The Eddington-Chandrasekhar Confrontation

The pursuit of knowledge through scientific inquiry can be both challenging and rewarding. As Sir Arthur Stanley Eddington noted, “The subject is a fair field for the struggle to gain knowledge by scientific reasoning; and, win or lose, we find the joy of contest.”

Mathematics and astronomy have long been intertwined, yet discrepancies between mathematical predictions and astronomical observations can arise. The exploration of stars and their life cycles has always captivated astronomers and astrophysicists alike.

A young prodigy, Subrahmanyan Chandrasekhar, made significant strides in this field by establishing a crucial parameter for determining stellar density through Fermi-Dirac statistics. He also identified a crucial mass threshold, now known as the Chandrasekhar limit, which determines whether a star will ultimately collapse into a neutron star or a black hole.

Early Life

Subrahmanyan Chandrasekhar, an Indian-American astrophysicist, began his education at home, where his father taught him physics and mathematics, while his mother instructed him in Tamil. A transformative lecture by Arnold Sommerfeld inspired him to write his first research paper titled _The Compton Scattering and the New Statistics_ in 1929. Chandrasekhar graduated with a physics degree from Presidency College, Madras, in 1930. That same year, he received a scholarship to pursue graduate studies at the University of Cambridge under Ralph Fowler's guidance.

During his lengthy sea voyage to England, Chandrasekhar contemplated white dwarfs—the remnants of stars that have exhausted their nuclear fuel. He integrated the principles of special relativity into his previous findings about stellar density and concluded that a star exceeding a specific mass, approximately 1.44 times that of the Sun, could not remain a white dwarf. This critical mass is referred to as the "Chandrasekhar limit."

Though now widely accepted, this idea faced skepticism in its early days, particularly from a prominent scientist. Chandrasekhar later shared the Nobel Prize in Physics in 1983 for his theoretical contributions to understanding stellar structure and evolution.

Upon arriving at Cambridge, he presented his findings through two papers—one addressing non-relativistic degenerate configurations, and the other focusing on relativistic effects and critical mass—to his advisor, who subsequently forwarded one of them, titled _The Highly Collapsed Configurations of a Stellar-Mass_, to Edward Arthur Milne for evaluation. Both scientists were curious about the fate of stars that exceeded the Chandrasekhar limit and whether other stages existed beyond being a white dwarf.

Despite their work being well-received, Milne sought to publish the findings in the Monthly Notices of the Royal Astronomical Society in 1931. Chandrasekhar completed his doctorate in 1933 after a challenging examination by Fowler and Eddington.

Eddington’s Criticism

Eddington, a strong proponent of Einstein's theories, anticipated Chandrasekhar’s insights on white dwarfs to resolve a longstanding debate with Milne regarding stellar models. The two often engaged in discussions, sharing meals at Cambridge's high table.

Milne posited that a star's core consisted of degenerate material, surrounded by gas that conformed to ideal gas laws, while Eddington argued that stars behaved like a perfect gas. At a Royal Astronomical Society meeting in 1929, Eddington dismissed Milne's theory, stating:

> “I have not read professor Milne’s paper, but I hardly think it is necessary, for it would be absurd for me to pretend that professor Milne has the remotest chance of being right.”

In another paper, he added:

> “It is difficult to discuss this paper. Professor Milne did not enter into detail as to why he arrives at results so widely different from my own; and my interest in the rest of the paper is dimmed because it would be absurd to pretend that I think there is the remotest chance of his being right.”

Milne retorted in _The Analysis of Stellar Structure_:

> “Sir Arthur Eddington has dug a most valuable trench into unknown territory. But he has encountered a rocky obstacle which he cannot get around. If he would make the mental effort to scramble up the sides of the trench he would find the surrounding country totally different from what he had imagined and the obstacle entirely an underground one.”

Chandrasekhar’s Contributions

Chandrasekhar's findings indicated that stars exceeding the critical mass would behave as perfect gases, aligning with some of Eddington's arguments. However, his conclusions contradicted Eddington's assertion that all stars ultimately become white dwarfs.

Admiring both scientists, Chandrasekhar believed a comprehensive derivation of the equation of state for stellar masses under various conditions was necessary to resolve their dispute. In 1934, he developed the exact solution for the equation of state (polytropic stars) using extensive numerical methods.

He authored two papers and submitted them to the Royal Astronomical Society in 1935, where he was invited to present his work. Eddington attended, prepared to challenge him. Although Chandrasekhar believed they were on amicable terms, he was unprepared for the ensuing confrontation.

After detailing his findings, Eddington delivered a critical address titled _Relativistic Degeneracy_, disputing the physical interpretations of Chandrasekhar's theory and branding it as a conceptual error:

> “The formula is based on a combination of relativity mechanics and non-relativity quantum theory, and I do not regard the offspring of such a union as born in lawful wedlock. I think there should be a law of Nature to prevent a star from behaving in this absurd way!”

Chandrasekhar left the meeting disheartened, feeling that his years of labor had been disregarded. The audience’s perception shifted in favor of Eddington's assertions, leading Chandrasekhar to question why Eddington had encouraged him to complete his calculations if he intended to undermine him publicly.

Eddington’s Dominance

Eddington's views were widely accepted, partly due to his established authority and reputation within the astronomical community, and partly due to his rigorous conclusions. However, neither Eddington's nor Chandrasekhar's theories had direct observational support.

