Episode 11 - The atomic hypothesis

Tomlin Hawthorne

Take a glass of water. Suppose you could put a tiny mark on every molecule in it, so you'd know them again.

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Now pour the glass into the sea. And wait. Wait until the currents have stirred your water evenly through every ocean on Earth. The Pacific, the Arctic, all of it.

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Then go to any beach, anywhere, and dip your glass in.

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How many of your marked molecules are in it?

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None, surely. Or one, if you're lucky?

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Over a thousand.

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That puzzle is from Lord Kelvin, about a hundred and fifty years ago. And the answer tells you the one thing you most need to know about atoms: there are more molecules in a glass of water than there are glasses of water in all the seas. A lot more. Today's question is how anybody found that out, given that for almost the whole of history, nobody could see an atom, and a good many serious people thought they were a fairy story.

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Welcome to Part Three. Last time you played two tones together, 440 and 442, and heard them throb, twice a second. Two waves sliding in and out of step. And perhaps you made a wine glass sing, in which case I hope the neighbours were understanding.

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Part Three is five episodes with a single destination. We're going to find out why time only runs one way. Why you can scramble an egg and not unscramble it, why you remember yesterday and not tomorrow. It is, I think, the deepest thing in this series. But to get there we need atoms. So: atoms.

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And we begin with a poem.

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Around 55 BC, a Roman named Lucretius wrote a poem in six books called On the Nature of Things. We know almost nothing about him. It's a poem about physics, in seven thousand lines of Latin hexameter, and its purpose is to cure you of the fear of death.

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His argument is this. Everything that exists is made of tiny, indestructible particles, too small to see, moving for ever through empty space. They collide, they hook together, they come apart. A tree, a mountain, a person: each is a temporary arrangement. When you die, your particles simply go on to be something else. There's no one left to suffer. So there's nothing to fear.

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He got the idea from the Greeks, from Democritus and Epicurus, who called the particles atoms, meaning uncuttable. But Lucretius has the best single piece of evidence in the ancient world, and it's something you've seen.

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He says: watch a beam of sunlight coming into a dark room. You'll see specks of dust dancing in it. And look how they move. They don't just drift. They jitter. They jerk about, change direction for no reason, as though being knocked by something. And they are, he says. They're being struck by particles too small to see. The dance of the dust is the visible sign of an invisible motion underneath.

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Keep that. A Roman poet, a sunbeam, some dust. It's going to come back in 1905 and settle the whole matter.

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The poem itself very nearly didn't survive. The early Church disliked it, for obvious reasons, and it vanished for a thousand years. Then in the winter of 1417 an out-of-work papal secretary called Poggio Bracciolini, whose hobby was hunting for lost books, found a copy in a monastery library in Germany. One copy. Stephen Greenblatt wrote a wonderful book about this called The Swerve. If Poggio had taken a different road that winter, we might know the poem only as a title.

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Now jump two thousand years on from Lucretius, to a lecture hall in California in 1961. Richard Feynman is giving the very first lecture of his famous course. And he asks his students a question.

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Suppose there were a catastrophe, and all scientific knowledge was destroyed. And you could pass on just one sentence to whoever came next. What sentence would hold the most information in the fewest words?

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His answer was the atomic hypothesis. Everything is made of atoms: tiny particles that never stop moving, that pull on each other when they're slightly apart, and push each other away when they're squeezed together.

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And he tells them that with a little imagination and thought, you can get a huge amount about the world out of that one sentence.

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Let's apply some. Why does ice melt? The particles are jiggling. Heat them and they jiggle harder, until they shake loose from their neighbours. Why does a puddle dry up? At the surface, now and then, a particle gets a hard enough knock to fly off. Why does that cool your skin when you sweat? Because it's the fastest ones that leave, and the slow ones stay behind. Why can you smell coffee from the next room? Particles of it are wandering through the air, bumping their way toward you.

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Solid, liquid, gas, evaporation, smell, pressure, the way things expand when they're warm. One sentence.

