Prof. CHANDRASEKHAR

 

The Nobel Laureate

 

A. RANGANATHAN

 

            BEFORE I DEAL with his life story as well as his scientific work, I wish to refer to an interview which gives us an idea of the Chan­drasekhar cast of mind. “My approach to objec­tives in science”, remarked Professor Chan­drasekhar in a memorable interview, “is rather like a sculptor who likes to create a structure, which has the stamp of his personality. Once he has finished the structure, he does not go on chiseling it here and there for the rest of his life”.

 

            Again the topics which have suited his temperament are - Stellar Structure, Stellar Dynamics, Radiative Transfer, Hydrodynamic and Hydromagnetic Stability, Ellipsoids, Post­Newtonian Approximations and Black Holes. His well-known style – The Chandrasekhar Style – is to change his field of specialization and to write the definitive work in the field at the end of each such period. Perhaps it is this Chandrasekhar Style which is the creative source of his scientific longevity. And in the process he has written a series of celebrated volumes: All Introduction to the Study of Stellar Structure (1939), Principles of Stellar Dynamics (1942), Radiative Transfer (1950), Plasma Physics (1960), Hydrodynamic and Hydromagnetic Stability (1961), Ellipsoidal Figures of Equilibrium (1969), and The Mathematical Theory of Black Holes (1983) which have won him such distinctions as the 1944 Fellowship of the Royal Society, the 1947 Adams Prize of Cambridge University, the 1952 Bruce Medal of the Astronomical Society of the Pacific, the 1953 Gold Medal of the Royal Astronomical Society, the 1957 Rumford Medal of the American Academy of the Arts and Science, the 1962 Royal Medal of the Royal Society of London, the 1962 Srini­vasa Ramanujan Medal of the Indian National Science Academy, the 1966 American National Academy of Science, the 1968 Padmavibushan Award of the Government of India, the 1971 Henry Draper Medal of the National Academy of Sciences, the 1973 Smoluchowski Medal of the Polish Physical Society, the 1974 Dannie Heineman Prize of the American Physical Society, the 1983 Nobel Prize for Physics and the 1984 Copley Medal of the Royal Society of London.

 

            And as a result of a heart problem (which necessitated major surgery and was happily solved) Chandrasekhar could not sus­tain his usual pattern of style on work for a while. For a work which ought to have been entitled The Post-Newtonian Approximations and the Stability of the Relativistic Stars was regretably never written. In the normal circum­stances, it ought to have published in 1975. And his spell in Chicago includes his tenure as the Editor of the Astrophysical Journal from 1952 to 1971.

 

            Subrahmanyan Chandrasekhar was born at Lahore on October 19, 1910. The first six years of his life were spent at Lahore. And two more years were spent at Lucknow before Chandrasekhar returned to Madras. He has a distinguished family background. His great grandfather – his father’s grandfather – had as a young man walked all the way from Trichinopoly to Nadia in Bengal, in order to study Nyaya. His father Shri C. S. Ayyar, was a member of the I.A. & A.S., – second to the Railways – and an authority on the Grammar of Carnatic Music. His uncle – his father’s younger brother – was Sir C. V. Raman, the first Asian scientist to win the Nobel Prize for Physics in 1930.

 

            As Lord Snow remarks somewhere, “As a rule, mathematical talent shows itself at a very early age”. Not surprisingly, Chandra was an accomplished mathematician even while studying at Hindu High School. The scene shifted to Presidency College, Madras – the same institution where his father and uncle studied – to do his Intermediate. And he joined the Physics Honours Course at Presi­dency College in 1927. Here it is necessary to stress that Chandrasekhar had a particularly distinguished career – academically speaking, as a student and as a research scientist. To sum it up in a phrase, it was due to Chandrasekhar’s interaction with Arnold Sommerfeld, Werner Heisenberg and M.N. Saha, as well as an ex­change of letters with Professor Ralph Fowler. At this point, one must emphasize the unique­ness of the Madras University Honours Course. For it allowed a good deal of academic free­dom in the pursuit of one’s chosen disciplines.

