Episode 36 - Antimatter and the strangest theory

Tomlin Hawthorne

True or false. There is antimatter in your kitchen.

Tomlin Hawthorne

Not in a laboratory, not at the edge of the universe, not in a science fiction film. Real antimatter, the stuff that annihilates ordinary matter on contact in a flash of pure energy. In your fruit bowl.

Tomlin Hawthorne

True. An ordinary banana gives off a particle of antimatter roughly once every hour or so.

Tomlin Hawthorne

Bananas contain potassium. A tiny fraction of all potassium is a radioactive kind. And now and then, when one of those atoms decays, it throws out an anti-electron. The anti-electron travels a fraction of a millimetre, meets an ordinary electron, and the two of them vanish in a pair of gamma rays.

Tomlin Hawthorne

This is completely harmless, and it's been going on in every banana ever eaten. But antimatter was only predicted in 1928, and only because a very quiet man refused to ignore half the answers to an equation. Today we meet him. And we'll finally find out how a ray of light knows the quickest path, which I've owed you since episode eight.

Tomlin Hawthorne

Last time you shook a box of coins, removed the heads, and did it again, and again. A hundred, fifty, twenty-five, twelve. That's the decay curve of every radioactive substance. No coin knew its turn, and the curve came out the same anyway.

Tomlin Hawthorne

We've now got two great theories of the twentieth century. Relativity, from Part Five: space and time are one fabric, and nothing outruns light. And quantum mechanics, from Part Six: particles are described by waves, and come in lumps. Each of them works superbly.

Tomlin Hawthorne

But they were built separately. Schrödinger's equation, the heart of quantum mechanics, doesn't respect relativity. It treats time in the old Newtonian way. That's fine for an electron drifting round an atom. It's not fine for one moving near the speed of light. So today's question: what happens when you put the two together?

Tomlin Hawthorne

The man who did it is the oddest character in this series, and there's some competition.

Tomlin Hawthorne

Paul Dirac was born in Bristol in 1902. His father was Swiss, a teacher of French, and a domestic tyrant. He insisted that Paul speak to him only in French, and in correct French. Paul found that he couldn't express what he wanted in French, so, as he put it, it was better for him to stay silent.

Tomlin Hawthorne

He stayed more or less silent for the rest of his life. His colleagues at Cambridge invented a unit, the dirac, defined as the smallest measurable amount of conversation: one word per hour. There are dozens of stories. After one of his lectures, the chairman invited questions. A man stood up and said: I didn't understand the equation in the top right-hand corner of the blackboard. Dirac said nothing. The silence stretched. The chairman, embarrassed, asked whether he would care to answer. Dirac said: that was not a question. It was a statement.

Tomlin Hawthorne

He had no small talk and apparently no hobbies, apart from long solitary walks, and climbing trees in a suit. He said he'd been taught at school never to begin a sentence without knowing how it would end. He once observed that he could never see why physicists wanted to read novels. He tried Crime and Punishment. His only comment was that the author had made a mistake, because the sun rises twice in one day.

Tomlin Hawthorne

And he's supposed to have said to Robert Oppenheimer, who wrote poetry: I don't see how you can do both. In science you want to say something nobody knew before, in words everyone can understand. In poetry it's the exact opposite.

Tomlin Hawthorne

I ought to resent that on your behalf. But I can't dislike him. He was, by every account, a person of complete honesty and no malice at all. And he had one guiding belief, which we met in episode seven. That a physical law must have mathematical beauty. He said that it was more important for an equation to be beautiful than for it to agree with experiment. If it was beautiful enough, the experiment would come round.

Tomlin Hawthorne

In 1928, at twenty-five, he put that belief to work.

Tomlin Hawthorne

He set out to find an equation for the electron that obeyed both quantum mechanics and special relativity. He didn't start from experimental data. He started from what the equation would have to look like to be consistent, and to be simple. It took him a couple of months, sitting at a small desk in his college room.

