Physics版 - Chandrasekhar’s role in 20th-century science |
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s***e
发帖数: 5242 | 1 by Freeman Dyson
12/2010
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 wa reflecting deeply on the meaning and purpose of
his work. His talk was one of a series of public lectures organized 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
Image copyright Penelope Fowler. Courtesy of Historical Photographs of China
, University of Bristol.
Figure 1
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.
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.
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 Structure and 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
Figure 2, Photo courtesy of the AIP Emilio Segre Visual Archives, V. Ya.
Frenkel collection
Figure 2
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 dwarf would 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 stars more 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 science that his
mastery of mathematics and physics would allow him to solve.
The decline and fall of Aristotle
Figure 3
Figure 3
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.
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 telescopes revealed 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 silver or 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 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 theory of 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 survey that revealed dark matter and
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
Figure 4, Image courtesy of NASA.
Figure 4
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 holes and 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.
Freeman Dyson is a retired professor at the Institute for Advanced Study in
Princeton, New Jersey.
References
1. S. Chandrasekhar, Truth and Beauty: Aesthetics and Motivations in
Science, U. Chicago Press, Chicago (1987).
2. S. Chandrasekhar, Astrophys. J. 74, 81 (1931).
3. J. R. Oppenheimer, H. Snyder, Phys. Rev. 56, 455 (1939).
4. See, for example, F. Zwicky, Morphological Astronomy, Springer, Berlin
(1957), sec. 8 and 9.
5. N. Bohr, J. A. Wheeler, Phys. Rev. 56, 426 (1939).
6. S. Chandrasekhar, Curr. Sci. 67, 495 (1994).
7. Ref. 2, reprinted in K. C. Wali, A Quest for Perspectives: Selected
Works of S. Chandrasekhar, with Commentary, vol. 1, Imperial College Press,
London (2001), p. 13. | s*******n
发帖数: 1474 | 2 Zwicky是天文领域一个独一无二的牛人, 以敏锐的洞察力和刻薄的人品著称
他把他在Palomar天文台的同事叫做“spherical bastard”
why? because“they are bastard in any way you look”
不过他对于现代天文学的贡献基本也只有Hubble等寥寥几人能相抗了。
Chicago
of
speakers
Marc
【在 s***e 的大作中提到】
: by Freeman Dyson
: 12/2010
: 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 wa reflecting deeply on the meaning and purpose of
: his work. His talk was one of a series of public lectures organized 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
| F**D
发帖数: 6472 | 3 问个题外话，你和Dr. Draine熟不?
【在 s*******n 的大作中提到】
: Zwicky是天文领域一个独一无二的牛人, 以敏锐的洞察力和刻薄的人品著称
: 他把他在Palomar天文台的同事叫做“spherical bastard”
: why? because“they are bastard in any way you look”
: 不过他对于现代天文学的贡献基本也只有Hubble等寥寥几人能相抗了。
:
: Chicago
: of
: speakers
: Marc
| d***n
发帖数: 194 | 4 Such articles about scientific giants are addicting... Part of the following
is also about Chandra and might be interesting:
http://www.springerlink.com/content/k6743707753k/front-matter.p | h********0
发帖数: 12056 | 5 My respect to Chandrasekhar is unlimited! | e********y
发帖数: 935 | 6 能不能摘要一下
following
【在 d***n 的大作中提到】
: Such articles about scientific giants are addicting... Part of the following
: is also about Chandra and might be interesting:
: http://www.springerlink.com/content/k6743707753k/front-matter.p
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