(then at least 2½ hours off ⏳) and on again: a nuclear reactor that nobody built, 2 billion years ago.
In 1972, a routine test at a French uranium plant found uranium that was missing a sliver of its fuel. The trail led to a mine in Gabon, where the rock itself had once run a nuclear reactor, switched on and off by groundwater. Its ashes are a ruler, too: a 2-billion-year-old test of whether the laws of nature change.
A nuclear reactor once ran itself, with nobody there to build it.
No engineers. No control rods. No off switch, except water. About 2 billion years ago, in what is now Gabon, in Africa, seams of uranium ore became natural nuclear reactors. Some of them ran for hundreds of thousands of years.
Nobody saw it. But the rock kept the evidence, and scientists read it like detectives. There are three clues:
🔍Missing uranium: fuel that had been burned.
⏱️Missing xenon: a gas that kept time.
🧽Samarium: a metal that burned as today's physics predicts.
Let's follow them. ☢️
🔍Chapter 1
The missing fuel
Uranium comes in two main kinds, or isotopes: common uranium-238, and rare uranium-235, the kind that burns in a nuclear reactor. Everywhere on Earth, uranium-235 makes up almost exactly the same share: about 0.72%.
In 1972, at the French uranium plant at Pierrelatte, an analyst made a routine check of a sample. It showed
0.7171%
instead of the usual 0.7202%. Tiny, but it meant that about 4 in every 1,000 uranium-235 atoms were missing. For a plant whose product is uranium-235, that was too much to shrug off.
The investigators followed the uranium back to a mine called Oklo, in Gabon. Its ore had produced about 700 tonnes of uranium with about 200 kg of uranium-235 missing: about 4 in every 100 of its uranium-235 atoms, ten times the shortfall in that first sample. One drill core had lost nearly 40% of its uranium-235. (The record, found later in one reactor zone, had lost about half.)
Chemistry can barely tell the two kinds apart, so whatever took the uranium-235 had to be nuclear. And the nuclear process that eats uranium-235 and mostly spares uranium-238 is fission, the splitting of atoms. Sure enough, the rock was full of fission's leftovers. About 3 months after the inquiry began in earnest, the answer was in: the missing fuel had been burned in chain reactions, long ago, inside the rock. 🤯
Stranger still, these reactors switched themselves on and off. One grain of rock, read with a model, suggests the rhythm: about 30 minutes on, then at least 2½ hours off. We'll get to that grain in Chapter 6.
🧪Chapter 2
How to be a reactor (if you're a rock)
When a uranium-235 atom swallows a slow neutron, it usually splits and throws out 2 or 3 new neutrons. If, on average, exactly one of them goes on to split another atom, the reaction keeps itself going: a chain reaction.
The catch: new neutrons fly out fast, and fast neutrons are poor at splitting uranium-235. Slow ones are far better at it, but on the way down many get swallowed by uranium-238 without splitting anything. So a reactor needs something to slow them down quickly, and nature had one on hand: water. A hydrogen nucleus weighs almost the same as a neutron, so, like one pool ball hitting another, each bump takes away, on average, half the neutron's energy.
George Cowan, writing about Oklo in 1976, boiled the recipe down to this:
Lots of uranium: at least 10% of the rock.
A seam at least half a metre thick, so the neutrons don't escape.
Water: about 6% of the rock's weight.
Few "poisons" that soak up neutrons, such as boron.
Enough uranium-235. That's the next chapter.
In 1953, George Wetherill and Mark Inghram reckoned a rich uranium deposit was "25 percent of the way to becoming a pile", the old word for a reactor. In 1972, someone remembered that prediction, and it all fell into place.
⏳Chapter 3
The fuel that burns down by itself
Both kinds of uranium are radioactive: they slowly decay by themselves. But uranium-235 decays about 6 times faster. Half of any uranium-235 decays every 704 million years; uranium-238 takes 4.5 billion.
So run the film backwards, and uranium-235 gets more common. Today it's 0.72%. About 1.95 billion years ago, when the Oklo reactors ran, it was 3.5%: for every uranium-235 atom in a lump of uranium today, there were about 7. When Earth formed, it was about 24%.
So nothing at Oklo was enriched. Every lump of uranium on Earth was about 3.5% uranium-235 back then. The rock was special, not the uranium.
And 3.5% is about what modern power stations use as fuel, typically 3 to 5%. With ordinary water to slow the neutrons, a natural reactor needs at least about 1%, and uranium fell below that about 400 million years ago.
Drag back in time and watch the fuel get richer 👇
The Oklo dot sits inside the band of power-station fuel, and the last 400 million years sit below the line that water needs. So no natural reactor run by water can start anywhere on Earth today.
Notice that the figure marks no other reactor era. Uranium was richer still before Oklo, so older reactors aren't ruled out, but whether any older deposit ever became one, nobody knows.
🦠Chapter 4
Life lit the fuse
Fuel-rich uranium was everywhere back then. Uranium-rich rock was not: a reactor needs uranium gathered into pockets of 10% of the rock or more. At Oklo, the gathering was done by oxygen.
Uranium dissolves in water when it's oxidised, and drops out as solid minerals when the oxygen is taken away. For Earth's first 2 billion years, the air and oceans held almost no free oxygen. Then oxygen, made by microbes that make their food from sunlight, began to build up in them, about 2.4 billion years ago.
Oxygen-rich water washed uranium out of old rocks. Deep underground, in sandstone that rivers had laid down in an old delta, that water met oil seeping from black shale. The oil took the oxygen away again, and the uranium came out as solid ore. In the reactor zones it reached 20–30% of the rock.
There were 15 to 17 reactor zones, depending on who counts: in two neighbouring mines, Oklo and Okélobondo, near Franceville, and at Bangombé, 30 km away. Mining has since dug them out; only the zone at Bangombé survives in place. No natural reactor has been found anywhere else.
Black shales in the same basin hold what may be fossils of colonies up to 12 cm across, 2.1 billion years old: possibly early life with many cells, their finders cautiously suggest.
One careful point: oxygen is how Oklo's uranium got gathered. It doesn't mean reactors were impossible before oxygen. Whether older rocks ever did the same, nobody knows.
♨️Chapter 5
A uranium geyser
A reactor with no operators needs a way to stop itself. At Oklo, it was the water:
Water fills tiny gaps in the rock and slows the neutrons. The chain reaction runs, and the rock heats up.
The water boils. Deep underground, under pressure, that happens well above 100 °C.
Steam has far fewer hydrogen atoms in the same space, so it hardly slows the neutrons. The reaction stops.
The rock cools, the steam turns back into water, the water seeps back, and it all starts again.
One twist: water also swallows a few neutrons, so a zone soaked completely full had more water than was ideal, and at first, losing a little water actually helped. The on-off loop took over once the water was down near the ideal amount.
Press play and watch the rock breathe, then make the water seep back faster or slower 👇
The long rest is set by how slowly the water finds its way back; the pulse itself changes much less. (The figure is a cartoon tuned to the rhythm read from the rock, not a model of any real zone.)
Now try "Water stays": the rock just boils steadily at full power. That's how George Cowan pictured Oklo in 1976. The xenon later showed that at least one zone pulsed.
How hot did the rock get? Scientists still argue: estimates for different zones run from about 100 °C to 400 °C.
The power was small: on average under 100 kilowatts, about what a few dozen toasters use. But the zones kept going for hundreds of thousands of years, some perhaps for up to 2 million, with no meltdown and no explosion.
