Episode 27 - An act of desperation

Tomlin Hawthorne

You have one of those glow-in-the-dark stars that children stick on bedroom ceilings. You hold it under a light, it soaks something up, and then it glows green in the dark.

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I'm going to offer you two ways to charge it.

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The first is a powerful red lamp. Really bright, uncomfortable to look at. You can hold the star under it for an hour.

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The second is a feeble violet light, so dim you can hardly see it. You get one second.

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Which one makes the star glow?

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The violet. One second of faint violet, and the star lights up. And the red lamp, the blazing one, for the whole hour? Nothing. Not a flicker. You could leave it there for a year.

Tomlin Hawthorne

That makes no sense. The red lamp is pouring in thousands of times more energy. If light is a wave, as we proved, more wave should do more. A big wave can do anything a ripple can.

Tomlin Hawthorne

This is the puzzle I left you with at the end of Part Four, wearing a different hat. Why can't a microwave oven give you a sunburn? Today we answer it. And the answer is where the old physics ends.

Tomlin Hawthorne

Welcome to Part Six. Last time, I hope, you listened to a small rising chirp, less than a second long, which was the sound of two black holes merging over a billion years ago. That was the far end of Einstein's world: the very large and the very heavy.

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Now we turn round and go down. Into the atom. And I want to be straight with you about what's coming. Relativity is strange, but it's a strangeness you can learn to picture. For the next eight episodes, there are things that can't be pictured, that the people who discovered them couldn't picture, and that nobody has pictured since. The mathematics works perfectly. It's the most accurate theory human beings have. And no one agrees on what it means.

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So if you find yourself thinking, that can't be right, I must have misunderstood: you probably haven't. Niels Bohr, who'll be with us for most of this, is supposed to have said that anyone who isn't shocked by quantum theory hasn't understood it.

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It begins quietly.

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The twenty-seventh of April, 1900. The Royal Institution in London, Faraday's old lecture theatre. Lord Kelvin is seventy-five, the grand old man of British science. He's the Kelvin of the temperature scale, the man who laid the Atlantic telegraph cable, the one who met Joule on his honeymoon. He gives a lecture with a splendid title: Nineteenth-Century Clouds over the Dynamical Theory of Heat and Light.

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His theme is that physics is in magnificent shape. The beauty and clearness of the theory, he says, is obscured only by two clouds.

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Cloud number one: nobody can detect the Earth's motion through the ether. That's Michelson and Morley. That cloud became relativity.

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Cloud number two is a technical problem to do with heat and light. That cloud became quantum mechanics.

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So, two small clouds on the horizon in the spring of 1900, and each of them turned out to be a hurricane. I think Kelvin deserves real credit. He's often mocked for complacency. But out of everything he could have picked, he picked the right two.

Tomlin Hawthorne

Let's look at the second cloud.

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It's about something you've known since you first watched a fire. Hot things glow. And the colour depends on the temperature. An iron poker in the coals goes a dull red. Hotter, it's orange. Hotter still, yellow, then white. A star that's hotter than the Sun is bluish. Potters and blacksmiths have judged temperature by eye for thousands of years.

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And here's the neat part: it doesn't matter what the thing is made of. Iron, clay, charcoal, a star. At the same temperature, they glow the same colour. So this is something universal, something about heat and light themselves, not about any particular material. That makes it exactly the kind of thing a physicist wants to explain.

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By 1900 the two great theories were ready to hand. Boltzmann's theory of heat: atoms jiggling, energy shared out among all the available motions. And Maxwell's theory of light: electromagnetic waves. Put them together, and you should be able to calculate the colour of a hot object.

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People did. And the answer was a catastrophe. It was later given that very name.

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Here's the trouble. Inside a hot oven, there can be light waves of every wavelength. Long ones, short ones, shorter ones still. And there's no limit to how short. So there are more possible short waves than long ones. In fact there are infinitely many. Boltzmann's rule says heat energy gets shared out equally among all the possibilities. So nearly all of it should go into the shortest waves. Ultraviolet, X-rays, gamma rays, without limit.

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In other words, the theory predicted that when you open your oven to check a cake, you should be killed instantly by a blast of gamma radiation. That any warm object should radiate infinite energy.

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Which doesn't happen. The cake is fine. The two best theories in physics, each tested a thousand ways, had been multiplied together, and the product was nonsense.

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Enter the most reluctant revolutionary in history.

