Thank you very much. I have to make one correction to the introduction. He said I made seminal contributions to our understanding of dark matter, as you will understand from the start. We do not understand what dark matter is, and so no contributions can be viewed as seminal. I have to say it's a pleasure to be here. This is my first first visit to Oxford and the past three days.
I've had a really enjoyable time walking around the town, talking with a variety of people in physics and astrophysics, and there's a long list of things I've learnt. I'm not too surprised because many of the things that I've learnt about astrophysics came from people here. For example, in James Bond, his books on Galactic Dynamics, which I would call the Rolls-Royce of theoretical astrophysics anyway, have had a great time visiting Oxford.
I'd like to come back again sometime to visit. I should also tell you that we just hired a new faculty member at Johns Hopkins, away from the University of Mississippi and University of Mississippi in Oxford, Mississippi. And so for the past year, like all the time, I keep hearing, Oh, back in Oxford, we did this back in Oxford, back in Oxford. And so when I came here, I was thinking grits. So it's not quite what I expected, but I've been really having a blast.
So in this talk, I will tell you about some spectacular science and about some lunacy. And what I'll try to tell you is that the lunacy is not completely crazy, and I'm going to unfortunately not give you a dramatic, definitive conclusion. I'm going to leave you with some uncertainty at the end, but that's the way it always is in science. There are things we know and things we don't know. So I also understand that Ray Rice was here giving this talk two years ago.
Ray always got the Nobel prise. Since then, I'm not Ray Weiss. There is only one Ray Weiss. And thank goodness the number of Ray Rice, this is not zero. So back almost forty three plus a few months ago, there was a spectacular announcement from the logo and Virgo collaboration who were searching for gravitational waves.
And after many years, they found them, and the gravitational waves they found were a signature, a signal from a pair of black holes that had merged in a burst of gravitational waves, as they did. So this was, I have to say, perhaps the most spectacular discovery I'd ever seen. Spectacular and definitive discovery I'd ever seen in science. Everybody agreed. There was a very quick Nobel prise went to Ray Rice, Barry Barish and Kip Thorne, the leaders and consumers of this project.
And they also got every other prise if there's a prise for physics. They got it, and deservedly so. It was also a spectacular coincidence because it was the discovery was almost. Precisely, actually, as precisely as you can possibly imagine, one hundred years after Albert Einstein developed his theory of general relativity and Isaac Newton, sorry, Albert Einstein's theory of general relativity is a theory of gravity. We all know about gravity. Will demonstrate.
That's gravity, things fall. It's not just that, it's also the Earth spinning around the sun, it's the moon spinning around the moon. It's the Solar System spinning around the centre of the Milky Way. It's the expansion of the universe. Everything that I just described can be everything that I just mentioned can be described as manifestations of Albert Einstein's theory of general relativity.
And this is a picture of what general relativity says the universe looks like, and I'll describe momentarily. But before I do so, I'm going to show you an equation. Now, I'm always told that in popular talks, you're not supposed to solve equations, but I feel compelled to show an equation because I'm a theoretical physicist. That is all we do is write down equations, and I believe that you all know what an equation is. An equation has three things in the middle.
There is an equal sign on the left hand side, there is something. And on the right hand side there something. And the point of the equation is to tell you that the thing on the left hand side is the same as the thing on the right hand side. So this is something that we call the Einstein Field Strength Tensor, and this is something that we call the stress energy tensor.
So in words, the left hand side describes the curvature of space and the thing on the right hand side describes the matter of content. So this is an equation that describes the picture that Einstein had for gravity in the universe. So Einstein surmised that when you place a massive object somewhere in the universe, it curves the spacetime around it and therefore other objects will fall or move subject to that curvature.
So there's an analogue that we can think of, which is not precise but is pretty good. Suppose I have a very large and very soft mattress, and I place a very heavy object right in the middle that will depress the mattress that looks something like this. So if I have that very heavy object depressing the mattress and then I put a smaller object over there, the object will fall into the very heavier object that is sort of roughly speaking, what Albert Einstein suggested.
The only difference being that instead of being a two dimensional surface, he posited that the curvature is for all three spatial dimensions, as well as the time dimension. So that idea is encapsulated in this beautiful and elegant equation. G equals team. You know, I remember when I first learnt this in college, my senior year, I was taking general relativity. I saw one of my professors in the hallway, I said.
General Tivoli, it's so elegant, know equals to me, and he said, yeah, but let's you know, that's what the rest of the year. So in words, this is what Einstein postulated. Spacetime tells matter how to move, and matter tells spacetime how to curve. So we place an object somewhere in space. And that curves the space, and then that curvature tells the other objects how to move. That's all there is to general relativity. Everything else is mathematics to make the statement quantitative.
