to regard them as hydrogen bombs because their layered-cake design did not enable them to ignite an arbitrarily large amount of fusion fuel. There was no way by this design to make, for example, a “doomsday weapon” thousands of times more powerful than Hiroshima.

But 30 Hiroshimas was not to be sneezed at, nor was deliverability. Joe-4 was an awesome weapon indeed, and Wheeler and other Americans heaved a sigh of relief that, thanks to their own, true superbomb, the new Soviet leader, Georgi Malenkov, could not threaten America with it.

On 1 March 1954, the Americans exploded their first LiD-fueled, deliverable superbomb. It was code named Bravo and like Mike, it relied on design calculations by the Wheeler and Los Alamos teams and used the Teller–Ulam invention. The explosive energy was 1300 Hiroshimas.

In March 1954, Sakharov and Zel’dovich jointly invented (independently of the Americans) the Teller–Ulam idea, and within a few months Soviet resources were focused on implementing it in a real superbomb, one that could have as large a destructive power as anyone might wish. It took just eighteen months to fully design and construct the bomb. On 23 November 1955, it was detonated, with an explosive energy of 300 Hiroshimas.

As Oppenheimer’s General Advisory Committee had suspected, in their opposition to the crash program for the super, these enormously powerful bombs—and the behemoth 5000-Hiroshima weapon exploded later by the Soviets in an attempt to intimidate John Kennedy—have not been very attractive to the military establishments of either the United States or the U.S.S.R. The weapons currently in Russian and American arsenals are around 30 Hiroshimas, not thousands. Although they are true hydrogen bombs, they are no more powerful than a large atomic bomb. The military neither needed nor wanted a “doomsday” device. The sole use of such a device would be psychological intimidation of the adversary—but intimidation can be a serious matter in a world with leaders like Joseph Stalin.

O n 2 July 1953, Lewis Strauss, a member of the Atomic Energy Commission who had fought bitterly with Oppenheimer over the crash program for the super, became the Commission’s chairman. As one of his first acts in power, he ordered removal of all classified material from Oppenheimer’s Princeton office. Strauss and many others in Washington were deeply suspicious of Oppenheimer’s loyalty. How could a man loyal to America oppose the super effort, as he had before Wheeler’s team demonstrated that the Teller–Ulam invention would work? William Borden, who had been chief counsel of Congress’s Joint Committee on Atomic Energy during the super debate, sent a letter to J. Edgar Hoover saying, in part: “The purpose of this letter is to state my own exhaustively considered opinion, based upon years of study of the available classified evidence, that more probably than not J. Robert Oppenheimer is an agent of the Soviet Union.” Oppenheimer’s security clearance was canceled, and in April and May of 1954, simultaneous with the first American tests of deliverable hydrogen bombs, the Atomic Energy Commission conducted hearings to determine whether or not Oppenheimer was really a security risk.

Box 6.2

Why Did Soviet Physicists Build the Bomb for Stalin?

Why did Zel’dovich, Sakharov, and other great Soviet physicists work so hard to build atomic bombs and hydrogen bombs for Joseph Stalin? Stalin was responsible for the deaths of millions of Soviet citizens: 6 million or 7 million peasants and kulaks in forced collectivization in the early 1930s, 2.5 million from the top strata of the military, government, and society in the Great Terror of 1937–39, 10 million from all strata of society in the prisons and labor camps of the 1930s through 1950s. How could any physicist, in good conscience, put the ultimate weapon into the hands of such an evil man?

Those who ask such questions forget or don’t know the conditions—physical and psychological—that pervaded the Soviet Union in the late 1940s and early 1950s:

1.   The Soviet Union had just barely emerged from the bloodiest, most devastating war in its history—a war in which Germany, the aggressor, had killed 27 million Soviet people and had laid waste to their homeland—when Winston Churchill fired an early salvo of the cold war: In a 5 March 1946 speech in Fulton, Missouri, Churchill warned the West about a Soviet threat and coined the phrase “iron curtain” to describe the boundaries that Stalin had established around his empire. Stalin’s propaganda machinery milked Churchill’s speech for all it could, creating a deep fear among Soviet citizens that the British and Americans might attack. The Americans, the subsequent propaganda claimed, * were planning a nuclear war against the Soviet Union, with hundreds of atomic bombs, carried by airplanes, and targeted on hundreds of Soviet cities. Most Soviet physicists believed the propaganda and accepted the absolute necessity that the D.S.S.R. create nuclear weapons to protect against a repeat of Hitler’s devastation.

2.   The machinery of Stalin’s state was so effective at controlling information and at brainwashing even the leading scientists that few of them understood the evil of the man. Stalin was revered by most Soviet physicists (even Sakharov), as by most Soviet citizens, as the Great Leader- —a harsh but benevolent dictator who had masterminded the victory over Germany and would protect his people against a hostile world. The Soviet physicists were frightfully aware that evil pervaded lower levels of the government: The flimsiest of denunciations by somebody one hardly knew could send one to prison, and often to death. (In the late 1960s, Zel’dovich recalled for me what it was like: “Life is so wonderful now,” he said; “the knocks no longer come in the middle of the night, and one’s friends no longer disappear, never to be heard from again.”) But the source of this evil, most physicists believed, could not be the Great Leader; it must be others below him. (Landau knew better; he had learned much in prison. But, psychologically devastated by his imprisonment, he rarely spoke of Stalin’s guilt, and when he did, his friends did not believe.)

3.   Though one lived a life of fear, information was so tightly controlled that one could not deduce the enormity of the toll that Stalin had taken. That toll would only become known in Gorbachev’s epoch of glasnost, the late 1980s.