⏱️Chapter 6
A stopwatch in a grain of rock
The rhythm comes from xenon, a gas. In 2004, Alex Meshik, Charles Hohenberg and Olga Pravdivtseva studied a sliver of mineral from reactor zone 13, about 4 mm across. It held about 800 million billion atoms of fission xenon in every gram, the most ever seen in a natural material, the team reports.
Fission doesn't make that xenon straight away. It makes tellurium, which turns into iodine, which turns into xenon. Xenon-136 arrives within a few minutes, xenon-134 an hour or two later, xenon-132 and xenon-131 after days, and xenon-129 after millions of years.
While the rock was hot, any xenon that formed escaped. When the water cooled to about 300 °C, tiny grains grew and locked in the tellurium and iodine still around. Their xenon was born inside the grains and stayed. So the grains are short of the xenons whose parents change fastest.
Slide the timings and watch xenon-134, the stopwatch hand 👇
In the figure, xenon-136 vanishes after any rest at all, because its parents last only a minute or so. The light ones are always kept. Xenon-134, whose parents live about an hour, is the stopwatch hand: how much of it survives tells how long the rock stayed hot. (The figure is a toy, much simpler than the researchers' model.)
Fitting their model, the team found pulses of about 30 minutes, with rests of at least 2½ hours in between.
How sure is that?
It's a model's reading of one grain, from one zone, and that zone may have been unusual. A major review takes it as typical, and a 1990 estimate also found rests of 2½ to 3 hours (though it assumed much longer pulses). But nobody knows whether the rhythm held for a reactor's whole life.
☢️Chapter 7
What the reactor left behind
How do you prove fission happened 2 billion years ago? With fingerprints. Fission makes the metal neodymium, but never neodymium-142. Subtract the natural neodymium, tagged by its neodymium-142, and what's left matches the neodymium made in modern reactors.
The reactors even made their own fuel. Uranium-238 that caught a neutron soon became plutonium-239, which decays (half of it every 24,000 years) back into uranium-235. About two-thirds of all the splitting burned the original uranium-235; most of the rest burned this home-made fuel. More than 2 tonnes of plutonium were made, and all of it decayed long ago.
The six zones known by 1976 alone released about as much energy as a large modern power reactor makes in 4 or 5 years: about 5 kg of mass turned into energy (this page's arithmetic).
The waste sat in the rock, with no containers, for 2 billion years. The rare earth metals, most of the zirconium, and ruthenium barely moved. Most of the caesium, strontium and barium left, though some caesium and barium were caught in tiny ruthenium-rich grains about 5 years after a reactor stopped. Plutonium moved only short distances before it decayed.
The honest lesson for nuclear waste: Oklo is an example, not a guarantee. The site stayed deep, low in oxygen and wrapped in clay.
🧽Chapter 8
A neutron sponge tuned to one note
The strength of electricity and magnetism is set by a pure number, the fine-structure constant, or α (alpha), about 1/137. It has no units, so a change in it would be a real change in the laws of nature. Some theories allow it to drift, and in 1976 Alexander Shlyakhter saw that Oklo could test it.
The key is samarium-149, a metal made by fission. It soaks up slow neutrons best at one particular energy, like a wine glass that rings at one note. That note is a tiny leftover sitting on top of a nuclear energy about 80 million times bigger, and part of that big energy is electric: the protons push each other apart. So if electricity had been even slightly stronger or weaker back then, the note would have moved.
The reactor's neutrons were spread right across that note, and they destroyed most of the samarium-149 that fission made. Had the note sat lower, among more slow neutrons, the reactor would have burned more; higher, less. So the samarium left in the rock records where the note was.
In the figure, the note is called a resonance. Its shift is in meV, a tiny unit of energy, and the burn rate σ̂ is in kilobarns (kb): how big a target each samarium nucleus made for the neutrons.
Drag the note and see if the rock still agrees 👇
Only shifts that keep the dot inside the band match the rock, and near zero that window is narrow. The reactor's temperature, still debated, moves the window a little. And far to the left, there's a second place where the curve dips back into the band.
So since the reactors ran, α has changed by less than about 1 part in 100 million, if nothing else changed at the same time. (Changes in the masses of quarks, the particles inside protons and neutrons, could move the note too.) The second window is a stranger answer, with a bigger change: other data argue against it, but it hasn't been fully ruled out.
🧐Chapter 9
The physicist who corrected himself
In 2004 the story took a turn. Two physicists, Lamoreaux and Torgerson, argued that earlier studies had assumed an idealised mix of neutron speeds. With what they considered a more realistic mix, they said, the samarium showed that α had changed, by at least 4.5 parts in 100 million.
In 2006, Lamoreaux teamed up with Gould and Sharapov to rebuild two reactor zones in a computer, following neutrons through realistic rock. The 2004 picture didn't fit the neutrons the rock records, and a real reactor built that way couldn't even have kept running. With realistic reactors, the change vanished.
So the claim was superseded by a new analysis that one of its own authors helped write, and other teams agreed: no sign of a change. That's science working: a surprise, a hunt for the hidden assumption, and a better model.
⚖️Chapter 10
Rock against clock
The rock makes one comparison: α then against α now. Spread over 1.95 billion years, its limit works out to about 6 parts in a billion billion per year (this page's arithmetic). That average only means something if the drift was steady.
Atomic clocks ask a different way. Clocks built on different atoms respond to α differently, so if α drifted, they would slowly drift apart. A 2023 comparison of optical clocks found no drift, to under 1 part in a billion billion per year: the clock limit Nº 1 lists, from the kind of clocks Nº 9 is all about.
Try the three ways nature's dial might have moved 👇
Per year, the clocks now win: they're about 8 times stricter than the rock. They overtook it by 2021; as recently as 2015, the rock was still ahead.
But they catch different things. If α changed early on and then stopped, today's clocks would see nothing; only the rock could catch it. If α wobbled back and forth quickly, as some ideas about dark matter predict, the rock would average the wobble away, and clocks, which watch for months and years, could catch it. You need both.
🕰️Chapter 11
The heir
The trick that made samarium a sharp ruler is now being built into clocks. The nucleus of thorium-229 has a tick that an ultraviolet laser can reach. Like samarium's note, that tick is a small leftover of huge nuclear energies with a big electric part, so it is about 1,000 times more sensitive to α than the best atomic clocks.
Two clocks locked to it were described in the journal Nature on 7 October 2026: one from TU Wien in Austria, working with Germany's PTB, and one from a team led by Tsinghua University in China. They're still far less steady than the best optical clocks. But the TU Wien clock has already hunted for quick wobbles in α, the kind some dark-matter ideas predict, about as sharply as the best atomic clocks, and found none. A slow drift over years is still to come. Early days. 🌱
The same trick, 2 billion years apart: samarium in a rock that ran itself, thorium in a crystal that keeps time.
Let's add it all up. 🧾
☢️ The reactor's logbook
Uranium-235 then1.95 billion years ago3.5%
Uranium-235 todaynatural uranium, almost everywhere0.72%
Reactor zonesGabon, depending on who counts15 to 17
Rhythmone grain, read with a model30 min on, ≥ 2½ h off
Average powera few dozen toasters< 100 kW
Plutonium madeall decayed since2+ tonnes
Change in αat most, if nothing else changed≈ 1 in 100 million
Natural reactors that could start todaywith water to slow the neutrons0
water on ✦ steam off ✦ the rock remembers
Deep under an old river delta in what is now Gabon, 2 billion years ago, water seeped into a seam of dark rock.