This was a remarkable idea because it had a number of observational consequences. First of all, it agreed and the limit of low mass objects and slowly moving objects with Einstein's. Sorry, Isaac Newton's theory of gravity from several hundred years before, but it said more. So one of the things that Albert Einstein realised almost immediately after developing this theory is that he could account for the perihelion,
the advance of Mercury. So Mercury spins around the Sun. And as Isaac and Isaac Newton's gravity and Isaac Newton's theory, planets orbit around the sun, or pseudo orbit around the Sun on ellipses, the close in on themselves. But it was observed at the time that by the time that Einstein was around, that Mercury's orbit does not close in on itself, but it actually processes or advances by about two degrees per cent.
And when Einstein described this system with this equation, he found that he could account for that perihelion advance. So that was the first indication that he was on the right track. The second indication was Eddington is famous eclipse experiment. So according to General Relativity, Light is affected by gravitational fields. So as a light ray passes by the sun, it gets deflected. It does not pass along a straight line.
And so if we were to look at a star that is very close to the Sun and that star was over here, it would seem that the star was actually over here. All right. The other way around, if the star was over here, the light from that star would come along a trajectory that derives from this direction. And it appears as the star was over here. And this was verified very shortly after Einstein's prediction, actually 100 years ago by Arthur Eddington.
So another prediction of Einstein's relativity that he realised fairly quickly after the development of the theory is the existence of gravitational waves, and this one took a hundred years to verify. So this is a picture of two stars that an audit orbit around each other.
And this is the gravitational field due to the stars. And if you look at the stars from these two, this pair of objects from this direction, the gravitational field you'll see is slightly different than the stars that the gravitational field, if you're looking from this direction because here it seems like if you got just, you know, one to two objects along the given line of sight here, it seems you have two objects that are sort of alongside each other.
And so as these as these massive objects spin around each other, the gravitational field that we will see will change in time. So these propagating perturbations in spacetime in the fabric of space are not too unfamiliar. So don't be too unfamiliar to you. All kinds of media can support waves. So for example, if I have a pond and I drop a pebble in the middle, that Pebble will induce perturbations to the surface of the water.
And what will happen is those disturbances will then propagate out as waves in the in the in the in the heights of the water. So here the medium is the water. We disturb the water by shaking something and when we shake it or move it, those disturbances are propagated through the medium and then seen over here. So suppose I had a small toy boat far away from this point in the water? The way I could actually detect that wave is by seeing the toy boat bounce up and down.
So if I were to move something over here up and down, that would cause a wave to propagate out, and I would detect that wave because a small boat over here would begin to shake up and down. Here's another example. Radio communications. Sorry, that's on radio communication. This is a string. Here's a second example. So suppose I have a string and I shake it up and down that disturbance and the string will propagate down the string as a wave.
And then if I have some beads on the wave over here, those beads will bounce up and down. So again, there's a medium which is here the string, which can propagate disturbances, disturbance, the disturbances can be set, the waves can be sent out by shaking this thing up and down and then detected by the motions they induced in these beads over here. Here's the radio communications, the same thing happens with radio communications and a radio transmitter.
I have an electron or a bunch of electrons, actually, and I shake those electrons up and down. Those electrons have associated with them electric fields. And as I shake the electron up and down, that disturbance gets propagated as a disturbance in the electric fields. The propagates over here. And then I detect that disturbance in electro that that wave like disturbance in the electromagnetic field through the motions that induces in the test electrons.
And this in turn over here. So I shake electrons. It sends a wave out in the electromagnetic field and then I detect that electromagnetic waves through the motions and induces and electrons in the receiving antenna. The other example I'd like to give, which I first gave when I give this talk in California because it's fairly familiar, is is earthquakes. So there I have a geophysical wave and it can be propagated and actually don't even live in California.
How many have you ever been sitting at home when a very large truck drove by? So they're the ground, which we think of is very, very stable and sturdy. There it is. It's not moving, we always think of the ground as very sturdy, but if a heavy truck comes by and a bumpy road and starts bouncing along, that can induce waves in the ground to propagate through the ground and then wind up shaking the house or building the trend and then shaking you.
So again, a bouncing object propagate waves in a medium or very sturdy medium like the Earth, the surface of the Earth, and then shake the house. Now there it takes a very, very massive truck to induce a wave because the ground is very, very rigid. It is not, though perfectly rigid if it was perfectly rigid. It doesn't matter how heavy the truck is, nothing would ever happen. But since it's extremely rigid, you need a perfectly rigid.