 

            Chandrasekhar’s career as a research scientist began in the wake of his meeting with Arnold Sommerfeld in 1928. Sommerfeld was a contemporary of Einstein and his students in­cluded such celebrities as Debye, Pauli, Bethe, Unsold and Heisenberg. Young Chandra told Sommerfeld that he had studied the English translation of his work on Atomic Structure and Special Lines. During this conversation Som­merfeld had introduced Chandra to the new world of contemporary physics – the discov­ery of wave mechanics by Schroedinger as well as the new developments triggered off by He­isenberg, Dirac, Pauli and others. He also gave him copies of his papers on the electron theory of metals – actually Sommerfeld had worked out the behaviour of electrons inside a metal by applying the Fermi-Dirac Statistics. This paper inspired Chandrasekhar to write his cele­brated paper Compton Scattering and the New Statistics.

 

            In fact Chandrasekhar postulated the inverse Compton Effect in respect of Stellar interiors where very high energy electrons exist. Indeed this paper – entitled Compton Scattering and the New Statistics – was published in the Proceedings of the Royal Society in Lon­don in 1929. His first paper on Thermodynam­ics and the Compton Effect with reference to the Interior of the Stars was published in the Indian Journal of Physics in 1928. Furthermore as a student he had published two more papers - The Ionization Formula and the New Statistics and on The Probability Method in the New Statistics Philosophical Magazine in 1930. And he also secured record marks in the Physics Honours of the Madras University in 1930 – First Class, First in the Madras Presidency.

 

            These achievements resulted in three developments:

 

            1. Young Chandra presented a prelimi­nary account of his Royal Society Paper at the January 1929 session of the Indian Science Congress. Soon Chandra has savoured the excitement of Raman’s discovery at Calcutta in 1929. And it was followed by a rewarding session with Heisenberg.

 

            2. Chandrasekhar attended the Indian Science Congress Association in Allahabad, in January 1930. By this time, he had elected to become a theoretical astrophysicist. Possibly because of the prize which was awarded to him: The Internal Constitution of the Stars by Eddington. It was pleasant surprise for Chan­drasekhar to be told by Saha that he was famil­iar with his work.

 

            3. The net result of all this work was obvious – Chandra was awarded the Govern­ment of India scholarship to do research at Trinity College, Cambridge.

 

            While dwelling on his career at Cam­bridge, I wish to discuss the Yeatsian concept of luck. “The English Poets” observed Yeats, “do not believe in luck”. For instance, accord­ing to Yeats, Wordsworth was lucky on two occasions in his life “that is when he composed his famous pieces: Tintem Abbey and The Ode on Intimations of Immortality. Einstein him­self was lucky, in this sense, during the first half of his career – the Quantun explanation of the photoelectric effect which won him the Nobel Prize for physics in 1921, the statistical law governing the phenomenon of Brownian Motion and the Special Theory of Relativity which neatly amalgamated space, time and matter into one fundamental unity, were written in 1906.

 

            He was lucky once again in 1916. For he was able to generalize the Special Theory to include the Gravitational Field in formulating his celebrated General Theory of Relativity. And yet Einstein was unable to unify electro­magnetic and gravitational forces even after several decades of hard work. In other words, one can be lucky or inspired once or twice in one’s life – there are, of course, exceptions to this rule like Shakespeare and Newton. Interestingly enough Sommerfeld’s initial response to Einstein’s Theory of General Relativity was not favourable. Einstein himself was not re­conciled to the uncertainty Principle of Heisenberg and the Bohr-Heisenberg Interpretation of Quantum Mechanics. And when luck deserts a creative genius, there is a sort of an intellec­tual hardening of the arteries!

 

            Combining Einstien’s Special Theory of Relativity and then the new Quantum Mechanics in 1930 (Chandra was then 19 while voyaging through the Mediterranean Sea), he demonstrated that if the mass of the star exceeded a certain critical mass (greater than approximately 1.4 times the mass of the sun) the star would not become a white dwarf. It would continue to collapse under the extreme pressure of gravitational forces. In 1935 (Chandra was a Fellow of Trinity, at that point of time), he established this criti­cal mass condition, currently known as Chandrasekhar’s Limit – based on rigorous mathematical reasoning – and reported the re­sults at a meeting of the Royal Astronomical Society of London. Chandrasekhar’s findings raised two fundamental questions: 1. What happens to the more massive stars when they continue to collapse? 2. Are there several ter­minal stages of stars other than that of white dwarfs?

