In 1946 Subrahmanyan Chandrasekhar gave a talk at the University of Chicago entitled“The Scientist.” 1 He was then 35 years old, less than halfway through his life and less than a third of the way through his career as a scientist,but already he was reflecting deeply on the meaning and purpose of his work. His talk was one of a series of public lecturesorganized by Robert Hutchins, then the chancellor of the university. The list of speakers is impressive, and included Frank Lloyd Wright, Arnold Schoenberg, and Marc Chagall. That list proves two things. It shows that Hutchins was an impresario with remarkable powers of persuasion, and that he already recognized Chandra as a world-class artist whose medium happened to be theories of the universe rather than music or paint. I say “Chandra” because that is the name his friends used for him when he was alive.
Basic science and derived science
Chandra began his talk with a description of two kinds of scientific inquiry. “I want to draw your attention to one broad division of the physical sciences which has to be kept in mind, the division into a basic science and a derived science. Basic science seeks to analyze the ultimate constitution of matter and the basic concepts of space and time. Derived science, on the other hand, is concerned with the rational ordering of the multifarious aspects of natural phenomena in terms of the basic concepts.”
As examples of basic science, Chandra mentioned the discovery of the atomic nucleus by Ernest Rutherford and the discovery of the neutron by James Chadwick. Each of those discoveries was made by a simple experiment that revealed the existence of a basic building block of the universe. Rutherford discovered the nucleus by shooting alpha particles at a thin gold foil and observing that some of the particles bounced back. Chadwick discovered the neutron by shooting alpha particles at a beryllium target and observing that the resulting radiation collided with other nuclei in the way expected for a massive neutral twin of the proton. As an example of derived science,Chandra mentioned the discovery by Edmond Halley in 1705 that the comet now bearing his name had appeared periodically in the sky at least four times in recorded history and that its elliptical orbit was described by Newton’s law of gravitation. He also noted the discovery by William Herschel in 1803 that the orbits of binary stars are governed by the same law of gravitation operating beyond our solar system. The observations of Halley and Herschel did not reveal new building blocks, but they vastly extended the range of phenomena that the basic science of Newton could explain.
The SS Pilsna, a member of the Lloyd Triestino fleet, sailed from India to Europe in the early 20th century. In 1930 Subrahmanyan Chandrasekhar sailed on the ship on his way to study with Ralph Fowler at Cambridge University. En route, he refined an earlier calculation of Fowler’s; the so-called Chandrasekhar limit implied by the new calculation was to have profound consequences.
The SS Pilsna, a member of the Lloyd Triestino fleet, sailed from India to Europe in the early 20th century. In 1930 Subrahmanyan Chandrasekhar sailed on the ship on his way to study with Ralph Fowler at Cambridge University. En route, he refined an earlier calculation of Fowler’s; the so-called Chandrasekhar limit implied by the new calculation was to have profound consequences.
Chandra also described the particular examples of basic and derived science that played the decisive role in his own intellectual development. In 1926, when Chandra was 15 years old but already a physics student at Presidency College in Madras (now Chennai), India, Enrico Fermi and Paul Dirac independently discovered the basic concepts of Fermi-Dirac statistics: If a bunch of electrons is distributed over a number of quantum states, each quantum state can be occupied by at most one electron, and the probability that a state is occupied is a simple function of the temperature. Those basic properties of electrons were a cornerstone of the newborn science of quantum mechanics. They paved the way to the solution of one of the famous unsolved problems of condensed-matter physics, explaining why the specific heats of solid materials decrease with temperature and go rapidly to zero as the temperature goes to zero.
Ralph Fowler, shown here in a 1931 photograph, wrote the seminal paper explaining the properties of white dwarf stars that inspired Subrahmanyan Chandrasekhar’s revolutionary calculation. Fowler and other important English astrophysicists did not accept the validity of the new work.
Ralph Fowler, shown here in a 1931 photograph, wrote the seminal paper explaining the properties of white dwarf stars that inspired Subrahmanyan Chandrasekhar’s revolutionary calculation. Fowler and other important English astrophysicists did not accept the validity of the new work.