Neutrons slowed in the water, found uranium, and split it, and the rock grew warm.
The water boiled away, and the rock went quiet, and cooled, and the water came back.
There was nobody to see it, only the microbes that had put oxygen into the air.
But the rock kept the receipts, in missing uranium and xenon and samarium, until a routine test in France noticed.
Nature ran a nuclear reactor 2 billion years before we built one, and the rock kept the logbook.
Nº 13 · ∫ Full version
Thirty minutes on
About 1.95 billion years ago, in what is now Gabon, seams of uranium ore became natural nuclear reactors. Groundwater in the rock slowed the neutrons enough to sustain a chain reaction; the heat boiled the water away and the reaction stopped; the rock cooled, the water seeped back, and it began again. Xenon locked in one grain from one reactor zone, read with a model, gives the rhythm: about thirty minutes on, then at least two and a half hours off. The reactors were found in 1972, as uranium that was missing a sliver of its uranium-235. Their ashes are also a ruler for the laws of physics: they limit any change in the fine-structure constant α over the last two billion years to about one part in a hundred million, provided the quark masses did not change much more than α did.
This page explains how a French laboratory noticed the missing fuel; what a chain reaction needs; why it could happen then, when all uranium was as rich as power-station fuel, and there, where oxygen made by life had gathered the uranium; how water switched the reactors on and off; how isotopes of xenon timed the pulses; how the reactors bred their own fuel, and what became of their waste over two billion years; how samarium-149 turned the rock into a test of the fine-structure constant, and how a 2004 claim that it had changed was corrected; how the rock compares with atomic clocks; and why the thorium-229 nuclear clocks described on 7 October 2026 use the same trick.
This is the ∫ Full version, with the equations, caveats and sources. New to the idea? Start with the ✨ Simple version.
Numbers marked "this page's arithmetic" were computed for this page from the cited inputs; they are not published results. Figures 2 and 3 are this page's cartoon and toy models; Figure 4 uses one resonance and an idealised neutron spectrum. Uranium isotope shares are by number of atoms, not by weight.
Results are as of 24 October 2026.
Part IThe missing fuel
Chapter 1A shortfall of four in a thousand
In May 1972, H. Bouzigues, an analyst at the French uranium plant at Pierrelatte, measured a routine sample of natural uranium, in the form of uranium hexafluoride, and found 0.7171% uranium-235. The value expected was 0.7202%.1,2 (Davis, Gould and Sharapov's review dates the start of the inquiry to June 1972.3)
The difference is 0.0031 percentage points. Put another way, about four in every thousand uranium-235 atoms were missing (this page's arithmetic: 0.43%). For a plant whose product is uranium-235, that was too much to shrug off.
The investigators ruled out contamination with depleted uranium from the enrichment process and followed the material back along the supply chain: to the Mounana mill near Franceville, in Gabon, and to the ore of the nearby Oklo mine. Ore shipped since 1970 had yielded about 700 tonnes of uranium with about 200 kilograms of uranium-235 missing, about 4% of the uranium-235 it should have held and roughly ten times the shortfall in the Pierrelatte sample (this page's arithmetic). Stored drill cores were stranger still: one held only 0.44% uranium-235, 61% of the normal share (this page's arithmetic).1 The review by Davis and colleagues cites an ore sample at 0.600%.3 The record came later, from zone 13: in 2018 Evan Groopman and colleagues reported uranium with a uranium-235 to uranium-238 ratio of 0.3655%, about half the normal value and the most depleted natural uranium of any known material.4
Chemistry can barely tell uranium-235 from uranium-238. They are the same element, which is why enrichment needs enormous plants.1 A drill core with nearly 40% of its uranium-235 gone needed a nuclear explanation, and the nuclear process that removes uranium-235 in preference to uranium-238 is fission. The depleted parts of the vein were rich in fission products, with the isotope patterns that fission leaves, and those products were almost absent elsewhere. About three months after the inquiry began in earnest, the French Atomic Energy Commission (CEA) had its answer: the missing uranium-235 had been burned in chain reactions, long ago, inside the rock.1 The CEA announced it on 25 September 1972.3
Not everyone believed it at first; Cowan recalls that American scientists greeted the announcement with scepticism.1 By June 1975, when the International Atomic Energy Agency held a symposium on "the Oklo phenomenon" in Libreville, the capital of Gabon, about 70 investigators from 20 countries had joined the work.1,2
The full answer turned out stranger than a reactor. It was a reactor that switched itself on and off. One grain of rock, read with a model, suggests the rhythm: about thirty minutes on, then at least two and a half hours off (Chapter 6). This page follows the clues in order: missing uranium, missing xenon, and samarium that burned as today's physics predicts.
Chapter 2What a reactor needs
When a uranium-235 nucleus absorbs a slow neutron, it usually splits into two lighter nuclei and releases, on average, about 2.5 new neutrons.1 If exactly one of them, on average, goes on to cause another fission, the reaction sustains itself. The multiplication factor k, the number of neutrons in one generation divided by the number in the generation before, is then 1. Below 1 the reaction dies away; above 1 it grows.
Fission neutrons are born fast. On their way down to slow speeds, many are captured by uranium-238 without causing fission, at the particular energies where it absorbs strongly; slowed all the way to "thermal" speeds, in step with the jostling of the surrounding atoms, they are far more likely to split uranium-235. A moderator does the slowing. Hydrogen slows neutrons faster than any other nucleus, because a proton has almost the same mass as a neutron: in each collision a neutron loses, on average, half its energy.1 Water is full of hydrogen, and nature supplies it for free.
Reactor physicists split k into four factors:
k∞ = η ε pfη: neutrons released per neutron absorbed in the fuel; ε: the small bonus from fast fission of uranium-238; p: the probability that a neutron escapes capture by uranium-238 while it slows down; f: the share of thermal neutrons absorbed in the fuel rather than in anything else. The subscript ∞ means an infinitely large reactor, from which no neutrons leak.
Here the formula is a picture, not a calculation. More water raises p, because the neutrons slow down faster and spend less time at the energies where uranium-238 captures them. But hydrogen also absorbs neutrons, so more water lowers f. Between the two lies an optimum. And a real reactor must be large enough, or too many neutrons leak out of its edges.
George Cowan, writing in Scientific American in 1976, condensed the conditions at Oklo into a short recipe:1
Uranium
at least about 10% of the rock on average. The reactor zones held 20–30%, more than 50 times the surrounding ore.
Thickness
seams at least half a metre thick, so that the neutrons do not escape.
Water
about 6% of the rock by weight was the optimum for moderation.
Few poisons
no large amounts of neutron absorbers such as boron, lithium or some of the rare earths.
Enough uranium-235
the subject of Chapter 3.
