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0:12
Black holes are structures in the fabric of space and time itself, and they're amongst the most extraordinary objects that we know that exists in the universe. Despite the mathematical complexity in describing black holes, and the myriad ways in which black holes can form in the universe, we also know that they possess a very striking simplicity, which is one of the things I wanted to try and describe to you tonight. The modern conception of black holes began in 2000--
0:44
sorry, 1915-- and it took many years before the properties of black holes were properly understood, and longer again until we have found evidence that black holes exist. But we do know black holes exist, and in 2015, there was a dramatic confirmation of the existence of black holes, the first direct detection of black holes by the measurement of the gravitational waves emitted by a system of two black holes. This was a system of two black holes that were orbiting each other.
1:14
They coalesced to form a single black hole, and then that cataclysmic explosion when they formed that single black hole, they emitted a gravitational radiation. That gravitational waves moves through the universe and was measured by the LIGO experiment in 2015. That was the first direct detection of black holes. It was the first direct detection of a binary system of black holes. Before them we weren't sure that they existed. And it was also the first direct detection of gravitational waves.
1:44
So in short, that was a truly spectacular discovery, and that's something I want to tell you about in tonight's lecture.
1:53
In telling the story of black holes, we'll start with the beginning of the story of gravity, or the modern story of gravity, which is Isaac Newton. And citing from Isaac Newton, we'll moved to general relativity, Einstein's theory of gravity, which is our best theory of gravity, and it's the arena where most of the discussion of black holes will happen tonight. But we know that relativity is not the final story. It's not the most fundamental story of gravity.
2:20
We know there's a new chapter, and the new chapter must include quantum theory. So there is some way in which general relativity must be subsumed into a deeper, more fundamental structure. And I want to explain why black holes, and the properties of black holes, are the key theoretical laboratory for making that next step forward in the search for fundamental physics.
2:46
So I want to begin our journey in 1687, which is when Isaac Newton formulated his theory of gravity. And along with his laws and mechanics, that comprises, really, the beginning of modern fundamental physics. And Newton thought a lot about how things fall. So for example, this apple. Famously, he thought about how apples fall. And he realised that everything falls in a very similar way, and in fact, in exactly the same way. So that apple falls, as I've just demonstrated,
3:21
this ball similarly falls in the same way. And if I take this ball and impart a small transverse motion to it, it's still falling to the Earth in the same way the apple was. But because of the transverse motion I gave it, the actual orbit was slightly different. And Newton thought about this a lot, and from these simple observations, he made the breathtaking leap that the moon is also falling to the earth in exactly the same way the apple was
3:57
falling to the earth or this ball was falling to the earth. And he came up with an ingenious thought experiment, which hopefully I can convince you, following Newton, of why that's the case. So here is a picture that Newton drew, and it's a picture of a planet. I'm not quite sure why it has all these fissures in it. But in any case, he has a planet with a little volcano, a little mount on the top of it. And he imagined standing on top of that hill and throwing objects.
4:31
In fact, he thought of having a cannon and firing cannon balls from it. So starting from the point V, he fires a cannon. And if it was thrown at a small velocity, the cannonball would fall to the earth and end up at the point D. If you threw it a little further, it would end up-- sorry, a little faster-- it would end up at the point E. But in both cases, just like the ball I demonstrated a few moments ago, it's falling to the earth all the time.
5:01
Faster still, it would go up to point F, and then G. And if you took, at the surface of the earth, and I took that ball, and I was able to throw that ball at 7.9 kilometres a second, which, admittedly, I couldn't throw. But if it could be thrown, then it would keep falling to the earth the whole time, but it would never actually touch the earth. It would come back and make the orbit, which was the final line that Newton drew. So Newton understood that all of these orbits,
5:35
these closed motion of particles, like the moon, are actually objects that are falling. So from simple thought experiments of apples, he made this leap to the cosmos, and it was a brilliant, but simple, insight. But Newton didn't stop there. He made this mathematically precise. And in Newton's theory of gravity, he said that all objects, all masses, feel a gravitational force. There's a gravitational force between the apple and the earth. And we perceive that, as the motion of the apple
6:13
falling towards the earth, there's also a gravitational force between the earth and the moon. And we perceive that, because of the transverse motion, that the moon stays in a stable orbit.
6:28
Newton's theory is magnificent, and it held sway for over 200 years. This was our deepest, most fundamental understanding of gravity. It predicted the motion of all of the planets in the solar system, and it actually predicted the existence of a new planet, the planet Neptune. So by studying the motion of Uranus, and it's using the mathematics of his theory, people realised that it almost worked, that there were some small deviations. And those deviations would be accounted
7:03
for in Newton's theory if there was another planet in a further orbit, just outside the orbit of Neptune. And the theory was precise enough that you could predict. Well, astronomers predicted exactly where that planet should be, and it was found. So Newton's theory was quite spectacular. But there's something very odd about Newton's theory as well. And the odd thing is that the force, the gravitational force that Newton invoked, is instantaneously communicated.
