Gravitational Waves Prediction: The Follow-Up
An epic post on neutron stars, pulsars, King Kong, ice cream, and NANOGrav's stunning announcement that the International Pulsar Timing Array has finally found the Gravitational Wave Background
Well, I pressed send on my Gravitational Waves Predictions post on June 27th, at two minutes to midnight, the day before the big announcement on gravitational waves was due.
I said I would buy myself an ice cream if the results lined up with my predictions. So the big question is: DID I GET TO EAT THAT ICE CREAM???
Reader, I got to eat that ice cream.
SO, WHAT WERE THE RESULTS?
If you recall, my main prediction was that they would find a gravitational wave background signal, and that it would be stronger than they had expected.
(If you are new here, and have no idea what that last line means, no problem: My predictions post from June 27th gives loads of background on what gravitational waves are (spoiler alert: basically, ripples in spacetime itself, which, as they pass through the universe at the speed of light, pull everything ever-so-slightly apart, then push everything ever-so-slightly back together); how colliding supermassive black holes make REALLY BIG ripples in spacetime; why scientists have been using pulsars to look for them; what pulsars are; why all this matters; etc. Everything you need, to understand {or disagree with} and enjoy {or complain about} this extremely lengthy {but, I hope, juicy} piece. Just pop back and read it, then return here.)
Oh, I should also say, by the way, that my main prediction was not particularly brave or dramatic or way-out-there: a gravitational wave background was exactly what they’d been looking for, and they’d been hinting for weeks on social media that the results were going to be Really Fucking Interesting…
So, anyway, on the morning of June 28th, 2023, the American, European, Indian, Japanese, Australian, and Chinese teams of scientists who form the various groups behind the International Pulsar Timing Array simultaneously released five important new scientific papers – and that afternoon the largest and best-funded team behind the project, America’s NANOGrav, made the big announcement, live on Youtube.
Coordinated with this, a whole bunch of prepared pieces by science journalists, who’d seemingly been given early access to the results and sworn to secrecy, went live on all the major legacy media outlets – New York Times, Washington Post, Associated Press, Reuters, ABC, NPR, and on and on, the whole mainstream list.
This is an unusual level of pre-fight hype for a results release, but the results were, in fact, worth it: after fifteen years of gathering better and better data, they have finally detected the gravitational wave background, and the signal is indeed stronger than they expected.
I win.
Hand me the ice cream.
If you have only a casual interest in all this, no problem, you can leave now, and I’ll see you for the next post.
But if you’re interested, stick around, because I want to dive a little deeper (OK, a LOT deeper) into what a breakthrough result looks like, in an area like this, where we are working at the very outer limits of technology and science, attempting to detect the almost undetectable.
(Warning: This post ended up about 8,000 words long, so pace yourself. Maybe put on the kettle.)
WE HAVE BEEN TRYING TO DO THIS INCREDIBLY DIFFICULT THING SINCE WORLD WAR ONE
Einstein first predicted the existence of gravitational waves, back in 1916 – they are one of the weirder and more wonderful implications of General Relativity – but he went to his grave in 1955 certain that no one would ever be able to detect them, because the signals would be so ludicrously faint, and the technical challenges so absurdly difficult. (Of course, it didn’t help that Einstein didn’t really believe that black holes existed, even though his own theories predicted them.)
So, let’s return to that results announcement…
The press conference was a classic of its kind, firmly occupying that weird zone, which important astronomical results often occupy, where what happens is both earthshakingly significant, and also kind of drab and undramatic.
It’s kind of like having a friend dive down the back of the sofa, and stay there, rummaging around, for fifteen years, at the end of which he emerges screaming “HEY EVERYBODY! I FOUND IT! I FOUND IT!!!” And you try to see at what he is holding up, and it looks like an almost invisibly small fragment of a boiled sweet, covered in fluff. I mean, you can barely see it. “That’s it?” you say “After fifteen years?” And your friend is disgusted at your response and says “What do you mean, is that it? This changes everything!”, because, you know, it’s a magic sweet of some kind (OK, this metaphor is starting to fall apart, let’s wrap it up).
Anyway, likewise, with this. A team of the world’s best astronomers have finally emerged from down the back of the sofa.
Here’s what they found:
Yeah, it’s an earth-shaking discovery that looks like nothing at all. Look at those huge error bars.
AN ASIDE FOR BEGINNERS, ON ERROR BARS (SKIP THIS IF, IN AN IDYLLIC SUNLIT KITCHEN, AS A SMALL CHILD, YOUR SMILING GRANDMOTHER TAUGHT YOU ALL ABOUT ERROR BARS)
If you don't know what error bars are – hi mum! – they’re a way to illustrate the uncertainty of your result, when you are drawing a graph.
A quick example… If you were placing the top speeds of different things on a graph, then the top speed of, say, a rare form of giant squid who lives at the bottom of the deepest trench in the Atlantic Ocean would have pretty large error bars: we have very little data (we’ve hardly ever seen one), and so we just don’t know. But you have to put a dot on the graph! So we might put in a dot for 30 kilometres per hour (that’s our best guess, given the few glimpses we have had of the elusive squid, and what we know about other squid and their bursts of top speed), but we know that, realistically, it could be as low as 20 km/h, and it could be as high as 45 km/h: so we we would also put in a little horizontal bar (below the 30) at 20, and another little horizontal bar (above the 30) at 45. Those are the error bars: we think the real answer is likely to lie somewhere between them, between 20 and 45. How likely is likely? Let’s say, in this case, there’s a 95% chance. You write that on the graph too, to show that’s what the error bars indicate. (Of course, the real answer might even turn out to be 30! We could be lucky!)
Whereas the top speed of, say, light travelling through space, would have a firm confident dot, at 1,079,252,848.8 km/h (or if you prefer, the more familiar 299,792,458 meters per second), with basically no error bars, because we know the speed of light in a vacuum to an incredibly high degree of precision.