 

            Eddington was not able to grasp the far ­reaching consequences of an elegant application of Einstein’s Special Theory of Relativity, which was at the core of Chandrasekhar’s dis­covery. This was a trifle surprising, owing, to Sir Arthur Eddington’s impeccable credentials. Indeed Eddington made the great discovery that the luminosity of a star depends mainly on its mass. Obviously it is possible to determine the luminosity of a star when one calculates its distance. Apart from making this great discov­ery, Eddington led the expedition to the island of Principe off the coast of West Africa in 1919, in order to photograph the stars which were visible near the sun when it was eclipsed. Eddington’s verification of the Gen­eral Theory constitutes a part of modern scien­tific history. Again Eddington’s personal rela­tions with Chandrasekhar were cordial. Indeed Eddington and Milne were partly responsible for electing Chandrasekhar as a Fellow of the Royal Society in 1944.

 

            Perhaps the Eddington-Chandrasekhar controversy must be viewed in the larger perspective of scientific controversies. For, just as Niels Bohr was involved in an historic con­troversy with Einstein, so was Chandrasekhar engaged in an equally historic controversy with Eddington. Interestingly enough, the similari­ties are striking. Although Einstein rejected the statistical reasoning underlying the nature of the Quantum Theory. Similarly, according to Mccrea, Eddington who supported Einstein at a time when some great scientists did not accept the General Theory of Relativity rejected Chandrasekhar’s Theory of Stellar Degeneracy on the ground that Chandra did not treat the star as a single molecule in relativistic terms. The irony lay in the fact that Chandrasekhar’s Theory had contributed to the mathematical underpinnings governing the astrophysics of Black Holes as a logical extension of the Gen­eral Theory of Relativity.

 

            In his paper Beauty and the Quest for Beauty in Science, Chandrasekhar refers to the fact that Eddington made this remark in the wake of a controversial discussion: “You look at it from the point of view of the star; I look at it from the point of view of Nature”.

 

            Here are two characteristic judgements delivered by Prof. Chandrasekhar in his Centenary Lectures on Eddington at Trinity Col­lege, Cambridge, in 1982. “It is my judgement” says Prof. Chandrasekhar, “that Edding­ton’s greatest contribution to the General The­ory of Relativity is his wondrous treatment of the subject in his Mathematical Theory of Rela­tivity. I continue to use it”. Again, with that magnanimity of mind which characterized Niels Bohr’s attitude to Einstenian determin­ism, Chandrasekhar remarks: “I find it hard to understand why Eddington, who was one of the earliest and staunchest supporters of The Gen­eral Theory of Relativity should have found the conclusion that Black Holes may form during the natural course of the evolution of stars, so unacceptable”. And seen in historical perspective, the biographical essays written by Chan­drasekhar – on Ralph Fowler, Eddington, Milne, Einstein and Karl Schwarszchild – ­constitute a prism for a long view of the development of twentieth century astrophysics.

 

            As is well-known, Chandrasekhar stud­ied in detail what happens to a star at the end of its life. Having burnt itself out, due to the relativistic degeneracy of the electron, he was able to show that stars which have a mass which is less than 1.4 times the mass of the sun, will experience a gravitational collapse. The expression “Black Hole” was given to this phenomenon – nearly three decades after Chandrasekhar worked out the details using Quantum Mechanics and the Special Theory of Relativity by John Archibald Wheeler.

 

            Chandrasekhar started working in the area of General Relativity during the ’Seven­ties. His spectacular contribution in this area is the solution of the Dirac Equation in the ambi­ence of the Kerr Metric. “The Black Holes of Nature”, says Chandrasekhar, “are the most perfect macroscopic objects there are in the universe; the only elements in their construc­tion are our concepts of space and time. And since the General Theory of Relativity provides only a single unique family of solutions for their descriptions, they are the simplest objects as well”.

