Episode 26 - Black holes and ripples in spacetime

Tomlin Hawthorne

Suppose that, a moment from now, the Sun is replaced by a black hole. Same mass exactly. Just crushed down into a black hole, sitting where the Sun was.

Tomlin Hawthorne

What happens to the Earth?

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Most people say: we get sucked in.

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We don't. Nothing happens to the Earth's orbit. Nothing at all. We'd go on circling that spot, once a year, exactly as before. It would get very dark and very cold, and that would be a serious problem. But we wouldn't fall in, any more than we're falling into the Sun now.

Tomlin Hawthorne

A black hole isn't a cosmic plughole. From a distance, it's just a mass. It's what happens close up that's strange. Today we go close up. And then we'll listen to two of them collide.

Tomlin Hawthorne

Last time you drew a triangle on an orange with three right angles in it. Two hundred and seventy degrees, where Euclid allows only a hundred and eighty. That's how a creature living on a surface could find out the surface is curved, without ever stepping off it. And it's what we've done with spacetime.

Tomlin Hawthorne

We ended with Einstein's theory of gravity. Mass bends spacetime; things follow the straightest paths through the bend. This is the last episode of Part Five, and the question is the natural one. What happens when gravity wins completely?

Tomlin Hawthorne

Two stories to begin with. Both are about people who followed the mathematics somewhere nobody wanted to go.

Tomlin Hawthorne

The first. It's the winter of 1915, on the Russian front. Karl Schwarzschild is a German astronomer, forty-two, the director of an observatory. When the war broke out he volunteered, though he was over age. He's been calculating shell trajectories for the artillery.

Tomlin Hawthorne

In November, Einstein publishes his equations. They're fearsomely difficult. Einstein himself has only found approximate solutions and doubts an exact one is possible. A copy of the paper reaches Schwarzschild in the east. And within weeks, in between his duties, he's found one. The exact shape of spacetime around a single round mass, like a star. He writes it up and posts it to Einstein, with a note saying that, as you see, the war has been kind enough to let me take this walk in the land of your ideas, in spite of the heavy gunfire.

Tomlin Hawthorne

Einstein was amazed. He read the paper to the Prussian Academy himself.

Tomlin Hawthorne

Schwarzschild had by then developed a rare and agonising disease of the skin. He was sent home, and died in May 1916.

Tomlin Hawthorne

But there was something odd in his solution. If you took the mass and imagined it squeezed into a small enough ball, the mathematics went wild. At a certain distance from the centre, time seemed to stop. Everyone, including Schwarzschild and Einstein, took that as a curiosity. No real object could be that compressed.

Tomlin Hawthorne

The second story. The summer of 1930. A steamship is on its way from Bombay to England, and on board is a nineteen-year-old from Madras, Subrahmanyan Chandrasekhar, on his way to study at Cambridge. To pass the time, he's doing a calculation.

Tomlin Hawthorne

He's thinking about what happens to a star when it runs out of fuel. It was known that a dead star shrinks, under its own gravity, into a dense ball about the size of the Earth, called a white dwarf, and that it's held up at that size by a kind of pressure from its electrons. We'll meet that pressure in Part Six.

Tomlin Hawthorne

Chandrasekhar asks: what if the star is heavier? He puts relativity into the sums. And he finds that the electron pressure has a limit. If the dead star is more than about one and a half times the mass of the Sun, the pressure can't hold. Nothing stops the collapse. The star just keeps shrinking.

Tomlin Hawthorne

He spent four years making sure. In January 1935 he presented the result to the Royal Astronomical Society in London. And immediately afterwards, the most famous astronomer in the world got up to respond. It was Arthur Eddington. The hero of our last episode. The man who'd proved Einstein right.

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And Eddington tore it to pieces. He made jokes. He said the result was absurd, that the star would go on shrinking and shrinking until gravity was strong enough to hold in its own light, and that there should be a law of nature to prevent a star from behaving in this ridiculous way. The audience laughed. Chandrasekhar was twenty-four.

Tomlin Hawthorne

Eddington had no real argument. He just didn't like where it led. And such was his standing that for years nobody would publicly take the young man's side, though several physicists told him privately that he was right. Chandrasekhar left England, went to Chicago, changed fields, and didn't work on the problem again for decades.

Tomlin Hawthorne

He was right. He received the Nobel Prize for it in 1983. He'd waited forty-eight years. And he was always gracious about Eddington, which is more than I'd have managed.

Tomlin Hawthorne

So what is it that both of them had found?

Tomlin Hawthorne

Let's build one. To throw something off the Earth so that it never comes back, you have to throw it at eleven kilometres a second. That's called the escape velocity. Rockets have to reach it.

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Now squeeze the Earth. Same mass, smaller ball. You're standing on the surface, closer to the centre, where the bend in spacetime is steeper. The escape velocity goes up.

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Keep squeezing. Squeeze the entire Earth down to the size of a marble. At that point, the escape velocity at the surface reaches three hundred thousand kilometres a second. The speed of light.

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And nothing goes faster than light. So nothing gets out. Not a rocket, not a radio signal, not a ray of light. Whatever's inside is cut off from the rest of the universe for good.