Two years later, in 1928, the famous German professor Arnold Sommerfeld, one of the chief architects of quantum mechanics, visited Presidency College. Chandra was well prepared. He had read and understood Sommerfeld’s classic textbook, Atomic Structureand Spectral Lines. He boldly introduced himself to Sommerfeld, who took the time to tell him about the latest work of Fermi and Dirac. Sommerfeld gave the young Chandra the galley proofs of his paper on the electron theory of metals, a yet-to-be-published article that gave the decisive confirmation of Fermi-Dirac statistics. Sommerfeld’s paper was a masterpiece of derived science, showing how the basic concepts of Fermi and Dirac could explain in detail why metals exist and how they behave. The Indian undergraduate was one of the first people in the world to read it.
Two years after his meeting with Sommerfeld, at the ripe old age of 19, Chandra sailed on the steamship Pilsna to enroll as a graduate student at Cambridge University. He was to work there with Ralph Fowler, who had used Fermi-Dirac statistics to explain the properties of white dwarf stars—stars that have exhausted their supply of nuclear energy by burning hydrogen to make helium or carbon and oxygen. White dwarfs collapse gravitationally to a density many thousands of times greater than normal matter, and then slowly cool down by radiating away their residual heat. Fowler’s triumph of derived science included a calculation of the relation between the density and mass of a white dwarf, and his result agreed well with the scanty observations available at that time. With the examples of Sommerfeld and Fowler to encourage him, Chandra was sailing to England with the intention of making his own contribution to derived science.
A sea change
Aboard the Pilsna, Chandra quickly found a way to move forward. The calculations of Sommerfeld and Fowler had assumed that the electrons were nonrelativistic particles obeying the laws of Newtonian mechanics. That assumption was certainly valid for Sommerfeld. Electrons in metals at normal densities have speeds that are very small compared with the speed of light. But for Fowler, the assumption of Newtonian mechanics was not so safe. Electrons in the central regions of white dwarf stars might be moving fast enough to make relativistic effects important. So Chandra spent his free time on the ship repeating Fowler’s calculation of the behavior of a white dwarf star, but with the electrons obeying the laws of Einstein’s special relativity instead of the laws of Newton. Fowler had calculated that for a given chemical composition, the density of a white dwarfwould be proportional to the square of its mass. That made sense from an intuitive point of view. The more massive the star, the stronger the force of gravity and the more tightly the star would be squeezed together. The more massive stars would be smaller and fainter, which explained the fact that no white dwarfs much more massive than the Sun had been seen.
To his amazement, Chandra found that the change from Newton to Einstein has a drastic effect on the behavior of white dwarf stars. It makes the matter in the starsmore compressible, so that the density becomes greater for a star of given mass. The density does not merely increase faster as the mass increases, it tends to infinity as the mass reaches a finite value, the Chandrasekhar limit. Provided its mass is below the limit, physicists can model a white dwarf star with relativistic electrons and obtain a unique mass-density relation; there are no models for white dwarfs with mass greater than the Chandrasekhar limit. The limiting mass depends on the chemical composition of the star. For stars that have burned up all their hydrogen, it is about 1.5 times the mass of the Sun.
Chandra finished his calculation before he reached England and never had any doubt that his conclusion was correct. When he arrived in Cambridge and showed his results to Fowler, Fowler was friendly but unconvinced and unwilling to sponsor Chandra’s paper for publication by the Royal Society in London. Chandra did not wait for Fowler’s approval but sent a brief version of the paper to the Astrophysical Journal in the US. 2 The journal sent it for refereeing to Carl Eckart, a famous geophysicist who did not know much about astronomy. Eckart recommended that it be accepted, and it was published a year later. Chandra had a cool head. He had no wish to engage in public polemics with the British dignitaries who failed to understand his argument. He published his work quietly in a reputable astronomical journal and then waited patiently for the next generation of astronomers to recognize its importance. Meanwhile, he would remain on friendly terms with Fowler and the rest of the British academic establishment, and he would find other problems of derived sciencethat his mastery of mathematics and physics would allow him to solve.
The decline and fall of Aristotle
Astronomers had good reason in 1930 to react with skepticism to Chandra’s statements. The implications of his discovery of a limiting mass were totally baffling. All over the sky, we see an abundance of stars cheerfully shining with masses greater than the limit. Chandra’s calculation says that when those stars burn up their nuclear fuel,there will exist no equilibrium states into which they can cool down. What, then, can a massive star do when it runs out of fuel? Chandra had no answer to that question, and neither did anyone else when he raised it in 1930.