7:37
So with this apple, if I move the apple, the force between the earth and the apple is instantaneously communicated. It doesn't take a little split second for it to be communicated, it's instantaneous. And this troubled Newton, instantaneous action at a distance. And I want to put up this fragment of a letter that Isaac Newton wrote to Bentley in 1692. Bentley was the Master of Trinity College in Cambridge. And I was actually fortunate enough to see this volume at the Wren Library, just a couple
8:17
of months ago. And I found it very moving to see Newton's handwriting, and I felt a physicality, a connection, spanning us across these centuries, that separating us in time. In this letter, somewhere towards the bottom, Newton said something quite extraordinary, so I've highlighted it here. It says, "that gravity should be innate, inherent, and essential to matter, so that one body may act upon another at a distance through a vacuum without the mediation of anything else,
8:52
is, to me, so great an absurdity that I believe no man who has in philosophical matters, any competent faculty of thinking, can ever fall into it." So this action of distance is disturbing him at this very deep, fundamental level, and it's worth registering this for a moment. So at the very foundations of his theory, he's troubled. But nevertheless, despite his troubles and those obstacles, he's been able to build his theory. And the theory, as I was just saying, is truly magnificent.
9:24
It's not a hodgepodge theory. It's a great theory. And it's a little template, I think, for how often progress can happen in theoretical physics. One doesn't necessarily have the big picture and the complete picture, and there can be troubling aspects in your understanding, but it's the creative act to be able to pierce through the void and come through and create some new body of knowledge, even though you have at the back of your mind some deep reservations that this is not the final story
9:53
and that things will change.
9:58
The next chapter began in 1905. 1905, Einstein came up and developed his special theory of relativity. And one of the aspects of the special theory of relativity is that Einstein discovers it and he said the universe has a speed limit. And the speed limit is 300,000 kilometres per second. That's the speed of light. At this point, Newton's theory, which has just been happily existing as the most fundamental understanding of gravity, suddenly ran into a contradiction, or a paradox.
10:34
If forces instantaneously communicated in his theory, and Einstein says that nothing goes faster than speed of light, something has to give.
10:45
In a remarkably short amount of time, Einstein himself was the one who worked out what the next step was. In 1915, Einstein developed his general theory of relativity, and he swept away completely the notion that gravity is a force. There is no force of gravity in Einstein's theory of relativity. Instead, gravity is the manifestation of the curvature of space and time, space-time. So we can draw some pictures to get some intuition and understanding of what this means.
11:23
So imagine that space is a rubber sheet and you place a heavy object into the rubber sheet, like a shot put, it would curve the rubber sheet, much like in the picture of the earth curving the space in the picture that you can see. So the Earth's0 curving space around it, and now the moon is orbiting the earth, not because of force pulling on it, but just like a marble rolling on that curved rubber sheet. If there was no friction, that ball, the moon, the marble,
11:54
would just roll around on that rubber sheet indefinitely. So the slogan of general relativity is that matter curves space and time, and curved space-time informs how matter moves.
12:13
It's important to understand and emphasise that general relativity doesn't prove Newton's theory is wrong. That's not the way science progresses. What Einstein did, or what his theory does, is subsumes Newton's theory into a deeper, more profound structure. And if you take the domain in which Newton's theory was developed, essentially, the solar system, then Einstein's theory, as a very good approximation, does reduce to Newton's theory. So Einstein's theory incorporates Newton's theory.
12:49
It extends it. It makes new predictions. And one of the most stunning predictions it makes is that there exists black holes.
13:02
Two or three weeks after Einstein wrote down these field equations, Karl Schwarzschild, who was a German scientist who was in the Prussian front, a soldier on the Prussian front, and a few weeks after Einstein wrote down these field equations, he found the first black hole solution.
13:23
A black hole is a region of space and time in which, once you go inside the black hole, you can never escape. The boundary of the black hole is called the event horizon. So if we imagine we're in a spaceship and we cross the event horizon, going from the outside to the inside of the black hole, once past the event horizon, no matter how you fire rockets, you're always going to stay inside the black hole. Similarly, if you shine a light beam-- you shine a torch, or any other light beam--
13:56
from inside the black hole, it necessarily stays inside the black hole and won't ever emanate past the boundary of the black hole, the event horizon. So since light can't come from inside to the outside, out black. They don't emit any light.