So the yellow dots here show their best, highly educated, guesses at the signals they have extracted from all the noise, but the real signals could be anywhere inside those error bars; anywhere between the short horizontal lines above and below each dot. More data should tighten up those bars over time, but right now (as you can see) there's a lot of uncertainty.
But but but… When you put together all those uncertain signals, even when you account for the wide margins of error… it forms the magical shape they were looking for; the shape that means it can only be the gravitational wave background. That shape is called the Hellings-Downs curve (after Ronald W. Hellings and George S. Downs, who predicted it in 1983).
BUT FIRST I WANT TO TALK ABOUT PULSARS, AGAIN
OK, before I dig into the Hellings-Downs curve (and how it provides extremely strong evidence that we have indeed found the gravitational wave background), I’m going to explain the whole process of how we use pulsars to measure gravitational waves – again, even though I kind of did so in the last post – because I think I can explain it slightly better this time. (I was in a rush, on deadline, last time.)
AN IRRITATED READER WITH A PHD IN ASTROPHYSICS WRITES:
Why do you explain all these basic things in such excruciating detail?
I REPLY:
Because neither of my parents – though intelligent, and interested in the world – were able to finish high school (thanks to one dead father, and one absent father, and thus the necessity of making a living while still basically kids). I want them to be able to understand this fascinating stuff, and right now nobody is explaining it in language they can understand. (Yes, they watch popular science programs, but such programs tend to assume at least a high-school science background –which is fair enough, as otherwise it would take the program forever to explain anything – and so my parents end up saying “It sounded very interesting but we didn’t understand it.”)
And it’s not just my parents. I want fourteen-year-old me to be able to understand it; I spent a lot of my childhood in the adult section of our local library, reading books by, and for, highly educated adults who assumed a basic level of knowledge I simply did not have at the time, and it was incredibly frustrating. I mean, I get it; those books were not written for me; but I don’t want young people (or people without a deep educational background) who read my work to suffer that frustration. These, by the way are a typical couple of lines from the NANOGrav paper I’m trying to explain:
"A frequentist test statistic built directly as a weighted sum of interpulsar correlations yields p = 5 × 10−5 to 1.9 × 10−4 (≈3.5σ–4σ). Assuming a fiducial f−2/3 characteristic strain spectrum, as appropriate for an ensemble of binary supermassive black hole inspirals, the strain amplitude is ${2.4}_{-0.6}^{+0.7}\times {10}^{-15}$ (median + 90% credible interval) at a reference frequency of 1 yr−1.”
Again, I get it, it’s a scientific paper, they are writing for their peers, using specialised technical language that is perfectly well understood by those peers – but people out in the world without PhDs in astrophysics need to know this stuff too. It contains important basic truths about our universe. (All of space-time wobbles like jelly! Or Jell-O, if you are an American.) And most coverage of this extremely important paper, for a general audience, in newspapers like the New York Times, has only a thousand or so words to give the full background, explain all the results, and deliver lots of quotes from the scientists involved. It must as a consequence, understandably, give a rather shallow level of explanation. Stuff gets skimped on. Here’s the New York Times, for example, explaining pulsars in their coverage of the announcement:
“Pulsars act like cosmic clocks, emitting beams of radio waves that can be periodically measured on Earth.”
And that’s basically it. I mean, it’s true, but you can’t really see a pulsar, or how intensely weird it is (or how astounding it is that we can now extract profound information from one), in your head, after reading that line. And it’s a thrill, to finally see a pulsar in your head.
My posts end up 5,000 words long, 6,000 words long, 7,000 words long, because I want to go one level deeper. Help you to see reality more clearly. To get you to that thrill-point. (And if you know all this shit already, that’s fine; just skip it.)
LET’S START AGAIN: PULSARS!
So, a pulsar is a very special kind of neutron star…
NO, WAIT, LET’S START EVEN EARLIER: NEUTRON STARS!
OK. Remember, the reason stars are big and fluffy and relatively stable, is because two forces are in balance: the gravitational pressure that is pulling everything in towards the centre, and the radiation pressure (from the fusion of elements, under that gravitational pressure, at their core) that is pushing everything out from the centre.
A neutron star is formed when a star larger than our sun (but not TOO much larger) finally runs out of that fuel. Without fuel to cause fusion to generate radiation to push against gravity, gravity wins – pretty abruptly – and it collapses, very fast. And keeps on collapsing: there is nothing to stop it, at this point.
Its actual atoms pancake under the incredible pressure of the collapse, with some (negative) electrons forced in so close to (positive) protons that they merge, to become (neutral) neutrons (this also creates a neutrino, which you can immediately forget about, as it simply whizzes off into the wild black yonder, carrying away some excess energy). So a neutron star is an incredibly small, smooth, dense, collapsed star, that was once larger than our sun, but is now made up mostly of neutrons, all jammed together, with no gaps, until the whole star takes up less space than… I’m not going to say Manhattan again. Fuck Manhattan. Everybody always says Manhattan. Grrrrrrrrr.
A GRUMPY ASIDE ABOUT POPULAR SCIENCE WRITING
One of the things that makes reading most popular science writing about the cosmos so infuriatingly dull is that most popular science writers just keep recycling the same few visual aids. You-could-fit-a-neutron-star-into-Manhattan. A-teaspoon-of-neutron-star-would-weigh-the-same-as-Mount-Everest. Only a few writers, like Tim Urban of Wait But Why?, bother to come up with fresh ones…
Also! (Now that I think about this further, about why I am reluctant to use Manhattan here…) God damn it! Likening the size of a neutron star to Manhattan – when you are trying to get people to see how absurdly small a neutron star is – is lousy writing, because we generally think of Manhattan as LARGE, not small; for most normal people, it is filed away in the part of our brains marked “BIG FUCKERS”.
Some of this is straightforwardly physical: if you are in Manhattan, you are overwhelmed by noise, by people; you are staring up all the time, at very large numbers of the biggest buildings you have ever seen (assuming you haven’t been to China, or Dubai); the roads are ridiculously wide and busy, Central Park is impressively vast, you are blown away by the scale of everything.