The answer was discovered in 1939 by J. Robert Oppenheimer and his student Hartland Snyder. They published their solution in a paper, “On Continued Gravitational Contraction.” 3 In my opinion, it was Oppenheimer’s most important contribution to science. Like Chandra’s contribution nine years earlier, it was a masterpiece of derived science, taking some of Einstein’s basic equations and showing that they give rise to startling and unexpected consequences in the real world of astronomy. The difference between Chandra and Oppenheimer was that Chandra started with the 1905 theory of special relativity, whereas Oppenheimer started with Einstein’s 1915 theory of general relativity. In 1939 Oppenheimer was one of the few physicists who took general relativity seriously. At that time it was an unfashionable subject, of interest mainly to philosophers and mathematicians. Oppenheimer knew how to use it as a working tool, to answer questions about real objects in the sky.
Oppenheimer and Snyder accepted Chandra’s conclusion that there exists no static equilibrium state for a cold star with mass larger than the Chandrasekhar limit. Therefore, the fate of a massive star at the end of its life must be dynamic. They worked out the solution to the equations of general relativity for a massive star collapsing under its own weight and discovered that the star is in a state of permanent free fall—that is, the star continues forever to fall inward toward its center. General relativity allows that paradoxical behavior because the time measured by an observer outside the star runs faster than the time measured by an observer inside the star. The time measured on the outside goes all the way from now to the end of the universe, while the time measured on the inside runs only for a few days. During the gravitational collapse, the inside observer sees the star falling freely at high speed, while the outside observer sees it quickly slowing down. The state of permanent free fall is, so far as we know, the actual state of every massive object that has run out of fuel. We know that such objects are abundant in the universe. We call them black holes.
Subrahmanyan Chandrasekhar’s discovery of a limiting mass for an ideal white dwarf appeared in a two-page paper 7 published in 1931. The limiting value of 0.9 solar mass is different from the modern value, which is 1.5 solar masses. The difference results from Chandra’s using an obsolete estimate of the chemical composition of the star.
Subrahmanyan Chandrasekhar’s discovery of a limiting mass for an ideal white dwarf appeared in a two-page paper 7 published in 1931. The limiting value of 0.9 solar mass is different from the modern value, which is 1.5 solar masses. The difference results from Chandra’s using an obsolete estimate of the chemical composition of the star.
With several decades of hindsight, we can see that Chandra’s discovery of a limiting mass and the Oppenheimer-Snyder discovery of permanent free fall were major turning points in the history of science. Those discoveries marked the end of the Aristotelian vision that had dominated astronomy for 2000 years: the heavens as the realm of peace and perfection, contrasted with Earth as the realm of strife and change.
Chandra and Oppenheimer demonstrated that Aristotle was wrong. In a universe dominated by gravitation, no peaceful equilibrium is possible. During the 1930s, between the theoretical insights of Chandra and Oppenheimer, Fritz Zwicky’s systematic observations of supernova explosions confirmed that we live in a violent universe. 4 In the same decade,Zwicky discovered the dark matter whose gravitation dominates the dynamics of large-scale structures. After 1939, astronomers slowly and reluctantly abandoned the Aristotelian universe as more evidence accumulated of violent events in the heavens. Radio and x-ray telescopesrevealed a universe full of shock waves and high-temperature plasmas, with outbursts of extreme violence associated in one way or another with black holes.
Every child learning science in school and every viewer watching popular scientific documentary programs on television now knows that we live in a violent universe. The “violent universe” has become a part of the prevailing culture. We know that an asteroid collided with Earth 65 million years ago and caused the extinction of the dinosaurs. We know that every heavy atom of silveror gold was cooked in the core of a massive star before being thrown out into space by a supernova explosion. We know that life survived on our planet for billions of years because we are living in a quiet corner of a quiet galaxy, far removed from the explosive violence that we see all around us in more turbulent parts of the universe. Astronomy has changed its character totally during the past 100 years. A century ago the main theme of astronomy was to explore a quiet and unchanging landscape. Today the main theme is to observe and explain the celestial fireworks that are the evidence of violent change. That radical transformation in our picture of the universe began on the good ship Pilsna when the 19-year-old Chandra discovered that there can be no stable equilibrium state for a massive star.