A very, very heavy truck will shake the ground and then you will feel that disturbance because it's going to then shake you. And it turns out that space time is no different. We always think of space time as rigid all the way, going back to Galileo. Any position in this room, I can specify in terms of three points. How far is it from that wall? How far is it from that wall and how far above the ground? And so we can all draw in our heads, an imaginary grid of lines?
And to us, that grid is perfectly rigid. It turns out that that's not true. It is extremely rigid, but it is not perfectly rigid. And if I were to have extremely massive objects. Those are extremely massive objects could disturb the rigidity of the space. And so this is a movie that shows how this works. So we all know that the Earth spins around the sun. Jupiter spins around the sun. There are binary stars, which are two stars that are gravitationally bound that spin around each other.
And as it turns out, as we now know, thanks to go, there are also binary black holes that are very massive objects and forget forget about the black holes. For now, just suppose I have two very massive objects that are in orbit around each other. The gravitational field due to that, pair of objects will change with time because these things are not steady and are not static in space, they're actually moving around.
So if I were to look at the gravitational field due to these two massive objects at some distance over here, I would see the gravitational field changing with time. And those wavelength disturbances are exactly analogous to the wavelength disturbances in the ground on a very heavy truck passes by. So such gravitational waves were postulated by Einstein's general relativity simply as a consequence of his postulate that it's of that spacetime could curve.
So this was 100 years ago, plus three years that I've thought about this, this gravitational waves propagate at the speed of light. They can carry energy just like electromagnetic waves, just like the wave in the ground when the truck drives by and then winds up shaking you. That motion has energy, so that wave has carried some energy. Likewise, gravitational waves can carry energy also like electromagnetic waves.
These gravitational waves we've actually known or had indirect evidence exist as of 19 as of the early 70s. And actually, I think one of the core discoveries of that system is here. So not that system of pulsars, the discover of pulsars is here that the people did. This work were at Princeton, actually University of Massachusetts at the time. So it turns out that there are very, very massive complex stars called neutron stars, and some of them are actually in binary orbits. So a pair of them.
And there was one system of two such neutron stars that were discovered, and it was seen that the orbital period was slowly increasing. Because this binary neutron star was emitting gravitational waves and those gravitational waves were carrying energy away, driving the neutron star to a higher period, sort of a longer a shorter period orbit, a higher frequency or so.
As of nineteen ninety three, there was already a Nobel prise given for work 20 years earlier, actually 10 to 20 years earlier that demonstrated indirectly the existence of gravitational waves. But still? We had not yet detected gravitational waves directly. So how do you detect a gravitational wave? So I already told you it's analogous to everything else.
We detect electromagnetic waves through the motion it induces in a test electron, we can detect a gravitational wave propagating through the ground through the motion of induces in the building that we're in. We detect a wave on the surface of a pond through the motion induces a toy boat. And likewise, gravitational waves can be detected through the characteristic motions that they induce in a set of test masses. Here is an overly dramatic representation of what might happen.
So the Earth is held together by its own soft gravity. If a gravitational wave were to pass by, that would change the gravitational field that the Earth is immersed in and out, induce some motions and threaten the Earth. So this is a sort of cartoonish movie of what would happen if a gravitational wave passed by the Earth do not be alarmed. This effect is magnified by. A billion billion billion, more or less, a little less than a billion dollars billion.
So well back in the early 70s, Ray Weiss and Kip Thorne and Ron Driver and others began to think about how you would actually detect a gravitational wave that was not quite so large and amplitude. And they came up with an idea called laser interferometry. And this is actually the mechanism that's used to detect these gravitational waves and for which the Nobel prise was awarded. So basically. What happens is you have a laser that emits a beam of light.
This is a half silver mirror that then splits that light beam in two, so one beam goes in this direction, the other half of the beam goes over here. This mirror over here in this mirror then reflect the light back and then the light is combined. Now, if a gravitational wave propagates in a direction perpendicular to the plane of this, of these of this interferometer, what will happen is that this mirror will move towards move in this direction while this mirror moves away and then vice versa.
So these will begin to shake, but the shake out of phase. And then this movie is going to show you how that phase is, how that motion is detected. So the light beam goes out in both directions and split when a gravitational wave passes, these things move. And then the last part I didn't tell you is that when the light? Combines light is a wave. And if that light then combines in phase. The beam over here will be bright, and if it's out of phase, it'll be faint.