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So here's the puzzle. If the idea is that good, and it had been around since Democritus, why did it take until the twentieth century for scientists to agree that atoms exist?

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Because for most of that time there wasn't any evidence. The Greeks had an argument. They didn't have a measurement.

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The measurements start with chemistry, around 1800. A Quaker schoolteacher in Manchester, John Dalton, noticed that when elements combine, they do it in fixed proportions. Water is always eight parts oxygen to one part hydrogen, by weight. Never seven and a half. It's as if the stuff comes in units, like eggs in a box. You can have a dozen or two dozen. You can't have a dozen and a bit.

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That was suggestive. And chemists spent the nineteenth century using atoms very happily, drawing molecules as little balls and sticks.

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But plenty of physicists weren't convinced. The balls and sticks, they said, are a handy way to do the bookkeeping. That doesn't make them real. You've told me yourself they're too small ever to be seen. Why should I believe in them?

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The leader of the sceptics was Ernst Mach, an Austrian physicist and philosopher. We'll meet him again; he had a large influence on the young Einstein. Mach held that science should deal only in what can be observed. Anything else was metaphysics. And whenever a colleague mentioned atoms, he had a stock reply. He'd ask: have you seen one?

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And I want to defend Mach, a little, because he's about to lose and he doesn't deserve to look silly. He was being rigorous. Science had been burned before by invisible things that explained everything: the fluid of heat, the fluid of electricity, a whole cellar full of imaginary substances. His demand for evidence was the right demand. He was wrong about atoms. He wasn't wrong to ask.

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The man on the other side was Ludwig Boltzmann, in Vienna, who had built a whole theory of heat on the assumption that atoms are real. He spent decades being told he was doing philosophy. We'll hear his story in two episodes' time, and it doesn't end well.

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So that's where things stood in 1900. A brilliant idea, hugely useful, and no proof.

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Now, back to the sunbeam.

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In 1827 a Scottish botanist, Robert Brown, was looking through his microscope at pollen from a wildflower, suspended in water. Tiny grains were spilling out of the pollen, and he noticed they wouldn't keep still. They trembled and wandered about, endlessly, in every direction.

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His first thought was the natural one for a botanist: they're alive. This is some kind of vital force. But Brown was careful. He tried pollen from plants that had been dead a hundred years. Same jitter. He tried things that had never been alive at all. Powdered glass. Soot. Ground-up rock. He even, and I love this, got hold of a fragment of the Sphinx and ground that up. It jittered too.

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So it wasn't life. It was something about small particles in water. And nobody knew what. It was filed away as a curiosity called Brownian motion, and it sat there for seventy-eight years.

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In 1905, a patent clerk in Bern picked it up. This is Einstein's extraordinary year, when he published four papers, any one of which would have made a career. We'll come to the others. This one is the least famous and, in a way, the most satisfying.

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Einstein reasoned like this. Suppose water really is made of molecules, and they really are in constant motion, as Boltzmann says. Then a grain floating in the water is being hit from all sides, all the time. Billions of impacts a second.

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Most of the time they cancel. As many from the left as from the right. But not exactly. In any given instant, just by chance, there'll be a few more hits on one side than the other. And if the grain is small enough, that tiny imbalance will be enough to shove it. Then the next instant, a shove another way.

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So the grain should wander. A staggering, aimless path, like someone coming home from the pub. And Einstein did more than say so. He worked out exactly how far the grain should wander in a given time. And his formula had a number in it that everyone wanted: how many molecules there are in a given amount of water.

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So you could turn it round. Measure how far the grains wander, and you can count the atoms.

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In Paris, a physicist called Jean Perrin did it. It was painstaking work: watching single grains through a microscope, marking their positions every thirty seconds, for hours. The wandering matched Einstein's formula precisely. And he counted the atoms. He got about six hundred thousand billion billion molecules in eighteen grams of water. A six with twenty-three zeros.