14:17
One of the ways in which black holes conform is in the final stages of evolution of stars. And evolution of star is a battle. It's a battle, on the one hand, between the matter of wanting to collapse in on itself, and the pressure caused by the thermonuclear reactions happening deep inside the core of the sun, holding that pressure, the force of gravity, at bay. So for most the evolution of the star, those two forces, using that Newtonian language, the force of gravity pulling the matter in
14:53
and the pressure pushing it out, are at equilibrium. But as the nuclear material is exhausted, the nuclear fuel is exhausted inside the star, if the star is big enough, it will collapse in on itself and a supernova will happen. That will collapse in and then explode off and, again, if the star is big enough, there will be a core of matter inside the interior of the star that will keep collapsing in on itself and will form a black hole.
15:32
One of the most extraordinary facts about general relativity and these black holes is, despite the complexity of what I've just said, how a black hole can form-- after all, the star could be 20 solar masses, 50 solar masses-- you think of the complexity of the supernova explosion, how much matter is ejected, and so on and so forth, the final black hole that is created is specified by two numbers, its mass and its spin. All the other information about the black hole--
16:07
sorry, all the other information about how the black hole was formed-- is lost, and you just left with those two numbers. Actually, to be more precise, there's three numbers, and exactly three. So now this is a fact. The third number is the electric charge, but in practise, the electric charge in astrophysical black holes is going to be extremely small, or non-existent, because charge will naturally neutralise the black hole very quickly. But the mathematics of relativity says it's specified
16:37
by three, and in practise, it will be just the mass and the spin, which will determine the properties of the black hole. So that's what I wanted to mention. That's what I mentioned at the beginning of the lecture, that black holes, in general, extremely are extremely simple.
16:57
If black holes are black, how do we detect them? Here is, I quickly add, an artist's impression of a star in a black hole. It's a companion system, a binary system. And the black hole is spinning. And you can see that it's stripped off, or it is continuing to strip off, matter from the star. And as it strips off the matter, because the black hole is rotating, that matter gets swirled around the black hole and starts to form, heat up from a plasma.
17:37
In fact, that plasma, as it generates magnetic fields, it also shoots up these jets along the axis of the direction which it's spinning.
17:49
This plasma reaches very high temperatures and starts to emit X-rays. And the first indirect detection of black holes came from measuring the X-rays produced by black holes, as in this picture.
18:07
We now know that there's many black holes in the universe by these indirect tests. And in particular, there's a supermassive black hole at the centre of our galaxy-- our galaxy, the Milky Way. It's in the constellation of Sagittarius, and it weighs three or four million times the mass of our sun.
18:30
In fact, most galaxies in the universe we think has a similar sized black hole, or even bigger. There's another very beautiful piece of indirect evidence for the existence of this black hole in the centre of our galaxy. So here is a picture of-- I'm going to run a little video, and it's a video of the motion of stars right at the centre of our galaxy. It was taken over 14 years, and the red cross is the place where we think the supermassive black hole exists,
19:13
and there's no light being emitted from that region. So the date was taken from 1992 to 2006, and let's have a look at it.
19:29
So one thing I should quickly add. This is not a simulation. Often, you see simulations, but this is real data. This is real observations of individual stars around the centre of our galaxy. And if I just stop at about here, you see we have these nice elliptical orbits of these stars going around the central object. And by studying the detailed shape of those orbits and the time taken for the stars to go around a complete orbit, we can use the mathematics of general relativity
20:03
to deduce what the mass of the object is that they're orbiting, and that's three to four million times the mass of our sun. And in addition, if I just take it a little bit forward, there's two orbits that get extremely close to the central object, but don't hit whatever it is. So we know the size, as well as the mass, and we know of no other object that can weigh three or four million times the mass of the sun and squeeze into that amount of space, except a black hole.
20:39
So we believe there is a black hole at the centre of our galaxy.
20:50
So these are the indirect ways to check the existence of black holes. Let me come on to the direct way. In 1916, just one year after Einstein formulated his theory of general relativity, he realised that general relativity predicts that gravitational waves exists. As matter moves through space and time, it forms gravitational waves. And the picture you can have in your mind is that as you move your hand through the surface of a pond, you form ripples on the surface of the pond.
21:26
Similarly, as mass moves through space and time , it forms gravitational waves. In fact, as we're moving around, we're forming gravitational waves. However, these gravitation waves of the motion of ourselves are extremely tiny.
21:45
The gravitational waves caused by the Earth orbiting the sun are also extremely tiny. As the Earth orbits the sun, it's emitting gravitational waves in all directions, and you can calculate what the total amount of power is from all those gravity waves. So imagine you gather them all together and say, how powerful is that? That would be powerful enough just to light up a light bulb. So even though these are existing, the sun and the earth is only producing these tiny, tiny little ripples
22:21
in space and time. There's a reason for why these are so small. And the reason is that gravity is an extremely weak force. So I'm going to use the Newtonian language because it's convenient here. We're not used to thinking of gravity as being weak. For example, if we jump, we fall to the ground and it feels like gravity is pulling us down with a strong force. But we can do a very simple experiment which compares gravity, and the strength of gravity, to another force.