And what happens is when this what happens is when these things move the lights. Received at this detector oscillates. So this is the basic idea of the measurement. We take this interferometer, we send out a beam, and if these two mirrors change in distance, move and distance by an amount comparable to the wavelength of light, then the brightness of the signal over here will change. So this experiment was actually done.
The detection was done by the local collaboration, Legault was working very closely with Virgo, which is a French and Italian government built laser. LIGO's an American and international American led project. They're also at least three other detectors that are being constructed for future measurements Geo, Tomah and Ajio. And there's also one being constructed in India LIGO India site.
The signal, though, that there was initially detected was detected primarily by a legal action, exclusively biological. This is a US led project. There were two detectors built, not just one. One was built in the state of Washington and one was built in the state of Louisiana. And the reason is that this is such a ridiculous thing to look for, and the signal is so faint that if you saw such a signal with just one detector and claim to discover anything, no one would ever believe you.
But if two detectors separated by a few thousand miles saw exactly the same gravitational wave signal exactly the same time, then you might believe that it was something more than just, you know, lightning striking in Seattle, Washington, or a heavy truck driving by one of the protective one of the two detectors. These detectors are four kilometres long, so here is the place where the laser is started.
Here is one of the mirrors, and here's another one of the mirrors. So the latest sent out in this direction, this direction than recombined over here. This is the detector in Louisiana. And this is a picture of the detector along the Strip. It's four kilometres in that direction. This is the other detector in the state of Washington. And this is a movie provided by the logo collaboration disclaimer, I had absolutely nothing to do with this.
I cannot be assigned any credit whatsoever for any of this. I like to show this because I think it's just absolutely mind boggling what they actually detected. So here is a video that shows what they detected. So this, I'm going to tell you, is an atom. That is the nucleus and this is the electron around an atom. And so here is what they actually detected. So there's the electron spinning around the nucleus now we zoom into the atomic nucleus.
This is an atomic nucleus, a bunch of protons and neutrons. And the magnitude of the motion that they detect over those four kilometres is that. So I have to show you the slide. And a second. So this is not easy. And I have to tell you that I was at Caltech from 1999 to 2011 and my office was right down the hall way from the people working on. I mean, there were people working like all over the place, but a bunch of the local leadership was right down the hall for me.
And so I'd hear about logo all the time. And any time I heard them talk about detecting gravitational waves, the following picture came into my mind. So this is a poster, a picture from Werner Herzog movie Fitzcarraldo, which is about a crazy guy in Brazil. In the eighteen hundreds who for some reason wants to take a ship over a mountain. And any time they talk to me, that's the first image that popped in my mind.
And so I was completely stunned when they reported the detection reported in February 2016, the detection that they made in September two thousand fifteen of an actual gravitational wave signal. So this is a plot of the displacement. Of. The test masses of those mirrors as a function of time and one of these detectors in the state of Washington, another detection detector several thousand miles away. So this. How it. Since of show, yes.
Now, that's actually not the movement to say this is what I want to show you. So this is actually a plot of the. Displacement of the Mirror. In one detector in the state of Washington, another detector several thousand miles away as a function of time on some particular time on September 14th, 2015, I think it was the evening. So the textures went up and down and up and down and up and down, up and down very more rapidly, very high amplitude, and then the signal sort of died away.
And the same thing here is in Livingston. So one does not need to do any complicated statistical analysis to see that something is going on here. As it turns out, you do have to do some fairly complicated mathematical general relativity to show that this is exactly what you would expect from the merger of two black holes. So I've been saying black hole a few times, but I haven't yet told you what a black hole actually is. So this was another spectacular consequence of general relativity.
I have to tell you, it's absolutely amazing that this silly little equation, Jimi, you know, equals team, you know? Could lead to so many novel and spectacular results and consequences. So this is another consequence of general relativity. It predicts the existence of black holes, a black hole you can think of as the densest possible object. So. The Earth is a massive object that is round, and it has some radius and we live on the surface of the Earth.
And if I were to throw a ball in the air or any object this thing, it would probably go up and then come back down. But if I had a really good arm and I could throw a ball with a velocity greater than 11 kilometres per second. That ball would escape the gravitational field of the Earth and then run off to infinity. If I were to do this from the surface of the Sun, that escape velocity is 600 kilometres per second. If, however, I had an object that was so massive and so small, so dense.
Well, sorry, I should say that the denser the object gets, the higher the escape velocity gets. So if I had a certain object that was so dense that the escape velocity was bigger than the speed of light. We know that nothing can travel faster than the speed of light. No light could ever be emitted from that object. In fact, nothing could ever escape from that object. So that's what a black hole is.