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Max Planck was forty-two, a professor in Berlin. He came from a long line of lawyers, pastors and scholars. He was upright, formal, deeply conservative by temperament, a fine pianist who might have been a professional musician. As a young man, choosing a career, he'd asked a physics professor for advice, and was told not to bother with physics: the subject was nearly finished, with only a few gaps left to fill.

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He went in anyway. He said he didn't want to discover new things, only to understand the foundations properly.

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Planck had been working on the glowing-oven problem for six years. The experimenters in Berlin had by now measured the glow extremely carefully, the actual amount of each colour at each temperature. In October 1900 Planck found a formula that matched their curve perfectly. He got it, by his own account, by inspired guesswork. He presented it at a meeting. One of the experimenters stayed up all night checking it against his data and came round the next morning to say it was exactly right, at every point.

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So now he had the right answer and no idea why it was right. He said later that the next eight weeks were the hardest work of his life.

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And in December, he found a way to derive his formula. But only by making an assumption so peculiar that he could hardly bring himself to write it down.

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He had to assume that the atoms in the walls of the oven can't give out or take in energy in any amount they like. They can only do it in lumps. Fixed packets. And the size of the packet depends on the colour of the light. For red light, a small packet. For blue light, a bigger one. For ultraviolet, bigger still.

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In symbols it's the shortest important equation in physics. E equals h f. The energy of one packet, equals the frequency of the light, times a fixed number. That number is now called Planck's constant, and written h.

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See how this cures the catastrophe. The very short waves, the gamma rays, come in enormous packets. An atom in a warm oven simply doesn't have enough energy to pay for even one. It's like a vending machine that only sells one item, and it costs a million pounds. Nobody buys. So the short waves never get their share, and the infinity goes away.

Tomlin Hawthorne

Planck presented this on the fourteenth of December, 1900. That's usually given as the birthday of quantum physics. He called his packets quanta, which is just Latin for amounts.

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And he didn't believe it. I want to stress that. He thought it was a mathematical trick, a bit of scaffolding that would turn out to be unnecessary. He described it afterwards as an act of desperation. He'd tried everything else. A theory had to be found, he said, at any cost.

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He spent the next ten years trying to get rid of his own discovery, to fit the lumps back into ordinary smooth physics. He couldn't.

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But it isn't zero. And everything in the next eight episodes follows from the fact that it isn't zero.

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For five years, almost nobody took Planck's lumps seriously. Including Planck. Then somebody did, and you can guess who.

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It's March 1905, in the patent office in Bern. This is the first of the four great papers of that year, three months before relativity. And it's the only one of them that Einstein himself, in a letter to a friend, called very revolutionary.

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Planck had said: atoms give out and take in light energy in lumps. He thought that was something odd about atoms. The light itself, once it's out, is a nice smooth Maxwell wave.

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Einstein said: no. Take it at face value. The light itself is made of lumps. A beam of light is a hail of tiny packets of energy, each one a single indivisible unit. Later they were named photons. A photon of blue light carries more energy than a photon of red light. And a brighter light doesn't have bigger photons. It has more of them.

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This was heresy. Light is a wave. Young proved it in 1801 with his two slits. Maxwell explained what kind of wave. Hertz made radio waves on a bench. For Einstein to say that light comes in particles was to go back a century.

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But he had a piece of evidence. It was an effect that had been known for nearly twenty years and that nobody could explain. If you shine light on a clean piece of metal, electrons get knocked out of it. It's called the photoelectric effect. It's how a solar panel works, and the sensor in a camera.

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And it behaves very strangely. Shine red light on the metal: no electrons come out. Make the red light brighter. Still none. Make it blinding. None.

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Now shine a faint ultraviolet light. Electrons fly out at once. Immediately, with no delay, even if the light is so dim you can barely detect it.

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You'll recognise that. It's the glow-in-the-dark star. And it's the sunburn.

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On the wave theory, this is impossible. A wave delivers its energy smoothly. A bright red light delivers a lot. It ought to be able to shake an electron loose eventually, like the sea working at a harbour wall.

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On Einstein's picture, it's obvious. Here's the image I'd use. Each electron is a ball sitting in a ditch. To get it out, you have to give it one kick, hard enough to clear the bank. Light arrives as individual kicks. A photon of red light is a gentle tap. It's not enough. And it doesn't matter how many gentle taps you deliver. A million taps, each too weak, never add up to one kick, because the ball settles back between them. A photon of ultraviolet is a hard kick. One is enough. And a dim ultraviolet light just means the kicks are few and far between. But each one that arrives does the job.