Tomlin Hawthorne

That's a black hole. The name was popularised by John Wheeler in 1967. Before that they were called frozen stars, or completely collapsed objects, which hadn't caught on.

Tomlin Hawthorne

The boundary, the point of no return, is called the event horizon. And here's the first thing to get straight about it. It isn't a surface. There's nothing there. No wall, no membrane. It's a place, like the Arctic Circle is a place. A line on the map of spacetime. If you were falling into a really large black hole, you'd cross the horizon without noticing anything whatever. No jolt, no sign.

Tomlin Hawthorne

But you'd have crossed. And here's the best way I know to feel what that means. Outside a black hole, you can move about freely in space, but you're carried helplessly forward in time. You can't stop tomorrow from coming. Inside the horizon, the bending of spacetime is so extreme that those roles are, in a sense, exchanged. The direction toward the centre becomes like the direction toward the future. You can no more avoid the centre than you can avoid next Wednesday. It isn't that the pull is too strong to resist. It's that every possible path, every direction you could point a rocket, leads inward. Out isn't on the map any more.

Tomlin Hawthorne

Now the second strange thing, and it comes from episode twenty-two. Suppose I stay safely far away and watch you fall in. And you've kindly agreed to wave at me once a second.

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Remember that time runs slow near a mass. As you get closer to the horizon, I see your waves arriving further and further apart. One every two seconds. Every minute. Every year. The light from you gets stretched, redder and redder, dimmer and dimmer. And I never see you cross. From my point of view, you slow down, and fade, and freeze at the edge, for ever.

Tomlin Hawthorne

From your point of view, you sailed straight through in a perfectly ordinary few seconds.

Tomlin Hawthorne

Which of us is right? You know the answer by now. Both. Those are two honest accounts by two observers, and there's no third account that overrules them.

Tomlin Hawthorne

And at the centre? The equations say that everything that fell in is crushed to a point of no size and infinite density. That's called a singularity. Hardly any physicist believes it. When a theory gives you infinity as an answer, it's usually the theory telling you that it's been pushed beyond where it works. Something else must happen in there. We don't know what. I'll come back to that at the end.

Tomlin Hawthorne

One piece of vocabulary you'll have heard. Spaghettification. Near a small black hole, gravity is so much stronger at your feet than at your head that you'd be drawn out into a long thin string well before you reached the horizon. Physicists did choose that word. Near a very large black hole, oddly, it's gentler at the horizon, and you'd get in intact. There's a consolation.

Tomlin Hawthorne

For fifty years all that was mathematics. Einstein himself wrote a paper in 1939 arguing that such things couldn't form in the real world. That same year, Robert Oppenheimer, yes, him, published a calculation showing that a heavy enough star, when it dies, would collapse exactly this way. Then the war came and he had other things to do.

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What changed minds was evidence. Black holes can't be seen. But the things near them can.

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At the very centre of our own galaxy, twenty-six thousand light-years away, there's a patch of sky that astronomers have watched for thirty years. There are stars there, and they're moving. One of them goes round in an orbit that takes sixteen years, and at its closest approach it's travelling at three per cent of the speed of light. It, and all the others, are circling a single point. And at that point there's nothing to see.

Tomlin Hawthorne

From the orbits, you can weigh the thing they're going round, just as Newton would have. It has four million times the mass of the Sun, in a space smaller than our solar system, and it's dark. Two astronomers, Andrea Ghez and Reinhard Genzel, shared a Nobel Prize for that in 2020. There's a giant black hole at the middle of the Milky Way. There seems to be one at the middle of nearly every large galaxy.

Tomlin Hawthorne

And in April 2019, we got a picture. A collaboration called the Event Horizon Telescope linked radio dishes in Hawaii, Arizona, Mexico, Chile, Spain and at the South Pole, so that together they acted like a single telescope the size of the Earth. They recorded so much data that it couldn't be sent over the internet. It was flown to the processing centres on hard drives. The South Pole's had to wait for the end of the Antarctic winter.

Tomlin Hawthorne

They pointed it at a galaxy fifty-five million light-years away. And the image is a blurry, lopsided ring of orange light with a dark centre. The glow is hot gas swirling round at close to the speed of light. The dark middle is the shadow of a black hole six and a half billion times the mass of the Sun. It's the size and the shape that Einstein's equations said it would be.

Tomlin Hawthorne

A century of algebra, and there it was, on the front page of every newspaper in the world.

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Now for the other thing I promised. The sound.

Tomlin Hawthorne

If spacetime can be bent, it can be shaken. Einstein saw this in 1916. Any mass that's accelerating, two stars whirling round each other, say, should send out ripples in the fabric of space and time, spreading at the speed of light. As a ripple passes, it stretches space in one direction and squeezes it in the other, then the reverse.

Tomlin Hawthorne

He also worked out how big the effect would be, and concluded that it was so absurdly small that nobody would ever detect it. He even changed his mind, twenty years later, and wrote a paper saying the waves didn't exist. A reviewer found the mistake. Einstein was furious, and then quietly fixed it.