It's an object that is so dense that its gravitational field is so strong that not even light can escape. These objects have been postulated for close to over 100 years to postulates, exist for over a hundred years. There have been pretty there's been pretty good evidence for the existence of astrophysical black holes for several decades. But no direct evidence. But it turns out that if you have a black hole.
It's conceivable you might have pairs of black holes, I told you that many stars are in binaries. Our star is actually pretty unusual in that it has no gravitationally bound companion. Most stars are gravitationally and systems are binary systems that are gravitationally bound. And so it's conceivable that if black holes exist, they might also have. There might be black hole binaries.
So here is another movie similar to the one that I showed you before of the gravitational field of two black holes. Let me see. So as this gravitational as these black holes spin around, they emit gravitational waves, those gravitational waves carry away energy. And as they carry away energy, the pair of binary black holes becomes more tightly bound, the distance becomes between them becomes smaller and the orbital frequency increases.
They start to spin around each other more rapidly and the emission of gravitational waves becomes more intense. So I'll show that to you again. So you'll see that early times. The gravitational wave signal is fairly weak, but as these things spiral in and emit more energy and the orbital frequency increases, the intensity of the gravitational wave signal becomes greater. So it becomes brighter in gravitational waves and the frequency increases.
So this is a calculation that you can do given me a new equals team, you know? And I have to say a lot of computational resources and the result of such a calculation is a gravitational wave signal that looks exactly like this. Interestingly enough, Lego had two ways to look for gravitational waves, and the simple way was just to wait for something to go bump in the night, and that's what happened. In this case, they didn't do any general relativity, they didn't do any black hole modelling.
They just noticed that something happened. And then afterwards they went back to those gravitational wave templates that were obtained from mathematical relativity, and they found that the signal they saw agreed precisely with black holes. They were as stunned as the rest of the world, and they spent a long, long time all thousand members of the collaboration trying to figure out anything else that could mimic such a signal.
And it turns out that this is a bona fide, genuine binary black hole merger the first direct evidence we've ever obtained for the existence of black holes and spectacular evidence of that. From the details of that gravitational wave signal, they were able to infer that the first black hole was thirty six times as much of the sun. The second one made twenty nine times as much as the Sun. The final black hole where it sixty two times the mass of the Sun.
I'm assuming you can all add thirty six and twenty nine. Which turns out to be 65 three solar masses. Was released as gravitational wave energy. You remember another famous Einstein equation is e equals m c squared. An object of a given mass has a certain amount of energy. There is equivalent equivalence between mass and energy. So approximately five percent of the rest mass energy of the system was emitted in the form of gravitational waves.
And they also were able to infer that this thing was about a billion light years away. This. Has no relevance to the talks. No direct relevance, but it's a great picture. This is actually a bona fide simulation of what the galaxy would look like. When we look out in the night sky, we see a bunch of stars from the southern hemisphere. We see a Milky Way. This is a bona fide simulation of what a night sky would look like if there was a pair of binary black holes pretty close by in the foreground.
And actually, it's not a picture, it's a movie, and this is what that night sky would look like if you were fairly close to the binary black hole system near merger. So there you have it. And. The merger is about to happen. Uh, there it is. And you still see some residual emotions over here. Actually, the thing that surprised me when I first saw this movie is how quickly it once it emerges, it just turns into a spherical black hole.
That ringtone is very, very quick. So everything I've told you until now is spectacular science, and now comes the lunacy. So I should say I wrote this paper three years ago. A lot of people paid attention. And ever since then, when I go to conferences and Rundle colleagues, I say, Do you really think primordial black holes are the dark matter? Really believe? So where do these black holes come from?
So here is the most likely answer with very, very great certainty, although not absolute certainty. These black holes, or at least the majority of the now 15 binary black hole systems that they've observed, probably are the remnants of stars. So The Sun is a star. It's a very or fairly ordinary star. And over the past hundred years, especially over the past 70, I would say we've learnt a lot about how stars evolve and stars can be low mass and stars can be high mass.
And roughly speaking, this is a picture that you would find in the astronomy class. Roughly speaking, small stars evolve and after they use up all the nuclear fuel that powers them, you know, the light from the Sun comes from nuclear reactions of this at the centre of the Sun. So star sign because they are burning nuclear fuel.
When that nuclear fuel runs out, though, they can't support themselves against gravitational collapse and the lower mass stars turn into something called the white dwarf, which is pretty interesting, but not quite as interesting as what happens to huge stars. Those evolved to neutron stars if they're pretty massive and if the really massive they evolve to black holes.