22:55
And it's a very simple experiment, but it's an important experiment. It involves a magnet and a paperclip. And obviously, just like the beginning of the lecture, if we drop the paperclip, it falls to earth under the influence of gravity. But I can compare the gravitational force of the whole of the planet Earth on that paperclip to the electromagnetic force on this tiny little magnet. And we know what will happen. It holds it up.
23:31
And it's a simple observation, but it's a profound one. It tells us that gravity is extremely weak. It's just that when all the other forces are not around, gravity is the only one left, and it dictates what's going on.
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So gravity is weak. Gravitational waves are very small. If we're going to have any hope of detecting gravitational waves, we're going to have to look for a cataclysmic explosion. And a cataclysmic explosion is the coalescence of two black holes.
24:10
So we imagine we have a system of two black holes, perhaps formed like the picture we had before-- one went supernova, formed the black hole, and then the companion star later also formed a supernova and turned into a black hole. And those black holes were rotating, spinning on their own axes, but they're also rotating around each other.
24:34
Because of the simplicity of black holes, specified by their mass and their spin, we can calculate how much gravitational waves would be admitted by the system. If every black hole was different and a highly complicated individual object, we wouldn't be able to do this. But that simplicity of black holes allows us to calculate the gravity waves that are produced.
25:03
And here is a prediction from general relativity of the gravity waves that are produced. So we're imagining the two black holes orbiting each other. Their emitting gravitational waves. As they emit the gravitational waves, they lose energy and they get closer and closer to each other, and they eventually inspiral and form a single black hole. So on this graph, on the vertical axis, I've got the strength of the gravitational waves, and on the horizontal axis, it's a time scale.
25:39
And you'll notice that the time scale is in roughly tenths of seconds. So we're looking at the very final part of the coalescence of these black holes. For millions of years, they'll be actually rotating around each other, producing gravitational waves at a constant frequency, like on the left-hand side of the graph. As they get closer, in the final inspiral and coalescence, the frequency of the gravitational waves goes up and the amplitude goes up. They form a single black hole, and then
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the strength of the gravitational waves dies away.
26:25
In fact, this frequency of these gravitational waves being produced in this process of almost the same as audio frequency. So people talk about the gravitational waves signals using the analogy of sound. So the frequency is constant, and then as they coalesce, it goes up in frequency and louder, and then it suddenly rings down. So it's called a chirp and ring down. So it would be something like wooop. That's a sound version of that graph, if you don't like looking at graphs.
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The point here is that the simplicity those black holes and general relativity allows us to determine that signal.
27:12
So we know, out of prediction from Einstein's theory of relativity, of what gravity waves are produced, gravitational waves, are produced by these systems. How do we measure them?
27:24
The technique is laser interferometry. And being a theorist, I love the fact that I can now play around with some equipment here, and hopefully not break it. What I brought in is a laser interferometer. And maybe if we can just have-- yeah, the picture there, let me just switch this on.
27:55
It should just start warming up in a second. OK right. So what have we got here? I've got it in a black box. It's not very dangerous, but it's a little bit dangerous. So you can't see it, but you can see from above what's happening. We have the laser here, and it's emitting a laser beam straight out the end here. And this little object here is a beam splitter. So half of the light gets reflected up here to a mirror, which then gets reflected back, and then will go straight forward.
28:30
And the other half will go through to this mirror and then come back to the splitter and then go off in this direction. So there is a coherent laser light beam that's split into two beams and then is sent down in this access. So let's have a look what happens.
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And if we can have the lights down. There are the two beams I mentioned. And something interesting happens if we manipulate them So they're sitting on top of each other. This is the phenomenon of interference. Light is a wave, and just like water waves on a pool-- on the surface of a pond, or something like that-- interferes, light wave also interferes. The point about this set up is that this interference pattern is very sensitive. And if you change the geometry a little bit,
29:39
fire a sound wave, then you see that the interference pattern changes. This is exactly the principle that's being used in the LIGO experiment to detect gravitational waves. Taking laser beams, interfering them, and then seeing when the gravitational wave comes in, that the interference pattern has moved. So can I have the lights back up again? Thank you.
30:15
And can we have the slides back as well? Thank you. So here is a photograph, two photographs, of two detectors. One in Hanford in Washington, the upper left-hand side of the United States, and the other one in Livingston in Louisiana, down in the lower right. And the pictures above them are pictures of the two jet LIGO detectors. And you can see that there's two long arms, and down each of those arms, which are actually four kilometres long, a laser beam is being sent.
