Episode 14 - The arrow of time

Tomlin Hawthorne

I'm going to describe two short films. Each lasts five seconds. And for each one, I'd like you to tell me whether I'm playing it forwards or backwards.

Tomlin Hawthorne

Film one. A green baize table. A white ball rolls in from the left, strikes a red ball, and stops. The red ball rolls off to the right.

Tomlin Hawthorne

Forwards or backwards?

Tomlin Hawthorne

Film two. A kitchen floor, with a mess of yolk and shell on it. The mess draws itself together, the shell closes round it, and a whole egg leaps up into a waiting hand.

Tomlin Hawthorne

Forwards or backwards?

Tomlin Hawthorne

The second one's backwards. You knew instantly. A child would know.

Tomlin Hawthorne

The first one, you can't tell. If I reversed it, you'd see a red ball roll in from the right, hit a white ball and stop, and the white one roll away. That's an ordinary shot.

Tomlin Hawthorne

So here's today's question. If the simple film has no direction and the egg film does, where does the direction of time come from? And why can you remember what you had for breakfast, and not what you'll have for dinner?

Tomlin Hawthorne

Last time, ten coins in a mug, shaken twenty times. If you did it, your list is mostly fours, fives and sixes, with a few threes and sevens, and no tens at all. You'd have to do it about a thousand times to expect a single ten. That heap in the middle is entropy: the summaries that can happen in the most ways are the ones you see.

Tomlin Hawthorne

And from that we got the Second Law. Left alone, things move toward the states that can happen in more ways. Today we ask what that has to do with time. I should say that this episode goes deeper than most. If it makes your head swim a little, that's the correct response. It does it to me.

Tomlin Hawthorne

Saint Augustine, in the eleventh book of his Confessions, stops in the middle of a meditation on Genesis and asks: what, then, is time? And he says something that everyone who has thought about this has wanted to quote ever since. If nobody asks me, I know. If I try to explain it to someone who asks, I don't.

Tomlin Hawthorne

And then he pushes on, and it gets worse. The past, he says, doesn't exist. It's gone. The future doesn't exist. It isn't here yet. And the present? The present has no length. The moment you try to catch it, it's already the past. So time is made of two things that aren't and one thing that has no size. And yet we measure it, we feel it pass, we say a sermon was long.

Tomlin Hawthorne

I think that's one of the most honest pages in philosophy. And the feeling he's circling is the one we need to explain. Time seems to flow. It seems to have a direction. The past is fixed and gone; the future is open and coming. That difference between the two directions is so basic to being alive that we hardly notice it's there.

Tomlin Hawthorne

Physics has its own word for it. In 1927 the English astronomer Arthur Eddington, who'll have a starring role when we get to Einstein, was giving a set of lectures in Edinburgh. He needed a name for this one-way quality of time, and he called it time's arrow. And he pointed out that space has nothing like it.

Tomlin Hawthorne

Nothing like it in space. That's a good way to feel the strangeness. In space you can go left or right, forward or back, and no direction is special. You can retrace your steps. In time you can't. There's one direction, and we're all being carried along it at one second per second, facing backwards, watching the past recede.

Tomlin Hawthorne

So where does the arrow come from?

Tomlin Hawthorne

The obvious place to look is the laws of physics. Surely somewhere in the rule book there's a line that says: time goes this way.

Tomlin Hawthorne

There isn't. And this is the first shock of the episode.

Tomlin Hawthorne

Go back to the billiard balls. Newton's laws govern that collision, and Newton's laws don't know which way time is running. If a film of something obeys Newton's laws, the reversed film obeys them too. Every bit as well.

Tomlin Hawthorne

And it's not only Newton. The laws of electricity and magnetism are the same. Einstein's relativity is the same. Quantum mechanics, in the way that matters here, is the same. There's a tiny wrinkle in the behaviour of some exotic particles, which I'll mention and set aside, because it has nothing to do with eggs.

Tomlin Hawthorne

At the level of the fundamental laws, there's no arrow. The rule book reads the same forwards and backwards. Take any process the laws allow, reverse the motion of every particle, and you get another process the laws allow.

Tomlin Hawthorne

So the laws permit the egg to unscramble. They permit the smashed glass to leap back on to the table. Every atom in that reversed film would be doing something perfectly legal.

Tomlin Hawthorne

And yet. One film you believe and one you don't.