So we actually expect there to be a whole bunch of black holes out there in the universe because we see a whole bunch of stars in those stars don't live forever. So that is probably what these black holes are still stars like the Sun, the Sun weighs one solar mass by definition, and there are heavier stars out there, the stars. When you see stars, there are about 100 up to 100 solar masses.
But the abundance of the more massive stars is hugely suppressed compared to the abundance of the lower mass stars. And so if you were to tell me, well, wow, we're going to see gravitational wave signal from a binary black hole merger, if you told me that back three and a half years ago, I would have said, Well, I'm guessing there's going to be five to 10 solar masses.
But it wasn't. Both of these black holes were nearly 30 times the mass of the Sun. And so this was at the time, a little bit surprising. Why is it that the fees are still the remnants? There'll be so much heavier than a typical stellar mass. So I'm not a stellar astrophysicist. I'm a cosmologist, and much of my time is spent thinking about the dark matter, and I was sitting around the lunch table with a bunch of my post-docs and students. And they also think about dark matter.
And so we start to wonder whether these black holes they saw might have something to do with the dark matter in the universe. So here's my rough, my quick primer on dark matter. We live in a galaxy called the Milky Way, and we can't actually take a picture of the galaxy that looks like this because we live in the middle of it. But there are plenty of other galaxies, like our own spiral galaxies to look sort of like this some blob of light.
And these things are the light comes from stars. And the galaxy is a gravitationally bound system of, say, 10 billion stars. And the galaxy only extends out to about, you know, some 10000 light years in distance. But there are still satellites of this galaxy. There can be gas clouds or dwarf galaxies that orbit around this galaxy. And we can measure the velocities at which these satellites spin around these galaxies.
And if Newton's laws were the entire story to gravity or general relativity was all there was to gravity. And if there was nothing in this galaxy beyond the stars that we see, we would expect the velocities at which satellite to spin to decrease that large radii for the same reason the Pluto. Which is not a planet anymore, spins around the sun far more slowly than does the Earth, and Mercury spins around the sun much more quickly.
So things that are further away from the galaxy should spin around with a smaller velocity. It turns out, though, that's not the case. And this discovery in this form was made by Vera Rubin, who is an astrophysicist who made this discovery in the early 1970s and others. And I also, since their astrophysicist here, I should advertise there is going to be a workshop to honour Vera Rubin and her science at Georgetown University next month.
If anybody's interested to attend, so this when it was discovered is a huge mystery, why is it that these things at large distance are spinning around so much more rapidly than they should? If this is all the matter in the galaxy and the inference that we make from this measurement, as well as from a huge array of other astronomical and cosmological observations, is that this galaxy and all galaxies, as far as we can tell, are immersed in a halo of some mysterious dark matter.
And we have absolutely no idea what the stuff is. So all I can tell you about dark matter with certainty. Is we know how it is distributed. We know how to distribute in galaxies through detailed measurements like this. We know how it's distributed throughout the universe today. We know very well how it's distributed in the early universe. Its existence is not a question. It is there and we know very much where it is and where it isn't. It is dark. So by this, I mean, it emits no light.
And it also absorbs no light. There's actually been no evidence for dark matter, apart from its gravitational effects on the stuff that we see for many years, and I would say they still are leading candidates involve new elementary particles. And 10 years ago, if I was here giving this talk, I would have been telling you that's going to be weakly interacting massive particle. It's got to be weakly interacting metaphorical. There's nothing else it can be. It's got to be a new elementary particle.
And next week, you're going to hear a talk by one of the leading figures in the detection or attempts to detect particle dark matter. But we don't know that it's an elementary particle. We still have no empirical evidence to support this hypothesis, although we can't disprove it. We've been looking for a number of years and 10 years ago. When I gave this talk, I would have said as soon as the Large Hadron Collider turns on it, CERN, we are going to see this new elementary particle.
Well, the Large Hadron Collider turned on about eight, seven or eight years ago, and they have not yet found anything. As you know, absence of evidence is not evidence of absence. However, it's starting to get disappointing that they haven't found anything yet. And so theorists over the past few years have started to wonder whether we should be thinking of alternative hypotheses. And that led us to consider the possibility that the black holes that likely detected are the dark matter.