Plus, it’s hard to separate it out mentally from New York City as a whole, a city of eight million people, in a vast metropolitan area of 20 million people that sprawls across the state borders into New Jersey, western Connecticut and northeastern Pennsylvania. It doesn’t matter that you might, intellectually, know that Manhattan is simply an island, with an area of 59 square kilometres, which is not a lot; all the emotions we feel about Manhattan are forms of AWE – or, sure, revulsion, or anxiety, or glee, or fear – but whatever they are, they are mostly sparked by its SCALE. All the IMAGES we associate with Manhattan are BIG, often EPIC: it’s the fall of the Twin Towers; it’s Spiderman swinging for miles along skyscraper canyons; it’s King Kong climbing the Empire State Building. King Kong is dwarfed by Manhattan! And when the most ambitious, epic, sprawling scientific project of all time was getting a code name (a project so BIG Christopher Nolan could make a $100,000,000 movie about it eighty years later, and find a huge audience for it), they called it the Manhattan Project.
All of which means Manhattan is a TERRIBLE choice when you want to summon an image of smallness in somebody’s mind. It makes mathematical/logical sense, but it doesn’t make human/emotional sense – and you can communicate far more clearly if you can line up your reader’s logical and emotional responses so that they both point in the same direction.
I HATE SCIENCE WRITERS THEY DON’T UNDERSTAND HOW PEOPLE THINK
OK, yeah, I have convinced myself. We need a new way to visualise the size of neutron stars. Let me do some quick research…
(Disappears. Hurries back.)
Anchorage! Capital city of America’s least-densely populated state, Alaska! Population of the urban area 290,000! Where my wonderful (Alaskan) wife
went to high school! Nobody files Anchorage in the “BIG FUCKERS” section of their brain. (Plus, Anchorage (small!) is helpfully set against the vastness of Alaska (BIG!), which reinforces Anchorages’s smallness in our minds…)Let me double-check…
Yes, the developed urban area of Anchorage is roughly 32 kilometers from east to west, and about 21 kilometers from north to south. Which is larger than the 20 kilometer diameter of a typical neutron star, so you could easily fit a neutron star into Anchorage.
Alternatively, you could fit fourteen neutron stars into the Anchorage metropolitan area (which includes Anchorage and the neighbouring Matanuska-Susitna Borough, and has an area of 1,706 square miles, or 4,420 square kilometres). Fourteen! Every member of the Anchorage Seawolves men’s ice hockey team actually on the ice (six), plus the opposition players on the ice (six), plus the referee (one) could bring their own neutron star to a game at the cosy little Chuck Homan Ice Rink, and park those thirteen neutron stars in the Anchorage metropolitan area… and still have room for another neutron star.
Now we’re getting somewhere. Move over, Manhattan, Anchorage is the new unit of comparison for neutron stars. Neutron stars are small. Like Anchorage. (Not fucking Manhattan.)
END OF GRUMPY ASIDE ABOUT POPULAR SCIENCE WRITING, AND THE CORRECT UNIT OF SIZE FOR VISUALISING NEUTRON STARS
OK, where were we?
Yes. Neutron stars are small, and dense.
And weirdly smooth, for a star.
I know this post is already getting long, but I have to riff on this, sorry. The smooth thing. I want you to see it in your head. I want you to feel it with your fingertips.
AN ENTHUSIASTIC ASIDE ABOUT HOW SMOOOOOOOOOOOOOOOOOTH NEUTRON STARS ARE…
I read about neutron stars all the time, and yet it is almost never mentioned in those pieces that their surface is essentially smoother than glass.
Yeah. Rub the screen of your phone, now. Really feel how absurdly, silkily smooth it is. A neutron star is smoother than that.
Why? Well, let’s start with a normal star, so we’ll have something to compare a neutron star to. The gravity on the surface of our own big fuzzy star, the sun, is only 28 times higher than the gravity on the surface of the Earth – even though our sun contains 333,000 times more mass than the Earth. How come? Because our sun, though ridiculously big (you could pack roughly a million Earths into it), is not very dense. It’s mostly made of two very light gases, hydrogen and helium (in their extremely hot, and thus even less dense, plasma form), which means it’s made mostly of space. (The average cubic meter of the Earth contains four times more matter, and thus mass, than does the average cubic meter of the sun.) So all that matter in the sun is reeeaaaalllly spread out: as a result, the sun has a surface that is pretty far from its centre, which means the gravity drops off a lot. (Even if you are standing on the surface of the sun, most of the sun’s matter isn’t NEAR you – the centre of the sun is 696,000 kilometers away, which is nearly twice the distance from the Earth to the Moon – so it can’t pull too hard on you.)
But a neutron star, having packed all the matter of a star twice as massive as the sun into a space as small as… well, you know… has a gravitational field that is off the scale. (Remember, it’s getting very close to the gravitational field strength of a black hole. If this star was any more massive, it would BE a black hole.) If you could, somehow, stand on the surface of a neutron star, you would be standing EXTREMELY CLOSE TO ALL OF THE MATTER IN THAT NEUTRON STAR. So the gravity on the surface of an average neutron star is, very roughly, a couple of hundred billion times stronger than on the surface of the Earth, and it pulls everything as far down as it can go, and spreads it all out, until everything is as flat as it can possibly get. If you managed to stand on a weighing scales on the surface of a neutron star, it would, very briefly, show you that you now weighed over a hundred times more than every single person on earth put together.
And then the neutron star’s gravity would smash apart every feeble chemical bond in every molecule in your body, and pull every one of your atoms individually down to the star’s surface extremely fast, and quite possibly crush the protons and electrons together so tightly they too would convert into neutrons, and smear those neutrons one deep all over the incredibly tight, dense surface of the star until it was perfectly smooth again.
It’s not TOTALLY smooth; they think that, due to its huge electromagnetic field, it probably has some mountains. But the highest mountains on the surface of a neutron star are only, at maximum, a couple of millimeters tall.
Millimeters.