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It's being sent and there's a big mirror at the end of one arm. There's a big mirror at the end of another arm. And the light's coming back, and it's being interfered, much in the same way we just demonstrated here, at that central detection facility at the apex of the two arms. If a gravitational wave comes through this system, it tends to squeeze one of the arms, makes a little bit shorter, makes the other arm longer, or vise versa.
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The gravitational waves that were caused by the two black holes colliding, that were observed in 2015, changed the length of these arms, these four kilometre arms, by 1,000th the size of an atomic nucleus.
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This is truly breathtaking engineering. All vibrations-- for example, me hitting the table, just like a few moments ago-- would completely swamp the signal. All seismic vibrations-- all vibrations of machinery in the laboratory, et cetera-- all of that has to be shielded away by elaborate and sophisticated engineering. And once that's happened, you have this perfectly stable system. If a gravitational wave comes in, it produces a signal. And you're waiting for the movement of 1,000th of the size
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of the diameter over four kilometres.
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One of the key aspects of this experiment is that there should be two. The distance between the two detectors is about 3,000 kilometres. So given that gravitational waves move at the speed of light, the time taken-- the gravitational wave will hit one of the detectors first, and it will hit the second one a little bit later. And a little bit later is exactly quantifiable. It's about 10 milliseconds. So if a gravitational wave signal has come in, the two signals, when you move them
33:04
on top of each other separated by 10 milliseconds, should be the same. And in the lower right-hand of the figure of the image, that is actually the real data that was published by the LIGO experiment, saying we have detected gravitational waves. Now, it's true that there's a lot of noise there, but the main feature that I want you to pick up on is that they are exactly in phase, especially towards the latter part of the event. They're exactly in phase.
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You can see that constant frequency process, the increasing amplitude, the chirp, and then the ring down.
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As I said before, this was the first direct detection of black holes, the first direct detection of gravitational waves, and the first direct detection of a binary system of black holes. So if you think about it for a moment, it's very hard to know that you have a binary system of black holes. A black hole and a star, you look for X-rays, and you also see the light coming from a star. But if you have just two black holes, they might be producing X-rays from some remnant, accretion
34:19
that surrounds them. But you wouldn't know if that's one black hole or two black holes. So this is the first direct evidence that there are binary systems of black holes in the universe.
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I've blown your mind once, hopefully, about the engineering feat. I want to blow your mind again.
34:41
By studying that signal and comparing it to the theoretical observations predictions from general relativity, we know that the masses of the two black holes were 36 times the mass of our sun and 29 times the mass of our sun. In fact, before this experiment, we didn't know such black holes of that mass existed. They coalesced to form a black hole, which weighs 62 times the mass of our sun. So there's one equation in this talk, and here it is. 36 plus 29 minus 62, and that's 3.
35:19
So after they coalesced, there was three times the mass of the sun of matter that was ejected into gravitational waves.
35:31
And the amount of energy that is, you use the famous E equals mc squared equation of Einstein. And that was released in a tenth of a second, which was that final chirp on the graph that I showed before. The amount of power that was produced in that moment was 3 times 10 to the 49 watts. Even if you have facility with numbers-- you're a mathematician or you're a physicist-- when you get numbers like this, 10 to the 49, that's 1 with 49 0's following it, you lose intuition. This is a huge number.
36:15
So you can try and think about, what's a powerful object that you know about in the universe? You might begin on earth with powerful objects, nuclear reactors, for example. Forget that. Let's go to the sun. Let's think of the sun for a moment. All of the power from the sun reaching us about 90 million miles away, driving all of life on Earth, that power, the total power emitted by the sun, is about 10 to the 24 watts, 1 followed by 24 0's. So this is much, much more powerful than all
36:52
of the power emitted by the sun. In fact, it's more power emitted by all of the stars, not just in our galaxy, but in all of the galaxies in the universe.
37:12
So when I mentioned cataclysmic explosion earlier, this simplicity of space-time, just the mass and the spin swirling around each other, that rearrangement of space and time into a single black hole is truly cataclysmic, and that's despite the fact that gravity is weak, in the sense that I was describing it before.
37:39
We also know that the event happened about 1.3 billion light years away. That means the gravitational waves were emitted about 1.3 billion years ago and then arrived at Earth in 2015. And I find that kind of poetic. 1.3 billion years ago, Earth had just evolved from single celled organisms to multicellular organisms. And we wait a little bit longer, and multicellular organisms become fish and reptiles. Dinosaurs come, dinosaurs go. Mammals come, evolve. Humans evolve. Isaac Newton comes.
38:25
Einstein comes. We start building this detector. And I say we because it is we. It is humanity who does this. We build this detector, and finally, when it's ready to go, it has its upgrade, we switch it on. And actually very soon after the upgrade, we switched on. Bang, the signal is there, coming towards us.