4.   Many Soviet physicists were “fatalists.” They didn’t think about these issues at all. Life was so hard that one merely struggled to keep going, doing one’s job as best one could, whatever it might be. Besides, the technical challenge of figuring out how to make a bomb that works was fascinating, and there was some joy to be had in the camaraderie of the design team and the prestige and substantial salary that one’s work brought.

* Beginning in 1945, American strategic planning did, indeed, include an option—if the U.S.S.R initiated a conventional war—for a massive nuclear attack on Soviet cities and on military and industrial targets; see Brown (1978).

Wheeler was in Washington on other business at the time of the hearings. He was not involved in any way. However, Teller, a close personal friend, went to Wheeler’s hotel room the night before he was to testify, and paced the floor for hours. If Teller said what he really thought, it would severely damage Oppenheimer. But how could he not say it? Wheeler had no doubts; in his view, Teller’s integrity would force him to testify fully.

Wheeler was right. The next day Teller, espousing a viewpoint that Wheeler understood, said: “‘In a great number of cases I have seen Dr. Oppenheimer act ... in a way which for me was exceedingly hard to understand. I thoroughly disagreed with him in numerous issues and his actions frankly appeared to me confused and complicated. To this extent I feel that I would like to see the vital interests of the country in hands which I understand better, and therefore trust more. . . . I believe, and that is merely a question of belief and there is no expert-ness, no real information behind it, that Dr. Oppenheimer’s character is such that he would not knowingly and willingly do anything that is designed to endanger the safety of this country. To the extent, therefore, that your question is directed toward intent, I would say I do not see any reason to deny clearance. If it is a question of wisdom and judgment, as demonstrated by actions since 1945, then I would say one would be wiser not to grant clearance.”

Almost all the other physicists who testified were unequivocal in their support of Oppenheimer—and were aghast at Teller’s testimony. Despite this, and despite the absence of credible evidence that Oppenheimer was “an agent of the Soviet Union,” the climate of the times prevailed: Oppenheimer was declared a security risk and was denied restoration of his security clearance.

To most American physicists, Oppenheimer became an instant martyr and Teller an instant villain. Teller would be ostracized by the physics community for the rest of his life. But to Wheeler, it was Teller who was the martyr: Teller had “had the courage to express his honest judgment, putting his country’s security ahead of solidarity of the community of physicists,” Wheeler believed. Such testimony, in Wheeler’s view, “deserved consideration,” not ostracism. Andrei Sakharov, thirty-five years later, came to agree. ⁴

Black-Hole Birth: Deeper Understanding

N ot only did Wheeler and Oppenheimer differ profoundly on issues of national security, they also differed profoundly in their approach to theoretical physics. Where Oppenheimer hewed narrowly to the predictions of well-established physical law, Wheeler was driven by a deep yearning to know what lies beyond well-established law. He was continually reaching, mentally, toward the domain where known laws break down and new laws come into play. He tried to leapfrog his way into the twenty-first century, to catch a glimpse of what the laws of physics might be like beyond twentieth-century frontiers.

Of all the places that such a glimpse might be had, none looked more promising to Wheeler, from the 1950s onward, than the interface between general relativity (the domain of the large) and quantum mechanics (the domain of the small). General relativity and quantum mechanics did not mesh with each other in a logically consistent way. They were like the rows and columns of a crossword puzzle early in one’s attempts to solve it. One has a tentative set of words written along the rows and a tentative set written down the columns, and one discovers a logical inconsistency at some of the intersections of rows and columns: Where the row word GENERAL demands an E, the column word QUANTUM demands a U; where the row word RELATIVITY demands an E, the column word QUANTUM demands a T. Looking at the row and column, it is obvious that one or the other or both must be changed to get consistency. Similarly, looking at the laws of general relativity and the laws of quantum mechanics, it was obvious that one or the other or both must be changed to make them mesh logically. If such a mesh could be achieved, the resulting union of general relativity and quantum mechanics would produce a powerful new set of laws that physicists were calling quantum gravity. However, physicists’ understanding of how to marry general relativity with quantum mechanics was so primitive in the 1950s that, despite great effort, nobody was making much progress.

Progress was also slow on trying to understand the fundamental building blocks of atomic nuclei—the neutron, the proton, the electron, and the plethora of other elementary particles that were being created in particle accelerators.

Wheeler had a dream of leaping over these impasses and catching a simultaneous glimpse of the nature of quantum gravity and the nature of elementary particles. Such a glimpse, he thought, might come from seeking out those places in theoretical physics where paradoxes abound. From resolving a paradox comes deep understanding. The deeper the paradox, the more likely that the understanding would probe beyond twentieth-century frontiers.

It was in this spirit that, soon after emerging from the superbomb effort, Wheeler, with Harrison and Wakano, filled in the missing gaps in our knowledge of cold, dead stars (Chapter 5 ); and it was in this spirit that Wheeler contemplated the resulting “fate of great masses.” Here was a deep paradox of just the sort Wheeler was seeking: No cold, dead star can be more massive than about 2 Suns; and yet the heavens seem to abound in hot stars far more massive than that—stars which some day must cool and die. Oppenheimer, in his straightforward way, had asked the well-established laws of physics what happens to such stars, and had got (with Snyder) an answer that seemed outrageous to Wheeler. This reinforced Wheeler’s conviction that here, in the fates of great masses, he might catch a glimpse of physics beyond twentieth-century frontiers. Wheeler was right, as we shall see in Chapters 12 and 13 .