(In fact, the very latest research claims that even the tallest mountains might only be fractions of a millimeter tall…)
OK, end of aside on the smoothness of neutron stars.
More importantly for our story, some of these absurdly tiny, dense, smooth, neutron stars, once they have collapsed (from a size larger than our sun to a size smaller than Anchorage!), end up spinning at hundreds or even thousands of times a second. (There is a complicated subplot here, about binary stars – two stars that orbit each other, very common in our universe – and how after the first star blows up, collapses, and becomes a neutron star, the surviving normal star can feed gas to the spinning neutron star, helping it to spin up faster and faster over time, which is why the fastest ones spin so fast, but this is already too long and detailed, so let’s leave all that out. Forget I said anything.)
Basically, neutron stars spin so fast because they have to conserve the entire original angular momentum – the amount of spin – that was previously found in a star larger than our sun. (Plus, sometimes, a whole bunch more spin from the gas from a neighbouring star they may have gulped down since.) That absolutely demented rate of spin, given they still contain some charged particles, means they generate an absolutely EPIC magnetic field. How epic? At least a hundred million times stronger than the Earth’s magnetic field, and potentially faaaaaar more; in the case of the monstrous neutron stars called magnetars, a trillion times stronger than the earth’s magnetic field. That kind of field can deform nearby atoms into long, thin cylinders – a hydrogen atom can be squeezed down to something 200 times narrower than its normal diameter… but let’s not go there, it’s a whole other post…
So, that epic magnetic field pulls some of the few remaining electrons etc free of the surface of the neutron star, or rips them from nearby gas, accelerates them to nearly light speed, and slams them back into the star’s magnetic polar cap…
WAIT, WHAT’S A POLAR CAP?
OK, you know how, with a bar magnet, all the magnetic field lines emerge from one end (one pole) of the magnet, swoop out and around, and reenter at the other end (other pole) of the magnet? Well, the magnetic field of a pulsar does the same. And the “polar cap” is the area where all the magnetic field lines touch the surface of the star – an area that, in a rapidly spinning neutron star, can be just a few hundred meters, or less, across. (The faster the spin, the tighter the field lines at the pole, and the smaller the magnetic polar cap.)
So you have COSMIC LEVELS OF ENERGY, tightened up by the magnetic field lines, focused to an outrageous density, and slammed at close to the speed of light into this absurdly small, human-scale area, like some demented special effect in a Marvel movie. It’s Ragnarök in a parking lot.
That releases a lot of energy, which has to GO somewhere, so such stars constantly emit enormously bright, powerful jets of energy from their magnetic poles as they spin, directed (again) into a tight beam by the magnetic field.
And if the axis of their magnetic field is offset from their axis of rotation (that is, if their magnetic North Pole – their Ragnarök parking lot – isn’t located at their demure, geographical, this-is-the-point-I-spin-around North Pole), then that beam of energy whips around like the rotating light on a police car, but waaaay faster.
And if that beam of light happens to shine in the direction of Earth at any point, as it whizzes around… we can see it (when the light eventually arrives), as a pulse of light, every time it whips past us – hundreds of times a second.
That’s a millisecond pulsar.
So how can we use that to measure gravitational waves?
Because that pulse is so incredibly regular, that, back here on Earth (as gravitational waves move through the pulsar and then us), we can actually detect these slight variations, these slight delays and speedings up, as the spacetime between us and the pulsar stretches and contracts.
So, to sum up: a pulsar can act as an incredibly accurate clock – one that seems to speed up and slow down, as it moves (fractionally) towards us and (fractionally) away from us, when passing gravitational waves stretch the spacetime between us. And that’s how we measure gravitational waves.
I know, I’m over-explaining this, and repeating some of what I said in my last post; let’s move on. (But it’s so INTERESTING! Plus, I want everyone to be able to see this clearly in their heads and understand it, not just take it on faith.)
So what are we measuring here, on this graph? (Which I’m going to paste in again, because you’ve probably forgotten it by now.)
THAT GRAPH AGAIN
We are measuring those very slight variations in the time it takes a beam of light to reach us from an incredibly rapidly flashing millisecond pulsar. In fact, we are measuring roughly 68 different millisecond pulsars (they add more at intervals, so this figure is a moving target) – 68 different weird, dense, rapidly spinning stars (each just the size of Anchorage! And smoother than glass! With mountains on their surface only millimetres high! Maybe less!) Though mostly located relatively nearby, in our own local Milky Way galaxy, these millisecond pulsars are spread all across the sky. And each of them has a characteristic, highly regular (very fast) speed at which it flashes.
BUT THERE AREN’T 68 DOTS ON THE GRAPH
I know. That’s because those pulsars have been organised into groups, or bins, based on how far apart they are from each other in the sky. (Marked “Pulsar Sky Separation (degrees)” on the graph.) Imagine the sky divided into slices, like a pizza. There’s one dot per slice of sky; that is, each dot represents the bin of pulsars found in that slice of sky, all averaged out.
If you are looking straight ahead at the first bin of pulsars – that is, at all the pulsars in the first slice of sky – then the pulsars in the second bin (the second slice of sky) are on average, whatever, ten or fifteen degrees away. (Too tired to work it out exactly; I’m doing a last round of proof-reading/fact-checking and I’m knackered… This post, much as I love it, has now taken a month and I just want to get it out.)
Remember, a millisecond pulsar should pulse EXTREMELY regularly and reliably. (Momentum is always conserved, so a spinning star that dense and massive can’t just speed up and slow down.) So those slight variations mean that the pulsar that you are looking at, directly in front of you, is probably being wobbled by gravitational waves.
That is, the distance between you and the pulsar is being expanded and contracted, very slightly, by many incredibly faint gravitational waves coming from all directions, rippling through spacetime. The expansion of the spacetime between you and the pulsar delays the arrival of the pulse of light from the pulsar (because it now has slightly further to travel). The contraction of the spacetime between you and the pulsar speeds up the arrival of the pulse of light from the pulsar (because it now has less far to travel). But the distance, from crest to trough, of the waves we are looking for, is measured in light years; it’s a hell of a distance, akin to the distance between our sun and the nearest few stars. And, as gravitational waves travel at the speed of light, that means each wave takes several years to arrive. Which means you have to measure those pulsars for years before you can be sure you have detected a signal.