Tomlin Hawthorne

The equation he found is very short. You can write it in one line with half a dozen symbols. It's carved on his memorial stone in Westminster Abbey. And when he saw what was in it, it was better than he'd hoped. It explained, with no extra assumptions, a property of the electron called spin, which until then had been tacked on by hand. It gave exactly the right value for the electron's magnetism. A colleague said that the equation seemed to know more than its author.

Tomlin Hawthorne

But there was something else in it. Something he hadn't put there and didn't want.

Tomlin Hawthorne

The equation had twice as many solutions as it should. Half of them described the electron. The other half described something with negative energy. An electron with less than nothing.

Tomlin Hawthorne

That's absurd. If such states existed, every electron in the universe would tumble down into them, giving off light for ever.

Tomlin Hawthorne

The sensible thing would have been to throw those solutions away. Call them unphysical. Mathematics often gives you answers that don't apply. If I ask how long the side of a square field is, and its area is a hundred, the algebra gives me ten and minus ten, and I don't lose sleep over the minus ten.

Tomlin Hawthorne

Dirac didn't throw them away. The equation was too beautiful to be half wrong. He worried at it for three years, tried one explanation and then another. And in 1931 he came to a conclusion that he found, I think, embarrassing. He published it in a rather roundabout way.

Tomlin Hawthorne

The extra solutions describe a new kind of particle. One that nobody had ever seen. It would have exactly the same mass as the electron, and exactly the opposite charge. Positive where the electron is negative. He called it an anti-electron.

Tomlin Hawthorne

And he went further. If it met an ordinary electron, the two would annihilate. Both would disappear, and their mass would turn into light.

Tomlin Hawthorne

Nobody much liked this. Pauli was scathing. Bohr was unconvinced.

Tomlin Hawthorne

The next summer, in California, a young physicist named Carl Anderson was photographing the tracks of rays from space as they passed through a chamber of mist inside a strong magnet. The magnet bends the path of a charged particle one way if it's negative and the other way if it's positive.

Tomlin Hawthorne

On the second of August 1932, he got a photograph of a track. It was as thin as an electron's track. It curved by the amount an electron's would. And it curved the wrong way.

Tomlin Hawthorne

A positive electron. He hadn't read Dirac's paper. He just saw it. It was named the positron.

Tomlin Hawthorne

I'd like you to register how extraordinary that is. Nobody had seen any hint of this in nature. A man sat at a desk, demanded that his equation be consistent and beautiful, and the equation told him that the universe contains a kind of matter nobody had imagined. And it does.

Tomlin Hawthorne

Dirac got the Nobel Prize the following year, at thirty-one. He seriously thought of turning it down, because he dreaded the publicity. Rutherford pointed out that refusing a Nobel Prize would get him a great deal more.

Tomlin Hawthorne

So. Antimatter. It's been made to sound exotic. It's this.

Tomlin Hawthorne

Every kind of particle has a partner. Same mass, opposite charge. The electron has the positron. The proton has the antiproton. You can even make an anti-atom: a positron going round an antiproton is antihydrogen. They've made it at CERN and kept it in a magnetic bottle for a quarter of an hour.

Tomlin Hawthorne

And when a particle meets its partner, they annihilate. That's E equals m c squared in its purest form. Not the tenth of a per cent you get from a nuclear reaction. All of it. A hundred per cent of the mass, converted to energy.

Tomlin Hawthorne

That's why it isn't lying about. Any antimatter that turns up meets ordinary matter almost at once, and is gone.

Tomlin Hawthorne

And it's in use. If you've ever had, or known anyone who's had, a PET scan in a hospital: the P stands for positron. The patient is given a sugar with a radioactive atom attached, one of the kind that gives off positrons. The sugar goes to wherever in the body is using most energy. A tumour, for instance. Each positron travels about a millimetre, finds an electron, and annihilates into two gamma rays, flying off in exactly opposite directions. A ring of detectors catches the pairs and works out where they came from.

Tomlin Hawthorne

So thousands of times a day, around the world, doctors look for cancer by putting antimatter inside people and watching it annihilate. Dirac's embarrassing extra solutions.

