White dwarfs, dark acts and bad blood

Empire of the Stars
July 15, 2005

A feud drove one astrophysicist's restless career, says Roger Penrose

Over the past century, remarkable progress has been made in our understanding of the Universe and its contents. In 1917, about two years after he introduced the field equations of general relativity, Einstein turned his attention to cosmology and began to apply these equations to the universe as a whole. In 1922, the Russian mathematician Alexandr Friedmann found the first plausible cosmological solutions, his universe models originating in the singularity that we now refer to as a Big Bang, in line with the 1929 observations of Edwin Hubble that the Universe is in a state of expansion.

Most cosmologists now believe that about 90 per cent of the material content of the Universe is some unknown substance referred to as "dark" matter and that the remaining 10 per cent - "ordinary" matter - is mainly hydrogen, with a significant contribution from helium and much smaller amounts of other elements. There is also a very large contribution from what is sometimes called "dark energy". But this can be consistently regarded as arising from the presence of Einstein's cosmological constant in the field equations (suggested in 1917, although he subsequently had second thoughts).

The material that is directly visible to us consists mainly of stars (including the Sun), and for many centuries the detailed nature of these distant light sources remained mysterious. However, a great deal is now known with considerable confidence about these ubiquitous entities, and this body of understanding constitutes a major part of the burgeoning subject of theoretical astrophysics. There is, indeed, a remarkable accord between the theory and observational evidence coming from many kinds of observation.

The key figure in this area from about 1906 until his death in 1944 was the Englishman Sir Arthur Stanley Eddington, a superb populariser of science as well as the originator of much of the subject of astrophysics. He was one of the first to understand Einstein's general relativity, and he led an expedition to the equatorial Atlantic island of Principe, just after the First World War, to take advantage of an eclipse of the Sun to verify Einstein's prediction that the Sun's gravitational field would cause a bending of light. Eddington is one of the main players in Arthur I. Miller's remarkable Empire of the Stars .

The other main player - and, indeed, the central character in this book - is Subrahmanyan Chandrasekhar (Chandra), who, when he first encountered Eddington, was a young and brilliant Indian student of mathematics and physics. At the age of 19, he came to Cambridge from Madras to work with Ralph Fowler, an astrophysicist colleague of Eddington's. At an early stage of his sea voyage to the UK, he came to an important realisation about white dwarf stars (enormously dense but dim and tiny bodies), such as the mysterious companion to the bright star Sirius. What Chandra calculated was that if such a star has a mass greater than a certain value - a value not very different from that of our own Sun - it would not be able to sustain itself against its own gravitational attraction and would collapse inwards without any agency being available to stop it.

In Cambridge, Chandra developed his ideas in much further detail, and was soon on friendly terms with Eddington, Fowler and many other leading astrophysicists and mathematicians. At a meeting of the Royal Astronomical Society in London, on January 11, 1935, Chandra gave a lecture on the maximum mass of white dwarfs. Eddington was due to speak after him. No one knew what he might say, but Chandra anticipated some useful or interesting commentary on his own talk. In any case, Chandra felt confident, because he was sure of his facts and had checked everything, in his normal meticulous way. What he did not expect was the devastating attack that ensued.

Eddington claimed that the basis on which Chandra's calculations were made was in fact completely wrong, and the young scientist was made to look a fool.

Some words of explanation are needed here. In 1926, Fowler had shown that the famous Pauli exclusion principle, which forbids any two electrons from being in the same state ("degeneracy pressure"), could prevent an extremely dense core of material, under extreme external pressure, from collapsing in on itself, and by this means he proposed that the core of a white dwarf star, of any mass whatever, could sustain itself under gravitational collapse.

But Chandra had realised that this would cease to be the case if the effects of Einstein's special relativity were taken into account, in cases where the electron velocities approach that of light. Accordingly, for a large enough mass, such degeneracy pressure would not be able to hold the star apart. There being no other means for halting its collapse, the star would appear to continue indefinitely inwards to achieve an infinite compression and an infinite density - a singularity. Chandra himself was less dogmatic in his speculation about the final state of the star, writing rather enigmatically that "one is left speculating on other possibilities".