Wheeler had fire in his belly—a deep, unremitting need to know the fate of great masses and learn whether their fate might unlock the mysteries of quantum gravity and elementary particles. Oppenheimer, by contrast, seemed not to care much in 1958. He believed his own calculations with Snyder but showed no need to push further, no drive for deeper understanding. Perhaps he was tired from the intense battles of the preceding two decades—weapons design battles, political battles, personal battles. Perhaps he was overawed by the mysteries of the unknown. In any event, he would never again contribute answers. The torch was being passed to a new generation. Oppenheimer’s legacy would become Wheeler’s foundation; and in the U.S.S.R., Landau’s legacy would become Zel’dovich’s foundation.

I n his 1958 Brussels confrontation with Oppenheimer, Wheeler asserted that the Oppenheimer–Snyder calculations could not be trusted. Why? Because of their severe idealizations (Figure 6.3 above). Most especially, Oppenheimer had pretended from the outset that the imploding star has no pressure whatsoever. Without pressure, it was impossible for the imploding material to form shock waves (the analogue of breaking ocean waves, with their froth and foam). Without pressure and shock waves, there was no way the imploding material could heat up. Without heat and pressure, there was no way for nuclear reactions to be triggered and no way to emit radiation. Without outpouring radiation, and without the outward ejection of material by nuclear reactions, pressure, or shock waves, there was no way for the star to lose mass. With mass loss forbidden from the outset, there was no way the massive star could ever reduce itself below 2 Suns and become a cold, dead, neutron star. No wonder Oppenheimer’s imploding star had formed a black hole, Wheeler reasoned; his idealizations prevented it from doing anything else!

In 1939, when Oppenheimer and Snyder did their work, it had been hopeless to compute the details of implosion with realistic pressure (thermal pressure, degeneracy pressure, and pressure produced by the nuclear force) and with nuclear reactions, shock waves, heat, radiation, and mass ejection. However, the nuclear weapons design efforts of the intervening twenty years provided precisely the necessary tools. Pressure, nuclear reactions, shock waves, heat, radiation, and mass ejection are all central features of a hydrogen bomb; without them, the bomb won’t explode. To design a bomb, one had to incorporate all these things into one’s computer calculations. Wheeler’s team, of course, had done so. Thus, it would have been natural for Wheeler’s team now to rewrite their computer programs so that, instead of simulating the explosion of a hydrogen bomb, they simulated the implosion of a massive star.

It would have been natural, that is, if the team still existed. However, the team was now disbanded; they had written their PMB-31 report and had dispersed to teach, do physics research, and become administrators at a variety of universities and government laboratories.

America’s bomb design expertise was now concentrated at Los Alamos, and at a new government laboratory in Livermore, California. At Livermore in the late 1950s, Stirling Colgate became fascinated by the problem of stellar implosion. With encouragement from Edward Teller, and in collaboration with Richard White and later Michael May, Colgate set out to simulate such an implosion on a computer. The Colgate–White–May simulations kept some of Oppenheimer’s idealizations: They insisted from the outset that the imploding star be spherical and not rotate. Without this restriction, their computations would have been enormously more difficult. However, their simulations took account of all the things that worried Wheeler—pressure, nuclear reactions, shock waves, heat, radiation, mass ejection—and did so by relying heavily on bomb design expertise and computer codes. To perfect the simulations required several years of effort, but by the early 1960s they were working well.

One day in the early 1960s, John Wheeler rushed into a relativity class at Princeton University that I, as a graduate student, was taking from him. He was slightly late, but beaming with pleasure. He had just returned from a visit to Livermore, where he had seen the results of the most recent Colgate, White, and May simulations. With excitement in his voice, he drew diagram after diagram on the blackboard, explaining what his Livermore friends had learned:

When the imploding star had a small mass, it triggered a supernova explosion and formed a neutron star in just the manner that Fritz Zwicky had speculated thirty years earlier. When the mass of the star was much larger than the 2-Suns maximum for a neutron star, the implosion—despite its pressure, nuclear reactions, shock waves; heat, and radiation—produced a black hole. And the black hole’s birth was remarkably similar to the highly idealized one computed nearly twenty-five years earlier by Oppenheimer and Snyder. As seen from outside, the implosion slowed and became frozen at the critical circumference, but as seen by someone on the star’s surface, the implosion did not freeze at all. The star’s surface shrank right through the critical circumference and on inward, without hesitation.

Wheeler, in fact, had already come to expect this. Other insights (to be described below) had already transformed him from a critic of Oppenheimer’s black holes to an enthusiastic supporter. But here, for the first time, was a concrete proof from a realistic computer simulation: Implosion must produce black holes.

Was Oppenheimer pleased by Wheeler’s conversion? He showed little interest and little pleasure. At a December 1963 international conference in Dallas, Texas, on the occasion of the discovery of quasars (Chapter 9 ), Wheeler gave a long lecture on stellar implosion. In his lecture, he described with enthusiasm the 1939 calculations of Oppenheimer and Snyder. Oppenheimer attended the conference, but during Wheeler’s lecture he sat on a bench in the hallway chatting with friends about other things. Thirty years later, Wheeler recalls the scene with sadness in his eyes and voice.

I n the late 1950s, Zel’dovich began to get bored with weapons design work. Most of the really interesting problems had been solved. In search of new challenges, he forayed, part time, into the theory of elementary particles and then into astrophysics, while keeping command of his bomb design team at the Installation and of another team that did subsidiary bomb calculations at the Institute of Applied Mathematics, in Moscow.

In his bomb design work, Zel’dovich would pummel his teams with ideas, and the team members would do calculations to see whether the ideas worked. “Zel’dovich’s sparks and his team’s gasoline” was the way Ginzburg described it. As he moved into astrophysics, Zel’dovich retained this style.

Stellar implosion was among the astrophysical problems that caught Zel’dovich’s fancy. It was obvious to him, as to Wheeler, Colgate, May, and White in America, that the tools of hydrogen bomb design were ideally suited to the mathematical simulation of imploding stars.

