Episode 04 - Galileo, Inertia, and the Art of the Thought Experiment

Tomlin Hawthorne

You're holding a ball on a string, whirling it round your head in a circle, like a slingshot. At some point the string snaps. Which way does the ball go? Does it carry on curving for a bit, as though it remembers the circle? Does it fly straight outward, away from you? Or something else? Picture it and choose.

Tomlin Hawthorne

When researchers put questions like this to university students in the 1980s, a large share got it wrong. Including students who had passed physics. They gave the answer that a medieval scholar would have given, and I'd bet a fair number of you just did too. Today we find out why, and who fixed

Tomlin Hawthorne

it.Last time I left you with a cloud to weigh. If you took an ordinary fair-weather cloud to be about a kilometre across, a kilometre each way, that's a billion cubic metres. Half a gram of water in each. Five hundred tonnes. Five hundred tonnes. That's a fully loaded jumbo jet, give or take, hanging over the picnic. It stays up because it's spread out into droplets so tiny that the air holds them, the same way dust hangs in a sunbeam. It's the mouse from episode two again. Small things barely notice gravity. And your heart: around three billion beats. A few times the billion seconds we talked about. You've used a good number of them already, and I'm grateful you're spending some here. Today's question sounds like the dullest one in the series. What does a moving object do when you leave it alone? Let me introduce our man through the theatre, since that's where he'd have wanted to be introduced. Galileo Galilei was born in Pisa in 1564, the same year as Shakespeare. His father was a musician and a rather combative music theorist. Galileo himself played the lute, wrote literary criticism, drew well, and was, by every account, tremendous company and completely unable to leave an argument alone. He gave his opponents nicknames. He once wrote a satirical poem about the requirement that professors wear gowns. In 1632 he published the book that got him tried by the Inquisition. And I want to tell you about its form, because it's not what you'd expect. It's not a treatise. It's a play. Four days of conversation in a palace in Venice, among three characters. There's Salviati, who is brilliant and patient and says what Galileo thinks. There's Sagredo, an intelligent man of the world with no stake in the matter, who asks the questions you'd ask. And there's the third one, who defends the traditional view, the view of Aristotle and of the Church. He is earnest, and he is always one step behind. Galileo named him Simplicio. Now, Galileo's defence was that this was a reference to Simplicius, a respected ancient commentator. Which is true. It is also true that in Italian the name sounds exactly like "simpleton," and that Galileo had put one of the Pope's own favourite arguments into Simplicio's mouth, near the end, where nobody could miss it. The Pope had been his friend. This is, I think, the most expensive joke in the history of science. Galileo spent the last nine years of his life under house arrest. Brecht wrote a great play about all this, Life of Galileo, and it's worth knowing that he wrote it twice. In the first version, from the late 1930s, Galileo's recantation is cunning: he gives in so he can go on working in secret. Then came Hiroshima, and Brecht rewrote the ending. In the later version Galileo condemns himself. He had a chance to make science answer to the people, he says, and he handed it to the powerful instead. We'll come back to that in episode twenty-four, when it stops being about the seventeenth century. Aristotle taught two things about motion that everybody believed.

Tomlin Hawthorne

One: heavy things fall faster than light ones. A stone beats a feather. Obviously.

Tomlin Hawthorne

Two: a thing only keeps moving if something keeps pushing it. A cart stops when the horse stops. Obviously. You believed both of these as a child. Part of you believes them now. So let's watch what Galileo does to each. And notice that he uses no equipment at all. He does it by thinking, in a way that I'd say nobody had quite thought before. Take the first claim. Heavy falls faster. Galileo, speaking through Salviati, says: fine. Let's suppose that's true and see where it leads. Take a big heavy stone and a small light one. By your rule, the big one falls fast and the small one falls slowly. Now tie them together with a short cord and drop the pair. What happens? Well, the small stone wants to fall slowly. So it lags behind, and it tugs back on the big one, like a child being dragged along by a parent. The pair should fall slower than the big stone alone. But hang on. The two stones tied together make one object. And that object is heavier than the big stone was. So, by your rule, it should fall faster than the big stone alone. Slower and faster. Both. From the same assumption.

Tomlin Hawthorne

That can't be. So the assumption is false. The only way out is that the big stone and the small stone fall at the same rate, and then tying them together changes nothing, which is what you'd hope from a piece of string. I still find it startling. He hasn't dropped anything. There's no tower. The famous story about the Leaning Tower of Pisa was told by a devoted assistant decades later, and it may or may not have happened. He has shown that the old idea contradicts itself. It was never possible, and for two thousand years nobody had noticed. This is a thought experiment. It's one of the strangest tools in science and we'll meet it again and again. Einstein was the great master. You imagine a situation, carefully, and you find that your own beliefs won't fit inside it together. Now, your objection. The feather. A feather does fall slower than a stone. I've seen it. Yes. Because of the air. And Galileo said so. He predicted that in a place with no air, a feather and a lump of lead would fall side by side. He couldn't test it. But three hundred and thirty years later, somebody did. In August 1971, at the end of the Apollo 15 mission, the astronaut David Scott stood on the Moon in front of a television camera, holding a geological hammer in one hand and a falcon feather in the other. He let go of both. They fell together, slowly, because the Moon's gravity is weak, and landed in the dust at the same moment. And Scott said, more or less: how about that. Mr Galileo was correct. Please go and watch it. It's forty seconds long. It's the most expensive demonstration ever performed, and he had brought the feather specially. Now the second claim, which is the bigger one. Things stop unless you keep pushing. Here Galileo did do experiments, of a quiet kind. He rolled balls down ramps. Picture a ramp sloping down, then a flat bit, then a ramp sloping up, like a wide letter V with a flattened bottom. Let a ball go from a certain height on the left. It rolls down, across, and up the other side. How high does it get? Nearly as high as it started. Not quite, because of friction. But the smoother he made the ramp and the ball, the closer it came. He guessed that with no friction at all, it would reach exactly the height it started from. Now make the right-hand ramp less steep. The ball still climbs to the same height. But to get there it has to travel further along. Make it shallower still. Further again. Now comes the leap. Make the right-hand ramp completely flat. The ball is trying to get back to its starting height. It can never reach it. So how far does it roll?

