Small controversy, stellar credit

Had Arthur Stanley Eddington permitted his mindset to be liberal enough, he would have got the credit of predicting the existence of black holes

As in any field, science too has its share of controversies. One may at first wonder why this should be so since science and scientists pride themselves on rational thinking and factual evidence. The reason is that incomplete evidence can lead to ambiguity and hence divergence of interpretations while rational thinking based on a wrong theory will, obviously, be misleading.

The historic controversy in 1935 between Subrahmanyan Chandrasekhar, then a budding scientist, and Arthur Stanley Eddington, a distinguished veteran with many contributions in the field of astrophysics, illustrates how
disagreements on a major scale can arise and be aired in public.
S. Chandrasekhar, nephew of Nobel laureate C.V. Raman and a brilliant scholar in his own right, went to Cambridge in 1930 for higher studies. While on the ship to England, Chandrasekhar was taken up by the problem of white dwarf stars and arrived at an explanation of how such stars maintain their equilibrium. A star like the Sun is held in equilibrium under two opposing forces. The mass of the star generates a powerful gravitational force which tends to pull the star inwards. There is an opposing force which prevents this catastrophic contraction. This force is generated by the thermonuclear fusion reaction
going on in the interior of the star.
While this is a good working theory for a typical star, it leads to a logical question: What happens to a star that has exhausted all its nuclear fuel?
We expect the star to contract under gravity. Indeed, there are many such stars which are very small, say with a radius of about a per cent of the radius of the Sun. Known as white dwarfs, these stars maintain their equilibrium in spite of the lack of thermonuclear reactions. Where does the pressure (to oppose gravity) come from?
Cambridge physicist R.H. Fowler had demonstrated that this pressure came from the quantum effect first noted by Wolfgang Pauli. Known as the Pauli Exclusion Principle, this effect arises from the limit imposed by the science of quantum mechanics on how closely one can pack a given volume with subatomic particles, like the electrons. Pauli’s prescription for close packing leads to a new kind of pressure called the degeneracy pressure since matter so packed is called degenerate matter.
Fowler’s analysis showed that the star can maintain its equilibrium in this way and white dwarfs were the ideal stars to whom this model applied.
Chandrasekhar was aware of this work but felt that it had missed a subtle effect that might become important in determining the equilibrium of a white dwarf. A rough and ready way of seeing this effect is through the analogy of a bucket being filled with water. The first drops of water occupy the lowest level in the bucket. As you fill in more and more water, the level of water rises and later drops occupy higher levels. Likewise, when a limited space is being filled with electrons, as the density of the electrons rises, the later batches have higher energy. And higher energy means the electrons move faster. With high enough energy the electrons may be moving at speeds close to that of light and hence they would be subject to the special theory of relativity proposed by Einstein in 1905. Fowler, instead, had continued to rely on Newtonian dynamics. This was the subtle effect that Chandrasekhar wanted to investigate. How would it change Fowler’s results?
During his stay in Cambridge as a research student, Chandrasekhar extensively studied this problem and finally came to a startling conclusion. He found that if one takes into account the effects of degeneracy of matter as well as its special relativistic behaviour, there is a critical mass above which there is no equilibrium state for a star. Equilibrium is possible only below this limit and the star can exist as a white dwarf. Thus the relativistic degeneracy places a mass limit on white dwarf stars.
When he submitted a scientific paper on this result for publication to the Royal Astronomical Society (RAS), he was asked to make a presentation of it in the next meeting of the society. These meetings are held on the second Friday of every month, and papers considered important are invited for presentation.
On the evening before the meeting, at the Fellows’ dinner in Trinity College, Chandrasekhar ran into Eddington, whose pioneering work on stars had inspired research on stellar structure. Eddington told him that as his paper was important he had asked the secretary of the society to allot more time for it. Evidently, Chandrasekhar got the impression
that Eddington was favourably inclined towards his work.
The next evening at the RAS meeting Chandrasekhar made his presentation and the president, as expected, called upon Eddington to comment. And here Chandrasekhar received a big shock. For, Eddington severely criticised the work, saying that there was no such thing as relativistic degeneracy. Moreover, he ridiculed the idea of a mass limit for white dwarfs.
He said: “The star (with mass exceeding the mass limit) has to go on radiating and radiating and contracting and contracting until, I suppose, it gets to a few km radius, when gravity becomes strong enough to hold in the radiation, and the star can at last find peace.” And further added that there should be a law of nature to prevent a star from behaving in this absurd way.
Why did Eddington not give an inkling of his violent opposition to Chandrasekhar’s conclusion the previous evening? Instead he chose to give the impression of friendly support. But the irony is that the behaviour of stars that he considered absurd applies to black holes.
In short, had Eddington permitted his mindset to be liberal enough, he would have got the credit of predicting the existence of black holes, objects whose
strong gravitational pull even holds back their own light.
It took many years for the astronomical community to realise that in the above controversy, Chandrasekhar had been right and Eddington wrong. The mass limit is now recognised as the Chandrasekhar Limit. This work is prominently cited in Chandrasekhar’s Nobel Award in 1983.

The writer, a renowned astrophysicist, is professor emeritus at Inter-University Centre for Astronomy and Astrophysics, Pune University Campus

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