Tomlin Hawthorne

So it isn't the amount of light that decides what it can do. It's the size of the individual packet. And the size of the packet is set by the colour.

Tomlin Hawthorne

Now I can finally answer the question from episode twenty.

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A bond between two atoms in your DNA takes a certain amount of energy to break. One photon of ultraviolet light carries about that much. So a single ultraviolet photon can snap a bond. That's sunburn, and, with bad luck, it's how skin cancer starts.

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A photon of visible light carries a bit less. Mostly not enough.

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And a photon of microwaves, or of the radio waves from a phone mast, carries about a millionth as much. It's not that it would take a million of them. No number of them will do it. They can jostle the molecules and warm you up, which is how the oven cooks. They cannot break a chemical bond, however many there are. The red lamp can't charge the star.

Tomlin Hawthorne

That's why the kind of light matters more than the amount. It's a real and useful thing to know. And you can only know it once you accept that light comes in lumps.

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Hardly anybody did accept it. For years.

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The great American experimenter Robert Millikan thought Einstein's idea was reckless. He described it as bold, not to say reckless, and he set out to prove it wrong. He spent ten years on it, building what he called a machine shop in a vacuum, to measure exactly how the energy of the ejected electrons depends on the colour of the light.

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In 1916 he published. Einstein's equation was right in every detail. Millikan confirmed it to within half a per cent and said, in the same paper, that he still couldn't believe the theory behind it. That's an honest scientist.

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And in 1913, when Planck and others wrote to recommend Einstein for a prestigious position in Berlin, they praised him to the skies, and then added an apology. That he may sometimes have missed the target in his speculations, as for example in his hypothesis of light quanta, shouldn't be held too much against him.

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When Einstein was finally given the Nobel Prize, in 1921, it wasn't for relativity, which the committee still thought too speculative. The citation was for the photoelectric effect.

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So here's where we stand, and it's uncomfortable. In episode ten, I showed you that light is a wave. Two slits, bright and dark stripes, light plus light making darkness. I told you the case was closed. In this episode, I've shown you that light comes in particles. Lumps that arrive one at a time and deliver single kicks.

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Both of those are established by experiment. Neither is going away. And a wave and a particle are not the same kind of thing. A wave is spread out. A particle is in one place.

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I'm not going to resolve that today. In two episodes' time we'll put the two together in a single experiment, and you can watch what happens.

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The myth of the week is a phrase. A quantum leap. Politicians use it, and advertisers, to mean a giant stride forward.

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A quantum is the smallest possible amount of something. A quantum leap is the tiniest change there can be. I don't expect to win this one. But the next time a company announces a quantum leap in customer service, you'll know what they've actually promised.

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And the question to take away.

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Planck didn't believe his own discovery. Late in life he looked back and drew a moral that's become famous. He said that a new scientific truth doesn't win by persuading its opponents and getting them to see the light. What happens is that the opponents eventually die, and a new generation grows up that's used to it.

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Sixty years later, a historian called Thomas Kuhn built a whole theory of science on roughly that observation. That science doesn't advance by steady accumulation. It goes along inside a framework that everybody shares, until the framework breaks, and then there's a revolution, and the old guard never really converts.

Tomlin Hawthorne

Is that fair? Is it true of the cases we've seen? Mach never accepted atoms. Eddington never accepted Chandrasekhar. But Planck himself came round, slowly. So did Millikan. Is science more like a courtroom, where evidence decides, or like a succession of generations? And is your own field any different?

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Your challenge. Find something that glows in the dark. A sticker, a watch dial, a toy. Take it into a dark room.

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Try to charge it with red light. A bicycle rear lamp is good, or a phone screen showing pure red, held right against it. Give it a full minute. Then look.

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Now give it two seconds of the phone's white torch, which has blue in it. Or better, a violet or ultraviolet light if you have one. Look again.

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You'll have seen, with a child's sticker, the thing that Einstein got the Nobel Prize for. Each bit of that glowing material is a ball in a ditch. And red light, however much of it, only taps.

Tomlin Hawthorne

Next time. We know matter is made of atoms. In 1909, in Manchester, a New Zealander fires some particles at a sheet of gold foil to see what an atom looks like inside. What he finds is so alarming that, by the physics of the day, every atom in the universe ought to collapse in less than a billionth of a second.