Tomlin Hawthorne

In the 1970s, a small group of physicists decided to try to catch one. Chief among them were Rainer Weiss at MIT, and Kip Thorne and Ronald Drever at Caltech. It took forty years and over a billion dollars, and for most of that time a good many of their colleagues thought it was hopeless.

Tomlin Hawthorne

What they built is called LIGO. There are two of them, one in Louisiana and one in Washington State, three thousand kilometres apart. Each is a giant letter L, with arms four kilometres long. A laser beam is split and sent down both arms, bounced off mirrors at the ends, and brought back together. You'll recognise it: it's Michelson and Morley's instrument, the one that failed to find the ether. If a gravitational wave passes, it makes one arm a tiny bit longer and the other a tiny bit shorter, and the returning beams slip out of step.

Tomlin Hawthorne

How tiny? The machine has to detect a change in the length of a four-kilometre arm of about one-thousandth of the width of a proton. That's like measuring the distance to the nearest star to within the width of a human hair. The mirrors have to be shielded from lorries on distant roads, from waves on the coast, from the jostling of the atoms in the mirrors themselves.

Tomlin Hawthorne

On the fourteenth of September, 2015, the upgraded detectors had just been switched on. They weren't yet officially running. Just before noon, central European time, a young researcher in Germany, monitoring the data, saw a signal come through. First in Louisiana. Seven thousandths of a second later, in Washington. It was so clean that his first thought was that someone was testing the system with a fake. He rang round. Nobody was.

Tomlin Hawthorne

The signal lasted a fifth of a second. It's a wave that rises in pitch and loudness and then stops. When you turn it into sound, it's a soft, rising whoop. A chirp.

Tomlin Hawthorne

Here's what it was. One point three billion years ago, when life on Earth was little more than single cells, in a galaxy far away, two black holes had been circling each other. One was about thirty-six times the mass of the Sun, the other about twenty-nine. They'd been spiralling inward for ages. In the last fraction of a second they were whirling round each other hundreds of times a second, at half the speed of light. And then they merged.

Tomlin Hawthorne

The black hole that was left had a mass of sixty-two Suns. Thirty-six plus twenty-nine is sixty-five. Three Suns' worth of mass was missing.

Tomlin Hawthorne

You know where it went. E equals m c squared. Three times the mass of the Sun was turned into pure energy, in the form of gravitational waves, in about a fifth of a second. For that instant, that one event was putting out more power than all the stars in the visible universe combined. And none of it was light. It was a silent shudder in the shape of space.

Tomlin Hawthorne

That shudder spread outward for one point three billion years. It passed through the Earth on a Monday morning, stretching and squeezing the whole planet, and you, by less than the width of an atomic nucleus. And two machines, switched on a few days earlier, felt it.

Tomlin Hawthorne

Weiss, Thorne, and the project's director, Barry Barish, got the Nobel Prize two years later. Hundreds of these events have been detected since.

Tomlin Hawthorne

I want to say why this matters so much. For the whole of human history, everything we've known about the universe beyond the Earth came to us as light. Galileo's telescope, radio dishes, X-ray satellites: it's all light, of one colour or another. We've been watching a silent film. In 2015, for the first time, we heard something. It's a new sense. And the first thing we heard was two black holes colliding, an event that gives off no light at all. Nobody knows what else we'll hear.

Tomlin Hawthorne

And the question to take away, and to end Part Five on.

Tomlin Hawthorne

At the centre of a black hole, general relativity predicts a singularity. Infinite density. And everybody agrees that this means the theory has broken. It's predicted its own failure.

Tomlin Hawthorne

I find that rather admirable in a theory. Most systems of thought don't come with a marked edge. But is it a weakness or a strength? When Newton's theory broke down, at Mercury, it didn't warn you. It just gave a slightly wrong number. Einstein's tells you exactly where it stops working. What would it be like if other disciplines had theories that did that?

Tomlin Hawthorne

And what does the breakdown tell us? It tells us that inside a black hole, where things are both very heavy and very small, you need gravity and the physics of the very small at the same time. And we don't have a theory that does both. That's the biggest unsolved problem in physics. It's episode forty-eight.

Tomlin Hawthorne

Your challenge is a pleasure. Search for the LIGO chirp. The laboratory has put the sound of that first detection online. It's less than a second long. Play it a few times. It's rather faint and low, and there's usually a second version shifted up in pitch so it's easier to hear.

Tomlin Hawthorne

And as you listen, remind yourself what it is. That's not an artist's impression. That's the actual motion of the mirrors, turned into sound. You're hearing space ring, from something that happened a billion years before the dinosaurs.

Tomlin Hawthorne

That's the end of Part Five. Space and time are one thing, and it bends, and it rings.

Tomlin Hawthorne

Next time we begin Part Six, and we go the other way, down, into the atom. I should warn you. Relativity is strange, but it's the kind of strange you can get used to. What's coming isn't. It starts with a cautious German professor, in the last weeks of the year 1900, doing something he later described as an act of desperation. And with a puzzle I left you: why can't a microwave oven give you a sunburn?