So we’re not measuring the waves directly, but rather their effect on the rapidly blinking light from the millisecond pulsars. Their effect over many many years.
But it’s a small effect – it’s changing the distance to the pulsar by literally one in a quadrillion, which is one in a million billion, or if you like numbers, 1 in 1,000,000,000,000,000; which adds up to just a few meters per lightyear. Plus – and this creates a huge detection problem – other things can affect that light beam as it travels to Earth: the pulsar might wobble very slightly (those pesky mountains!); the light might pass through clouds of gas, or the solar wind; and so on. Those things all mess with the lightbeam too, and create noise that can be a thousand times louder than the signal we are looking for.
Which brings us (at last) to the extremely cool thing about gravitational waves, that allows us to detect them, to tell them apart from all the other things that might affect the light: Gravitational waves have what is called, mathematically, a "quadrupole" nature.
AN IRRITATED NORMAL PERSON WRITES:
What? Do you think I have a PhD in cosmology or what?
I REPLY:
Jesus, give me just one second dad, I’m going to explain. Quadrupole; four poles. Which basically means they can’t just change things north-to-south, without also changing things east-to-west.
This means that as they streeeeeetch spacetime longer in the north-south direction, they are simultaneously squeezing spacetime shorter in the east-west direction.
This is a real bastard to visualise in three dimensions, so let’s cheat, and visualise it, simplified, in two dimensions. Get out the trusty rubber sheet…
Imagine an area of spacetime as a square rubber sheet: write “north” “south” “east” and “west” on the respective edges. Now let’s send a gravitational wave through it, that pulls north and south apart: simultaneously, east and west will move closer together. That is, to get longer north-south, our rubbery sheet of spacetime must simultaneously get shorter east-west.
That means that a gravitational wave, as it moves, waves in two different directions at once, and they are, as a mathematician would put it, anti-correlated.
Here’s a description in fairly mathematical language (with notes):
As you increase the angular separation from the first pulsar (that is, as you move your eye, or telescope, across the sky, away from that first pulsar, to sample another pulsar, and another, and another), the signal you get from those other pulsars becomes less and less correlated with the original signal (that is, stretches in the spacetime you are observing start to become squeezes), until by the time you are pointed at ninety degrees to the first pulsar, the signal is anti-correlated. (That is, by the time you’ve moved 90 degrees, maximum north-south stretch has become maximum east-west squeeze – or vice versa.)
That’s the bit on the graph where the curve falls BELOW the line.
Which means that, as signals arrive late from any pulsars directly in front of you, they arrive early from any pulsars off to either side of you. And as they begin to arrive early from the pulsars in front of you, they start to arrive late from the pulsars to your left and right.
Then, though, as you continue to swing further across the sky (starting to turn your back on the original pulsar), the signals you detect start to correlate more and more with the original pulsar signal again, until by the time you have your back fully to the original pulsar, they are strongly correlated again (but at half the intensity – see next sentence for why), because you are looking in the stretching, north-south direction again.
However, as the two pulsars are now far apart from each other, and positioned in opposite directions from you-the-observer, the exact waves they are experiencing (from all the random gravitational waves sloshing about the universe) only overlap half as much as would those experienced by two pulsars right beside each other, right in front of you. (The math on this is kind of horrible, but if you want to wade deep into the swamp, here’s a great paper on it.)
But here’s the big, fat, juicy, luscious, important thing: only a gravitational wave background signal can give you that odd curve in the results.
They’ve found it.
THE DIFFERENCE BETWEEN “STRONGER THAN EXPECTED” AND “STRONG”
The signal they have detected is stronger than they expected; but that doesn’t mean it’s strong. (Similarly, if you built a sensitive listening device in your bedroom that, to your surprise, managed to pick up the sound of a feather falling to the ground on the far side of the world, the signal you received might be LOUDER than you expected, but it still wouldn’t be LOUD.)
Indeed, when I say “They have finally detected it”, healthy, red-blooded, meat-eating scientists swoon to the floor and have to be brought back to consciousness with smelling salts, AND RIGHTLY SO, because I am using the sloppy, unscientific language of a normal human being, like the barbarian outsider that I am: it’s more scientifically accurate to say that they have found evidence for the existence of the gravitational wave background, significant to 3σ (pronounced 3 sigma); which means there is roughly a three-in-a-thousand chance that randomness could produce this result, by mistake, with no gravitational waves involved. (In fact this result is a little better than 3 sigma, and probably has roughly a one-in-a-thousand times chance it might have happened randomly.) The informal requirement for proof in physics, where you can say, “yep, we have detected it, now give us our ice creams” without a ton of qualifiers, is usually five sigma (5σ), which would mean the chance of random bullshit generating this result would be roughly one in three and a half million.
And scientists are not being prissy when they urge this level of caution: we’re operating right at the edge of the possible here. Get anything wrong, at any stage, when what you are looking for is already so faint and hard to find, and you can generate a false positive that could throw the whole field off track. (When looking for something this weak, it’s surprisingly easy to accidentally leak some fake signal into the noise. The LIGO gravitational wave detector in Louisiana is so sensitive that it has to be protected from alligators bumping into the outside of the building.)
Plus, the whole field is traumatised by the painful mistakes made by earlier teams of researchers in this area. Particularly painful was the excited announcement, made in March 2014, by the team operating the BICEP2 radio telescope at the South Pole. They thought they had found unmistakable evidence of huge, extremely early and thus extremely ancient, gravitational waves – traces of evidence captured in swirls of polarised light from the Cosmic Microwave Background Radiation.