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And then he counted them a dozen other ways, by completely different methods, and got the same number every time. That was what did it. One measurement can be a fluke. Thirteen that agree can't.

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The sceptics gave way almost at once. Perrin got the Nobel Prize in 1926. Mach, as far as anyone knows, never changed his mind. And Lucretius had been right about the dust. The dance in the sunbeam really is the invisible showing itself, though I should say that the motes you see with the naked eye are mostly riding air currents. You need a microscope to see the true jitter. But he had the idea exactly.

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An atom is about a ten-millionth of a millimetre across. Ten rungs down the ladder from episode two. But that doesn't land. So here's the story I like best, because someone held the answer in his hands and didn't know it.

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Benjamin Franklin, in the 1770s, was in London. He'd heard the old sailors' tale that pouring oil on rough water calms it. And being Franklin, he tried it. He went to the pond on Clapham Common, on a windy day, and poured on a teaspoon of oil.

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And he watched it spread, with what he called surprising swiftness, until it had calmed about half an acre. A patch the size of eight tennis courts, smooth as a mirror.

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Now think like a physicist. One teaspoon. Half an acre. Why did it stop there? Why not a whole acre?

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Because it couldn't get any thinner. It had spread until it was a single molecule thick, and a layer can't be thinner than one molecule.

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So do the estimate. A teaspoon is five cubic centimetres. Half an acre is two thousand square metres. Divide the volume by the area and you get the thickness: about two and a half billionths of a metre.

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That's the length of an oil molecule. Franklin had measured it, in 1774, with a teaspoon and a pond. He didn't take the last step. Nobody did, for another hundred years.

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And today we can simply look. Since the 1980s there have been microscopes that feel their way across a surface with a needle one atom wide at the tip, and build up a picture. In 2013, a team at IBM used one to push individual molecules around on a sheet of copper, photographed each arrangement, and strung the photos together into a film. It's called A Boy and His Atom. It's a minute long. A stick figure, made of a few dozen molecules, bounces a ball that is a single one. It holds the record as the smallest film ever made.

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Have you seen one? Yes, Professor Mach. Here's a film.

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The myth of the week is a subtle one, and it catches almost everybody. It's the idea that an atom is a tiny piece of the stuff, with all the properties of the stuff.

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That an atom of gold is a very small, shiny, yellow, heavy thing. That a molecule of water is wet.

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It isn't. A single gold atom has no colour. Colour is something that happens when light meets a crowd of them. A single water molecule isn't wet. Wetness is how billions of them slide over each other and cling to your skin. One molecule doesn't have a temperature, either. Temperature, as we'll see next time, is an average over a multitude.

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The properties of the world you live in, hard and soft, hot and cold, wet and dry, mostly aren't properties of atoms. They're properties of crowds. Nobody is a traffic jam.

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Remember this, because it's the hinge of the next four episodes. And in the last part of the series it comes back as one of the biggest questions there is.

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The question to take away.

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Mach said: I will not believe in what I cannot observe. That sounds like the very definition of scientific caution. And it led him wrong.

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So when is it reasonable to believe in something you can't see? You must have views on this, because the humanities and the social sciences are full of such things. The unconscious. Social class. The market. National character. Nobody has seen any of them. Some of them, you'll think, are as real as atoms, and some are caloric fluid.

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How do you tell? What was it about atoms that finally earned belief? I'd suggest it was the thirteen different roads that led to the same number. But I'd like to know whether you think that test would work on the unconscious.

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Your challenge this week is the gentlest yet. Two glasses of water, one cold from the fridge, one hot from the kettle. Let them stand a minute until the water is completely still. Then put a single drop of food colouring, or ink, into each. Don't stir.

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Watch what happens, and in which glass it happens faster. Then ask yourself what is doing the stirring.

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And find A Boy and His Atom. It's a minute of your life.

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Next time, we follow the jiggling. What is heat? What is cold? And why did a twenty-eight-year-old French engineer, who thought he was writing about steam engines, turn out to have discovered a law that governs the fate of the universe?