New ideas confront the old order
It has always seemed strange to me that the work of the three main pioneers of the violent universe—Chandra, Oppenheimer, and Zwicky—received so little recognition and acclaim at the time when it was done. Those discoveries were neglected, in part, because all three pioneers came from outside the astronomical profession. The professional astronomers of the 1930s were conservative in their view of the universe and in their social organization. They saw the universe as a peaceful domain that they knew how to explore with the standard tools of their trade. They were not inclined to take seriously the claims of interlopers with new ideas and new tools. It was easy for the astronomers to ignore the outsiders because the new discoveries did not fit into the accepted ways of thinking and the discoverers did not fit into the established astronomical community.
In addition to those general considerations, which applied to all three of the scientists,individual circumstances contributed to the neglect of their work. For Chandra, the special circumstances were the personalities of Arthur Eddington and Edward Arthur Milne, who were the leading astronomers in England when Chandra arrived from India. Eddington and Milne had their own theories of stellar structure in which they firmly believed; both of those were inconsistent with Chandra’s calculation of a limiting mass. The two astronomers promptly decided that Chandra’s calculation was wrong and never accepted the physical facts on which it was based.
Zwicky confronted an even worse situation at Caltech, where the astronomy department was dominated by Edwin Hubble and Walter Baade. Zwicky belonged to the physics department and had no official credentials as an astronomer. Hubble and Baade believed that Zwicky was crazy, and he believed that they were stupid. Both beliefs had some basis in fact. Zwicky had beaten the astronomers at their own game of observing the heavens, using a wide-field camera that could cover the sky 100 times faster than could other telescope cameras existing at that time. Zwicky then made an enemy of Baade by accusing him of being a Nazi. As a result of that and other incidents, Zwicky’s discoveries were largely ignored for the next 20 years.
The Chandra X-ray Observatory is one of several telescopes casting an eye on the violent universe. Chandra is seen here loaded in the Columbia space shuttle a few days before its 23 July 1999 launch.
The Chandra X-ray Observatory is one of several telescopes casting an eye on the violent universe. Chandra is seen here loaded in the Columbia space shuttle a few days before its 23 July 1999 launch.
The neglect of Oppenheimer’s greatest contribution to science was mostly due to an accident of history. His paper with Snyder, establishing in four pages the physical reality of black holes, was published in the Physical Review on 1 September 1939, the same day Adolf Hitler sent his armies into Poland and began World War II. In addition to the distraction created by Hitler, the same issue of the Physical Review contained the monumental paper by Niels Bohr and John Wheeler on the theoryof nuclear fission—a work that spelled out, for all who could read between the lines, the possibilities of nuclear power and nuclear weapons. 5 It is not surprising that the understanding of black holes was pushed aside by the more urgent excitements of war and nuclear energy.
Each of the three pioneers, after a brief period of revolutionary discovery and a short publication, lost interest in fighting for the revolution. Chandra enjoyed seven peaceful years in Europe before moving to America, mostly working, without revolutionary implications, on the theory of normal stars. Zwicky, after finishing the sky surveythat revealed dark matterand several types of supernovae, became involved in military problems as World War II was beginning;ultimately, he became an expert in rocketry. Oppenheimer, after discovering the most important astronomical consequence of general relativity, turned his attention to mundane nuclear explosions and became the director of the Los Alamos laboratory.
When I tried in later years to start a conversation with Oppenheimer about the importance of black holes in the evolution of the universe,he was as unwilling to talk about them as he was to talk about his work at Los Alamos. Oppenheimer suffered from an extreme form of the prejudice prevalent among theoretical physicists, overvaluing pure science and undervaluing derived science. For Oppenheimer, the only activity worthy of the talents of a first-rate scientist was the search for new laws of nature. The study of the consequences of old laws was an activity for graduate students or third-rate hacks. He had no desire in later years to return to the study of black holes, the area in which he had made his most important contribution to science.Indeed, Oppenheimer might have continued to make important contributions in the 1950s, when black holes were an unfashionable subject, but he preferred to follow the latest fashion. Oppenheimer and Zwicky did not, like Chandra, live long enough to see their revolutionary ideas adopted by a younger generation and absorbed into the mainstream of astronomy.
