Arthur Eddington: The Man Who Weighed Stars and Saved Einstein

When general relativity landed in late 1915, almost nobody in Britain wanted to hear it. It was a German theory during a war with Germany. British observatories were run by men who had grown up on Newton. Few in Cambridge could even read the mathematics.

Eddington could. The Chief Assistant at the Royal Observatory, a former Senior Wrangler at Trinity, he had the mathematical horsepower and — as a Quaker — a stubborn belief that science shouldn't care which side of the Channel it came from. He persuaded the Astronomer Royal, Frank Dyson, to plan an expedition around a total solar eclipse predicted for 29 May 1919. The eclipse would sweep across the Atlantic, and a few minutes of totality would let them photograph stars in the Hyades cluster right beside the darkened Sun.

Einstein's prediction was specific: a light ray grazing the Sun's limb should bend by 1.75 arcseconds — exactly twice what a naive Newtonian analysis of light-as-particle gave. The Hyades stars, if photographed against an eclipsed Sun, should appear displaced outward compared to the same stars photographed at night, months earlier.

Eddington sailed to Príncipe, a volcanic island off Africa's west coast. Andrew Crommelin led a parallel team to Sobral, in northern Brazil — two sites to insure against weather. On eclipse day, clouds smothered Príncipe until the final minutes; Eddington snapped sixteen plates and only two proved usable. They were enough.

Six months later, at a joint meeting of the Royal Society and the Royal Astronomical Society in Piccadilly, Dyson announced the verdict: the starlight had bent by an amount consistent with general relativity, not with Newton. The New York Times ran it on the front page under a six-deck headline: LIGHTS ALL ASKEW IN THE HEAVENS. Einstein, almost unknown outside physics, became overnight the most famous scientist on Earth. Eddington's cloud-rescued plate — the Dyson, Eddington, and Davidson photograph — remains one of the great confirmations in the history of science.

Having helped save Einstein, Eddington turned to a harder problem. Nobody knew what the inside of a star looked like. It was 1920. Stellar spectra gave you the surface — temperature, composition, a little about motion. Everything below that was speculation.

Eddington reasoned his way down. A star, he argued, is a ball of gas — not solid, not liquid, not some exotic phase. Gravity pulls inward. Something must push outward to hold it up. Gas pressure alone is not enough for a star as massive as the Sun; the interior temperatures are too extreme and the matter too ionised. The missing force was radiation pressure — photons streaming out from the hot core, shoving on the plasma like a slow, steady wind from below.

From this single insight he extracted the mass–luminosity relation: more massive stars have to be dramatically brighter, because gravity squeezes them hotter in the middle. The theory predicted a curve, and the data — once it came — fell almost exactly on it. A 10-solar-mass star shines about 10,000 times brighter than the Sun, not ten times; the exponent is roughly 3 to 4. His 1926 book The Internal Constitution of the Stars laid the whole picture out, and is, remarkably, still readable today as a textbook.

There was one giant puzzle left: what powered it all? Eddington computed how fast the Sun would cool if it were burning coal, or contracting gravitationally — the Kelvin–Helmholtz estimate Lord Kelvin had pushed in the nineteenth century. The answer was millions of years, not the billions that geology and biology were demanding. Eddington argued that four hydrogen atoms fusing into one helium atom would release the missing energy — a correct pointer at fusion almost two decades before Hans Bethe worked out the CNO cycle in detail. When critics objected that the Sun wasn't hot enough for such reactions, Eddington replied, famously: "We do not argue with the critic who urges that the stars are not hot enough for this process; we tell him to go and find a hotter place."

What happens when radiation pressure wins? You get the Eddington limit — the maximum luminosity a star can sustain in hydrostatic equilibrium. Above it, outward radiation pressure on the ionised gas exceeds gravity's inward pull, and the star's outer layers are literally driven off into space as a wind.

For pure hydrogen, the limit works out to roughly L_Edd ≈ 3.2 × 10⁴ × (M/M☉) × L☉. A 100-solar-mass star can shine up to about 3 million Suns before it starts to shed itself. Most stars sit comfortably below their limit. A handful of the most massive sit right up against it — the luminous blue variables like Eta Carinae, P Cygni, and S Doradus, which flicker near the edge and periodically erupt in shells of gas visible for centuries.

Eddington derived all this from first principles in 1926. The same equation sets an upper bound on how fast a black hole can swallow gas: push matter onto a black hole past the Eddington limit and the resulting accretion luminosity blows the rest of the infalling gas away before it can fall. Quasars are typically quoted as fractions of their Eddington rate. An entire language of modern high-energy astrophysics is Eddington's 1926 notation.

In 1930, a 19-year-old prodigy named Subrahmanyan Chandrasekhar calculated during his boat voyage from India to England that a white dwarf above about 1.4 solar masses could not exist as a stable object. Electron degeneracy pressure, once you corrected it for special relativity, was not strong enough to hold up such a star against its own gravity. Something else had to happen — the star had to keep collapsing.

He brought the result to Cambridge, where Eddington was the grand old man of stellar astrophysics. At a Royal Astronomical Society meeting in January 1935, Chandrasekhar presented his limit. Eddington rose immediately after and demolished it in public, calling the result "stellar buffoonery" and insisting there must be a law of nature preventing such an absurd outcome as an infinitely collapsing star. Chandrasekhar, humiliated, turned away from white dwarfs and spent decades on other problems.

Eddington was wrong. Chandrasekhar was right, and there is no such law. Above his eponymous limit, a white dwarf becomes a neutron star, or, if it is massive enough, a black hole. Chandrasekhar eventually received the 1983 Nobel Prize, partly for the work Eddington had once mocked. The episode is a permanent reminder that even the century's greatest astrophysicist can be catastrophically wrong — and a warning about how heavy the opposition of a senior figure can sit on the field.

Between the war and his death in 1944, Eddington wrote a series of books for general readers that together sold more than a million copies — an unthinkable figure for popular science at the time. Stars and Atoms (1927), The Nature of the Physical World (1928), The Expanding Universe (1933): each was part astrophysics lecture, part philosophical meditation on what physics implies about knowledge, chance, and reality.

He had a gift for the memorable phrase. On the strangeness of physics at small scales: "Not only is the universe stranger than we imagine, it is stranger than we can imagine." On time and entropy: the image of the arrow of time — a phrase he coined in 1927 — remains the standard shorthand, used daily by every physicist who talks about thermodynamic irreversibility. On fuel: "A star is drawing on some vast reservoir of energy by means unknown to us... this reservoir can scarcely be other than the subatomic energy which, it is known, exists abundantly in all matter." That was 1920. The first fusion experiments were decades in the future.

He was also prone to mystical detours. His late work on a "Fundamental Theory" tried to derive the constants of nature from pure number — the famous claim that the fine-structure constant had to be exactly 1/137, which it doesn't. That project didn't age well. The popular books, and The Internal Constitution of the Stars, did.

Eddington is in almost everything we see. Every star in the sky is held up by the balance he first quantified between gravity and radiation. Every luminous blue variable, every quasar blowing gas off an accreting black hole, every estimate of how long the Sun has left — all of it runs through his 1920s papers. The main-sequence band on the Hertzsprung–Russell diagram, the mass–luminosity law, the temperature scale of stellar interiors: the whole vocabulary of stellar astrophysics starts with him.

And the whole empirical foundation of Einstein's spacetime, at least for the first decade of its life, came from a cloud-strafed photograph on a cocoa plantation in West Africa.