To puzzle out the details of realistic stellar implosion, Zel’dovich collared several young colleagues: Dmitri Nadezhin and Vladimir Imshennik at the Institute of Applied Mathematics, and Mikhail Podurets at the Installation. In a series of intense discussions, he gave them his vision of how the implosion could be simulated on a computer, including all the key effects that were so important for the hydrogen bomb: pressure, nuclear reactions, shock waves, heat, radiation, mass ejection.

Stimulated by these discussions, Imshennik and Nadezhin simulated the implosion of stars with small mass—and verified, independently of Colgate and White in America, Zwicky’s conjectures about supernovae. In parallel, Podurets simulated the implosion of a massive star. Podurets’s results, published almost simultaneously with those from May and White in America, were nearly identical to the Americans’. There could be no doubt. Implosion produces black holes, and does so in just the way that Oppenheimer and Snyder had claimed.

T he adaptation of bomb design codes to simulate stellar implosion is just one of many intimate connections between nuclear weapons and astrophysics. These connections were obvious to Sakharov in 1948. Upon being ordered to join Tamm’s bomb design team, he embarked on a study of astrophysics to prepare himself. My own nose was rubbed into the connections unexpectedly in 1969.

I never really wanted to know what the Teller-Ulam/Sakharov–Zel’dovich idea was. The superbomb, one that by virtue of their idea could “be arbitrarily powerful,” seemed obscene to me, and I didn’t want even to speculate about how it worked. But my quest to understand the possible roles of neutron stars in the Universe forced the Teller–Ulam idea onto my consciousness.

Zel’dovich, several years earlier, had pointed out that gas from interstellar space or a nearby star, falling onto a neutron star, should heat up and shine brightly: It should become so hot, in fact, that it radiates mostly high-energy X-rays rather than less energetic light. The infalling gas controls the rate of outflow of X-rays, Zel’dovich argued, and conversely, the outflowing X-rays control the rate of infall of gas. Thereby, the two, gas and X-rays, working together, produce a steady, self-regulated flow. If the gas falls in at too high a rate, then it will produce lots of X-rays, and the outpouring X-rays will strike the infalling gas, producing an outward pressure that slows the gas’s fall (Figure 6.4a). On the other hand, if the gas falls in at too low a rate, then it produces so few X-rays that they are powerless to slow the infalling gas, so the infall rate increases. There is just one unique rate of gas infall, not too high and not too low, at which the X-rays and gas are in mutual equilibrium.

This picture of the flow of gas and X-rays disturbed me. I knew full well that if, on Earth, one tries to hold a dense fluid such as liquid mercury up by means of a less dense fluid such as water below it, tongues of mercury quickly eat their way down into the water, the mercury goes whooshing down, and the water goes whooshing up (Figure 6.4b). This phenomenon is called the Rayleigh–Taylor instability. In Zel’dovich’s picture, the X-rays were like the low-density water and the infalling gas was like the high-density mercury. Wouldn’t tongues of gas eat their way into the X-rays, and wouldn’t the gas then fall freely down those tongues, destroying Zel’dovich’s self-regulated flow (Figure 6.4c)? A detailed calculation with the laws of physics could tell me whether this happens, but such a calculation would be very complex and time consuming; so, rather than calculate, I asked Zel’dovich one afternoon in 1969, when we were discussing physics in his apartment in Moscow.

Zel’dovich looked a bit uncomfortable when I raised the question, hut his answer was firm: “No, Kip, that doesn’t happen. There are no tongues into the X-rays. The gas flow is stable.” “How do you know, Yakov Borisovich?” I asked. Amazingly, I could not get an answer. It seemed clear that Zel’dovich or somebody had done a detailed calculation or experiment showing that X-rays can push hard on gas without Rayleigh–Taylor tongues destroying the push, but Zel’dovich could not point me to any such calculation or experiment in the published literature, nor would he describe for me the detailed physics that goes on. How uncharacteristic of him!

A few months later I was hiking in the high Sierras in California with Stirling Colgate. (Colgate is one of the best American experts on the flows of fluids and radiation, he was deeply involved in the late stages of the American superbomb effort, and he was one of the three Livermore physicists who had simulated a star’s implosion on a computer.) As we hiked, I posed to Colgate the same question I had asked of Zel’dovich, and he gave me the same answer: The flow is stable; the gas cannot escape the force of the X-rays by developing tongues. “How do you know, Stirling?” I asked. “It has been shown,” he replied. “Where can I find the calculations or experiments?” I asked. “1 don’t know ...”

6.4 (a) Gas falling onto a neutron star is slowed by the pressure of outpouring X-rays. (b) Liquid mercury trying to fall in the Earth’s gravitational field is held back by water beneath it; a Rayleigh–Taylor instability results. (c) Is it possible that there is also a Rayleigh–Taylor instability for the infalling gas held back by a neutron star’s X-rays?

“That’s very peculiar,” I told Stirling. “Zel’dovich told me precisely the same thing—the flow is stable. But he, like you, would not point me to any proofs.” “Oh! That’s fascinating. So Zel’dovich really knew,” said Stirling.

And then I knew as well. I hadn’t wanted to know. But the conclusion was unavoidable. The Teller–Ulam idea must be the use of X-rays, emitted in the first microsecond of the fission (atomic bomb) trigger, to heat, help compress, and ignite the superbomb’s fusion fuel (Figure 6.5). That this is, indeed, part of the Teller–Ulam idea was confirmed in the 1980s in several unclassified American publications; otherwise I would not mention it here.