Today the recipe cannot work with ordinary water. Natural uranium is 0.72% uranium-235, and a reactor fuelled with it needs a better moderator: heavy water, or very pure graphite stacked in a carefully built lattice, as in Enrico Fermi's pile in Chicago in December 1942. Neither occurs in nature.1
Two papers had foreseen the possibility. In 1953 George Wetherill and Mark Inghram estimated that a rich pitchblende deposit was "25 percent of the way to becoming a pile" (as Cowan quotes them), and noted that uranium-235 had been about 3% of uranium two billion years ago.1 In 1956 Paul Kuroda set out the conditions for a natural chain reaction: a deposit larger than the distance a fission neutron travels, about two-thirds of a metre; enough uranium-235; a moderator; and few poisons.5,2 He found no sign of one in the samples he could examine, which did not include Oklo.3 In 1972, Meshik writes, the explanation at the CEA fell into place when someone recalled the prediction published nineteen years earlier.2
Part IIWhy then, why there
Chapter 3The uranium clock
Both uranium isotopes are radioactive, and uranium-235 decays faster: its half-life is 703.8 million years, against 4,468 million years for uranium-238.6 Its decay rate is 6.35 times larger (this page's arithmetic), so the further back you go, the larger its share. Starting from today's average ratio in terrestrial zircons, 1 atom of uranium-235 for every 137.818 atoms of uranium-238,7 the share t years ago follows from
R(t) = R0 e(λ235 − λ238) t, f = R / (1 + R)R: the ratio of uranium-235 atoms to uranium-238 atoms; R0 = 1/137.818; λ = ln 2 / half-life; f: the share of uranium-235. Uranium-234, 0.0055% of natural uranium, is left out.
Today f is 0.720%. At 1.95 billion years ago it was 3.5% (this page's arithmetic; 3.42–3.64% across the uncertainty of the date). For every uranium-235 atom in a lump of uranium today, the same lump held 6.8 then. When Earth formed, about 4.54 billion years ago, the share was about 24%.
The date matters, so this page always pairs the share with it. The best age for the reactions is 1,950 ± 40 million years, from the work of Ruffenach and colleagues on samples from reactor zone 2. Older estimates of 1.7–1.8 billion years came from potassium–argon and rubidium–strontium ages that are now read as later alteration of the rocks.3,8
Nothing at Oklo was enriched. At any one moment, uranium everywhere on Earth had almost the same share of uranium-235; the uranium at Oklo was ordinary for its day. What was special was the rock around it.
The share sets a threshold. With ordinary water as the moderator, Cowan put the minimum for a plausible natural reactor at about 1% uranium-235.1 Natural uranium fell below 1% about 400 million years ago (Cowan; this page's arithmetic gives 0.40 billion years). Oklo's 3.5% was far above that: about the enrichment of the fuel in a modern light-water power reactor, typically 3–5%. Meshik calls it roughly the level used in most nuclear power stations.2
Figure 1 draws the share against time, on a logarithmic scale, with the 1% line and the band of modern reactor fuel. Drag back from today, or tap a moment, and watch where the curve crosses each line.
Figure 1⏳ Try it
Wind back the uranium clock
Drag back in time
Uranium-235 share
Uranium-235 atoms then, per atom today
With water as the moderator
The share of uranium-235 in natural uranium, f = R/(1 + R) with R(t) = R0 e(λ235 − λ238)t, R0 = 1/137.818 (Hiess et al. 2012) and half-lives of 703.8 and 4,468 million years; uranium-234 is ignored. Log scale. The dashed line at 1% is the minimum for a plausible natural reactor moderated by water (Cowan 1976); the band at 3–5% is the enrichment of modern light-water reactor fuel. The share has been below 1% for the last 400 million years (shaded; this page's arithmetic). The Oklo reactions are dated to 1,950 ± 40 million years ago (Ruffenach, via Davis et al. 2014). The oxygen marker is the Great Oxidation Event, 2.45 to 2.32 billion years ago: at Oklo, oxygen-rich water dissolved and concentrated the uranium; whether older deposits ever went critical is unknown.Uranium-235 burns down faster than the rest of uranium, so the further back you go, the richer every lump of uranium was. Drag back in time, or tap a moment. Above the dashed line there is enough uranium-235 for water to run a reactor; the band is what modern power plants use. Oklo ran when nature's own uranium was as rich as power-plant fuel.
The Oklo dot sits inside the band of power-station fuel, and the last 400 million years, shaded, lie below the line for water. The older part of the curve, to the left, is deliberately not shaded. Uranium was richer still long before Oklo, and whether any older deposit ever went critical is not known; the oxygen marker belongs to the next chapter.
So no natural reactor moderated by water can start anywhere on Earth today. A different idea, a large natural reactor at the centre of the Earth (a "georeactor"), has been tested with geoneutrinos, the antineutrinos from radioactive decay inside the planet: the Borexino experiment excludes one with more than 2.4 TW of power at Earth's centre, at 95% confidence.9
Chapter 4Life lit the fuse
Rich uranium was everywhere two billion years ago. Uranium-rich rock was not. To build a reactor, nature had to gather uranium into pockets of 10% or more. At Oklo, the gathering was done by oxygen.
Uranium comes in two common chemical states. Oxidised, it dissolves in water; reduced, it does not, and it comes out of solution as minerals such as uraninite.1 For Earth's first two billion years, the air and the oceans held almost no free oxygen. The Great Oxidation Event, dated to 2.45–2.32 billion years ago in the framing of El Albani and colleagues, is when oxygen made by photosynthetic microbes began to accumulate.10
At Oklo, oxygen-rich water leached uranium out of older rocks. The host rock was sandstone laid down in a river delta, but the ore formed later, deep underground. In the generally accepted model, during deep burial, about 4 km down, oil migrated from the overlying black shales into the top of the sandstone, while oxygenated fluids mobilised the uranium in a conglomerate lower down; later, where the two fluids met in fractured patches that acted as oil traps, the uranium came out of solution as uraninite.8,11 The ore was deposited about 2,050 ± 30 million years ago, in sediments laid down about 2.1–2.2 billion years ago.8,3 The reactor zones themselves held 20–30% uranium, in Cowan's account more than 50 times the rest of the ore.1 Their thin cores hold up to 80% uraninite in clay, and part of that was the reactors' own doing: hot water dissolved the quartz of the sandstone, the rock collapsed, and the uranium was packed tighter.8
Oklo and Okélobondo are adjacent mines near Franceville, in the Haut-Ogooué province of south-eastern Gabon; another zone lies at Bangombé, 30 km away (Meshik gives about 35 km).3,2 The number of reactor zones depends on who counts: Gauthier-Lafaye counts 14 at Oklo and Okélobondo plus one at Bangombé, Meshik and colleagues count 16 at Oklo and Okélobondo, and other authors give 17.3,12 Cowan, in 1976, knew six. More were found over the following years, five of them after 1982, which were studied from 1989 in a European research programme.1,13
The same basin holds another surprise. Black shales of the Francevillian series, about 2.1 billion years old, contain structures up to 12 cm across that their discoverers read as fossils of colonial organisms that grew in oxygenated water. They present them, cautiously, as possible early multicellular life; whether the structures are biological at all is still debated.10
No natural reactor has been found anywhere else. Davis and colleagues call the Oklo deposits the only known place on Earth where all the conditions for chain reactions came together,3 and this page found no later discovery. One caution. Oxygen is how Oklo's uranium was gathered. It does not show that natural reactors were impossible before oxygen: older uranium was richer still, and whether any older deposit ever went critical is unknown.
All the zones at Oklo and Okélobondo have since been mined out; only the zone at Bangombé survives in place. Reactor zone 10, about 400 m below the surface, was the best preserved,3 and its samples, with those of zone 2, underpin the modern analyses of Chapters 10 and 11.
