Episode 17 - Maxwell: Let there be light

Tomlin Hawthorne

A history question. What was the most significant event of the nineteenth century?

Tomlin Hawthorne

Take a moment. You've got plenty to choose from. The defeat of Napoleon. The revolutions of 1848. The abolition of slavery. The American Civil War. The unification of Germany. Darwin.

Tomlin Hawthorne

Here's an answer you may not have considered. It was given by Richard Feynman, to a room of undergraduates in the early sixties. Look back from ten thousand years in the future, he said, and the event of the nineteenth century that will stand out is James Clerk Maxwell working out the laws of electricity and magnetism. Next to that, he said, the American Civil War will look like a local matter.

Tomlin Hawthorne

Now, that's a physicist talking, and physicists have been known to overrate physics. But I'd like to spend this episode seeing whether he might have a case. Because what Maxwell found, in the same decade as that war, is the answer to a question people had been asking since Genesis. What is light?

Tomlin Hawthorne

Last time, I asked you to wave a fridge magnet round your phone and watch the compass needle chase it. And then, if you were feeling bold, to touch a wire to a battery and see the needle kick. Electricity making magnetism. And we met Faraday, who showed it works the other way too: a moving magnet makes electricity. And who looked at iron filings and decided that the space around a magnet is not empty. It holds a field.

Tomlin Hawthorne

He had the vision. What he couldn't do was write it down in the language physicists use. For that, the story needs one more person.

Tomlin Hawthorne

James Clerk Maxwell was born in Edinburgh in 1831. That's the very year Faraday pushed the magnet into the coil. He grew up on his family's estate, Glenlair, in the hills of south-west Scotland, an only child, endlessly curious. His mother's letters describe a small boy who had to know how everything worked, and whose constant question, in broad Galloway Scots, was: what's the go of that? And if the answer didn't satisfy him: but what's the particular go of it?

Tomlin Hawthorne

His mother died when he was eight. At ten he was sent to school in Edinburgh, and arrived wearing clothes his father had designed, for practicality, and shoes with square toes, and speaking with a country accent. The other boys named him Dafty. It stuck for years.

Tomlin Hawthorne

At fourteen, Dafty wrote a paper on how to draw certain mathematical curves using pins and string. It was read to the Royal Society of Edinburgh by a professor, because the author was thought too young to present it himself.

Tomlin Hawthorne

He was not a remote figure. He wrote comic verse all his life, some of it rather good, and sang it to the guitar. He was devout, gentle, funny in a sideways manner that people sometimes took a minute to catch. He worked out that Saturn's rings can't be solid and must be made of countless small lumps, which was confirmed by a space probe a hundred and twenty years later. He took the first colour photograph, in 1861. It's of a tartan ribbon, naturally.

Tomlin Hawthorne

And in his twenties he did something his colleagues thought eccentric. He read Faraday. Properly. He'd been advised not to bother: Faraday had no mathematics, the lines of force were a crutch. Maxwell read him anyway, and decided that Faraday was the one who'd understood, and that the lines of force were the truth, and that his own job was to translate.

Tomlin Hawthorne

It took him about ten years. What he ended with was a set of equations. In their modern form there are four. And between them they contain everything that was known, and is known, about electricity and magnetism. Let me tell you what the four say, in words. They're simpler than their reputation.

Tomlin Hawthorne

One. Electric charges create electric fields. The field points away from positive charges and toward negative ones.

Tomlin Hawthorne

Two. Magnetic field lines never begin or end. They always loop round and close on themselves. Which is another way of saying: there's no such thing as a north pole without a south. Cut a magnet in half and you get two magnets.

Tomlin Hawthorne

Three. A changing magnetic field creates an electric field. That's Faraday's discovery. The magnet moving into the coil.

Tomlin Hawthorne

Four. An electric current creates a magnetic field. That's Ørsted and his compass.

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So far, Maxwell's a translator. He's taken fifty years of other people's experiments and put them into four tidy lines.

Tomlin Hawthorne

And then he looks at the four lines, and something bothers him.

Tomlin Hawthorne

It's the kind of thing that would bother you, if you'd been listening to episode seven. It's a matter of symmetry.

Tomlin Hawthorne

Look at number three. A changing magnetic field makes an electric field.

Tomlin Hawthorne

Now, where's the partner to that? Shouldn't there be a line that says: a changing electric field makes a magnetic field? Number four doesn't say that. Number four says a current does, an actual flow of charge along a wire. It says nothing about fields changing in empty space.

Tomlin Hawthorne

The set is lopsided. Magnetism changing can make electricity. But electricity changing, with no wire and no current, apparently does nothing.