Tomlin Hawthorne

You know the answer now, from last time. The difference isn't in the laws. It's in the counting. The unbroken egg is a state that can happen in relatively few ways. The mess on the floor can happen in vastly more. Going from few to many is overwhelmingly likely. Going from many to few would need a conspiracy of every molecule at once.

Tomlin Hawthorne

So here's the first conclusion, and I'd like to state it carefully. Every single thing that distinguishes the past from the future, everything that lets you tell a film is running backwards, is a case of entropy increasing.

Tomlin Hawthorne

Try it. Think of a process that only goes one way. Ice melting in a drink. Smoke spreading from a candle. A ball bouncing lower and lower. A person growing old. A sound dying away. In every case, something concentrated is spreading out. Energy, or matter, moving from the few-ways state to the many-ways state.

Tomlin Hawthorne

And think of the processes that look fine either way. A planet orbiting. A pendulum swinging in a vacuum. Two balls colliding. Those are the ones where entropy isn't changing.

Tomlin Hawthorne

The arrow of time is the Second Law. As far as anyone can tell, that's all it is.

Tomlin Hawthorne

But now we have to be careful, because there's a trap here, and Boltzmann himself was caught in it.

Tomlin Hawthorne

A colleague of his in Vienna, a man named Loschmidt, pointed it out, in a friendly way. He said: Ludwig, your argument is that there are more disordered states than ordered ones, so things tend to become disordered. Lovely. But your argument doesn't mention which direction in time you're going. It works just as well backwards.

Tomlin Hawthorne

Think about it. Take a half-melted ice cube in a glass. Boltzmann's counting says: there are far more ways for it to be more melted than less. So in the future, it'll probably be more melted. Correct.

Tomlin Hawthorne

But run the same logic toward the past. There are far more ways for it to have been more melted than less. So in the past, it was probably more melted too?

Tomlin Hawthorne

That says the ice cube most likely formed spontaneously, out of lukewarm water, a moment ago. Which is absurd. We know it used to be a bigger ice cube. Somebody took it out of a freezer.

Tomlin Hawthorne

So the counting argument, alone, isn't enough. It explains why entropy goes up toward the future. It doesn't explain why entropy doesn't also go up toward the past. To get the arrow, you need one more ingredient. You need to add a fact.

Tomlin Hawthorne

The fact is: entropy was lower before.

Tomlin Hawthorne

The ice cube melts toward the future because it started as a solid ice cube. It was in a special, few-ways state, and it's been unwinding ever since. The arrow doesn't come from the laws. It comes from the starting point.

Tomlin Hawthorne

So: why was there an ice cube? Because of a freezer, which was run by a power station, which burned coal. And the coal is ancient forest, stored sunlight, concentrated and tidy. And the Sun is a ball of hydrogen that's been slowly spreading its energy into space for five billion years. And the hydrogen came from...

Tomlin Hawthorne

You see where this is going. Every bit of order you trace back comes from some earlier, greater order. The ice cube borrows it from the freezer, the freezer from the coal, the coal from the Sun. Entropy today is low because yesterday it was lower. And the day before, lower still.

Tomlin Hawthorne

Follow that chain all the way back, and it ends in one place. The Big Bang. Nearly fourteen billion years ago, the universe began in a state of extraordinarily, almost unbelievably low entropy. And everything that has happened since, every star, every storm, every egg, every thought, has been that original order running down.

Tomlin Hawthorne

Philosophers have a name for this: the Past Hypothesis. It's the assumption that the universe started out in a very special state. Without it, none of the reasoning about time's arrow works. With it, everything does.

Tomlin Hawthorne

I want to show you how far this reaches, because it's easy to nod at and miss.

Tomlin Hawthorne

Why do you remember the past and not the future?

Tomlin Hawthorne

A memory is a record. And think about what a record is. A footprint on a beach, say. You see the footprint and conclude: somebody walked here. Why are you entitled to conclude that? The laws of physics would allow the sand grains to have jumped into that shape by chance. But that's fantastically unlikely. Far more likely that there was an earlier, more ordered state of affairs, a person with a foot, and the print is what it left.

Tomlin Hawthorne

But notice: that reasoning only works because you're assuming the past was more ordered than the present. If entropy were equally likely to have been higher in the past, the footprint would tell you nothing. It'd be just as likely to be a fluke.

Tomlin Hawthorne

So every record, every trace, every fossil, every photograph, every memory in your head, is only a record because of the low-entropy past. Records point one way in time because entropy does. There are no footprints from the future, for the same reason there are no unbroken eggs rising from the floor.