Part IIIHow it ran
Chapter 5A uranium geyser
A reactor with no operators needs a way to stop itself. At Oklo it was the water. With water in the pores of the ore, k exceeded 1 and the power rose. The heat raised the temperature until the water boiled; deep burial kept it under pressure, so it boiled well above 100 °C. Steam holds far fewer hydrogen atoms in a given volume than liquid water, so it moderates far less. k fell below 1 and the chain reaction died. The rock cooled, the steam condensed, water seeped back, and the cycle began again.1,2
There is a twist at the start. A zone saturated with water held more than the optimum, so it was over-moderated: at first, the heat that drove some of the water off moved the zone towards the optimum and raised k.1 The on-and-off picture applies once the water content was near or below the optimum. From there, losing water meant losing the reaction.
Figure 2 is a cartoon of that feedback, not a model of any real zone. Press Play to run twelve hours, or drag along the chart; then change how fast the water seeps back.
Figure 2♨️ Try it
A reactor that switches itself off
Press play
power (share of full)water in the porestemperature
Reactor
Power, share of full
Water in the pores
Model time
On / off at this setting
A cartoon of the feedback, not a reconstruction of any reactor zone (this page's model). Reactivity ρ = a(W − Wc) − b(T − Tamb) rises with the water fraction W in the pores and falls with temperature; the power follows ρ with a lag; the temperature cannot exceed the boiling point, where surplus heat makes steam; steam drives water out of the pores, and water seeps back only after the steam has condensed. Parameters are tuned to about 30 minutes on and 2.5 hours off; temperatures and powers are nominal, and real temperatures are disputed (100 to 400 °C in different analyses). Power is shown as a share of the model's full power; "on" means above half of it, timed over the last complete cycle. The chart begins three model hours into a run that starts with the pores full and the rock at 200 °C, once the rhythm has settled. With "water stays", expulsion and condensation lag are switched off and the model settles into steady boiling, as Cowan pictured the reactors in 1976 (Petrov proposed pulses in 1977); the pulses were read from xenon in one zone (Meshik et al. 2004; Figure 3). Over its whole life a zone averaged under 100 kW (Cowan 1976).Water slows the neutrons so they can split uranium. The splitting heats the rock until the water boils away, and without water the reaction stops. The rock cools, the water seeps back, and it starts again. Press play, or drag along the chart. Then make the water come back faster or slower, and see what sets the long rest. (A cartoon, tuned to the rhythm read from the rock.)
The long rest is set by the slow return of the water, and the pulse itself changes much less. In this cartoon the pulses need the steam to push water out of the pores; if the water stays, it settles into steady boiling at constant power.
That was how Cowan pictured the reactors in 1976: the power levelling off and staying roughly constant. In 1977 Yuri Petrov proposed a pulsed regime instead, driven by the loss of moderation as steam voids formed.14,3 The xenon of Chapter 6 says that at least one zone did pulse. Slower regulators worked too: neutron poisons such as lithium and boron, which burned out early, and the gradual fall in the share of uranium-235 as the fuel was used up.1
How hot did the rock get? Nobody agrees. Older work gave 200–400 °C.8 Davis and colleagues describe conditions similar to those in a modern pressurised-water reactor, but they also report later analyses that point lower: 182 ± 80 °C for zone 3, and 100 ± 30 °C for zone 10 from a reanalysis of lutetium thermometry that rests on an uncertain nuclear input.3 Meshik's phosphate grains formed at about 300 °C.2 The temperature matters again in Chapter 10.
The power was modest. From the accounting of Naudet at the CEA, Cowan gives a total of about 15,000 megawatt-years of energy from about 6 tonnes of uranium-235, for the six zones known then. On average it was under 100 kW, "a few tens of kilowatts" in Cowan's words, and at 100 kW the energy would have lasted 150,000 years.1 Meshik compares the output with a few dozen toasters.2 Zones 10 and 13 and the zone at Bangombé ran for 100,000 to 300,000 years by the estimates of Hidaka and Holliger, as Davis and colleagues report them.3 A 2026 compilation by Hidaka and colleagues, which counts 16 zones in all (14 at Oklo, one at Okélobondo and one at Bangombé), gives about 240,000 years for zone 13 but 0.6 to 2.2 million years for five other zones, including 1.6 million for zone 10, several times the earlier estimate for that zone.15 The estimates depend on the method: across the zones, they run from about 100,000 years to about two million. In all that time, Meshik notes, there was no meltdown and no explosion.2
Chapter 6The xenon stopwatch
The rhythm comes from xenon. In 2004 Alex Meshik, Charles Hohenberg and Olga Pravdivtseva, of Washington University in St. Louis, analysed a fragment of rock from reactor zone 13: a uranium-free aluminium phosphate about a millimetre thick and four millimetres across.12,2 It held about 8 × 1017 atoms of fission xenon per gram, the highest concentration, the team reports, ever seen in a natural material.12,16
Fission does not make these xenon isotopes directly. It makes tellurium, which decays to iodine, which decays to xenon, and each chain has its own delay. Xenon-136 appears within a few minutes of fission, xenon-134 an hour or two later, xenon-132 and xenon-131 after days, and xenon-129 only after millions of years, because its iodine parent lives so long.2
Xenon is a gas. While the rock was hot, the xenon that formed escaped. When the water cooled to about 300 °C, the aluminium phosphate crystallised and trapped the tellurium and iodine still around; their xenon was born later, inside the grains, and stayed. So the grains are short of xenon-136 and xenon-134, whose parents had mostly decayed before the grains closed, and relatively rich in xenon-132, xenon-131 and xenon-129.2
Figure 3 is a toy version of that logic, much simpler than the researchers' model. Set how long the pulse lasted and how long the rock stayed hot before the grains closed, and watch how much of each xenon isotope ends up kept.
Figure 3⏱️ Try it
Read the xenon stopwatch
Set the timing
kept in the grainescaped as xenon while hotstill telluriumstill iodinethe inferred timing (in this toy)sorting by mass insteadsorted by weight instead
Xenon-136 kept
Xenon-134 kept
Xenon-132 kept
A toy model in the spirit of Meshik, Hohenberg and Pravdivtseva (2004), not their model. Fission at a constant rate during the pulse makes tellurium, which decays to iodine and then xenon (half-lives: 136Te 17.6 s, 136I 83.4 s; 134Te 41.8 min, 134I 52.5 min; 132Te 3.20 d, 132I 2.30 h; 131Te 25.0 min, 131I 8.03 d; 129Te 69.6 min, 129I 16.1 million years). Xenon made while the rock is hot escapes; when aluminium phosphate grows, the tellurium and iodine still present are trapped and their xenon stays (Meshik 2005). Bars: the share of each chain's fission yield kept. Ignored: independent fission yields of iodine and xenon, the 131mTe branch, washing by water and repeated cycles, so real grains kept some xenon-136 that this toy does not. Dashed ticks: this toy at the inferred timing, 30 minutes on and 2.5 hours off. A mass-dependent process would remove 136Xe twice as much as 134Xe relative to 132Xe; the measured pattern does not, which rules it out (Meshik 2005). “Compare” draws that pattern as dashed bars, matched to the toy's 134Xe/132Xe with the loss compounding per two mass units: 136Xe/132Xe = (134Xe/132Xe)2.Fission doesn't make xenon straight away: it makes tellurium, which turns into iodine, which turns into xenon, each step with its own delay. While the rock is hot, xenon escapes. When it cools, tiny mineral grains grow and lock in whatever hasn't become xenon yet. So the heavy xenons, whose parents change fastest, go missing. Slide the timings, press play, and watch xenon-134, the stopwatch hand. (A toy: real grains kept a little xenon-136.) Then ask what sorting atoms by weight would have left instead.
