Episode 21 - The trouble with the speed of light

Tomlin Hawthorne

You're on a train doing a hundred kilometres an hour. You walk toward the front at five. How fast are you going, as seen by someone on the platform?

Tomlin Hawthorne

A hundred and five. Easy. Speeds add.

Tomlin Hawthorne

Now a harder one. The train is going at half the speed of light. It's a very good train. You're standing at the back with a torch, and you shine it toward the front.

Tomlin Hawthorne

The light leaves your torch at the speed of light. How fast is that light going, as measured by someone on the platform?

Tomlin Hawthorne

One and a half times the speed of light. That's what addition says. That's what Galileo says, and Newton, and common sense.

Tomlin Hawthorne

And it's wrong. The person on the platform measures that light going at the speed of light. Exactly. Not a whisker more. And so do you, on the train. You both get the same number for the same beam, though one of you is moving at half the speed of light relative to the other.

Tomlin Hawthorne

That can't be right. And it is. Today is about how one young man, in 1905, decided to believe it, and what he had to give up in exchange.

Tomlin Hawthorne

Welcome to Part Five. Last time I asked you to wrap your phone in kitchen foil and call it. Silence. The waves can't get through a metal skin. And to trace a voice message from one phone to another and name the physics at every step. If you managed most of it, you now understand the plumbing of the modern world better than nearly everyone who uses it.

Tomlin Hawthorne

Part Five is six episodes on relativity. I'll tell you now that there's no difficult mathematics in it. What's difficult is that it asks you to let go of something you didn't know you were holding. So let's go slowly.

Tomlin Hawthorne

Bern, Switzerland, 1905. There's a clock tower in the middle of the old town, one of the great mechanical clocks of Europe, with a parade of little bears that comes round on the hour. A couple of hundred yards along the same street, on the third floor of the Postal and Telegraph building, is the Federal Office for Intellectual Property. The patent office.

Tomlin Hawthorne

At a high desk in room eighty-six sits a technical expert, third class. He's twenty-six. He has a wife, Mileva, who studied physics with him, and a one-year-old son. He has untidy dark hair and a moustache and, by the accounts of his friends, a loud, barking laugh.

Tomlin Hawthorne

He's there because he couldn't get a university job. He'd graduated from the Zurich Polytechnic five years earlier, and of the students in his section he was the only one not offered a junior post. His professors hadn't warmed to him. He skipped lectures, he argued, he read what he liked. One of them, his mathematics teacher, remembered him later as a lazy dog who never bothered about mathematics at all. He wrote to professors across Europe asking for a position, and for the most part they didn't write back. For a while he gave private lessons, with an advertisement in the paper offering a free trial.

Tomlin Hawthorne

The patent job came through a friend's father. And Einstein, I should say his name, loved it. He could do a day's work in a few hours, and keep his own calculations in the desk drawer, which he called his department of theoretical physics. He'd shut it quickly when footsteps came.

Tomlin Hawthorne

Now, here's something a historian named Peter Galison noticed, and I think it's a lovely piece of detective work. What kind of patents were crossing that desk? Switzerland made clocks. And the hot problem of the day, with railways and telegraphs spreading everywhere, was how to make distant clocks agree. If it's noon in Bern, when exactly is it noon in Geneva? You need that to run trains without collisions. The world had only just been divided into time zones, twenty years before, for precisely this reason. And the patent applications coming in were for schemes to synchronise clocks by sending electrical signals between them.

Tomlin Hawthorne

So every working day, Einstein was reading about how to decide whether two clocks in different places show the same time. Keep that in mind.

Tomlin Hawthorne

Now the physics. There are two things you already know, and they don't fit together.

Tomlin Hawthorne

The first is from episode four. Galileo's ship. Shut yourself in a cabin below decks on a ship that's sailing smoothly, and there's no experiment you can do to tell whether you're moving. The butterflies fly the same. The water drips straight. Steady motion can't be felt. The laws of physics are the same in the moving cabin as on the shore.

Tomlin Hawthorne

And one consequence is that speed is always relative to something. There's no such thing as how fast you're really going. You're doing zero relative to your chair, a thousand miles an hour relative to the centre of the Earth, sixty-seven thousand relative to the Sun. And speeds add in the obvious way. A hundred, plus five, is a hundred and five.

Tomlin Hawthorne

The second thing is from episode seventeen. Maxwell's equations. Four lines that describe electricity, magnetism and light. And out of those four lines falls a speed. Three hundred thousand kilometres per second. The speed of light.