Tomlin Hawthorne

Maxwell had more than a feeling. He'd found a case where the old equations gave nonsense, where they contradicted themselves. But the cure he chose was the symmetrical one. He added a term to the fourth equation. Nobody had measured it. No experiment had asked for it. He put it in because the mathematics was broken without it and whole with it.

Tomlin Hawthorne

The new fourth line reads: an electric current, or a changing electric field, creates a magnetic field.

Tomlin Hawthorne

Now watch what happens. This is one of the great moments.

Tomlin Hawthorne

Suppose, somewhere in empty space, an electric field changes. Say I shake a charge.

Tomlin Hawthorne

By the new rule four, a changing electric field creates a magnetic field, close by.

Tomlin Hawthorne

But that magnetic field has just appeared. It wasn't there a moment ago. So it's changing. And by rule three, a changing magnetic field creates an electric field, a little further on.

Tomlin Hawthorne

And that electric field is new. So it's changing. So it creates a magnetic field, further on again.

Tomlin Hawthorne

Which creates an electric field. Which creates a magnetic field.

Tomlin Hawthorne

Each one gives birth to the other. And the whole thing moves outward, away from the charge I shook, through empty space. It needs no wire. Once it's launched, it doesn't even need the charge. It carries itself.

Tomlin Hawthorne

It's a wave. A wave in Faraday's fields. The equations, with that one extra term, say that such waves must exist.

Tomlin Hawthorne

And they say more. They say how fast the wave travels.

Tomlin Hawthorne

There are two numbers in Maxwell's equations that have to be measured. One tells you how strong the electric force is: how hard two charges push on each other. You measure it with charged metal plates on a bench. The other tells you how strong the magnetic force is: how hard two wires carrying current pull on each other. You measure it with coils and a balance.

Tomlin Hawthorne

These are numbers from a laboratory. Brass, glass, wire, wax. Nothing to do with light. Nothing to do with speed at all.

Tomlin Hawthorne

And Maxwell's equations said: combine those two numbers in a certain simple way, and you get the speed of the wave.

Tomlin Hawthorne

In 1862 he did the sum. He was at Glenlair for the summer, and the story goes that he had to wait until he got back to London to look up the comparison, because he didn't have the reference book in the country.

Tomlin Hawthorne

His wave travelled at about three hundred and ten thousand kilometres per second.

Tomlin Hawthorne

A French physicist, Fizeau, had measured the speed of light a few years earlier, with a spinning toothed wheel and a mirror on a hill five miles away. He got about three hundred and fifteen thousand.

Tomlin Hawthorne

Those are the same number. To within the errors of the day, they're the same.

Tomlin Hawthorne

Two measurements of how hard charges push and wires pull, made on a workbench, give you the speed of light.

Tomlin Hawthorne

Maxwell wrote, and he put it in italics, which he almost never did, that we can scarcely avoid the conclusion that light consists of waves in the same medium that causes electric and magnetic phenomena.

Tomlin Hawthorne

Light is an electromagnetic wave. That's what it is. A ripple of electric and magnetic field, each regenerating the other, crossing space at three hundred thousand kilometres a second.

Tomlin Hawthorne

Every time you've seen anything, a face, a page, a star, what's entered your eye is a train of Faraday's fields, shaken loose from some jiggling charge and carrying itself to you.

Tomlin Hawthorne

This is the second great unification in the history of physics. The first was Newton's: the heavens and the Earth obey the same law. This one says that electricity, magnetism and light, three subjects that had been studied separately for two thousand years, are one subject. Amber, lodestone and the rainbow.

Tomlin Hawthorne

And think back to the last episode. Faraday said the field is real. Here's the proof. Sunlight is a piece of field that left the Sun eight minutes ago. The charges that made it are ninety-three million miles behind. If the field were just a bookkeeping device for forces between charges, it couldn't do that. It's out there on its own, crossing the dark, carrying energy. You can feel it on your face.

Tomlin Hawthorne

Nothing in the equations says the wave has to be the size that light is. You could shake a charge slowly and get a long, lazy wave. Or fast and get a short one. Light should be just one stretch of an enormous range of electromagnetic waves, most of them invisible.

Tomlin Hawthorne

Maxwell didn't live to see that tested. He died in 1879, of stomach cancer, at forty-eight. The same illness, at the same age, as his mother. It's the year Einstein was born.

Tomlin Hawthorne

The test came eight years later, in Germany. A young professor, Heinrich Hertz, built an electrical circuit with a small gap in it, across which he could make sparks jump. A spark is charge slamming back and forth, very fast. If Maxwell was right, that should send out waves.

Tomlin Hawthorne

Across the room, he set up a plain loop of wire, also with a tiny gap. Not connected to anything. And he darkened the room, and looked at the gap in the loop through a magnifying glass.

Tomlin Hawthorne

When the sparks jumped in the circuit, tiny sparks jumped in the loop. Across the room. With nothing in between.