And in fact, Stephen Hawking wrote a paper in 1974 showing that the early universe, the Big Bang, could have plausibly produced some primordial black holes. Here are my collaborators. They are an assorted set of post-docs and students. And Adam Riess, who is a colleague at Johns Hopkins. So here's the question. We wrote this paper, we sat around for a while wondering whether we should actually post it online because it seemed kind of ridiculous and speculative,
but not completely ridiculous. And there's a reason why we actually wrote the paper. It's easy enough to sit around the table and say, hey, maybe it's dark matter, but then we actually did a calculation, which is what we're paid to do. And we found a very, very surprising result. So we know from the laws of gravity that if we have two black holes that pass by each other, there's some chance that they will merge and form a, but they will form a binary and then merge.
That's a straightforward calculation and straightforward to calculate how probable it is, the two black holes that pass by each other are going to form a binary merge. We also, thanks to the efforts of cosmologists over the past few decades, have pretty good ideas about how the dark matter on the galactic halo is distributed. So this is a picture not of a galaxy, but this is a picture of the distribution of dark matter within a galaxy.
The what we believe to be the distribution of dark matter in the galaxy, given cosmological simulations and there are there's more dark matter in the son of the galaxy, less dark matter away from the centre of the galaxy, and the dark matter is also distributed in sub clumps.
And so what we did is we took this distribution of dark matter. We passed with all the dark matter is made up of 30 solar mass black holes, and then we calculated the rate at which these black holes would merge and give you a gravitational wave signals if all the dark matter is made of 30 solar mass black holes. And when we did that calculation, we found this incredible coincidence that that number was done on the gravitational of the binary merger rate inferred from light.
So that's why we wrote this paper to point out this very interesting coincidence. Since then, this paper has received a lot of attention. We've had people help us out, a number of theorists have shown said, Oh yeah, primordial black holes. It's very easy to produce primordial black holes in the early universe. In fact, 30 solar masses is just what we expect and just with the right abundance.
This is a collection of words. You are not expected to understand the meanings of any of this meaning of any of these words. I do not understand the meaning of any of these words. Some of them, I understand, but not all of them. The point is, some theoretical physicists believe that this is actually a plausible. Candidate for the dark matter. Since then, though, a number of astrophysicists have ruled out of written paper saying that this is a ridiculous idea for dark matter.
So some people show that using measurements of the cosmic microwave background you can rule this out is a dark matter candidate. Dwarf galaxy dynamics quasar lending x rays from galactic black hole supernova stars as pulsar timing. The list goes on and on. All these papers are really nice. The ideas are great. I think each one of them comes with a caveat, and I believe that there's no paper that I can point to that says that tells me I have to stop thinking about this idea.
But all of them are very interesting astrophysics and could lead to novel ways to detect. Or test this idea, the primordial black holes are the dark matter. So I'm going to tell you briefly about one idea that my colleagues came up with to try to test the idea of whether these primordial black holes are the dark matter. So as you know, it's the job of theorists to propose theories and come up with hypotheses for answers to questions.
But we're also supposed to provide mechanisms to test those hypotheses. And ultimately, the hypothesis the primordial black holes are the dark matter is not going to be determined by a bunch of theorists sitting around a room arguing it's going to be determined by experiments and observations. So one such observation experiment that we suggested you could do involves these very intriguing objects called fast radio bursts.
So these fast radio bursts were detected roughly 20 years ago. Over the past few decades, about 20 something of them have been detected. Just last year, a new Canadian telescope that was designed in part to detect them has discovered about 20 more of these and is expected to discover thousands more within the next few years. And the basic idea is that a fast radio burst is what it sounds like, it's a radio burst that is very, very fast.
So you have a radio telescope. People are pointing radio telescopes in the sky, and they notice that there were just blips of radio frequency radiation coming from somewhere in the sky, and those blips lasted less than a millisecond. We do not know where these things come from. Plenty of theoretical astrophysics around the world have various ideas and hypotheses, but we do not know where they come from, but there's pretty good evidence that they come from far away.
They come from other galaxies at cosmological distances. So if primordial black holes were the dark matter, there's some chance that the light from one of these fast radio bursts could pass near the trajectory of the light from one of these fast radio bursts as it travels to us. This is a telescope. It's not a peace sign. So if the introductory passes by a black hole, there's a chance that it could be gravitationally lensed.
Remember, I told you about Ellington's experiment, where the light trajectory from a target gets bent, so it's introductory of light from a star can be burnt. If that trajectory passes by, a very massive object might get burnt in this direction and might actually get burnt in this direction. So if there's a black hole along the line of sight to a given fast radio burst, we might actually see not just one, but two images of the fast radio burst.