Feeling unable to defend himself adequately, Chandrasekhar sought counsel from an expert. He reached out to his Belgian colleague, Leon Rosenfeld, who worked under Niels Bohr in Denmark. In a letter, he expressed:

> “… I have been spending months on my stellar structure work with the hope that for once there will be no controversy. Now that my work is completed, Eddington has started this “howler” and of course Milne is happy. My work has shown that his (Milne’s) ideas in many places are wrong, but my work depends on the relativistic degenerate formula and Milne can now go ahead. The result is that there is going to be a long period of stress and confusion, and if somebody like Bohr can authoritatively make a pronouncement in the matter, it will be of the greatest value for further progress in the subject.”

Chandrasekhar sought Bohr's assistance to clarify doubts surrounding his work. He shared Eddington's manuscript with Bohr, who forwarded it to Wolfgang Pauli. Both expressed their support for Chandrasekhar's theory privately but did not want to publicly engage in the controversy.

Chandrasekhar attempted to counter Eddington's critiques in a joint paper with Christian Møller. The following year, physicist Rudolf Peierls substantiated the claims Eddington dismissed in his own paper, _Note on the Derivation of the Equation of State for a Degenerate Relativistic Gas_. Peierls also challenged Eddington's misunderstandings of Chandrasekhar's work in another paper co-authored with Paul Dirac and Maurice Pryce, stating:

> “In a recent paper, Eddington raises an objection against the customary use of the Lorentz transformation in quantum mechanics, … when applied to … the behavior of a degenerate gas. This objection seems to us to be mainly based on a misunderstanding, and our purpose here is to show that the practice of theoretical physicists on this point is quite consistent.”

Eddington persisted in his critiques, seizing every opportunity to undermine Chandrasekhar's work. In a 1936 invited lecture, he remarked:

> “… put the stars back in precisely the same difficulty from which Fowler had rescued them. The small stars could cool down all right and end their days as dark stars in a reasonable way. But above a certain mass … the star could never cool down, but must go on radiating and contracting until heaven knows what becomes of it. That did not worry Chandrasekhar; he seemed to like the stars to behave that way and believes that is what really happens. But I felt the same objections as earlier to this stellar buffoonery; at least it was sufficient that there must be something wrong with the physical formula used.”

During a meeting of the International Astronomical Union in July 1939, Eddington approached Chandrasekhar after the proceedings concluded and said, “I’m sorry if I hurt you this morning. I hope you are not angry with what I said.” To which Chandrasekhar replied, “You have not changed your mind. Have you?” Eddington admitted he hadn’t, prompting Chandrasekhar to respond, “What are you sorry about, then?” before walking away.

Frustrated by the ongoing attacks on his theory and the lack of authoritative support from figures like Bohr, Pauli, and Dirac, Chandrasekhar decided to abandon his struggle for validation and shift focus to other research areas. He published the book _An Introduction to the Study of Stellar Structure_ in 1939 and redirected his interests.

Reflecting on these experiences 45 years later, Chandrasekhar recounted:

> “I knew the assistant secretary, Miss Williams… rather well, and she used to send me the program ahead of the meeting. And on Thursday evening I got the program and found that immediately after my paper Eddington was giving a paper on ‘Relativistic Degeneracy.’ I was really very annoyed because, here Eddington was coming to see me every day, and he never told me he was giving a paper.”

He continued, recalling a conversation with Eddington:

> “Then I went to dine in College and Eddington was there. Somehow I thought Eddington would come to talk with me. After dinner, I was standing by myself in the Combination Room where we used to have coffee, and Eddington came up to me and asked me, ‘I suppose you are going to London tomorrow?’ I said, ‘Yes.’ He said, ‘You know your paper is very long. So I have asked the secretary to give you a half-hour for your presentation instead of the customary 15 minutes.’ I said, ‘That’s very nice of you.’ And he still did not tell me. So I was a little nervous as to what the story was.”

At a tea event before a meeting at Burlington House, Chandrasekhar and relativist McCrea engaged Eddington in conversation, who, when asked about Relativistic Degeneracy, only teased, “That’s a surprise for you,” and walked away.

In a 1977 interview, Chandrasekhar reflected on Eddington's derision of his theories:

> “Eddington gave an hour’s talk, criticizing my work extensively and making it into a joke. I sent a note to Russell [Henry Norris Russell was presiding], telling him I would wish to reply.”

Russell's response was a terse, “I prefer that you didn’t,” leaving Chandrasekhar without an opportunity to defend himself while enduring the audience's pitying glances.

This narrative highlights how personal biases, authority, and entitlement can sometimes overshadow logic and objectivity in the realm of science, much as they do in other aspects of life.

Despite the turmoil, the personal rapport between Chandrasekhar and Eddington remained intact, as they exchanged amicable correspondence from 1938 to 1943. In his obituary for Eddington delivered at the University of Chicago, Chandrasekhar remarked:

> “Posterity may rank Eddington, next to Karl Schwarzschild, as the greatest astronomer of our time. I believe that anyone who has known Eddington will agree that he was a man of the highest integrity and character. I do not believe, for example, that he ever thought harshly of anyone. That was why it was so easy to disagree with him on scientific matters. You can always be certain that he would never misjudge you or think ill of you on that account. This cannot be said of others.”

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