6.5 Schematic diagram showing one aspect of the Teller–Ulam/Sakharov–Zel’-dovich idea for the design of a hydrogen bomb: A fission-powered explosion (atomic bomb trigger) produces intense X-rays that somehow are focused onto the fusion fuel (lithium deuteride, LiD). The X-rays presumably heat the fusion fuel and help compress it long enough for fusion reactions to occur. The technology for focusing the X-rays and other practical problems are so formidable that by knowing this piece of the Teller–Ulam “secret,” one is only an infinitesimal distance along the way toward building a working superbomb.

W hat converted Wheeler from a skeptic of black holes to a believer and advocate? Computer simulations of imploding stars were only the final validation of his conversion. Far more important was the destruction of a mental block. This mental block pervaded the world’s community of theoretical physicists from the 1920s through the 1950s. It was fostered in part by the same Schwarzschild singularity that was then being used for a black hole. It was also fostered by the mysterious, seemingly paradoxical conclusion, from Oppenheimer and Snyder’s idealized calculations, that an imploding star becomes frozen forever at the critical circumference (“Schwarzschild singularity”) from the viewpoint of a static, external observer, but it implodes quickly through the freezing point and on inward from the viewpoint of an observer on the star’s surface.

In Moscow, Landau and his colleagues, while believing Oppenheimer and Snyder’s calculations, had severe trouble reconciling these two viewpoints. “You cannot appreciate how difficult it was for the human mind to understand how both viewpoints can be true simultaneously,” Landau’s closest friend, Evgeny Lifshitz, told me some years later.

Then one day in 1958, the same year as Wheeler was attacking Oppenheimer and Snyder’s conclusions, there arrived in Moscow an issue of the Physical Review with an article by David Finkelstein, an assistant professor at a little known American university, the Stevens Institute of Technology in Hoboken, New Jersey. Landau and Lifshitzread the article. It was a revelation. Suddenly everything was clear. ⁵

Finkelstein visited England that year and lectured at Kings College in London. Roger Penrose (who later would revolutionize our understanding of what goes on inside black holes; see Chapter 13 ) took the train down to London to hear Finkelstein’s lecture, and returned to Cambridge enthusiastic.

In Princeton, Wheeler was intrigued at first, but was not fully convinced. He would become convinced only gradually, over the next several years. He was slower than Landau or Penrose, I believe, because he was looking deeper. He was fixated on his vision that quantum gravity must make nucleons (neutrons and protons) in an imploding star dissolve away into radiation and escape the implosion, and it seemed impossible to reconcile this vision with Finkelstein’s insight. Nevertheless, as we shall see later, in a certain deep sense both Wheeler’s vision and Finkelstein’s insight were correct.

S o just what was Finkelstein’s insight? Finkelstein discovered, somewhat by chance and in just two lines of mathematics, a new reference frame in which to describe Schwarzschild’s spacetime geometry. Finkelstein was not motivated by the implosion of stars and he did not make the connection between his new reference frame and stellar implosion. However, to others the implication of his new reference frame was clear. It gave them a totally new perspective on stellar implosion.

David Finkelstein, ca. 1958. [Photo by Herbert S. Sonnenfeld; courtesy David Finkelstein.]

The geometry of spacetime outside an imploding star is that of Schwarzschild, and thus the star’s implosion could be described using Finkelstein’s new reference frame. Now, Finkelstein’s new frame was quite different from the reference frames we have met previously (Chapters 1 and 2 ). Most of those frames (imaginary laboratories) were small, and all portions of each frame (top, bottom, sides, middle) were at rest with respect to each other. By contrast, Finkelstein’s reference frame was large enough to cover simultaneously the regions of space-time far from the imploding star, the regions near it, and all regions in between. More important, the various parts of Finkelstein’s frame were in motion with respect to each other: The parts far from the star were static, that is, not imploding, while the parts near the star were falling inward along with the imploding star’s surface. Correspondingly, Finkelstein’s frame could be used to describe the star’s implosion simultaneously from the viewpoint of faraway static observers and from the viewpoint of observers who ride inward with the imploding star. The resulting description reconciled beautifully the freezing of the implosion as observed from far away with the continued implosion as observed from the star’s surface.

In 1962, two members of Wheeler’s Princeton research group, David Beckedorff and Charles Misner, constructed a set of embedding diagrams to illustrate this reconciliation, and in 1967 I converted their embedding diagrams into the following fanciful analogy for an article in Scientific American.

Once upon a time, six ants lived on a large rubber membrane (Figure 6.6). These ants, being highly intelligent, had learned to communicate using signal balls that roll with a constant speed (the “speed of light”) along the membrane’s surface. Regrettably, the ants had not calculated the membrane’s strength.

One day five of the ants happened to gather near the center of the membrane, and their weight made it begin to collapse. They were trapped; they could not crawl out fast enough to escape. The sixth ant—an astronomer ant—was a safe distance away with her signal-ball telescope. As the membrane collapsed, the trapped ants dispatched signal balls to the astronomer ant so she could follow their fate.

The membrane did two things as it collapsed: First, its surface contracted inward, dragging surrounding objects toward the center of the collapse in much the same manner as an imploding star’s gravity pulls objects toward its center. Second, the membrane sagged and became curved into a bowl-like shape analogous to the curved shape of space around an imploding star (compare with Figure 6.2).

6.6 Collapsing rubber membrane populated by ants provides a fanciful analogue of the gravitational implosion of a star to form a black hole. [Adapted from Thorne (1967)]

The membrane’s surface contracted faster and faster as the collapse proceeded. As a result, the signal balls, which were uniformly spaced in time when dispatched by the trapped ants, were received by the astronomer ant at more and more widely spaced time intervals. (This is analogous to the reddening of light from an imploding star.) Ball number 15 was dispatched 15 seconds after the collapse began, at the precise moment when the trapped ants were being sucked through the membrane’s critical circumference. Ball 15 stayed forever at the critical circumference because the membrane there was contracting with precisely the speed of the ball’s motion (speed of light). Just 0.001 second before reaching the critical circumference, the trapped ants dispatched ball number 14.999 (shown only in the last diagram). This ball, barely outracing the contracting membrane, did not reach the astronomer ant until 137 seconds after the collapse began. Ball number 15.001, sent out 0.001 second after the critical circumference, got inexorably sucked into the highly curved region and was crushed along with the five trapped ants.