 

            Highlighting his philosophical razor, William of Ockham, proclaimed during the early fourteenth century, that in slicing the world into categories, “thou shall not multiply entities unnecessarily”. He might have been happy when Dirac explained the mathematical theory of the Spin 1/2 Electron in the first half of this century. Furthermore, this was contin­ued by the 1976 Chandrasekhar solution of the Dirac Equation – formulated in 1928 and which represents the Spin 1/2 particles like the Electron and the Neutron – separable in the Kerr Geometry. The theory of the Gravita­tional Perturbations of the Kerr Black Hole is of considerable complexity and it has been tackled in a characteristically masterly style by Professor Chandrasekhar. And just as the Dirac Equation had set off a tidal wave in theoretical physics, so can Chandrasekhar’s mathematical theory of Black Holes be re­garded as one of the greatest achievements in the history of astronomy.

 

            In his Shakespeare, Newton and Beethoven or Patterns of Creativity, Prof. Chandrasekhar says that “on reading Shelley’s A Defence of Poetry, the question insistently occurs why there is no similar A Defence of Science written by a scientist of equal endowment”. In trying to answer this question, one could think of at least four works – ­G.H. Hardy’s A Mathematician’s Apology, J. Bronowski’s The Common Sense of Science and The Visionary Eye, Chandrasekhar’s own Truth and Beauty.

 

            Chandrasekhar’s work Truth and Beauty, ranges from essays in biography to the dialogue of the scientific and literacy cultures, from a discussion of the patterns of beauty con­stituting Shakespeare’s Plays and Sonnets, Newton’s Principia, Beethoven’s Sympho­nies, Milne’s Kinematical Theory of Relativity and Einstein’s General Theory of Relativity to the defence of scientific values. The volume concludes with sensitive assessments of Karl Schwarzchild and Arthur Stanley Eddington as well as an aesthetic response to the two major areas in the Mathematical Theory of Relativity. Prof. Chandrasekhar himself has made and continues to make memorable contributions to these two areas of Relativistic Astrophysics –the Mathematical Theory of Black Holes and the Mathematical Theory of Colliding Waves. Throughout Prof. Chandrasekhar has success­fully attempted, in a manner which many readers will doubtless find intellectually stimulat­ing, to bring out the relations between aesthet­ics and scientific motivations.

 

            Together, these essays reveal Prof. Chandrasekhar in at less formal, more immedi­ate mode – as one of the most distinguished scientist-aestheticians of our time. Indeed, these essays constitute a splendid body of work – an aesthetically meaningful complement to the scientific classics for which Prof. Chandra­sekhar speaks in Truth and Beauty with the kind of quiet authority that makes his Shelley-­inspired defence of scientific values a classic for our time.

 

            At this point, a distinction ought to be made between the great scientist-writers like Eddington, Jeans, Haldane, Raman, Chan­drasekhar, Weinberg, Weisskopf, and the sci­ence writers. Furthermore, like Madame Cu­rie, Albert Einstein and C.V. Raman, Chan­drasekhar is a brilliant expositor. For in­stance, Madame Curie’s account of the discov­ery of radium, Einstein’s formulation of the special theory of relativity in his paper on the “Electrodynamics of Moving Bodies”. Raman’s paper “On the Molecular Scattering of Light in Water and the Colour of the Sea” as well as his Lectures on Physical Optics, and Chan­drasekhar’s description of the White-dwarf state of stars are memorable pieces of scientific writing.

 

            It is not only for his technical brilliance that Chandrasekhar is pre-eminent. He is even more celebrated for his literary sensibility which informs such elegant pieces and exposi­tions as The Story of Two Atoms, Marian Smoluchowski as the Founder of the Physics of Stochastic Phenomena, The Scientist, As­tronomy is Science and in Human Culture, Einstein and General Relativity - Historical Perspectives, Beauty and the Quest for Beauty in Science and Einstein’s General Theory of Relativity and Cosmology (published in the Encyclopaedia Britannica).