38:49
I also want to emphasise at this point that gravitational waves, observations that we've had, and there's been three more since then, there was just one two days ago. You may have noticed that in the news-- it's not just verifying that Einstein was right. It's not verifying that, oh, black holes really do exist, confirming what we knew. That's all true, but the really exciting thing is it's a new type of astronomy that's being created. We now have a new window at looking at the universe.
39:18
Not through electric electromagnetic radiation, like in the telescopes we've been using, but by gravitational waves. And we're going to learn more about black holes and their properties and their distribution, and we probably are going to learn things that are brand new that we haven't thought about before as well. So gravitational wave astronomy and observations over the next 10, 20, 30, 40 years is going to be an extremely exciting field in science, or fundamental science.
39:51
OK, so let's leave the observations and let's go back to some theoretical pondering. Let's return to the question about what happens inside a black hole. So the two figures here are Stephen Hawking, of course, and Roger Penrose, who in the '60s and early '70s really pioneered and laid the foundations for understanding the true properties of black holes, and in particular, what happens deep inside the black hole. If you cross into the event horizon, as I've said before,
40:25
you are never coming out past the event horizon. In fact, if you crossed a big enough black hole, you wouldn't even notice that anything was different. You would feel exactly the same as if I stood on this table and jumped off the table, so I would be in freefall for a moment. That sense of freefall would be exactly what you would feel, if the black hole was big enough, as you crossed the event horizon. As time went on, you would then find, actually, you would be squeezed and stretched.
40:58
It's called spaghettification. You'd be squeezed and stretched, and eventually, you would confront what's inside the black hole, this space-time singularity. And this space-time singularity is inevitable. And the picture I've drawn doesn't capture a key feature of space-time singularities. And the key feature of space-time singularities inside black holes is that they're singularities in time and not in space.
41:31
If a singularity was a point in space-- let's imagine it was in the centre of this room-- you have this strong sense that you should be able to avoid it. If you find your rocket, surely I could just move away from the space-time singularity. Why do I have to hit the space-time time singularity? That's true, and that's because space-time singularities and black holes are not of that form. Space-time singularity is a singularity in time, and you should think of a moment in time in the future
42:00
that you can't avoid. We can't avoid next Tuesday, and that's exactly-- not rough, exactly-- how you can't avoid the space-time singularity in a black hole. And it's this change of grammar that's actually important. A space-time singularity happens. You go inside the event horizon and the space-time singularity will inevitably happen. For the biggest black holes that we know of. It's of the order of 100 hours. Inside the black hole in the centre of our galaxy, it's about three hours, I think.
42:37
Or maybe it's one hour. It's roughly that.
42:43
Interestingly, the longest you have before the singularity happens is just to relax. You just freefall, and that's the longest you've got. Any other motion you do, if you switch on your rockets, it makes your-- the singularity happens quicker. I think there's a life lesson there somewhere, but I'm not sure what it is.
43:09
But it's interesting. I think it's not emphasised enough, that one more level of that analogy with Tuesday is firing your rockets trying to avoid the space-time singularity would be exactly analogous to say, I'm going to hop in my car and I'm not sure which direction you are driving, but you just try and drive away from next Tuesday. It's meaningless. And similarly, that's exactly what's happening inside the black hole. So what is a space-time singularity? So a space-time singularity is where
43:44
the laws of general relativity break down. So general relativity is no longer valid at the space-time singularity. And at first hearing this, that sounds like a very bad thing. It sounds like general relativity is no longer-- it's somehow a flawed theory. It can't tell us what we need to know about what would happen deep inside a black hole. But, in fact, that's completely the wrong way of looking at it. What the space-time singularities are telling us is that there's an opportunity
44:18
for deeper insight into the fundamental laws of physics. We know that general relativity is not the theory of everything. After all, it doesn't describe any of the quantum forces, which we'll be discussing in a moment. So there must be a bigger theoretical framework, deeper fundamental physics, beyond general relativity. And what the result of Stephen Hawking and Roger Penrose says is that black holes are a great place to think about where you should go beyond our existing knowledge.
44:55
Black holes aren't the only place that space-time singularities exist. They also exist at the very beginning of the Big Bang. So if you look at all the galaxies today, they're all expanding away from each other. If you run the history of the universe backwards in time, those galaxies will be getting closer and closer and closer. And about 14 billion years ago, all of those galaxies would be on top of each other, and that would be the Big Bang. And that moment if the Big Bang, in the context
45:27
of Einstein's theory of general relativity, is a space-time singularity. So another place to think about fundamental physics beyond general relativity is the very beginning of the Big Bang, or the very early part of the universe.