In the toy, xenon-136 vanishes after any rest at all, because its parents have half-lives of only 18 and 83 seconds. The light isotopes are always kept. Xenon-134, whose parents live about an hour, is the hand of the stopwatch: the share of it that survives tells how long the rock stayed hot.
Could the pattern come instead from physical sorting by mass, such as diffusion? A mass-dependent process would deplete xenon-136 about twice as much as xenon-134, relative to xenon-132. The grain does not show that pattern, which rules physical sorting out.2
Fitting their model to the pattern, the team found pulses of about thirty minutes, separated by dormant periods of at least two and a half hours, with the different xenon isotopes giving much the same answer.12,2
That is this page's headline number, and it carries caveats. It is a model reconstruction, from one grain, in one zone. Davis and colleagues note that it applies strictly to zone 13 and take it as typical for all the zones.3 An older estimate agrees on the rest, though not on the pulse: in 1990 Kuroda had inferred an off time of 2.5 to 3 hours from the tellurium precursors, assuming that each on period was much longer than the rest.3 Nobody knows whether the rhythm held for the whole life of a zone. Zone 13 may also have been unusual: it ran for a shorter time than the five other zones that Hidaka and colleagues date (Chapter 5), and less of its fission came from uranium-235, which they read as partly fast-neutron operation. They suggest that its short life may be related to the pulsing the grain records.15
Taken at face value, the numbers are vivid (this page's arithmetic). A cycle of about three hours, on for a sixth of it, makes eight pulses a day. If all the energy came in pulses, each ran at about six times the average power: 180 kW during a pulse for an average of 30 kW.
Chapter 7The reactor that bred its own fuel
How do you prove that fission happened two billion years ago? By the isotope fingerprints it left. The cleanest is neodymium. Natural neodymium contains neodymium-142, which fission does not make, because the fission products of mass 142 stop at stable cerium-142. So the neodymium-142 in a sample shows how much natural neodymium is present. Subtract that natural part, correct for neutron capture, and what is left matches the neodymium made in modern reactors.1 The capture correction does double duty: it measures how many neutrons passed through the rock.
Uranium left traces of its own. About one uranium-235 nucleus in six that absorbs a neutron becomes uranium-236 instead of splitting (Cowan's figure). Uranium-236 decays to thorium-232, and thorium turns up in the reactor zones and almost nowhere else in the ore. A rarer reaction on uranium-238 leads, through a longer decay chain, to bismuth, which is likewise found only in the zones.1
The reactors also made fuel. Uranium-238 that captured a neutron became uranium-239, which decays within days to plutonium-239. Plutonium-239 has a half-life of about 24,000 years, and it decays back to uranium-235. In effect, the reactors bred fresh fuel from uranium-238. In Naudet's accounting, about two-thirds of all the fissions burned the original uranium-235, most of the rest burned uranium-235 bred this way, and a few per cent came from fast fission of uranium-238 and from plutonium-239 that split before it could decay.1 More than two tonnes of plutonium-239 were made, and all of it has long since decayed.2
Each zone received about 1021 neutrons per square centimetre over its life: an average flux of about 108 neutrons per square centimetre per second for a life of a few hundred thousand years (several times lower for the longer lives of the 2026 compilation, Chapter 5).3
Cowan's total for those six zones, 15,000 megawatt-years, is 4.7 × 1017 J: about five years of output from a large power reactor of 3 GW thermal (this page's arithmetic; Cowan compares it with four years of a large nuclear power plant).1 By E = mc2, about 5 kilograms of mass were turned into energy (this page's arithmetic: 5.3 kg from 15,000 megawatt-years, or 5.5 kg from 6 tonnes of uranium-235 at about 200 MeV per fission). Spread over hundreds of thousands of years, it averaged less than 100 kW, as Chapter 5 said.
Chapter 8Two billion years of storage
The reactors left their waste where it was made, with no containers and no engineers, for two billion years. What happened to it is a natural experiment in nuclear waste disposal.
Cowan's 1976 inventory sorted the elements into two groups.1 Near the zones stayed the rare earths and yttrium, most of the zirconium, ruthenium, rhodium, palladium, niobium and silver, some of the molybdenum and iodine, and traces of krypton and xenon. Most of the rubidium, caesium, strontium and barium left, and probably the cadmium.
Some of the leavers were caught on their way out. Evan Groopman and colleagues found fission caesium and barium locked in ruthenium-rich metal and sulfide grains, and dated the capture to 4.98 ± 0.56 years after the reactor stopped.4 Apart from what those grains caught, the caesium was flushed out with a characteristic time of 2.7 ± 0.6 years, while technetium largely stayed.17
Plutonium moved only on small scales. Where it decayed, it left uranium-235 behind, and that "naturally enriched" uranium traces where the plutonium went.8 This page gives no distance, because it found no primary measurement to quote.
Gauthier-Lafaye credits the preservation to the stability of the basin, to clays, and to reducing organic matter.11 That is the honest lesson. Oklo is an analogue, not a guarantee: some elements barely moved in two billion years, others left within a few years, and the site stayed deep, reducing and wrapped in clay. It shows which elements a repository has to worry about, and which conditions help.
Part IVA ruler for the laws of physics
Chapter 9Is the fine-structure constant constant?
The fine-structure constant sets the strength of electromagnetism:
α = e2 / (4πε0ħc) ≈ 1/137.036e: the elementary charge; ε0: the electric constant; ħ: the reduced Planck constant; c: the speed of light. α is a pure number, the same in every system of units.
Because α is a pure number, a change in it would be a real change in the laws of physics, not a change of units. Some theories allow it: dynamical models of dark energy, for example, can make α vary over cosmic time.18 So physicists look for a change wherever they can, over the longest times they can reach.
In 1976 Alexander Shlyakhter pointed out that the Oklo reactors could provide a very tight test.19,20 The idea is this. Some nuclei capture neutrons through resonances at very low energies, and the position of such a resonance depends on the electrostatic energy inside the nucleus. If α had been different when the reactors ran, a resonance would have sat at a different energy, and the reactor would have burned the isotope that owns it at a different rate. The isotope abundances in the rock still record what happened.
The quantity tested is
Δα/α = (αOklo − αnow) / αnowPositive if α was larger when the reactors ran.
In 1996 Thibault Damour and Freeman Dyson reanalysed published rare-earth data from Oklo, taking into account the large uncertainty in the temperature at which the reactors ran. They found −0.9 × 10−7 < Δα/α < 1.2 × 10−7, at 95% confidence.20
Chapter 10Samarium-149, tuned to one note
Samarium-149 swallows thermal neutrons greedily: at the standard thermal energy of 0.0253 eV this page's one-resonance model gives a capture cross section of 39,500 barns (the evaluated value is about 40,100), some 30,000 times the geometric size of the nucleus (this page's arithmetic). The reason is a resonance at 0.0973 eV. A neutron with that energy forms a short-lived excited state of samarium-150, which then usually sheds its energy as gamma rays. That state lies just above the energy needed to pull a neutron out of samarium-150, 7.987 MeV.21,22 So the resonance energy is a tiny difference between large nuclear energies: about 1 part in 80 million of the state's height above the ground state (this page's arithmetic).