From stellar structure to Shakespeare
Chandra would spend 5-10 years on each field that he wished to study in depth. He would take a year to master the subject, a few more years to publish a series of journal articles demolishing the problems that he could solve, and then a few more years writing a definitive book that surveyed the subject as he left it for his successors. Once the book was finished, he left that field alone and looked for the next topic to study.
That pattern was repeated eight times and recorded in the dates and titles of Chandra’s books. An Introduction to the Study of Stellar Structure (University of Chicago Press, 1939) summarizes his work on the internal structure of white dwarfs and other types of stars. Principles of Stellar Dynamics (University of Chicago Press, 1942) describes his highly original work on the statistical theory of stellar motions in clusters and in galaxies. Radiative Transfer (Clarendon Press, 1950) gives the first accurate theory of radiation transport in stellar atmospheres. Hydrodynamic and Hydromagnetic Stability (Clarendon Press, 1961) provides a foundation for the theory of all kinds of astronomical objects—including stars, accretion disks, and galaxies—that may become unstable as a result of differential rotation. Ellipsoidal Figures of Equilibrium (Yale University Press, 1969) solves an old problem by finding all the possible equilibrium configurations of an incompressible liquid mass rotating in its own gravitational field. The problem had been studied by the great mathematicians of the 19th century—Carl Jacobi, Richard Dedekind, Peter Lejeune Dirichlet, and Bernhard Riemann—who were unable to determine which of the various configurations were stable. In the introduction to his book, Chandra remarks,
These questions were to remain unanswered for more than a hundred years. The reason for this total neglect must in part be attributed to a spectacular discovery by Poincaré, which channeled all subsequent investigations along directions which appeared rich with possibilities; but the long quest it entailed turned out in the end to be after a chimera.
After the ellipsoidal figures opus came a gap of 15 years before the appearance of the next book, The Mathematical Theory of Black Holes (Clarendon Press, 1983). Those 15 years were the time during which Chandra worked hardest and most intensively on the subject closest to his heart: the precise mathematical description of black holesand their interactions with surrounding fields and particles. His book on black holes was his farewell to technical research, just as The Tempest was William Shakespeare’s farewell to writing plays. After the book was published, Chandra lectured and wrote about nontechnical themes, about the works of Shakespeare and Beethoven and Shelley, and about the relationship between art and science. A collection of his lectures for the general public was published in 1987 with the title Truth and Beauty. 1
During the years of his retirement, he spent much of his time working his way through Newton’s Principia. Chandra reconstructed every proposition and every demonstration,translating the geometrical arguments of Newton into the algebraic language familiar to modern scientists. The results of his historical research were published shortly before his death in his last book, Newton’s “Principia” for the Common Reader (Clarendon Press, 1995). To explain why he wrote the book, he said, “I am convinced that one’s knowledge of the Physical Sciences is incomplete without a study of the Principia in the same way that one’s knowledge of Literature is incomplete without a knowledge of Shakespeare.” 6
Chandra’s work on black holes was the most dramatic example of his commitment to derived science as a tool for understanding nature. Our basic understanding of the nature of space and time rests on two foundations: first, the equations of general relativity discovered by Einstein,and second, the black hole solutions of those equations discovered by Karl Schwarzschild and Roy Kerr and explored in depth by Chandra. To write down the basic equations is a big step toward understanding, but it is not enough. To reach a real understanding of space and time, it is necessary to construct solutions of the equations and to explore all their unexpected consequences. Chandra never said that he understood more about space and time than Einstein, but he did. So long as Einstein did not accept the existence of black holes, his understanding of space and time was far from complete.
When I was a student at Cambridge, I studied with Chandra’s friend Godfrey Hardy, a pure mathematician who shared Chandra’s views about British imperialism and Indian politics. When I came,Hardy was old and he spent most of his time writing books. With the arrogance of youth, I asked Hardy why he wasted his time writing books instead of doing research. Hardy replied, “Young men should prove theorems. Old men should write books.” That was good advice that I have never forgotten. Chandra followed it too. I do not know whether he learned it from Hardy.
This article is based on a talk I gave for the Chandrasekhar Centennial Symposium at the University of Chicago on 16 October 2010.
REFERENCES
Freeman Dyson is a retired professor at the Institute for Advanced Study in Princeton, New Jersey.