But the astronomer ant could never learn about the crushing. She would never receive signal ball number 15, or any signal balls emitted after it; and those just before 15 would take so long to escape that to her the collapse would appear to slow and freeze right at the critical circumference.

This analogy is remarkably faithful in reproducing the behavior of an imploding star:

1.   The shape of the membrane is precisely that of the curved space round the star—as embodied in an embedding diagram.

2.   The motions of the signal balls on the membrane are precisely the same as the motions of photons of light in the imploding star’s curved space. In particular, the signal balls move with the speed of light as measured locally by any ant at rest on the membrane; yet balls emitted just before number 15 take a very long time to escape, so long that to the astronomer ant the collapse seems to freeze. Similarly, photons emitted from the star’s surface move with the speed of light as measured locally by anyone; yet the photons emitted just before the star shrinks inside its critical circumference (its horizon) take a very long time to escape, so long that to external observers the implosion must appear to freeze.

3.   The trapped ants do not see any freezing whatsoever at the critical circumference. They are sucked through the critical circumference without hesitation, and crushed. Similarly, anyone on the surface of an imploding star will not see the implosion freeze. He will experience implosion with no hesitation, and get crushed by tidal gravity ( Chapter 13 ).

This, translated into embedding diagrams, was the insight that came from Finkelstein’s new reference frame. With this way of thinking about the implosion, there was no more mystery. An imploding star really does shrink through the critical circumference without hesitation. That it appears to freeze as seen from far away is an illusion.

T he embedding diagrams of the parable of the ants capture only some of the insight that came from Finkelstein’s new reference frame, not all. Further insight is embodied in Figure 6.7, which is a spacetime diagram for the imploding star.

Until now, the only spacetime diagrams we have met were in the flat spacetime of special relativity; for example, Figure 1.3. In Figure 1.3, we drew our diagrams from two different viewpoints: that of an inertial reference frame at rest in the city of Pasadena (with the downward pull of gravity ignored), Figure 1.3c; and that of an inertial frame attached to your high-speed sports car as you zoom down Pasadena’s, Colorado Boulevard, Figure 1.3b. In each diagram we plotted our chosen frame’s space horizontally, and its time vertically.

In Figure 6.7, the chosen reference frame is that of Finkelstein. Accordingly, we plot horizontally two of the three dimensions of space, as measured in Finkelstein’s frame (“Finkelstein’s space”), and we plot vertically time as measured in his frame (“Finkelstein’s time”). Since, far from the star, Finkelstein’s frame is static (not imploding), Finkelstein’s time there is that experienced by a static observer. And since, near the star, Finkelstein’s frame falls inward with the imploding stellar surface, Finkelstein’s time there is that experienced by an infalling observer.

Two horizontal slices are shown in the diagram. Each depicts two of the dimensions of space at a specific moment of time, but with the space’s curvature removed so the space looks flat. More specifically, circumferences around the star’s center are faithfully represented on these horizontal slices, but radii (distances from the center) are not. To represent both radii and circumferences faithfully, we would have to use embedding diagrams like those of Figure 6.2 or those of the parable of the ants, Figure 6.6. The space curvature would then show clearly: Circumferences would be less than 2π times radii. By drawing the horizontal slices flat, we are artificially removing their curvature. This incorrect flattening of the space is a price we pay to make the diagram legible. The payoff we gain is our ability to see space and time together on a single, legible diagram.

At the earliest time shown in the diagram (bottom horizontal slice), the star, with one spatial dimension absent, is the interior of a large circle; if the missing dimension were restored, the star would be the interior of a large sphere. At a later time (second slice), the star has shrunk; it is now the interior of a smaller circle. At a still later time, the star passes through its critical circumference, and still later it shrinks to zero circumference, creating there a singularity in which, according to general relativity, the star is crunched out of existence. We shall not discuss the details of this singularity until Chapter 13 , but it is crucial to know that it is a completely different thing from the “Schwarzschild singularity” of which physicists spoke from the 1920s through the 1950s. The “Schwarzschild singularity” was their ill-conceived name for the critical circumference or for a black hole; this “singularity” is the object that resides at the black hole’s center.

The black hole itself is the region of spacetime that is shown black in the diagram, that is, the region inside the critical circumference and to the future of the imploding star’s surface. The hole’s surface (its horizon) is at the critical circumference.

Also shown in the diagram are the world lines (trajectories through spacetime) of some particles attached to the star’s surface. As one’s eye travels upward in the diagram (that is, as time passes), one sees these world lines move in closer and closer to the center of the star (to the central axis of the diagram). This motion exhibits the star’s shrinkage with time.

Of greatest interest are the world lines of four photons (four particles of light). These photons are the analogues of the signal balls in the parable of the ants. Photon A is emitted outward from the star’s surface at the moment when the star begins to implode (bottom slice). It travels outward with ease, to larger and larger circumferences, as time passes (as one’s eye travels upward in the diagram). Photon B, emitted shortly before the star reaches its critical circumference, requires a long time to escape; it is the analogue of signal ball number 14.999 in the parable of the ants. Photon C, emitted precisely at the critical circumference,. remains always there, just like signal ball number 15 And photon D, emitted from inside the critical circumference (inside the black hole), never escapes; it gets pulled into the singularity by the hole’s intense gravity, just like signal ball 15.001.