Chandra was devastated by Eddington's attack. He inquired of many other important figures what they thought. His ideas received assent from Niels Bohr, Paul Dirac, Fowler, Leon Rosenfeld, Wolfgang Pauli and John von Neumann, but no one seemed willing to "go public". Chandra, in any case, suffered greatly from swings of confidence, and this encounter would appear to have had a lasting effect on him. In late 1936, he returned briefly to India to marry the charming and intelligent Lalitha Doraiswamy, whom he had left behind when he sailed to England. From there, the couple went to settle (after a short stop in Cambridge) at Yerkes Observatory in the US, where Chandra had accepted a job.

One effect of the onslaught seems to have been to initiate a pattern in Chandra's scientific activities for the rest of his life: he would keep changing his field. In 1938, he completed a comprehensive account of his understanding of the structure of stars (including white dwarfs), An Introduction to the Study of Stellar Structure . Then he moved to a new topic, the dynamics of systems of many stars, and in 1943 he published a comprehensive account, The Principles of Stellar Dynamics . Again he moved to a new topic and in 1950 produced another book, Radiative Transfer ; ditto in 1961 with Hydrodynamic and Hydromagnetic Stability ; and, in 1969, the Ellipsoidal Figures of Equilibrium .

Eventually, he began to steer himself back to the area that his original work on white dwarfs should have been aiming him towards, namely Einstein's general relativity - because the unstoppable collapse of a too-massive white dwarf star would lead, inevitably, to the very large gravitational fields that require this theory, Newtonian descriptions becoming inadequate. Chandra had previously no expertise in general relativity, but at the age of about 50 he determined to become an expert, which indeed he did. In 1971, he produced General Relativity and Relativistic Astrophysics .

His tortuous route to the resolution of the white dwarf problem finally led him to the study of black holes. By then, others had finally built up a robust theory, which he mastered and made significant contributions to, producing, in 1983, The Mathematical Theory of Black Holes . Even this did not quite tackle the singularity issue, which he began to address in his last phase of work in general relativity.

Empire of the Stars is a fascinating account of an important and moving story. It holds particular interest for me because many of those who feature in it are known to me, either personally or by reputation. I was, however, still somewhat unclear as to why Eddington should have chosen to be so devastating to a young and sensitive student on that day in 1935.

Miller makes the point that Eddington was by then very wrapped up with his own "fundamental theory" (involving things he called "E-numbers"), which he proposed using to explain many unknown features of the Universe, such as the exact number of protons it contains and the precise value of the fine structure constant (which Eddington claimed was exactly 1/137, after previously thinking it had to be exactly 1/136). So he would not countenance anything that might undermine this theory. I am quite prepared to believe this, as I have encountered many instances of passionate commitment by people to their pet theories. But Miller does not really make clear why the existence of black holes should be so devastating to Eddington's E-numbers.

In a general way, the book is much more valuable as a historical account of important events, the personalities involved in them and the implications of the events for those personalities than as an account of the scientific issues, especially those directly related to black holes and other aspects of general relativity. The suggestion that the collapsed star is somehow "still there" inside a black hole is frequently made in the book, as is the picture conjured up of "space closing around the collapsed star". These pictures do not really accord with what I would regard as a reasonable description. Even more disturbing is the dramatic description of "funnelling light" that appears in the second paragraph of the book's prologue. This does not accord at all with my own understanding, in which the passage through a black hole's horizon would be insidious in the extreme, with absolutely no evident indication that such an irreversible act has taken place.

Finally, in parts of the last chapter, many of the fanciful schemes that people put forward these days, such as time travel through wormholes, the creation of mini-black holes in the lab and even the plausibility of extraspatial dimensions, are too readily taken on board. I rather fear that people feel that black holes are so weird - yet seem to exist - that they license almost anything else. But when you get to understand them, black holes are not so weird, and we must in any case address the singularity issue with the Big Bang.

These relatively minor reservations aside, I enjoyed Empire of the Stars immensely and learnt a lot from it.

Sir Roger Penrose is emeritus professor of mathematics, Oxford University.

Empire of the Stars: Friendship, Obsession and Betrayal in the Quest for Black Holes

Author - Arthur I. Miller
Publisher - Little, Brown
Pages - 400
Price - £17.99
ISBN - 0 316 72555 2

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