Part of every nuclear energy is electrostatic: the protons repel each other. So the position of the resonance depends on α. Damour and Dyson estimated the shift as
ΔEr ≈ −(1.1 MeV) × Δα/αA larger α in the past would mean a lower resonance. The resonance energy is a difference: the excited samarium-150 nucleus that the neutron forms is slightly more spread out than samarium-149, so a larger α raises its electrostatic energy a little less. Davis and Hamdan (2015) find about 2.5 times more sensitivity with better nuclear parameters, reduced by corrections of no more than 25%.
A change in α of 1 part in 100 million would therefore move the resonance by about 11 meV with the Damour–Dyson estimate, or by 21–28 meV with Davis and Hamdan's, against a resonance energy of 97.3 meV (this page's arithmetic).20,23
The reactor's neutrons were spread right across the resonance. On a logarithmic energy scale, as reactor spectra are usually drawn, a thermal neutron spectrum peaks at 2kT, which equals 0.0973 eV at 291 °C; per unit energy, the flux peaks at kT, half that (this page's arithmetic). Either way, a shift of a few hundredths of an electronvolt changes how many neutrons samarium-149 swallowed.
Fission made samarium-149, and the neutrons then destroyed most of it. Comparing the samarium-149 that survives with the other samarium isotopes gives σ̂, the capture cross section averaged over the reactor's neutron spectrum. For zone 10, Gould, Sharapov and Lamoreaux deduced 85.0 ± 6.8 kilobarns (71.5 ± 10.0 kb for zone 2).22 If the resonance had sat lower, among more of the thermal neutrons, σ̂ would have been larger; if higher, smaller.
Figure 4 shows both halves of the argument: above, the resonance and the reactor's neutrons; below, the spectrum-averaged cross section against a shift of the resonance, with the band measured in zone 10. Drag the resonance, change the temperature, and see which shifts the rock allows.
Figure 4🧽 Try it
Move the note, change the burn
Drag the resonance
Sensitivity to α:
Change in α that would do this
Effective cross section, σ̂Samarium burn rate, σ̂
Against the rock
Top: the neutron-capture cross section of samarium-149 near its lowest resonance (one-level Breit–Wigner, Er = 0.0973 eV, Γγ = 60.5 meV, Γn(Er) = 0.533 meV, g = 9/16; this page's model gives 39,500 b at 0.0253 eV), and the reactor's neutron spectrum per logarithmic energy interval: a Maxwellian at the chosen temperature plus the epithermal tail with the index 0.15 measured for zone RZ10, joined smoothly near 5kT; its Maxwellian part peaks at 2kT, which is 0.0973 eV at 291 °C. Bottom: the spectrum-averaged cross section σ̂ against a shift Δ of the resonance, with the value inferred from samarium depletion in RZ10, 85.0 ± 6.8 kb, as a ±2σ band (Gould, Sharapov and Lamoreaux 2006). Where the curve lies in the band, the shift is allowed: there are two windows. Δα/α = −Δ/(1.1 MeV) (Damour and Dyson 1996) or with about 2.5 times the sensitivity (Davis and Hamdan 2015; 2.7 MeV here). One resonance and an idealised spectrum: this page's model reproduces the measured σ̂ at zero shift and both windows roughly (at 250 °C, about −15 to +14 and −101 to −89 meV, against −11.6 to +26.0 and −101.9 to −79.6 meV from full reactor models). The published limit, |Δα/α| < 1.1 × 10−8 at 95% confidence, needs only a weak, testable assumption about how the light-quark masses changed relative to α (Davis and Hamdan 2015); the earlier limits assume that only α changed.Samarium-149 soaks up neutrons best at one particular energy, like a glass that rings at one note (the tall peak). The reactor's neutrons (the wide blue hump) were spread right around that note. Drag the note left or right, as slightly stronger or weaker electricity would have moved it, and see how much samarium the reactor would have burned. Only shifts that keep the dot inside the band match what is in the rock.
Only shifts that keep the curve inside the band match the rock. Near zero, the allowed window is a few hundredths of an electronvolt wide, about 1 part in 100 million in α. The temperature moves the window, which is why the reactor model matters. And there is a second window.
Because σ̂ first rises and then falls as the resonance moves down, a single measured value allows two shifts. With full reactor models, Gould and colleagues found one window from −11.6 to +26.0 meV, which contains zero, and another from −101.9 to −79.6 meV, which would mean a Δα/α between 0.72 and 0.93 × 10−7 with the Damour–Dyson sensitivity (about 2.5 times smaller with Davis and Hamdan's).22 Fujii and colleagues reported a "rather strong but still tentative" indication, from gadolinium data, that the second window can be ruled out;24 Davis and colleagues, reviewing the field in 2014, judge that it is not ruled out on experimental grounds.3 The limits below use the window that contains zero.
Among the tightest published limits is Davis and Hamdan's, from 2015:23
|Δα/α| < 1.1 × 10−8 (95% confidence)Over the roughly 1.95 billion years since the reactors ran: about one part in a hundred million.
Two conditions come with it. The first is the reactor model: the temperature and the neutron spectrum shape σ̂ against the shift, and different models gave different answers (Chapter 11). The second is more basic. The resonance's position depends not only on α but also on the masses of the light quarks, relative to the energy scale of the strong force. Gould and colleagues' limit assumes that only α changed.22 Davis and Hamdan replace that with a weak, testable assumption about how the ratio of the light-quark mass to the strong-interaction scale changed, compared with α.23 Without such an assumption, Oklo limits a combination of α and the quark masses, as Flambaum and Shuryak showed.25
Chapter 11A claim, and its correction
In 2004 the story took a turn. Lamoreaux and Torgerson argued that the earlier analyses had assumed an idealised neutron spectrum, a pure Maxwell–Boltzmann distribution. With what they considered a more realistic spectrum, the samarium data implied a change: Δα/α of at least 4.5 × 10−8, at six standard deviations.26 At the time, some quasar observations had been read as showing a slightly smaller α in the distant past; Meshik noted that the Oklo claim pointed the opposite way.2
In 2006 Lamoreaux, with Gould and Sharapov, modelled zones 2 and 10 in detail with the Monte Carlo neutron-transport code MCNP, following neutrons through realistic geometries and materials. They showed that the disagreements among Oklo results came from different reactor models, which produced different neutron spectra.22 As a test of realism they used the measured epithermal index of the zones, a number that describes how many neutrons are still slowing down: the 2004 model, an infinite reactor, implied 0.53 against 0.15 measured, and a finite reactor with its composition would have been subcritical.22 Their result was consistent with no change: −0.24 × 10−7 ≤ Δα/α ≤ 0.11 × 10−7, at two standard deviations.
So the claim was superseded by a reanalysis that its own first author co-wrote. Other groups reached the same conclusion with their own reactor models:3
The 2000 row is their resonance shift, 4 ± 16 meV, divided by the Damour–Dyson sensitivity of −1.1 MeV (this page's arithmetic); they quote it as a rate over about 2 billion years, (−0.2 ± 0.8) × 10−17 per year. The 2006 Petrov, 2012 and 2014 rows are as tabulated in the review by Davis, Gould and Sharapov. Each bound depends on its authors' reactor model and on the assumption that only α changed (or, for Davis and Hamdan, a weak assumption about the quark masses).
This is what a maturing measurement looks like: a surprising result, a search for the assumption behind it, and a better model that the original author helped to build.
