Arthur Stanley Eddington

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   The protons at the centre of the Sun repel each other electrically and, at 15 million degrees, lack the energy to touch. They touch anyway, rarely, by tunnelling: without it the Sun would not burn, and its rarity is why the Sun burns slowly enough for life to have appeared.

   The Internal Constitution of the Stars · 1926

   The Sun is too cold for protons to touch, so they pass through the wall between them, rarely, and that rarity gives the Sun billions of years.

   In 1920 the astronomer Arthur Eddington proposed that stars shine by fusing hydrogen into helium. The objection came quickly. The centre of the Sun is about 15 million degrees. That sounds enormous, but for two protons it is not enough. Both carry a positive electric charge, so they repel each other, and the repulsion grows the closer they get. To come close enough to stick, classical physics would need a temperature several hundred times higher, of the order of ten billion degrees. Eddington answered his critics with an irony that became famous: let them go and find a hotter place. He was right that stars burn hydrogen, but he could not say how. The answer came in 1928 from another corner of physics: radioactivity. Some nuclei throw out an alpha particle, two protons and two neutrons stuck together. The particle is held inside by a wall of energy that, counted classically, it could not jump. George Gamow and, independently, Ronald Gurney and Edward Condon showed that the particle gets out by tunnelling. The calculation also explained a strange rule known for some time: a small difference in the particle's energy changes how long the nucleus lives by billions of billions of times. A year later Robert Atkinson and Fritz Houtermans turned the idea around: if a particle can tunnel out of a nucleus, it can tunnel in. That is how the protons in stars manage to touch. In the Sun, any given proton waits on average billions of years before it fuses: tunnelling is rare, and the next step, in which a proton turns into a neutron, is rarer still. But the Sun has so many protons that every second about 600 million tonnes of hydrogen become helium and about 4 million tonnes of mass turn into light and heat. The rarity is a stroke of luck. If protons got through easily, the Sun would have burnt its fuel long ago, and there would have been no time for life on Earth.

   “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.”

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