Tomlin Hawthorne

Now put those two together and listen for the clash.

Tomlin Hawthorne

Maxwell's equations give a speed. But speed relative to what? The equations don't say. They just give a number.

Tomlin Hawthorne

If Galileo's right, and speed is always relative to something, then Maxwell's number must be relative to something. And everyone knew what. The ether. That invisible substance filling all of space, the stuff that light was supposed to be a wave in. The speed of light is three hundred thousand kilometres a second relative to the ether, the way the speed of sound is three hundred and forty metres a second relative to the air.

Tomlin Hawthorne

Fine. But then Galileo's principle is in trouble. Because now there's a way to tell if you're really moving. Measure the speed of light. If you're moving through the ether, you'll get a slightly different answer in different directions. Light coming at you head-on will seem faster. Light catching you up from behind will seem slower. Your cabin below decks does have a window after all.

Tomlin Hawthorne

So one of them has to give. Either Galileo's principle fails for light, and there's a real, absolute state of rest, the ether. Or there's something wrong with our idea of how speeds combine.

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In 1887, somebody went to look.

Tomlin Hawthorne

Albert Michelson was born in a town in Prussia that's now in Poland, and brought to America as a small child. He grew up in gold-rush mining camps in California and Nevada, where his father kept a shop. He got into the Naval Academy by taking a train across the continent and waylaying President Grant on his morning walk. And he became obsessed with one thing: measuring the speed of light more accurately than anybody ever had.

Tomlin Hawthorne

In 1887, in Cleveland, Ohio, with a chemist called Edward Morley, he set out to detect the Earth's motion through the ether.

Tomlin Hawthorne

The Earth goes round the Sun at about thirty kilometres a second. So we're ploughing through the ether at at least that speed. That should make an ether wind, and light travelling into the wind should take a little longer than light travelling across it.

Tomlin Hawthorne

The difference would be minute. So they built an instrument of astonishing delicacy. A beam of light was split in two. One half went out and back in one direction, the other half out and back at a right angle to it. Then the two were brought together again. If one had been delayed, even by a tiny fraction of a wave, the pattern they made together would shift. It's interference, from episode ten.

Tomlin Hawthorne

To keep it steady they mounted the whole thing on a slab of sandstone five feet square, and floated the slab in a trough of mercury, so it could be turned without a tremor. Even so, a horse and cart passing in the street outside would ruin a reading. They worked at night.

Tomlin Hawthorne

They turned the slab slowly, watching for the pattern to shift as one arm and then the other faced into the ether wind.

Tomlin Hawthorne

Nothing. It didn't shift. They tried at different times of day. They tried at different seasons, when the Earth is moving in a different direction. Nothing. Light took the same time in every direction, as if the Earth were standing perfectly still in the ether.

Tomlin Hawthorne

It's the most famous experiment in physics that failed to find anything. Michelson thought of it as a disappointment for the rest of his life. He got the Nobel Prize anyway, the first American to win one in science.

Tomlin Hawthorne

For the next eighteen years, the best physicists in Europe tried to save the ether. Perhaps the Earth drags the ether along with it. Perhaps, and this was seriously proposed by two very distinguished men, objects moving through the ether get squashed in the direction of motion, by exactly the amount needed to hide the effect. The measuring rods shrink, so you can never catch the ether out.

Tomlin Hawthorne

These were clever ideas. They also had the smell of a conspiracy. Nature had an ether, and had arranged things so that no experiment could ever show it.

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He'd been turning it over for ten years. When he was sixteen, he said, he'd asked himself a question. What would I see if I could run alongside a beam of light, at the speed of light? By the old physics, I'd catch it up. I'd see a light wave standing still next to me. A frozen ripple of electric and magnetic field, hanging in space, not going anywhere.

Tomlin Hawthorne

But there's no such thing. Maxwell's equations don't allow a stationary light wave. It was the whole point that the changing fields keep each other going. So something was wrong with the idea of catching it up.

Tomlin Hawthorne

In the spring of 1905 he went to see his closest friend, Michele Besso, who worked at the patent office too, and talked the problem through for a whole afternoon. He went home defeated. The next morning he came back and, before even saying hello, said: thank you. I've completely solved the problem.

Tomlin Hawthorne

Five weeks later the paper was finished. It has no references to other scientists. At the end he thanks Besso.

Tomlin Hawthorne

Here's what he did. He took two statements, and he declared them both to be true, without exception.