This was Really Big News; such huge gravitational waves, so early in the life of the universe, would, as a bonus (if they existed), provide strong evidence in favour of Cosmic Inflation. Cosmic Inflation was (and is) the extremely popular but unproven theory that our universe expanded with incredible rapidity to an astonishing size in its earliest moments, and then slowed down considerably. To discover gravitational waves AND prove Cosmic Inflation would pretty much guarantee the team a Nobel Prize…
OUCH
But it turned out that the swirls of polarised light they had detected in the Cosmic Microwave Background Radiation hadn’t been bent out of shape by gravitational waves at the dawn of time. Instead, some of the Cosmic Microwave Background Radiation was being polarised slightly, at the last moment, as it passed through dust in our own Milky Way galaxy on its way to our telescopes.
They hadn’t found the secrets of the birth of the universe; they had found some dust.
They had to withdraw the claim, which was finally put out of its misery by an article in Nature on January 30th 2015, brutally titled “Gravitational waves discovery now officially dead”.
How traumatising was that? So traumatising that the final question the NANOGrav scientists were asked, in the otherwise relaxed and celebratory Q&A after the announcement, was:
“How do we know that this won’t be a BICEP2 type result?”
A jolt of shocked, nervous laughter shook the room; someone had voiced everyone’s secret fear out loud!
So, science is human, and human beings sometimes make mistakes based on faulty models.
But this result looks solid. Dr. Maura McLaughlin (the NANOGrav Physics Frontiers Center Co-Director) gave a very firm reply.
“Of course this is something that we have thought very long and very hard about. We do not want to be another BICEP 2… And for those folks at home, this was an experiment that announced a big discovery, and it ended up not being… real. We of course do not want to be in that position. We are very confident we are not going to go down that path.”
She is right. This is the real thing. The fact that it fits the Hellings-Downs curve is very, very positive. Plus, in general, it refines and improves on earlier, mushier signals that pointed in the same direction: it’s always good, with this kind of patient, multi-year search, if your result slowly emerges, with more and more clarity, from a huge number of observations, rather than appearing abruptly – which might just be due to one bad batch of data, or some freak event disturbing the equipment. (Goddamn space alligators.) And, even more reassuring – the same faint Hellings-Downs curve is now starting to appear (though even fainter, so far, than the NANOGrav signal) in entirely separate sets of data gathered from pulsars by the big joint European/Indian team, by the Chinese team, and by the Australian team.
But here we get to something which I find incredibly moving.
BUILDING A CATHEDRAL
To get to that three sigma result, that faintest of strong signals, required 15 years of observations, of more and more – eventually 68 or so – different pulsars, using, at various times, almost all of the world’s largest and most sensitive radio telescopes. Which meant that any single given observation of any given pulsar, or handful of pulsars, from any given telescope, on any given night, was not going to find anything. And they all knew that. All they could possibly do was add a single data point to a pile that others would add to, night after night, year after year… until, 15 years later, the data points were so numerous that a pattern started to emerge.
And that pattern, announced last month, is just the first, the smallest, the faintest evidence of something. It will take many more years of staring up at those spinning dots in the distant darkness to get a real picture, with details.
It is the data-collection equivalent of building a cathedral. Each stone carved is just another stone. But your work, your life, has meaning, because it is part of a greater project, aimed at heaven.
In one important respect, though, the data-collection of the International Pulsar Timing Array differs fundamentally from building a cathedral.
Cathedral building is a timeless project: there is a faith in the terrible beauty of the status quo. On the first day of construction, a mason strikes a chisel with a hammer, to remove a flake of stone, and the work has begun; two centuries later, his great-great-grandson strikes a chisel with a hammer, to remove a flake of stone, and the work is done.
BUILDING AN INTERNATIONAL PULSAR TIMING ARRAY
There is, instead, a faith in progress, a belief in the beauty of change, built into the story of the International Pulsar Timing Array. A faith in the ingenuity of the human mind, a faith in technology – our technology, for technology is our will, our desire, made manifest in matter. A generation of young scientists, like Chiara Mingarelli, and Stephen Taylor, and Michael Lam, and Thankful Cromartie, and Luke Kelley, and yes, Maura McLaughlin, began this quest for knowledge knowing their knowledge was inadequate, knowing their tools were inadequate, that they were inadequate: but trusting, having faith, that they could gain new knowledge on the journey, build new technologies – things never seen before on this earth – on the way to their goal.
And so, to get to this point, a generation of scientists spent years building earlier gravitational detectors that they knew in advance would not be sensitive enough to pick up anything; but they did it anyway, because building such inadequate detectors was the only way to move the science forward; to learn the necessary lessons; so that one day adequate detectors could be built.
Yes, that selfless devotion is indeed reminiscent of the cathedral builders of the Middle Ages.
A CYNIC WRITES:
Maybe they moved into a field that was hopelessly far away from getting any results because the existing successful fields were already too crowded. So it was simply a career move – just a longterm one.
Well, yes, a lot of the scientists involved would say that they chose the field because the existing fields were too crowded. Chiara Mingarelli says she moved out of LIGO (which measures the short, a-few-kilometer-long, gravitational waves made by small black hole mergers) after two years because it felt like mature science, and she wanted to make a breakthrough of her own, so she got involved with the International Pulsar Timing Array (which was hoping to measure the deeper, slower gravitational waves, many light-years long, made by the mergers of supermassive black holes). But isn’t that heroic? To throw yourself into the void, and trust that you will be able to come up with the designs, and build the machines, and write the software, and find the data, that will generate a whole new field of knowledge? To risk it all on a bet on yourself, and your friends? Isn’t that humanity at its best; its most hardworking, its most cooperative, its most optimistic?
There are hints of this everyday miracle – the miracle of making new things happen that lies at the heart of this kind of science – buried in the dry language of the press release:
“Initially, pulsar instrumentation was not precise enough to achieve the sensitivity needed for this experiment. The team worked to develop next-generation instrumentation for both the Arecibo and Green Bank telescopes. They scoured known pulsars to find those precise enough to enable the search for low-frequency gravitational waves and added them to the pulsar timing array. In parallel, there were advances in theory and breakthroughs in data-analysis techniques that are tuned and optimized for modern computing architectures.”