Chapter 12Rock against clock
Oklo measures one number: α then against α now. Divided by the time between, it becomes an average rate: 1.1 × 10−8 over 1.95 billion years is about 6 × 10−18 per year (this page's arithmetic: 5.6 × 10−18; with the 1.8 billion years that Davis and Hamdan use, 6.1 × 10−18). That rate means something only if the drift was steady.
Clocks measure the rate now. Different atomic transitions depend on α in different ways, so if α drifted, clocks of different kinds would slowly drift apart. Comparing two transitions of the ytterbium ion with each other, and with caesium clocks, over several years, Lange and colleagues found (1.0 ± 1.1) × 10−18 per year in 2021.28 Comparing optical clocks in 2023, Filzinger and colleagues found (1.8 ± 2.5) × 10−19 per year:29 a change below about 7 parts in 1019 per year at two standard deviations, the limit Nº 9 describes and Nº 1 prints beside the quasar test.
Figure 5 puts these limits on one ruler, as an average rate per year or as a total change since the reactors ran. Switch the view, and try the three ways α might have changed.
Figure 5⚖️ Try it
Rock against clock
Two ways to ask
Suppose α…
Show:
the Oklo rockatomic clocksprojection
Rock (2015)
Clocks (2023)
Clocks stricter by
Upper limits on a change of the fine-structure constant, as an average rate per year or as a total change over the 1.95 billion years since the Oklo reactors ran. Oklo (95% or 2σ): Damour and Dyson 1996, −0.9 to +1.2 × 10−7; Gould, Sharapov and Lamoreaux 2006, −0.24 to +0.11 × 10−7; Davis and Hamdan 2015, |Δα/α| < 1.1 × 10−8; converted to rates by dividing by 1.95 billion years, which assumes a steady drift (this page's arithmetic; the authors' rates use about 1.8 billion years and are about 8% larger). Clocks: Lange et al. 2021, (1.0 ± 1.1) × 10−18 per year, and Filzinger et al. 2023, (1.8 ± 2.5) × 10−19 per year, drawn as |value| + 2σ, and stretched over 1.95 billion years only as "if the drift were steady" (hatched). Dashed: a projection, a thorium-229 nuclear clock ratio held to 10−15 for a year with the sensitivity K = 5,900 (Beeks et al. 2025; uncertain by about 40%), this page's arithmetic. The Oklo limits assume that only α changed (Davis and Hamdan need only a weak assumption about the quark masses); the clock limits are for the present-day rate. The sketch above is qualitative. Tap a bar for its source.Two ways to ask whether nature's dial has moved. The rock compares 2 billion years ago with today. Clocks watch the dial right now, very closely, for a few years. Shorter bars mean a stricter test. Switch between "per year" and "in total", and try the three ways the dial might have moved: each method catches some and misses others. Tap a bar for its source.
Per year, the clocks now win. Taking two standard deviations, the 2023 clocks are about eight times tighter than the rock's average rate (this page's arithmetic: 6.8 × 10−19 against 5.6 × 10−18 per year, a ratio of 8.3), and the 2021 clocks had already overtaken it, by a factor of about 1.8. As recently as 2015, Davis and Hamdan could still write that the Oklo bound on the present-day rate was tighter than the best clock limit.23
But the two do not measure the same thing. If α changed early and then stopped, today's clocks would see nothing; only the rock, which compares then with now, could catch it. If α oscillated quickly, as some models of ultralight dark matter predict, the rock would average the oscillation away, while clocks that watch for months and years are built to catch it; Filzinger's paper is such a search,29 and so, over 20 seconds to a day, is the TU Wien thorium clock (Chapter 13). If the drift was steady, the clocks' limit stretched over 1.95 billion years would mean |Δα/α| < 1.3 × 10−9 (this page's arithmetic, and hypothetical). The rock and the clocks are complementary.
There is a third kind of look, which Nº 1 also prints: light from a quasar that crossed a gas cloud about 8.5 billion years ago shows the same α as today to about 1 part in a million.30 It reaches furthest back, with the loosest limit.
Chapter 13The heir: a clock in a nucleus
The trick that made samarium-149 a sensitive ruler is now being built into clocks. Thorium-229 has a nuclear excited state at only 8.36 eV, within reach of a vacuum-ultraviolet laser, at 148 nanometres. Like samarium-150's resonance, its energy is a small remainder left after large nuclear energies almost cancel, and those energies include a large electrostatic part. So the frequency of the transition responds to a change in α about 5,900 ± 2,300 times more strongly than α itself changes: about a thousand times more than the best atomic clocks.31
Two clocks with lasers locked to the thorium nucleus were described in Nature on 7 October 2026, one from TU Wien working with Germany's PTB and one from a team led by Tsinghua University. Their instabilities are 3 × 10−12 and 5 × 10−13 over one second, still far from the best optical clocks, as Nº 9 describes.32 The TU Wien clock is already a sensor. Its authors searched its frequency for the oscillations and drifts, on timescales from 20 seconds to a day, that some models of ultralight dark matter predict. Because the thorium nucleus is so sensitive, their limits on dark matter that would make α oscillate compete with the best atomic clocks, and for dark matter acting through the strong force they go beyond earlier limits.32 No nuclear clock has yet limited a slow drift of α over years.
A projection, not a result: if the ratio of a nuclear clock to an optical clock could be held to 10−15 over a year, it would resolve a drift of about 2 × 10−19 per year (this page's arithmetic: 10−15 divided by 5,900, ignoring the 40% uncertainty in the sensitivity). That is comparable with today's best clock limits, and it would need the crystal's temperature and the clock's other shifts under control at a level not yet shown.
The same physics, two billion years apart: a nucleus whose energy levels are balanced so finely that electromagnetism shows through. In Gabon it was samarium, in a rock that ran itself. In the laboratory it is thorium, in a crystal that keeps time.
Chapter 14Glossary and sources
Isotope
Atoms of the same element with different numbers of neutrons. Uranium-235 and uranium-238 are both uranium.
Fission
The splitting of a heavy nucleus into two lighter ones, releasing energy and a few neutrons.
Chain reaction, k
Fissions caused by neutrons from earlier fissions. k is the number of neutrons in one generation divided by the number in the one before; a reactor runs steadily at k = 1.
Moderator
A material that slows neutrons down: water, heavy water or graphite.
Thermal neutron
A neutron slowed until its energy matches the jostling of the surrounding atoms, a few hundredths of an electronvolt.
Neutron capture
A nucleus absorbing a neutron without splitting, usually releasing gamma rays.
Cross section, barn
The effective target area a nucleus presents to a neutron. 1 barn = 10−24 cm2; 1 kilobarn (kb) = 1,000 barns.
Resonance
A neutron energy at which a nucleus captures neutrons especially readily, because the neutron and nucleus form a short-lived excited state.
σ̂ (sigma hat)
A cross section averaged over a reactor's whole neutron spectrum.
Fission products
The lighter nuclei left by fission, and their decay products.
Breeding
Making new fissile fuel from uranium-238 in a reactor, here via plutonium-239 to uranium-235. Engineers keep "breeder" for a reactor that makes more fuel than it burns; Oklo made less, so strictly it was a converter.
Half-life
The time for half of a radioactive sample to decay.
Great Oxidation Event
The rise of free oxygen in Earth's air and oceans, beginning about 2.45 to 2.32 billion years ago; by some estimates oxygen stayed for good only from about 2.2 billion years ago.
Fine-structure constant, α
The pure number, about 1/137, that sets the strength of electromagnetism.
Δα/α
The fractional difference between α when the reactors ran and α now.
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