Tomlin Hawthorne

There's a deep puzzle here that I'll just name. If the laws treat matter and antimatter as mirror images, then the Big Bang should have made equal amounts of each. They should then have annihilated, completely, and left a universe with nothing in it but light. That didn't happen. There was a slight excess of matter, about one part in a billion, and that leftover is everything: every galaxy, every person. Nobody knows why. It's on the list for episode thirty-nine.

Tomlin Hawthorne

Now, Dirac's equation was a beginning. Because once you allow particles to be created and destroyed, an electron and a positron appearing out of energy and vanishing back into it, you need a whole new kind of theory. One in which the number of particles isn't fixed.

Tomlin Hawthorne

It took twenty years. It was finished just after the war, by three people working separately. Julian Schwinger, a dazzling New Yorker who gave lectures of terrifying polish. Sin-Itiro Tomonaga, working in the ruins of Tokyo, cut off from the rest of the world. And Richard Feynman.

Tomlin Hawthorne

The theory is called quantum electrodynamics. QED for short. It's the full quantum theory of light and electrons and how they affect each other. And it's the first of what are called quantum field theories.

Tomlin Hawthorne

Here's the basic picture. How do two electrons repel each other? Faraday said: through the field. QED says the field itself comes in lumps, photons, as we learned in episode twenty-seven. So one electron gives off a photon. The other absorbs it. And that exchange gives each of them a shove. All electric and magnetic force, the paperclip jumping to the magnet, your hand not passing through the table, comes down to charged particles tossing photons back and forth.

Tomlin Hawthorne

Feynman's contribution was a way of thinking about this that turned a nightmare calculation into something you could do on a napkin. He drew pictures. A line for an electron. A wiggly line for a photon. A dot where they meet. Each picture stands for one way a thing could happen, and there are simple rules for turning each picture into a number.

Tomlin Hawthorne

Two electrons could exchange one photon. Draw it. Or two photons. Draw that. Or one photon that, on its way across, briefly turns into an electron and a positron, which then annihilate back into a photon. Draw that too. To get the answer, you add up all the pictures.

Tomlin Hawthorne

They're called Feynman diagrams, and physicists have covered blackboards with them ever since. Feynman bought a van and had it painted with them. The story goes that when a stranger asked why the van had Feynman diagrams on it, the answer was: because the name's Feynman.

Tomlin Hawthorne

Now I can pay a debt.

Tomlin Hawthorne

In episode eight, I told you that light always takes the path of least time, like a lifeguard running to a swimmer. And I asked: how does it know? It looked like foresight. And I gave you a promissory note.

Tomlin Hawthorne

Here's Feynman's answer. The light doesn't take the quickest path. It takes every path.

Tomlin Hawthorne

I mean that as he meant it. To work out how light gets from a lamp to your eye, you have to consider every conceivable route. The straight one. A route with a kink in it. A route that goes to the ceiling and back. A route that loops round the Moon. All of them.

Tomlin Hawthorne

For each route, you draw a little arrow, like the hand of a clock. And the direction the arrow points depends on how long that route takes: the hand turns as the light travels.

Tomlin Hawthorne

Then you add all the arrows together, head to tail.

Tomlin Hawthorne

Now look at the wild routes. The one via the Moon, and the one that's a tiny bit different, take very different times. So their arrows point in quite different directions. Add up a great crowd of arrows pointing every which way, and they go round in circles and get nowhere. They cancel.

Tomlin Hawthorne

But near the quickest route, something special happens. That's the bottom of a valley. The neighbouring routes all take very nearly the same time. So their arrows all point very nearly the same way. Add them up and you get one long arrow.

Tomlin Hawthorne

So the only routes that count, in the end, are the ones bunched round the path of least time. Everything else has cancelled itself out.

Tomlin Hawthorne

That's how light knows. It doesn't. There's no foresight. It tries everything, and what we see is what survives the cancelling. It's interference again. It's the double slit, with infinitely many slits.

Tomlin Hawthorne

And Maupertuis, the man Voltaire ridiculed? His principle of least action comes out of this as a consequence. It's what quantum mechanics looks like from far enough away that you can't see the arrows.