45:44
Up until now, I've just been just describing gravity, but I now introduce another player into the game, which is the quantum world. All of fundamental physics rests on two pillars. On the one hand, Einstein's theory of general relativity, describing gravity. And on the other, the quantum world, which describes all of elementary particle physics-- electrons protons, neutrons quarks. All of the elementary particles that are observed in the particle accelerators, including
46:19
the Large Hadron Collider, are described by the quantum world. And there's something called the standard model of particle physics, which encapsulates our deepest understanding of elementary particles and their interactions. Both of these fundamental theories are extremely accurate and describe nature with exquisite precision and beauty, but they're mathematically inconsistent.
46:52
And that's a paradox when you first hear it, but it has a very simple explanation.
46:59
When I've been describing gravity, I've literally been forgetting about the quantum world. And we can do that because all of the quantum forces-- for example, the electromagnetic force is one of those forces-- are neutralised over the scales that I've been describing. So the only force that's important, using the Newtonian language of gravity on the scales of black holes and galaxies and so on, is gravity itself. And we use Einstein's theory of general relativity
47:30
and forget about the quantum world. Similarly, when people do experiments in Geneva at the Large Hadron Collider, they understand and appreciate that the gravitational interactions are extremely tiny compared to the interactions they're looking at. Think of the paperclip and the magnet. And they, again, pretend that gravity doesn't exist at all. They just pretend it's not there. So in both domains, we're approximating what's going on. The quantum world, we approximate
48:05
by saying there's no gravity. And in these descriptions of black holes and gravitational waves, and so on, we approximate by saying the quantum world doesn't exist. But nevertheless, we would like to do better than that. We would like to put these both together into a cohesive, logical framework. And the question remains, then, is how do we unify these two great pillars of knowledge? So in the rest of the talk, I want to just give you some flavour why we think black holes are the key laboratory,
48:40
or a key laboratory, for that next stage of unification in fundamental physics.
48:52
I can just tell you one thing about quantum theory to motivate what I wanted to say.
48:59
In quantum theory, the vacuum, empty space and time, is actually not as empty as you might think.
49:10
A way of thinking about it, it's a sea of virtual particles and anti-particles coming into existence out of nothing, literally nothing, existing for a little while, and then annihilating away to nothing. So in this picture, I've got-- a red arrow might represent an electron coming into being with its anti-particle, a positron. They exist for a little, short amount of time, and then they annihilate away. And we call these particles virtual, because they're not directly detected.
49:45
However, they can be indirectly detected, or their effects can be indirectly detected. And they can be measured, and we know that these are real, So our conception of what the vacuum is in quantum theory is changed from our naive picture.
50:03
Stephen Hawking asked the great question, in essence, what happens to these processes in the presence of a black hole? Now, Stephen Hawking did not have the theory of quantum gravity. This is a work in progress. But he's taking one component of the quantum theory and taking a component of general relativity, a black hole, and fusing them together to obtain some insight.
50:37
And by doing a specific calculation, he showed that the following happens. Away from the black hole, these processes, these virtual processes, continue much as they were happening as if there wasn't a black hole. But near the event horizon, occasionally one of these particles can be stripped off, one of the virtual particles can be stripped off, it goes inside the event horizon, and the singularity will happen for it. The other particle can escape away from the black hole.
51:19
And in this process, the particle that escapes turns into a real particle. So the net effect of this process is the black hole, with this virtual processes happening all over the place, is such that, effectively, the black hole is emitting particles.
51:41
And it's not just emitting particles in any old way. It's emitting them in a very precise way. It's emitting them it as if it was a hot object with a temperature. And this Stephen Hawking's famous Hawking radiation.
52:01
There's more. The properties of black holes obey a series of laws, which have the same form as the laws governing thermal systems. A thermal system is any system involving heat, so think of a steam engine.
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There's very precise laws that were developed in the 19th century to describe the physics of steam engines, and any objects involving heat.
52:33
And these laws have a great universality, that are another great achievement in the quest for understanding fundamental physics. They explain, for example, if you pump up a bicycle tyre, the valve will always get hot. If you release the valve and the air comes rushing out, the valve will get cold. If it's a hot, sunny day and you're in your kitchen and you think you'd like to be cooled down a bit, you might be tempted to open the fridge door and the cold air comes out.
53:04
But these laws that I'm describing would say if you do that, overall, the temperature the room will increase, because the heat being produced at the back of the fridge will always be bigger than the cold air coming out of the fridge, or the reduction of temperature. So these laws, they basically govern everything in everyday life with anything to do with heat. It's quite remarkable that black holes obey these same kinds of laws.
53:44
These laws of thermal systems were developed in the mid-19th century, before atoms were universally accepted as fundamental building blocks of matter.
53:58
When the atomic theory came along, people realised that it explained where these thermal those came from. The thermal laws have a microscopic explanation. So for example, take a hot cup of tea. It has heat. It has a temperature. But we from the point of view of atoms, that can be explained in terms of the individual motions of the atoms.