In other words, there were many years of struggle, many years where nothing was discovered, nothing could be discovered, but they worked on, they worked on.
I bow my head before such selfless sacrifice. There is a kind of nobility in that kind of science – a personal sacrifice made for the collective dream of knowledge – that I don’t pause to praise sufficiently often.
Some of the scientists, when they are allowed to step away from the dry language of the scientific paper and the scientific press release (where there is enormous cultural and social pressure to hide your emotions), definitely get the enormity of what they have achieved. Dr. Scott Ransom of the National Radio Astronomy Observatory put it pretty succinctly:
“We’re using a gravitational-wave detector the size of the galaxy that’s made out of exotic stars, which just blows my mind.”
And, as I predicted, it didn’t just detect a signal, it detected a strong signal (relative to what they had expected).
How strong? Well, in the this-is-really-exciting-but-if-I-show-my-excitement-they-will-shoot-me language of the press release:
“Detailed analysis of the background hum is already providing insights into how supermassive black holes grow and merge. Given the strength of the signal NANOGrav sees, the population of extremely massive black hole binaries in the Universe must number in the hundreds of thousands, perhaps even millions.”
BOOMING LOUD
Or as Dr. Luke Kelley (a lead author of the paper) put it, during the live announcement:
“The wavelengths of these gravitational waves span many many lightyears, so they are long in that sense. But the amplitudes of these gravitational waves – how much they are actually changing spacetime – are themselves very tiny. We mentioned one part in one quadrillion. However, compared to previous models of the expected gravitational background, that signal is booming loud, compared to what we thought we would see.”
I said it would be louder than they’d expected. Yep! Listen to Luke! Booming loud!
By the way, when I said the International Pulsar Timing Array has improved over the years, that can be hard to visualise.
Here are two beautiful graphs that shows how the Array has grown. (More accurately, two versions of the same graph, ten years apart.) Each vertical line of dots is a pulsar, and each of the dots comprising that vertical line is a measurement: as the years go by (as you move down horizontally, down through the years) there are more and more pulsars in the Array (more and more vertical lines), and the measurements get richer and richer, finer and finer.
Here is the graph after five years:
And here is the same graph again, after fifteen years:
So progress in this field is not linear, it is exponential: more and more pulsars each year; constantly improving technology and software. It took us fifteen years to get here (hell, it took 13.8 billion years to get here!), to this faint trace of a probable signal: we will go much, MUCH further, and see far more detail, in the next fifteen.
Remember, what we have invented here is something completely new: gravitational telescopes, of different designs, observing gravitational waves – ripples in fucking spacetime itself – at different wavelengths. We might look at light (a laser beam five kilometers long, for LIGO; a pulsar beam hundreds or thousands of lightyears long, for the International Pulsar Timing Array), in order to detect the gravitational waves, but those gravitational waves themselves have nothing to do with light: LIGO, and the International Pulsar Timing Array (plus the soon-to-be-launched LISA) are new types of telescope, observing an utterly new aspect of reality, to which our senses and the senses of every living thing on earth were previously completely blind.
BUT A TELESCOPE’S A TELESCOPE, RIGHT?
Wrong.
All telescopes previous to this measured some kind of light. Some measured the light we can see – that narrow, brilliant band which we interpret as red, orange, yellow, green, blue, and violet (all clustered tightly around those wavelengths produced in the greatest quantities by our sun, and the wavelengths our eyes therefore evolved to see). Some measured light we cannot see, because it’s too short (ultraviolet light; light above the wavelength we call violet) or too long (infrared light; light below the wavelength we call red). But if that light was new to humans, it was not new to life. Bees can see ultraviolet light. Snakes can see infrared light (the light the James Webb Space Telescope is designed to see).
Nothing living has ever previously seen a gravitational wave.
Maybe sit with that thought for a moment. (And maybe call it back to mind, whenever you hear someone say that human beings are insignificant blobs-of-matter-who-don’t-matter – or, alternatively just some dumb animal ruining the earth. No, we are something much-weirder-than-this – and we are doing something much, much weirder than that.)
Humanity, as a social animal, as an organism, as a being, HAS A NEW SENSE; has developed new sense organs. We can see gravity now, taste it, smell it.
Conventionally, we translate gravity waves into visual signals, because we are visual animals, but we have also translated them into sound waves – famously, the first gravitational waves ever detected, by LIGO, in 2015, as two black holes (of about 36 and 29 solar masses) merged, were at a frequency that was easily translated directly into sound waves; sound waves which made a rapidly rising sound (which abruptly cuts off) that they ended up calling a chirp. (Rising, because the frequency got rapidly higher, and the wavelengths thus rapidly shorter, in the very final second as the black holes spiralled faster and faster around each other. Abruptly cutting off at the moment they touch and immediately merge, becoming a single, new, bigger, black hole; no longer two, circling each other, and churning up spacetime.)
Here is that chirp, not adjusted for frequency in any way. Don’t seek to be blown away by the chirp itself (you won’t be, it is underwhelming); be blown away by the FACT THAT IT EXISTS AT ALL.
I could have adjusted the frequency upward a little, to make it “chirpier”, but I wanted you to hear it raw, unadjusted.
Besides, they went on to detect some REALLY chirpy mergers! Here is my favourite raw, unadjusted chirp, made by two neutron stars merging (on August 17th, 2017). (More details on that merger here, GW170817)
Oh, I downloaded these audio clips from the wonderful Gravitational Wave Open Science Center, and you can too, at this link.
Because I am using them here, under a Creative Commons Attribution 4.0 International License, I have to include this citation:
R. Abbott et al. (LIGO Scientific Collaboration and Virgo Collaboration), "Open data from the first and second observing runs of Advanced LIGO and Advanced Virgo", SoftwareX 13 (2021) 100658.