6.7 A spacetime diagram depicting the implosion of a star to form a black hole. Plotted upward is time as measured in Finkelstein’s reference frame. Plotted horizontally are two of the three dimensions of that frame’s space. Horizontal slices are two-dimensional “snapshots” of the imploding star and the black hole it creates at specific moments of Finkelstein’s time, but with the curvature of space suppressed.

It is interesting to contrast this modern understanding of the propagation of light from an imploding star with eighteenth-century predictions for light emitted from a star smaller than its critical circumference.

Recall (Chapter 3 ) that in the late eighteenth century John Michell in England and Pierre Simon Laplace in France used Newton’s laws of gravity and Newton’s corpuscular description of light to predict the existence of black holes. These “Newtonian black holes” were actually static stars with circumferences so small (less than the critical circumference) that gravity prevented light from escaping from the stars’ vicinities.

The left half of Figure 6.8 (a space diagram, not a spacetime diagram) depicts such a star inside its critical circumference, and depicts the spatial trajectory of a photon (light corpuscle) emitted from the star’s surface nearly vertically (radially). The outflying photon, like a thrown rock, is slowed by the pull of the star’s gravity, it draws to a halt, and it then falls back into the star.

The right half of the figure depicts in a spacetime diagram the motions of two such photons. Plotted upward is Newton’s universal time; plotted outward, his absolute space. With the passage of time, the circular star sweeps out the vertical cylinder; at any moment of time (horizontal slice through the diagram) the star is described by the same circle as in the left picture. As time passes, photon A flies out and then falls back into the star, and photon B, emitted a little later, does the same.

6.8 The predictions from Newton’s laws of physics for the motion of light corpuscles (photons) emitted by a star that is inside its critical circumference. Left: a spatial diagram (similar to Figure 3.1). Right: a spacetime diagram.

It is instructive to compare this (incorrect) Newtonian version of a star inside its critical circumference and the photons it emits with the (correct) relativistic version, Figure 6.7. The comparison shows two profound differences between the predictions of Newton’s laws and those of Einstein:

1.   Newton’s laws (Figure 6.8) permit a star smaller than the critical circumference to live a happy, non-imploding life, with its gravitational squeeze forever counterbalanced by its internal pressure. Einstein’s laws (Figure 6.7) insist that when any star is smaller than its critical circumference, its gravitational squeeze will be so strong that no internal pressure can possibly counterbalance it. The star has no choice but to implode.

2.   Newton’s laws (Figure 6.8) predict that photons emitted from the star’s surface at first will fly out to larger circumferences, even in some cases to circumferences larger than critical, and then will be pulled back in. Einstein’s laws (Figure 6.7) demand that any photon emitted from inside the critical circumference move always toward smaller and smaller circumferences. The only reason that such a photon can escape the star’s surface is that the star itself is shrinking faster than the outward-directed photon moves inward (Figure 6.7).

A lthough Finkelstein’s insight and the bomb code simulations fully convinced Wheeler that the implosion of a massive star must produce a black hole, the fate of the imploding stellar matter continued to disturb him in the 1960s, just as it had disturbed him in Brussels in his 1958 confrontation with Oppenheimer. General relativity insisted that the star’s matter will be crunched out of existence in the singularity at the hole’s center (Chapter 13 ), but such a prediction seemed physically unacceptable. To Wheeler it seemed clear that the laws of general relativity must fail at the hole’s center and be replaced by new laws of quantum gravity, and these new laws must halt the crunch. Perhaps, Wheeler speculated, building on views he had expounded in Brussels, the new laws would convert the imploding matter into radiation that quantum mechanically “tunnels” its way out of the hole and escapes into interstellar space. To test this speculation would require understanding in depth the marriage of quantum mechanics and general relativity. Therein lay the beauty of the speculation. It was a testbed to assist in discovering the new laws of quantum gravity.

As Wheeler’s student in the early 1960s, I thought that his speculation of matter being converted into radiation at the singularity and then tunneling its way out of the hole was outrageous. How could Wheeler believe such a thing? The new laws of quantum gravity would surely be important in the singularity at the hole’s center, as Wheeler asserted. But not near the critical circumference. The critical circumference was in the “domain of the large,” where general relativity must be highly accurate; and the general relativistic laws were unequivocal—nothing can escape out of the critical circumference. Gravity holds everything in. Thus, there can be no “quantum mechanical tunneling” (whatever that was) to let radiation out; I was firmly convinced of it.

In 1964 and 1965 Wheeler and I wrote a technical book, together with Kent Harrison and Masami Wakano, about cold, dead stars and stellar implosion. I was shocked when Wheeler insisted on including in the last chapter his speculation that radiation might tunnel its way out of the hole and escape into interstellar space. In a last-minute struggle to convince Wheeler to delete his speculation from the book, I called on David Sharp, one of Wheeler’s postdocs, for help. David and I argued vigorously with Wheeler in a three-way telephone call, and Wheeler finally capitulated.

Wheeler was right; David and I were wrong. Ten years later, Zel’-dovich and Stephen Hawking would use a newly developed partial marriage of general relativity and quantum mechanics to prove, mathematically, that radiation can tunnel its way out of a black hole—though very, very slowly (Chapter 12 ). In other words, black holes can evaporate, though they do it so slowly that a hole formed by the implosion of a star will require far longer than the age of our Universe to disappear.

T he names that we give to things are important. The agents of movie stars, who change their clients’ names from Norma Jean Baker to Marilyn Monroe and from Béla Blasko to Béla Lugosi, know this well. So do physicists. In the movie industry a name helps set the tone, the frame of mind with which the viewer regards the star—glamour for Marilyn Monroe, horror for Béla Lugosi. In physics a name helps set the frame of mind with which we view a physical concept. A good name will conjure up a mental image that emphasizes the concept’s most important properties, and thereby it will help trigger, in a subconscious, intuitive sort of a way, good research. A bad name can produce mental blocks that hinder research.