Tomlin Hawthorne

Forever. It never stops. There's nothing to stop it. This is the principle of inertia, and it is exactly backwards from Aristotle and from common sense. Motion doesn't need a cause. A moving thing, left alone, keeps moving, in a straight line, at a steady speed, for ever. What needs a cause is a change: speeding up, slowing down, turning. The cart doesn't stop because the horse stopped pushing. It stops because the ground and the axles are pushing back. Friction isn't the absence of a force. Friction is a force. Aristotle had been describing a world where something is always interfering, and took the interference for the nature of things. I find that a rather moving kind of mistake. It's not a failure to look. It's that the truth was hidden by something so constant that nobody could see it as a separate thing. I'll leave you to consider whether your own field has an equivalent.

Tomlin Hawthorne

So: the ball on the string. The string snaps. There is now nothing pulling the ball toward the centre. So it does what any object does when left alone. It goes straight. Not outward, not along the curve. Straight ahead along the direction it was travelling at the instant of the break, at a tangent to the circle. Like mud leaving a bicycle tyre.

Tomlin Hawthorne

One more scene from the play, and it's my favourite. The great argument of the age was whether the Earth moves. Copernicus said it spins once a day and circles the Sun. And the objection to this was excellent. If the ground is rushing eastward at hundreds of miles an hour, then drop a stone from a tower and it should land far to the west, because the tower has moved on while the stone was in the air. Birds should be left behind. There should be a howling permanent wind. None of that happens. Therefore the Earth is still. It's a good argument. Simplicio makes it. And Salviati answers with a ship. Shut yourself up, he says, with a friend, in the main cabin below decks on some large ship. Bring some flies and butterflies. Bring a bowl with fish in it. Hang up a bottle that drips, drop by drop, into a narrow-necked jar beneath. With the ship at rest in harbour, watch carefully. The butterflies fly equally to all sides. The fish swim without preferring any direction. The drops fall into the jar. You jump, and you go as far forward as back. Now have the ship set sail, as fast as you like, so long as the motion is smooth and steady. And watch again. Nothing changes. The drops still fall into the jar and not behind it, though the ship moves on while they're in the air. The butterflies don't get pressed against the back wall. You can't jump further toward the stern.

Tomlin Hawthorne

You know this. You've poured a drink on an aeroplane at five hundred miles an hour and it went into the cup. And that answers Simplicio. The stone dropped from the tower was already moving east, along with the tower and the air and you. By inertia it keeps that motion as it falls. We are all below decks on the Earth, and that is why we can't feel it move. This idea has a name: the principle of relativity. Steady motion is undetectable from the inside, so there's no such thing as "really" at rest. It's from 1632. When Einstein arrives in episode twenty-one, he won't be overthrowing this. He'll be taking it more seriously than anyone ever had, and following it to the point where time itself comes apart.

Tomlin Hawthorne

The myth of the week is the one from the top of the episode, and it has a name: impetus. It's the feeling that when you throw something, you put a kind of push inside it, a stock of oomph, which then gradually runs out. That's why the ball slows and stops: it's used up its push. And it's why people expect the ball from the snapped string to keep curving. It's got some curve left in it. This was the best theory of the fourteenth century, and most of us reinvent it by the age of six, because it fits experience so well. It's still wrong. Nothing gets used up. The ball slows because the air and the ground act on it. Take those away and it would cross the galaxy. If you gave the medieval answer at the start, don't feel bad. You've spent your whole life at the bottom of an ocean of air on a sticky planet. You'd need to have grown up in space to find Galileo obvious. A question to take away. The argument with the two stones used no data whatsoever. It was pure thought. And yet it told us something true about real stones. How is that possible? If you can learn about the world by thinking, why do we need experiments? And if we need experiments, what exactly was the argument doing? You have cousins of this in your own world. The counterfactual in history: what if the wind had favoured the Armada? The hypothetical in law, or in ethics: suppose a runaway tram. Are those the same kind of thing as Galileo's stones? Do they tell us about the world, or only about our concepts? And your challenge. Thirty seconds, one book, one sheet of paper. First, hold the book in one hand and the flat sheet in the other, at the same height, and drop them together. Predict first. You know what'll happen. Now put the sheet flat on top of the book, so it's lying on the cover, not stuck down. Drop the book. Before you do it: predict. Does the paper stay on the book all the way down, or does it lift off and flutter behind? Then do it, and ask yourself what the book did for the paper. Next time, an apple, a plague, and the most audacious sentence ever written about the Moon: that it is falling, right now, and has been for four billion years, and keeps missing.