It turns out that those two images are separated by an angular scale that's way too small to ever be resolved. But it turns out that the path length along this trajectory differs most generally from the path length along this trajectory. And so what you would see in this case is the fast radio burst from one trajectory, followed by a fainter echo from the other trajectory. And what we showed is that if if 30 solar mass primordial black holes are the dark matter.
After this Canadian telescope has been observing for several years and discovered several thousand of these things, about 10 of them should exhibit this echo. So this is a straightforward test that is going to be carried out. I don't know what the answer is going to be, but within a few years, we'll be able to tell definitively whether dark, primordial black holes are the dark matter or not. Now, I should say that about a year ago.
My collaborators and I did a calculation, so we've been thinking really hard about how to test the scenario, how to test the scenario, what can we do to figure out whether this is a real? This is really the dark matter or just a figment of our imagination. And we came across. Something that has sort of dampened my optimism about the scenario.
So this is work that was done with the post up Yasin Ali, who is now on the faculty at NYU, and another postdoc, Eli Kovac's, is now on the faculty, Ben-Gurion University. So if primordial black holes are the dark matter and they're distributed throughout the universe, they will have would have been distributed randomly throughout the early universe. And if I have a bunch of black holes that are distributed randomly, there will be some places where I have two of them.
There's just happen to be close by by chance. So if I have two black holes that are close by. Those black holes will form a binary that will form a gravitationally bound system. And so it is straightforward to calculate the fraction of primordial black holes that will actually be in primordial, gravitationally bound binaries. So we did this calculation. That's what we do for theoretical astrophysics, we calculate.
And it turns out that only a very tiny fraction of the primordial black holes make up are to be found in binaries. But there are actually quite a few of them in terms of total numbers and binaries. If they survive, long enough, will merge and produce gravitational wave signals. And we did the calculation of how many gravitational wave signals we would have expected to see with Lego from these primordial miners. And it turns out to be a hundred times as many as Lego seen.
So unless there's something that we're missing in the calculation, unless there's some unforeseen mechanism that disrupts these binaries after they're formed. My current belief is that this is a challenge, so challenging scenario to make work. My collaborator, Yacine, believes that there might be mechanisms that might disrupt this binary, so he doesn't. He knows he will not allow me to say that the scenario is ruled out.
But the way I would put it is that when we wrote our first paper three years ago, this was a scenario that was innocent until proven guilty. And now I would say that this hypothesis is guilty until proven innocent. So one final update the first miner black hole was discovered on September 14th, 2015. It was announced to the world in February 2016. Legault then had a long run. And discovered several more black hole binaries.
They've been shut down for about a year and they just turned back on started observing again a few weeks ago. And within the past few weeks, they've already detected like three or four binary black hole signals. So as of now, there are about 15 more black hole mergers. And if any of the legal people were here, if Ray Weiss were here, he would say, you should exhibit caution, don't over interpret the results. We don't understand all the systematics, we don't understand the distributions.
But if you actually look. The masses of the black holes that they've discovered have a whole range of masses, but there actually seems to be a preponderance of black holes that have masses that are close to 30 solar masses. So I don't say that this is evidence the primordial black hole binaries are primordial, black holes are the dark matter.
What I would say is that if we had not, if we had seen a bunch more binary black hole mergers and none of them, none of the rest of them had 30 solar masses, then I would say the scenario is highly unlikely. I don't want to say that this proves this scenario, but at least the scenario has not yet been killed. And it's an intriguing result regardless of whether the primordial black holes or stellar remnant black holes, because we really don't know where these things come from.
And the fact that they seem to be more massive than what we would have guessed five to 10 ish or broad mass distribution, I think, is intriguing. So. I'd like to conclude. So gravitational waves were discovered that a spectacular science, we're doing all kinds of interesting things with these observations and measurements. And there's going to be plenty more to come. I'm curious about the dark matter. I'd like to know what it is. I don't know what it is.
I have not made seminal contributions. I appreciate the compliment, but we're not in the winner's circle yet. So we've detected gravitational waves directly as of three years ago. We've seen several more. These are very bona fide astrophysical black hole signals. I forgot to mention you probably also saw also saw last month this image from the Event Horizon telescope of the of a black hole. The actual picture, the first picture of a black hole, which was pretty spectacular.
As I said, these are most likely related to the endpoint of stellar evolution, but the details we really don't know a whole lot about. The jury's still out as to whether the primordial black holes can make up the dark matter, we should still be pursuing other dark matter candidates like you'll hear about next week from Elena Asprilla. And this is always a true statement at the end of any science talk, we will learn more with forthcoming observations and experiments.
And I thank you very much for your interest and your attention.