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The Eddington-Chandrasekhar Debate: A Tale of Scientific Rivalry

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Chapter 1: The Human Element of Science

The journey of scientific discovery often involves a rich tapestry of personal interactions and intellectual debates. Sir Arthur Stanley Eddington once remarked, "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 are deeply intertwined, yet occasionally, theoretical conclusions can clash with empirical observations. The examination of stars and their life cycles has consistently been one of the most captivating areas within astrophysics.

A prodigious young mind named Subrahmanyan Chandrasekhar made a groundbreaking discovery that helped define the density of stars using Fermi-Dirac statistics. He introduced the concept of the 'Chandrasekhar limit'—a critical mass threshold that dictates whether a star will collapse into a neutron star or black hole.

Early Life

Subrahmanyan Chandrasekhar, an Indian-American astrophysicist, began his education at home. Under his father's guidance, he learned mathematics and physics, while his mother imparted knowledge of Tamil. A pivotal moment in his academic journey occurred when he attended a lecture by Arnold Sommerfeld, inspiring him to author his first research paper on "The Compton Scattering and the New Statistics" in 1929. He earned his physics bachelor's degree from Presidency College, Madras, in 1930, and shortly after received a government scholarship to study at the University of Cambridge under Ralph Fowler.

During his long voyage to England, Chandrasekhar contemplated white dwarfs—stellar remnants devoid of nuclear fuel. He integrated concepts from special relativity into his previous findings regarding stellar density, concluding that a star could not remain a white dwarf if its mass exceeded 1.44 times that of the Sun. This threshold is now recognized as the "Chandrasekhar limit."

Though celebrated today, the significance of his work was initially overshadowed by skepticism from established scientists. He would later share the Nobel Prize in Physics in 1983 for his theoretical contributions to stellar structure and evolution.

Upon arriving at Cambridge, Chandrasekhar presented two papers to his advisor: one focusing on non-relativistic degenerate configurations and the other addressing relativistic effects and critical mass. His advisor, Fowler, passed one of these papers, titled "The Highly Collapsed Configurations of Stellar Mass," to Edward Arthur Milne for evaluation.

Milne, however, posed several unanswered questions: What occurs when a star exceeds this mass limit? Are there subsequent stages beyond being a white dwarf? Despite the uncertainties, both he and Milne recognized the merit of Chandrasekhar's work, leading to its publication in the Monthly Notices of the Royal Astronomical Society in 1931. Chandrasekhar ultimately completed his doctorate in 1933 after navigating a rigorous examination led by Fowler and Eddington.

Eddington's Critique

Eddington, a staunch supporter of Einstein's theories, was eager to validate Chandrasekhar's findings on white dwarfs as a means to resolve a longstanding debate with Milne regarding stellar models. The two frequently discussed their research and shared meals at Cambridge's high table.

Milne proposed that a star's core consists of degenerate material, encased by matter adhering to perfect gas laws, while Eddington argued that stars function as perfect gases. In a 1929 Royal Astronomical Society meeting, Eddington dismissed Milne's ideas, 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."

He further noted in one of his publications:

"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 research posited that if a star's mass exceeds the critical limit, it behaves like a perfect gas, thereby supporting Eddington's claims. However, this did not align with Eddington's view that all stars inevitably become white dwarfs.

Admiring both scientists, Chandrasekhar believed a comprehensive derivation of the equation of state for stellar mass under general conditions was necessary to resolve their differences. By 1934, he achieved an exact solution to the equation of state for polytropic stars using extensive numerical techniques.

He submitted two papers to the Royal Astronomical Society in 1935 and was invited to present his findings. Unbeknownst to him, Eddington was prepared to critique him harshly. Chandrasekhar, expecting a cordial exchange, found himself unprepared for the onslaught that followed his presentation.

After discussing his solution, Eddington launched into a critical examination titled "Relativistic Degeneracy," claiming the theory was fundamentally flawed:

"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 feeling despondent, reflecting on the disparity between his expectations and reality. Observers began to echo Eddington's sentiments, leaving him disheartened. He questioned why Eddington had never privately communicated his skepticism and whether his encouragement had been a ruse to discredit him publicly.

Eddington's Authority

At that time, Eddington's ideas were widely accepted, not only due to his authority and reputation but also because of his rigorous reasoning. However, there was no conclusive observational data to validate Eddington's stance or to disprove Chandrasekhar's findings.

Feeling unable to counter Eddington's criticisms at meetings, Chandrasekhar sought guidance from an expert in the field, writing to his friend Leon Rosenfeld, who worked under Niels Bohr in Denmark. He expressed his frustrations about Eddington's critiques and the ongoing confusion surrounding his work.

"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. The result is that there is going to be a long period of stress and confusion..."

Chandrasekhar sought Bohr's intervention to clarify his work. He provided Bohr with Eddington's manuscript, which was then shared with Wolfgang Pauli. Both scientists expressed their agreement with Chandrasekhar's theory but were reluctant to engage in the ongoing controversy publicly.

Chandrasekhar attempted to counter Eddington's arguments in a joint paper with Christian Møller. The following year, physicist Rudolf Peierls validated aspects of Chandrasekhar's theory in a paper titled "Note on the Derivation of the Equation of State for a Degenerate Relativistic Gas." He criticized Eddington's misunderstandings in collaboration with Paul Dirac and Maurice Pryce, noting:

"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 continued to undermine Chandrasekhar's theories. In a 1936 lecture, he stated:

"… 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..."

At the International Astronomical Union meeting in Paris in July 1939, Eddington approached Chandrasekhar afterward 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 responded, "No." Chandrasekhar retorted, "What are you sorry about, then?" and walked away, feeling exhausted by Eddington's continual denigration of his work.

Frustrated by the lack of authoritative support from figures like Bohr, Pauli, and Dirac, Chandrasekhar decided to redirect his focus to other research areas. He authored "An Introduction to the Study of Stellar Structure" in 1939 and shifted his interests.

Reflecting on those tumultuous years, 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..."

In a 1977 interview, Chandrasekhar vividly recalled Eddington's mockery 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 sent back a note saying, 'I prefer that you didn't.' And so I had no chance even to reply; and accept the pitiful glances of the audience."

This narrative illustrates how personal biases, authority, and entitlement can overshadow reason and fairness within the scientific community, akin to other aspects of life.

Despite the animosity in their professional exchanges, the personal rapport between Chandrasekhar and Eddington remained intact. They continued to correspond amicably from 1938 to 1943.

In his obituary for Eddington 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."

Thank you for engaging with this account. I welcome any thoughts, feedback, or suggestions you may have!

If you enjoyed this narrative, consider showing your appreciation by giving it a clap or treating me to a cup of coffee ☕️🙂.

Chapter 2: The Legacy of the Debate

The first video, "Physics Beef: The White Dwarf Controversy between Subrahmanyan Chandrasekhar and Arthur Eddington," explores the intense scientific rivalry between these two influential figures in astrophysics, offering insights into their conflicting theories and personal interactions.

The second video, "A Story of Brutal Betrayal In Science | Eddington And Chandrasekhar," delves into the personal and professional betrayals faced by Chandrasekhar and their lasting impact on the scientific community.

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