Tomlin Hawthorne

Feynman wrote a short book explaining all this with nothing but little arrows. It's called QED: The Strange Theory of Light and Matter. It's four lectures, given to an audience with no physics. I'd put it on the shortest of short lists.

Tomlin Hawthorne

Two last consequences, and they're both large.

Tomlin Hawthorne

First. If particles can pop in and out of existence, then empty space isn't empty. Even in a perfect vacuum, the fields are still there, and by the uncertainty principle they can't be perfectly still. They jitter. Pairs of particles flicker into being and vanish again. The vacuum is a seething thing. And you can measure its effects: that jitter very slightly changes the magnetism of the electron and the energy levels of hydrogen.

Tomlin Hawthorne

And this is where QED earns its reputation. You can calculate the strength of the electron's magnetism, adding up thousands of diagrams. And you can measure it. The two agree to about one part in a trillion.

Tomlin Hawthorne

Feynman's comparison was that it's like measuring the distance from Los Angeles to New York and getting it right to the width of a human hair. It's the most precisely confirmed prediction in all of science.

Tomlin Hawthorne

Second, and this changes the whole picture. Why are all electrons identical? Not similar. Identical. Every electron in the universe has exactly the same mass and exactly the same charge. Two snowflakes differ. Two electrons don't.

Tomlin Hawthorne

In quantum field theory, there's an answer. There aren't really lots of separate electrons. There's one thing: the electron field. It fills all of space, like Faraday's field. And what we call an electron is a ripple in that field. A little lump of excitation. All electrons are alike for the same reason that all the notes of middle C are alike. They're the same field, doing the same thing in different places.

Tomlin Hawthorne

So here's the modern view, and it's the one I told you in episode sixteen that we'd arrive at. The world isn't made of particles. It's made of fields. A dozen or so of them, all filling the whole of space. Particles are what the fields look like when you look closely: the smallest possible ripples.

Tomlin Hawthorne

Faraday, with his iron filings, was more right than he could have dreamed.

Tomlin Hawthorne

The myth of the week is that a Feynman diagram is a picture of what happens. A little film of two electrons and a photon. It isn't. It's one term in a sum. One arrow. The actual event is all the diagrams together, and no single one of them took place.

Tomlin Hawthorne

And a bonus myth, since we're here: that antimatter falls upward. It's a lovely idea, and until recently nobody had checked. In 2023 an experiment at CERN let go of some antihydrogen atoms and watched. They fall down, like everything else.

Tomlin Hawthorne

And the question to take away.

Tomlin Hawthorne

Dirac trusted the beauty of his equation over the evidence, when there was no evidence. And he was right. It's the best case there is for the idea that beauty is a guide to truth.

Tomlin Hawthorne

But he also, later, rejected QED itself, the theory that grew out of his own work. He thought the mathematics used to tame its infinities was ugly, and that an ugly theory couldn't be correct. He went to his grave saying so. And QED is the most accurate theory we have.

Tomlin Hawthorne

So the same instinct that found antimatter also turned its back on the greatest success in physics. What does that tell you about taste as a guide? When is trusting your sense of form wisdom, and when is it vanity? You'll have seen both, in artists and in scholars.

Tomlin Hawthorne

Your challenge. Two things, both on paper.

Tomlin Hawthorne

One. Draw a Feynman diagram. Time goes up the page. Draw two lines coming up from the bottom, a little apart: two electrons. Halfway up, join them with a wiggly line: a photon passing between them. Then let the two lines continue up, leaning away from each other. That's the simplest picture of two electrons repelling.

Tomlin Hawthorne

Now draw a more complicated way for the same thing to happen. Two wiggly lines. Or a wiggly line with a small loop in the middle. There's no limit. Every one you can draw is part of the answer.

Tomlin Hawthorne

Two. Next time you eat a banana, have a thought for Dirac.

Tomlin Hawthorne

Next time. By 1960 physicists had found not three or four particles but hundreds, and nobody could remember their names. Then a man who loved languages and birdwatching sorted them out, and named the pieces after a line in Finnegans Wake. We'll meet the complete cast of the universe. It's shorter than you'd think.