…and this extremely long acknowledgement, below – but that’s kind of cool, because the acknowledgement lists off the startling number of organisations from around the world that it took to detect and record these chirps. Well worth reading. Firm evidence that we are indeed building a networked global mind that vastly transcends any single human mind – what Pierre Teilhard de Chardin called the Noösphere (and which my wife Solana Joy and I now call the Thinky-sphere – her excellent coinage – because only French Jesuits born in the 19th century who speak classical Greek know how to pronounce Noö, or know at a glance what it means.)
Here goes!
"This research has made use of data or software obtained from the Gravitational Wave Open Science Center (gwosc.org), a service of the LIGO Scientific Collaboration, the Virgo Collaboration, and KAGRA. This material is based upon work supported by NSF's LIGO Laboratory which is a major facility fully funded by the National Science Foundation, as well as the Science and Technology Facilities Council (STFC) of the United Kingdom, the Max-Planck-Society (MPS), and the State of Niedersachsen/Germany for support of the construction of Advanced LIGO and construction and operation of the GEO600 detector. Additional support for Advanced LIGO was provided by the Australian Research Council. Virgo is funded, through the European Gravitational Observatory (EGO), by the French Centre National de Recherche Scientifique (CNRS), the Italian Istituto Nazionale di Fisica Nucleare (INFN) and the Dutch Nikhef, with contributions by institutions from Belgium, Germany, Greece, Hungary, Ireland, Japan, Monaco, Poland, Portugal, Spain. KAGRA is supported by Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan Society for the Promotion of Science (JSPS) in Japan; National Research Foundation (NRF) and Ministry of Science and ICT (MSIT) in Korea; Academia Sinica (AS) and National Science and Technology Council (NSTC) in Taiwan."
Hurrah for the thinky-sphere!
Anyway, for weeks after the first detection in 2015, gleeful astronomers would greet each other in the corridors of their institutions by chirping at each other.
Like little birds.
What a beautiful, what a marvellous and unlikely, thing: humans imitating small black holes colliding; a sound which they had heard.
With gravitational waves, we are currently at the point optical telescopes were at when Galileo first observed a few of the largest moons of Jupiter and Saturn (and mistook the blurry rings of Saturn for two more huge moons, one either side of Saturn, almost touching it…)
It is finally possible to see something useful. Blurry… but something.
But there is so much more to see.
SO, WHAT DO I THINK THEY WILL EVENTUALLY SEE? (HIGH-RISK, HIGH-REWARD PREDICTION TIME!)
As long-term subscribers will know, I think our universe evolved; that is, the rich complexity of our specific universe is the result of a long evolutionary process, at the level of universes. Our universe is the extremely complex descendent of earlier, far more primitive, universes – just as (nested within this universe) human beings are the descendants of earlier, far more primitive DNA-based organisms, and (nested within human culture) Formula 1 racing cars are the descendants of earlier, far more primitive, horseless carriages. (With humans as the replicators.)
No highly complex self-regulating system we have come across on earth has ever spontaneously come into being fully formed – whether that’s a banking system, or a lizard, or a flat screen TV, or a rainforest – they are always iterated into being, through an evolutionary process, over many generations; why would the universe, of which these complex systems are mere subunits, be any different?
The unfolding of our particular universe since the Big Bang is therefore best seen as the rapid development of an evolved organism, rather than (as the mainstream paradigm has it), the arbitrary and random blunderings of a bunch of arbitrary and random matter blindly pushed around by a bunch of arbitrary and random laws.
I think you can make some pretty specific predictions about the early universe based on that. (By “early universe” here, I mean the first billion years of our universe, which were opaque to us until the development of the James Webb Space Telescope… and these new gravitational wave detectors.)
SO, HOW LONG IS THAT GOING TO TAKE?
My most radical and important prediction remains the same: the picture of our universe which gravitational waves will ultimately reveal is one in which supermassive black holes turn out to be fundamental: one in which supermassive black holes form first, in huge numbers, by direct collapse, before galaxies form, indeed before widespread star formation. Of any kind. It is these early, supermassive black holes that will then optimise our universe for star formation, rapidly building out galaxies around themselves, while building up their own size by swallowing more gas. (That means, by the way, that extremely early galaxies will be small, compact, dense, and dominated by the mass of their central supermassive black holes; only later will enough stars have been formed for the mass of the stars to dominate. And that is exactly what we are now starting to see.)
BUT HOW CAN WE DETECT THAT?
If there was indeed a phase transition at the very beginning of our universe, in which the incredibly smooth gas revealed by the Cosmic Microwave Background generated vast numbers of direct collapse supermassive black holes, then there should surely be traces of that astonishing event in the gravitational wave background. The semi-simultaneous creation of a couple of hundred million supermassive black holes is unlikely to have been completely symmetrical. (Symmetrical collapses – or expansions – don’t make gravitational waves.) If it happened sometime in the first fifty million years (but probably much earlier and tighter than that), it must have made waves.
And there is another exciting prediction that follows on from that: if supermassive black holes formed that early, in a small, dense universe that was only at the beginning of its expansion after the Big Bang, then supermassive black hole mergers would also occur far earlier, and in far greater numbers, than mainstream cosmology currently expects. In other words, supermassive black hole mergers will be front-loaded, with many of them happening inside the first couple of hundred million years. Those signals should, by the time they reach us, be significantly stretched by the expansion of our universe, the expansion of spacetime. That fingerprint should help us identify them.
One day, I predict, we will tease out both those specific signals from the Gravitational Wave Background.
And I will eat another ice cream.
This time, two scoops.
Literally wept reading your ode to the miraclulous nature of this achievement. I hope the scientists involved in this heroic undertaking read this, they deserve to bask in such validating recognition. Truly grateful to them and to you for making the discovery so exciting and accessible!
This is my favorite substack. Keep doing everything you are doing. It's amazing to watch and you have a brilliant way of making all this confusing scientific data/jargon easy to understand, even to a simpleton like me. It's still very early on, as you always say, but I'm willing to say that I believe this theory is more plausible than most any other theory of the universe, that I've come across at least. Can't wait for your next post Julian! Joy's post are also great treats while waiting. Egg on. Rock on. Let's keep evolving.