Tomlin Hawthorne

One. Galileo's principle. The laws of physics are the same for everybody in steady motion. There's no experiment that can tell you that you're really moving. No ether, no absolute rest. He didn't argue that the ether doesn't exist. He just said it was superfluous, and never mentioned it again.

Tomlin Hawthorne

Two. Maxwell's equations are among those laws. And they contain a speed. So that speed, the speed of light, must be the same for everybody in steady motion. Whoever you are, however you're moving, when you measure the speed of a beam of light, you'll get the same number.

Tomlin Hawthorne

Each of those was something physicists already more or less believed. Nobody had dared to believe both at once, because together they seem to be nonsense. They give you the torch on the train. The passenger says the light is moving away from her at the speed of light. The man on the platform says the same light is moving away from him at the speed of light. And they're moving relative to each other.

Tomlin Hawthorne

How can they both be right?

Tomlin Hawthorne

Einstein's answer is the hinge of modern physics, and he got it from thinking about clocks.

Tomlin Hawthorne

What is a speed? It's a distance divided by a time. So many kilometres, in so many seconds.

Tomlin Hawthorne

If two people in relative motion are going to get the same answer for the speed of the same beam of light, when by every ordinary expectation they shouldn't, then there's only one way out. They must disagree about the distance. Or about the time. Or both.

Tomlin Hawthorne

Everyone had assumed that a metre is a metre and a second is a second, for everybody. That time ticks along at one rate for the whole universe, like a great clock in the sky, and space is a fixed stage. Newton had said so explicitly. Nobody had ever thought of it as an assumption. It was just how things are.

Tomlin Hawthorne

Einstein said: that's the thing we have to give up. The speed of light is fixed. Space and time are what bend.

Tomlin Hawthorne

Next episode we'll see exactly how. I'll show you why a moving clock has to run slow, and you'll be able to see it for yourself, with nothing but a triangle.

Tomlin Hawthorne

The myth of the week is probably the most widespread misunderstanding of any scientific idea.

Tomlin Hawthorne

Einstein showed that everything is relative.

Tomlin Hawthorne

He showed almost the opposite. The whole theory rests on two things that are not relative at all. The laws of nature are the same for everyone. The speed of light is the same for everyone. Those are absolutes, and he held on to them so hard that everything else had to move.

Tomlin Hawthorne

He came to dislike the name relativity. He'd have preferred to call it the theory of invariants: the theory of what stays the same. Think how differently the twentieth century might have talked about it.

Tomlin Hawthorne

Because the name escaped. Within a few years people were saying that Einstein had proved there's no absolute truth, that it's all a matter of your point of view, in morals and in art as well as in physics. He hadn't. It has nothing to do with morals. If anything the lesson runs the other way: that beneath the things that vary from observer to observer, there's something that doesn't, and the job is to find it.

Tomlin Hawthorne

And the question to take with you.

Tomlin Hawthorne

Look at what he did. Everyone else was trying to fix the problem by adding something. A draggable ether. Shrinking rulers. Einstein fixed it by taking something away: an assumption about time so deep that nobody had noticed it was one.

Tomlin Hawthorne

What are the assumptions in your own field that are so basic nobody states them? The ones that aren't in the textbook because they're the paper the textbook is printed on? And how would you ever find them? Einstein found his, I think, because he had a habit of asking childish questions about adult things, and because he was sitting outside the profession, with nobody to tell him the question was naive.

Tomlin Hawthorne

Your challenge this week is a thought experiment. It's his.

Tomlin Hawthorne

You're holding a mirror at arm's length, looking at your own face. Now you start to move forward, faster and faster. Light has to leave your face, travel to the mirror, and come back.

Tomlin Hawthorne

Suppose you're moving at very nearly the speed of light. By the old way of thinking, the light from your face would struggle to get ahead of you. It would take longer and longer to reach the mirror. And at the speed of light itself, it would never get there. Your reflection would vanish.

Tomlin Hawthorne

So. Does it? If it does, you'd have a way to know you were moving, just by looking in a mirror, and Galileo's principle is dead. If it doesn't, then the light is still leaving your face at the speed of light relative to you, and something has to pay for that.

Tomlin Hawthorne

Decide which you'd rather give up. Einstein, at sixteen, was fairly sure he'd still see his face.

Tomlin Hawthorne

Next time, we find out what pays. Can two perfectly good clocks, both keeping perfect time, disagree? Yes. And one of the places it's happening is about twenty thousand kilometres above your head, right now, and your phone is correcting for it.