54:32
So heat is this disordered motion of the atoms. That's what it is, in terms of this atomistic big picture. And for example, the temperature of the tea is determined by the average speed of these atoms. So the atomic picture provided a deeper, more profound understanding of what these thermal laws were.
55:01
And that's the status of black hole thermodynamics, or thermal physics, at the moment. We know that they obey a series of laws, but we don't have the underlying picture of atoms of space and time which explains those laws. So that's one of the big outstanding question, what is the microscopic description in understanding of these thermal laws? What happens when the black hole emits its particles, more and more particles? Eventually, it will reduce to nothing.
55:43
And remember, I said in general relativity, black holes are very simple, that no matter how they were formed, from all the matter of the collapsing star, material in the star, they were then specified by the mass and the charge, the mass and the spin. If the black hole then evaporates, producing all this thermal radiation, it seems like we have a process in which information has turned into pure thermal radiation, and that goes against the grain of quantum theory.
56:17
That's a major outstanding question, what happens to the black hole as it fully evaporates?
56:27
A variation of that question is the singularity inside the black hole will be revealed when the black hole evaporates. So what is the nature of the singularity, and what is that? These new atoms of space and time tell us what that is and how it's resolved. This is the cutting edge of research into black hole physics today. So I just wanted to end the talk with some comments about string theory. So string theory is an attempt to unify quantum theory with Einstein's theory of general relativity.
57:08
And the fundamental idea of string theory is extremely simple. The idea is this. If you zoomed in into the atom, you would find a halo of electrons surrounding a nucleus of protons and neutrons. If you zoomed into the protons and neutrons, you would find quarks. If you zoomed further into the quarks, we don't know what you would find, but we think you'll find something, some deeper structure. But don't go to the next step, go all the way to the end, and what is the endpoint of that process?
57:45
And the end process, it's postulated, is that the fundamental building blocks are strings, these one dimensional filaments of energy which would have no further substructure. And one of the most appealing things in strings is that the different vibrations of the string would correspond to different elementary particles. So the one string, if it's vibrating, just like a violin string, one note would correspond to an electron, another note would correspond to a quark, another note
58:19
to a photon, a particle of light, and also another vibration would correspond to a graviton, a quantum particle of gravity.
58:34
So we don't know yet if string theory is correct, but research in string theory, or a large branch of research, is trying to address these questions of the thermal properties of black holes to have a deeper understanding of what black holes are, as well as to get evidence that string theory is actually on the right track, and it is the theory that unifies quantum theory and gravity.
59:07
So in tonight's lecture, I wanted to tell you several things. The first was that black holes are really cool. They're structures in the fabric of space and time itself. They have this beautiful simplicity, and they really are amongst the most extraordinary objects that exist in the universe. Black holes are real. We've had indirect evidence that black holes are real for a long time, but we now have this beautiful direct detection of black holes that was made by the LIGO experiments
59:38
in 2015, and then three times since then.
59:44
And this section of gravitational waves is presaging in a new era of astronomy. This is not the end of a story. Like many developments in physics, as one story ends, a new one opens up. And the new one that's opening up is this new era of astronomy using gravitational waves. For example, one of the things that we're going to do-- we, I include humanity in the we there-- is put satellites up in space, and they're going to be separated a million kilometres apart,
1:00:17
and we're going to be looking to the gravitational waves that might change the length, that million kilometres by 1,000th of the size of the diameter of a proton. It's breathtaking what we are thinking about doing, and it's being planned to be done in the next 20, 30, 40 years. So black holes are real, and finally, black holes are the way forward. By thinking about quantum theory, we know that there are thermal objects. We know there are space-time singularities, where
1:00:51
we need a quantum theory of gravity to tell us what's going on. And black holes, and thinking about their properties, is the arena in which we think that we can get the most insight in that next step.
1:01:08
The last point I wanted to make was a recurring theme that's gone throughout the talk is that, often, there's very long time scales between developments, both in theory-- development of fundamental theoretical physics over the scale of hundreds of years. Sometimes it's punctuated by rapid development, but often it's over the scale of 100 years-- and also, experimental verification. Predictions come up with new theories, but we sometimes have to wait 10, 20, 30,
1:01:41
again, up to 100 years before we get evidence and confirm the predictions. But that's the nature of the activity we are undertaking. And even though the progress can be slow, the clearest message that comes through is that progress does get made. We do make inexorable progress in obtaining a deeper understanding of the fundamental laws of physics, and I think that's surely one of the great intellectual and cultural achievements of all of humanity. Thank you.
1:02:20
So this is actually-- there'll be another talk-- it's actually another of the deep clues to how to unify quantum theory and gravity.
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