Subrahmanyan Chandrasekhar was born in Lahore on 19 October 1910. In the summer of 1930, aged nineteen, he sailed from Madras to England to begin research at Cambridge, and he spent the voyage doing a calculation.
The result was that a dead star cannot be arbitrarily heavy. Above a certain mass, nothing can hold it up, and it must go on collapsing.
Five years later the most eminent astrophysicist in the world stood up in front of the Royal Astronomical Society and made him a laughing stock for it.
The Calculation on the Boat
The question was what holds up a white dwarf.
A star like the Sun stays inflated because fusion in the core produces heat and pressure. When the fuel runs out, the pressure stops and gravity wins. The star collapses until something else stops it, and in 1926 Ralph Fowler had identified what: electron degeneracy pressure.
This comes from quantum mechanics rather than from heat. The exclusion principle forbids two electrons from occupying the same quantum state, so as matter is compressed the electrons are forced into higher and higher momentum states simply because the low ones are full. The resulting pressure does not depend on temperature at all. A white dwarf can cool forever and still resist gravity.
Fowler’s treatment implied that this works for any mass. Chandrasekhar noticed the gap. If you squeeze the electrons hard enough, they are pushed to speeds approaching that of light, and then special relativity has to be applied to them.
That changes everything, and it changes it in the worst possible direction. For a non relativistic degenerate gas, pressure rises with density as the power five thirds. For a fully relativistic one, it rises only as the power four thirds. The stiffness of the material falls, and at four thirds the balance against gravity becomes precarious rather than stable.
Work through it and there is a maximum mass. Chandrasekhar’s first figure was around 0.91 times the mass of the Sun; the refined value, with the right composition, is about 1.4. Above it, electron degeneracy pressure cannot win, whatever the star does.
The conclusion is not subtle, and he understood it at nineteen. A star that ends its life above that mass has nothing left to stop it.
The Meeting, 11 January 1935
Arthur Stanley Eddington was by then the dominant figure in the field. He had written The Internal Constitution of the Stars, the book that created stellar astrophysics as a quantitative subject. He had led the 1919 eclipse expedition that confirmed general relativity and made Einstein famous worldwide. He was the most effective scientific communicator in Britain, and at Cambridge he was, in practice, the arbiter of what counted as good astrophysics.
He had also been kind to Chandrasekhar personally, visiting him, encouraging him, and he had seen the proofs of the paper before the meeting.
Chandrasekhar presented his result. Eddington was scheduled to speak immediately afterwards, which Chandrasekhar had not been told, and he used his time to demolish it.
His argument was that combining special relativity with degeneracy in this way was illegitimate, a mixture of two theories that did not belong together, and that the result was therefore an artefact. His rhetorical flourish was the line that everybody remembers: that a star should not behave in this absurd way, and he thought there ought to be a law of Nature to prevent it.
The audience laughed. Chandrasekhar, twenty four, had no right of reply under the format of the meeting. He sat there while the room agreed with Eddington.
Eddington Was Wrong, and Everybody Competent Knew
The relativistic treatment of a degenerate electron gas is not controversial physics. It was not controversial in 1935 either, among physicists.
Chandrasekhar went to the people who would know. Wolfgang Pauli, whose exclusion principle it was, confirmed that the treatment was correct. Niels Bohr agreed. So did Rudolf Peierls and Léon Rosenfeld. Privately, the physics community was unanimous.
Publicly, almost none of them said anything. The dispute was taking place in astronomy, Eddington was an institution, and quantum physicists had their own field to attend to in the 1930s. Peierls and others eventually published technical notes supporting the result, but nobody with comparable standing went after Eddington in public.
Eddington never conceded. He kept up the objection for the rest of his life, in part because he was deep in his own unified fundamental theory by then and had commitments that Chandrasekhar’s result cut across.
What It Cost
The immediate cost was that Chandrasekhar left the subject.
He put the full treatment into his 1939 book An Introduction to the Study of Stellar Structure, moved to the University of Chicago, and turned to something else. Then he did it again, and again: stellar dynamics, radiative transfer, hydrodynamic and magnetohydrodynamic stability, ellipsoidal figures of equilibrium, general relativity, and finally the mathematical theory of black holes. Roughly a decade each, a book at the end of each, and then he would abandon the field entirely.
He described this as a deliberate way of working. It is also difficult not to read the first move as a young man being told that the most important thing he would ever do was absurd.
The larger cost was to the subject. The implication of the limit is that something must exist beyond a white dwarf, and the natural next questions are what stops the collapse and what happens if nothing does. In 1939 Oppenheimer and Snyder published the answer to the second one: continued gravitational collapse, with the star cutting itself off from communication with the outside universe. That paper describes a black hole.
It was almost entirely ignored for nearly thirty years. The war intervened, but so did the intellectual climate, in which the leading authority in stellar astrophysics had publicly declared that this whole direction was nonsense. Serious work on collapse only resumed in the 1960s, driven by pulsars, quasars and the discovery of X ray binaries, and the term black hole was not in general use until 1967.
Chandrasekhar said later that he thought the physics of collapse had been delayed, and that if his result had been accepted in 1935 astronomy might have got to these objects decades earlier. He was in a position to know, and he was not a man given to overstatement.
What the Limit Turned Out to Govern
The figure of 1.4 solar masses is now one of the most used numbers in astrophysics.
- Type Ia supernovae. A white dwarf pulling material from a companion approaches the limit, ignites its carbon, and detonates. Because the trigger is a fixed mass, these explosions have a nearly standard brightness, which makes them the distance markers used to measure the expansion of the universe. The discovery of dark energy in 1998 rests on them
- Neutron stars. The remnant above the limit collapses until neutron degeneracy stops it, at a density comparable to an atomic nucleus, packing more than a solar mass into a sphere a few kilometres across
- Black holes. Above the neutron star limit as well, nothing is left that can resist. The object photographed by the Event Horizon Telescope in 2019 is at the far end of the argument Chandrasekhar started on a boat
He received the Nobel Prize in Physics in 1983, forty eight years after the meeting, for the theoretical studies of the structure and evolution of stars.
The Part That Complicates the Story
It would be tidier if the two men had hated each other. They did not.
They continued to see each other, cycled and played tennis together, and Eddington went on supporting Chandrasekhar’s career in practical matters even while rejecting his result. Chandrasekhar said repeatedly, in interviews given decades later, that he never lost his affection or his admiration for Eddington, and he wrote about him with warmth.
That is what makes the episode worth telling. It is not a story about a villain. It is a story about how much damage a generous, brilliant, senior person can do by being confidently wrong in public, in a field where they are the standard of judgement, in front of people who will take their word for it rather than check.
Chandrasekhar’s last book, finished in his eighties, was Newton’s Principia for the Common Reader, in which he worked through Newton’s propositions one by one and restated them in modern terms. He had spent his life on the mathematics of collapse and he ended it going back through the geometry of the book where gravity was first written down.
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