Perhaps nothing was more influential in preventing physicists, between 1939 and 1958, from understanding the implosion of a star than the name they used for the critical circumference: “Schwarzschild singularity.” The word “singularity” conjured up an image of a region where gravity becomes infinitely strong, causing the laws of physics as we know them to break down—an image that we now understand is correct for the object at the center of a black hole, but not for the critical circumference. This image made it difficult for physicists to accept the Oppenheimer–Snyder conclusion that a person who rides through the Schwarzschild singularity (the critical circumference) on an imploding star will feel no infinite gravity and see no breakdown of physical law.

How truly nonsingular the Schwarzschild singularity (critical circumference) is did not become fully clear until David Finkelstein discovered his new reference frame and used it to show that the Schwarzschild singularity is nothing but a location into which things can fall but out of which nothing can come—and a location, therefore, into which we on the outside can never see. An imploding star continues to exist after it sinks through the Schwarzschild singularity, Finkelstein’s reference frame showed, just as the Sun continues to exist after it sinks below the horizon on Earth. But just as we, sitting on Earth, cannot see the Sun beyond our horizon, so observers far from an imploding star cannot see the star after it implodes through the Schwarzschild singularity. This analogy motivated Wolfgang Rindler, a physicist at Cornell University in the 1950s, to give the Schwarzschild singularity (critical circumference) a new name, a name that has since stuck: He called it the horizon.

There remained the issue of what to call the object created by the stellar implosion. From 1958 to 1968 different names were used in East and West: Soviet physicists used a name that emphasized a distant astronomer’s vision of the implosion. Recall that because of the enormous difficulty light has escaping gravity’s grip, as seen from afar the implosion seems to take forever; the star’s surface seems never quite to reach the critical circumference, and the horizon never quite forms. It looks to astronomers (or would if their telescopes were powerful enough to see the imploding star) as though the star becomes frozen just outside the critical circumference. For this reason, Soviet physicists called the object produced by implosion a frozen star —and this name helped set the tone and frame of mind for their implosion research in the 1960s.

In the West, by contrast, the emphasis was on the viewpoint of the person who rides inward on the imploding star’s surface, through the horizon and into the true singularity; and, accordingly, the object thereby created was called a collapsed star. This name helped focus physicists’ minds on the issue that became of greatest concern to John Wheeler: the nature of the singularity in which quantum physics and spacetime curvature would be married.

Neither name was satisfactory. Neither paid particular attention to the horizon which surrounds the collapsed star and which is responsible for the optical illusion of stellar “freezing.” During the 1960s, physicists’ calculations gradually revealed the enormous importance of the horizon, and gradually John Wheeler—the person who, more than anyone else, worries about using optimal names—became more and more dissatisfied.

I t is Wheeler’s habit to meditate about the names we call things when relaxing in the bathtub or lying in bed at night. He sometimes will search for months in this way for just the right name for something. Such was his search for a replacement for “frozen star”/“collapsed star.” Finally, in late 1967, he found the perfect name.

In typical Wheeler style, he did not go to his colleagues and say, “I’ve got a great new name for these things; let’s call them da-de-da-de-da.” Rather, he simply started to use the name as though no other name had ever existed, as though everyone had already agreed that this was the right name. He tried it out at a conference on pulsars in New York City in the late fall of 1967, and he then firmly adopted it in a lecture in December 1967 to the American Association for the Advancement of Science, entitled “Our Universe, the Known and the Unknown.” Those of us not there encountered it first in the written version of his lecture: “[B]y reason of its faster and faster infall [the surface of the imploding star] moves away from the [distant] observer more and more rapidly. The light is shifted to the red. It becomes dimmer millisecond by millisecond, and in less than a second is too dark to see . . . [The star,] like the Cheshire cat, fades from view. One leaves behind only its grin, the other, only its gravitational attraction. Gravitational attraction, yes; light, no. No more than light do any particles emerge. Moreover, light and particles incident from outside ... [and] going down the black hole only add to its mass and increase its gravitational attraction.”

Black hole was Wheeler’s new name. Within months it was adopted enthusiastically by relativity physicists, astrophysicists, and the general public, in East as well as West—with one exception: In France, where the phrase trou noir (black hole) has obscene connotations, there was resistance for several years.

1. It is near the town of Arzimas, between Cheliabinsk and the Ural Mountains.

2. After their successful test of a bomb based on the American design, the Soviets returned to their own design, constructed a bomb based on it, and tested it successfully in 1951.

3. Sakharov has speculated that this design was directly inspired by information acquired from the Americans through espionage, perhaps via the spy Klaus Fuchs. Zel’dovich by contrast has asserted that neither Fuchs nor any other spy produced any significant information about the superbomb that his design team did not already know; the principal value of the Soviet superbomb espionage was to convince Soviet political authorities that their physicists knew what they were doing.

4. Just for the record, I strongly disagree with Wheeler (though he is one of my closest friends and my mentor) and with Sakharov. For thoughtful and knowledgeable insights into the Teller–Oppenheimer controversy and the pros and cons of the American debate over whether to build the superbomb, I recommend reading Bethe (1982) and York (1976). For Sakharov’s view, see Sakharov (1990); for a critique of Sakharov’s view, see Bethe (1990). For a transcript of the Oppenheimer hearings, see USAEC (1954).

5. Finkelstein’s insight had actually been found earlier, in other contexts by other physicists including Arthur Eddington; but they had not understood its significance and it was quickly forgotten.