 

            Chandrasekhar is a professional astrono­mer who in recent years had devoted some of his time to the explanation of some trends in the history of astronomy. In his 1968 Nehru Memorial Lecture he rightly states that “since no astronomy at an advanced level can exist without actual computations of planetary and lunar ephemerides, it must be the first task of the historian of Hindu astronomy to search for such texts”. Here it is worth noting that David Pingree’s projected eleven-volume Census of the Exact Sciences in Sanskrit might well fill in certain gaps in the history of Indian sci­ence. However, in order to get a clear picture, Chandrasekhar’s Nehru Memorial Lecture ­Astronomy in Science and in Human Culture – ought to be studied, along with his signifi­cant review of Neugebauer’s A History of An­cient Mathematical Astronomy. For they not only reflect Chandrasekhar’s characteristic aes­thetic sensibility but also unveil the poetic vis­tas of the following Ptolemy verse:

 

            “I know that I am mortal and the crea­ture of a day

            But when I contemplate the intricate cir­cling spiral of the stars,

            No longer do my feet touch earth, but beside Zeus himself

            I take my fill of the immortal nectar of the gods”.

 

            Prof. Chandrasekhar’s 1975 Nora and Edward Ryerson Lecture on Shakespeare, Newton and Beethoven or Patterns of Creativ­ity is a significant contribution to the dialogue of the two cultures in our time. Here it is well to recall that Lord Snow, who concerned himself with the widening gap between science and the rest of our culture, in his Rede Lecture, sparked off an interesting controversy. Actu­ally, Lord Snow had not made a plea for uni­versal dilettentism but attempted to put an end to the cold war between the sciences and the humanities. And Snow’s casual observation that literary men did not know such concepts as the second law of thermodynamics, which to him constituted the scientific equivalent of “Have you read a play by Shakespeare” was character­ized as a “cheap journalistic infelicity” by F.R. Leavis in his polemical Richmond Lecture.

 

            The man of letters and the scientist are equally concerned with what Aldous Huxley termed as the need to “give a purer sense to the words of the tribe” at different levels of perception. Here it would be relevant to refer to Professor Chandrasekhar’s perceptive comment on the Heisenberg definition of beauty:

 

            “In a deeply moving essay on The Meaning of Beauty in the Exact Sci­ences, Heisenberg gives us a definition of beauty which I find most apposite. The definition, which Heisenherg says goes back to antiquity, is that “beauty is the proper conformity of the parts to one another and to the whole”. On reflection it does appear that this definition touches the essence of what we may describe as ‘beautiful’, it applies to King Lear, Misa Solemnis and the Principia”.

 

            And viewed in historical perspective it is clear that the dialogue of the two cultures is not a new phenomenon. For Wordsworth wrote that “if the time should ever come when what is now called science, thus familiarized to men, shall be ready to put on, as it were, a form of flesh and blood, the poet will lend his divine spirit to aid the transfiguration and will welcome the Being thus produced as a dear and genuine inmate of the household of man”. Furthermore, Shelley’s stellar vision in Helles:

 

            “Worlds on worlds are rolling ever

            From creation to decay

            Like the bubbles on a river

            Sparkling, bursting, borne away”

 

could be viewed as a poetic transcript of a monograph like Chandrasekhar’s An Introduc­tion to the Study of Stellar Structure.

 

            I conclude with a sentence from Chan­drasekhar’s essay on “Beauty and the Quest for Beauty in Science:

 

            “The translucence of the eternal splen­dour through material phenomena (for which Plotinus spoke) is made iridescent in such works as Jacobi’s Lectures on Dynamics, Boltmann’s Lectures on Theory of Gases, Sommerfeld’s Atomic Structure and Spectral Lilies, Dirac’s Principles of Quantum Mechanics and the various gems of exposition which Schroedinger wrote in his later years”.

 

            A sentence which could well be applied to some of Professor Chandrasekhar’s own works such as Radiative Transfer and The Mathematical Theory of Black Holes.

 

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