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He'd made what we now call radio waves. He showed they reflected, like light. They could be focused, like light. They travelled at the speed of light. They were light, of a colour a million times too long for the eye.

Tomlin Hawthorne

And Hertz, asked what use his discovery might have, said: none whatever. He said it was just an experiment that proved Maestro Maxwell was right. He died at thirty-six, seven years later. Within a decade of his death, a young Italian called Marconi had sent a signal across the Atlantic. The unit of frequency carries Hertz's name: one wave per second is one hertz.

Tomlin Hawthorne

So, Feynman's claim. Every radio and television broadcast. Radar. Mobile phones. Wi-Fi. X-rays in hospitals. The microwave in your kitchen. Fibre optics. The whole of electrical engineering, the grid, the motor, the generator. All of it is in those four lines, and nearly all of it was unimagined when he wrote them. I don't know how you weigh that against a war. But I don't think the comparison is silly.

Tomlin Hawthorne

There's one loose thread, and I need to show it to you, because it's going to unravel everything.

Tomlin Hawthorne

Waves, as we said in episode ten, are waves in something. Sound is a wave in air. A ripple is a wave in water. So what is light a wave in? What's doing the waving, in the empty space between here and the Sun?

Tomlin Hawthorne

Maxwell assumed there must be something. An invisible, weightless, perfectly transparent substance filling all of space. They called it the ether. It had to be extraordinarily stiff, to carry waves that fast, and yet the planets had to slide through it with no resistance at all. Maxwell believed in it. He wrote the entry on it for the Encyclopaedia Britannica.

Tomlin Hawthorne

And the equations gave one speed for light. Three hundred thousand kilometres a second. But speed relative to what? Relative to the ether, presumably.

Tomlin Hawthorne

Hold that thought. In four episodes' time a patent clerk is going to ask that question again, and decline to accept the answer.

Tomlin Hawthorne

The myth of the week is one I held myself as a child. That radio waves are a kind of sound. They're called radio, the thing they come out of makes noise, so surely they're noise.

Tomlin Hawthorne

They're not. They're light. Sound is air being squeezed; it travels at about a third of a kilometre a second and can't cross a vacuum. Radio is Maxwell's wave; it travels a million times faster and crosses a vacuum perfectly well. Your radio set catches the light and turns it into sound. The astronauts on the Moon could talk to Houston by radio. They couldn't have shouted to each other across a crater.

Tomlin Hawthorne

And the question to take away.

Tomlin Hawthorne

Maxwell added a term to an equation for the sake of consistency. And out of that came a prediction, nobody had been looking for it, that light is electromagnetic, and that there's a whole unseen spectrum. Mathematics, apparently, knew something about the world that no human did.

Tomlin Hawthorne

In 1960 the physicist Eugene Wigner wrote a famous essay about this, called The Unreasonable Effectiveness of Mathematics in the Natural Sciences. His point was that we have no right to expect it. Mathematics is something we make up, sitting in chairs. Why should the universe pay any attention?

Tomlin Hawthorne

There are a few answers on offer. That mathematics is the language the world is written in, which is what Galileo said. That we invent mathematics by abstracting from the world in the first place, so of course it fits. That we only notice the successes. Which do you find convincing? Is it unreasonable, or isn't it?

Tomlin Hawthorne

Your challenge this week is the best one in the series. You're going to measure the speed of light with a bar of chocolate.

Tomlin Hawthorne

You need a microwave oven and a large flat bar of chocolate. Take the turntable out of the microwave, so the plate can't rotate. That's essential. Put the chocolate on an upturned plate, flat. Heat it on full power for about twenty seconds. Watch it. Stop as soon as you see it start to melt in spots.

Tomlin Hawthorne

You'll find it has melted in a few separate places, with solid chocolate in between. Those are the hot spots of a standing wave, the same kind as on a guitar string. Measure the distance between the centres of two neighbouring melted spots. It should be about six centimetres.

Tomlin Hawthorne

That distance is half the wavelength. So double it: twelve centimetres. Now look on the back of the oven for a label giving its frequency. It'll say 2,450 megahertz. That's two thousand four hundred and fifty million waves per second.

Tomlin Hawthorne

Multiply the wavelength by the frequency. Twelve centimetres, times two thousand four hundred and fifty million. You should get something close to three hundred thousand kilometres per second.

Tomlin Hawthorne

You've measured the speed of light, in your kitchen, and you may now eat the apparatus.

Tomlin Hawthorne

Next time. If light is a wave, then colour is just wavelength. Red is a long wave, blue is a short one. That's what Newton's heirs say. And the greatest poet in the German language thought it was an outrage, and spent twenty years and a thousand pages trying to prove them wrong.