Tomlin Hawthorne

And it's the same with cause and effect. We feel that causes come before effects, that the past pushes the present. That lopsidedness isn't in the fundamental laws either. It's in the entropy gradient.

Tomlin Hawthorne

And the sense that the future is open and can be changed, while the past is closed.

Tomlin Hawthorne

So let me say it as plainly as I can. The reason you can remember this morning's breakfast, and not this evening's dinner, is connected, by an unbroken chain of reasoning, to the condition of the universe 13.8 billion years ago. The most intimate fact about your experience, that you live forwards, is a fact about cosmology.

Tomlin Hawthorne

I've known that for a long time and I still find it hard to hold in my head.

Tomlin Hawthorne

Now, an honest footnote, because a sharp listener will object.

Tomlin Hawthorne

The very early universe was a hot, smooth, almost perfectly uniform gas. Spread out evenly, same temperature everywhere. Didn't I say that's what high entropy looks like? That sounds like the heat death, not the beginning.

Tomlin Hawthorne

It's the right objection. The answer is gravity. For a gas in a box in your kitchen, spread-out is the many-ways state. But when gravity is in charge, as it is for a whole universe, it's the other way round. Gravity wants to clump things. A smooth, even gas is balanced on a knife edge. It has all its clumping still to do. So for the universe as a whole, smooth is the special state, and lumpy, stars and galaxies and black holes, is where it's heading. The early universe was like a pencil standing on its point.

Tomlin Hawthorne

And why did the universe begin that way?

Tomlin Hawthorne

Nobody knows.

Tomlin Hawthorne

That's not false modesty. It's one of the great open questions in physics, perhaps the greatest. There are proposals, and we'll look at one in episode forty-six. But the truthful position is that the arrow of time rests on a fact about the beginning of the universe that we can state and can't explain.

Tomlin Hawthorne

The myth of the week comes in two opposite flavours.

Tomlin Hawthorne

The first is that the direction of time must be written into the laws of nature. It's the natural assumption. It's wrong. The laws don't have a direction. The world does, because of how it started.

Tomlin Hawthorne

The second is the one you'll find in popular books with nebulae on the cover: that physics has shown time is an illusion. It hasn't. What physics has shown is narrower and stranger. The difference between past and future is real. It just isn't fundamental. It's like the difference between up and down. Up and down are perfectly real if you live on a planet. They aren't built into space. Anaximander saw that in episode one. Past and future may be the same kind of thing. Real for us, here, in a universe with a low-entropy beginning. And not built into time itself.

Tomlin Hawthorne

And the question to take away. It's Augustine's.

Tomlin Hawthorne

We've explained why time has a direction. We haven't explained why it seems to flow. Why there seems to be a moving present, a now, that slides along.

Tomlin Hawthorne

The physicist Carlo Rovelli thinks the flow is something we bring. That creatures like us, who store memories and make predictions, will inevitably experience a moving present, and that there's nothing in the world outside that corresponds to it. Others think that can't be the whole story, that the passing of time is the most undeniable thing we know, and a physics that leaves it out has left out something real.

Tomlin Hawthorne

You know Proust. For Proust the past isn't gone at all. It's all still there, stored, and a taste of cake dipped in tea can bring a whole lost world back entire. Is that closer to what the physics is telling us? That the past is as real as the present, and it's only our access to it that's so peculiar?

Tomlin Hawthorne

Your challenge. Two things.

Tomlin Hawthorne

One. Find six short video clips and watch each forwards and then reversed. Most phones will do it. A pendulum. A bouncing ball. Milk poured into tea. Someone walking. A wave on a beach. A spinning coin. Sort them into two piles: the ones where you can tell, and the ones where you can't. Then ask what every clip in the first pile has in common.

Tomlin Hawthorne

Two. A book. Alan Lightman's Einstein's Dreams. It's very short. It imagines thirty worlds, each with a different kind of time. One where time is a circle. One where it runs backwards. One where it sticks. It's a novel by a physicist, and it's the best thing I know for loosening your grip on the idea that time has to be the way it is.

Tomlin Hawthorne

Next time, the last episode of Part Three. A tiny imaginary creature, standing at a tiny door, who looked for over a century as though he could beat the Second Law with nothing but quick fingers. What finally stopped him wasn't energy. It was memory. And in working out why, we'll find out what information is, and take a guess at what life is.