“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.”Arthur Stanley Eddington · The Internal Constitution of the Stars · 1926 · Arthur S. Eddington, «The Internal Constitution of the Stars», Cambridge University Press, 1926, p. 301 (citat după surse secundare)
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.
Made simple: the window protons pass through. Think of the centre of the Sun as a huge crowd of runners bumping into one another. Most run at an ordinary speed, a few are faster, and very, very few are extremely fast. Between any two stands an electric wall. The ordinary speed (physicists say thermal energy) is about 1.35 kiloelectronvolts; the wall is around 1,000 kiloelectronvolts. No runner reaches the top of the wall. They all have to go through it.
Now combine two things that pull in opposite directions. The faster a proton is, the thinner the wall left in front of it, so it gets through more easily. But fast protons are very rare. The numbers below are ‘toy’ numbers, chosen only to show the shape:
PROTON SPEED HOW MANY (per million) CHANCE OF PASSING PRODUCT (how much it counts)
ordinary 600,000 1 in 10 billion very little
3 times faster 5,000 1 in 1 million more
6 times faster 25 1 in 10,000 THE MOST
12 times faster almost 0 1 in 100 almost nothingFusion comes from the middle: not from the ordinary protons (too weak), nor from the extremely fast ones (too few), but from a narrow band between them. Astronomers call it the ‘Gamow window’, after George Gamow, who first worked out how hard it is for a particle to pass through the electric wall of a nucleus. For the Sun, the window sits at a few times the ordinary energy.
What the table teaches: if the Sun warmed a little, the window would widen and it would burn faster; if it cooled, it would burn more slowly. That makes a star a thermostat: when it burns too hard it expands and cools, when it burns too weakly it contracts and heats up.
What was actually measured. The first evidence came from nuclei, not stars. The Geiger–Nuttall rule, found in 1911, said that nuclei which emit more energetic alpha particles live much shorter lives. The differences are enormous: polonium-212 emits alpha particles of almost 8.8 megaelectronvolts and half its atoms are gone in 0.3 millionths of a second; uranium-238 emits particles of only 4.3 megaelectronvolts and half its atoms are gone in 4.5 billion years. The energy is only twice as large, but the nucleus's life is over a hundred thousand billion billion times shorter. Gamow's tunnelling formula (1928) gave exactly this exponential fall. Ronald Gurney and Edward Condon published the same explanation the same year, in Nature.
For stars, Robert Atkinson and Fritz Houtermans showed in 1929 that tunnelling allows fusion at the real temperatures of stars. Hans Bethe described the reaction chains in 1938–1939 (the proton–proton chain and the carbon–nitrogen–oxygen cycle), for which he received the Nobel Prize in 1967.
Direct confirmation came only in our century. The reactions at the centre of the Sun produce neutrinos, particles that pass through the whole Sun and the Earth almost without stopping. In 2014 the Borexino detector, under the Gran Sasso mountain in Italy, measured the neutrinos from the first reaction of the proton–proton chain, exactly the one that depends on tunnelling, in numbers matching the energy the Sun gives off today. In other words: through neutrinos, we have seen the tunnelling happening right now in the heart of the Sun.
Why it matters The light and heat that keep life going on Earth exist only because the protons in the Sun pass, rarely, through a wall that classical physics declared impassable.