Our Universe & Others

0:00 The most famous you might have heard of his pie in the sky, and our artful universe, but I'll now pass on to John, who's going to speak on our universe and others. Thank you. Thank you. I think I need to put this on. That's correct. Well, welcome to the Newton Institute, if you haven't been here before. My job is to tell one of those extremely rare events, which is called our universe, and why it is that cosmologists take an interest in thinking about other types of universe as well. One of the reasons cosmology and the study of universes is a rather vast and difficult subject it's really not just about astronomy it's not just understanding the most famous you might have heard of pie in the sky and our art for the universe but I'll now pass on to John who's going to speak on our universe and others, thank you Thank you. I need to put this on. That's correct, yes. Well, welcome to the Newton Institute, if you haven't been here before. My job is to tell you something about one of those extremely rare events, which is called our universe, and why it is that cosmologists take an interest in thinking about other types of universe as well. One of the reasons cosmology and the study of universes is a rather vast and difficult subject is because it's really not just about astronomy, it's not just understanding the objects that one sees through telescopes, but about understanding the nature of space and time itself. Well, a few years ago, you can remember, people were much enamoured of the idea of time and the year 2000 and so forth, and there

2:30 was a famous physicist who once asked what was the definition of time and why did it exist, and his answer was that time exists to stop everything happening at once. Sorry, to stop everything happening at once. Well, for the counterpart to that, of relevance to us today, why does space exist? Space exists, I'm afraid, to stop everything happening in Cambridge. Now, the study of the universe became a subject for mathematicians and for physicists that had a theory, a way of making predictions about what whole universes would be like as a result of Einstein's development of a new theory of gravity that subsumed Newton's famous theory to make it relativistic, make it able to deal with very strong gravity fields, with things that move close to the speed of light. general theory of relativity. And it led to other scientists making rather dramatic predictions that the whole universe, everything that is on an astronomical scale, should be in a state of motion, should be expanding. Things should be moving away from one another at ever-increasing speeds. But at the end of the 1920s, this discovery was confirmed by observations of an American called Edwin Hubble. Hubble was a remarkable man. He began life, in effect, as a boxer. He then became a lawyer, and then he became an astronomer. People tend to go in the opposite direction nowadays. He was quite a good boxer, actually. He fought a draw against the world light heavyweight champion in an exhibition. He was a huge man, about six foot four and a half tall, and so his ideas really were much taken upon by other easily at conferences and so forth. But this is what he first found back in 1929. This is a plot of the speed at which distant sources of light are receding away from us, nebulae as they were called in Hubble's day, galaxies they will be called today. And here is the distance measured in light years, the distance that light can travel in one year at 186,000 miles per second. And you can see, even by astronomers' standards, this is a pretty good straight line. The deviations from the exact straight line are just because things have little local motions, just like the Earth does going around the Sun.

5:00 So on seeing here, the farther away you are, the faster things seem to be receding. Hubble's observations, by the way, would fit, the original observations, would sort of fit around in a little box the size of one of these dots close to the origin. So this shows you how hard people work in this subject. They've become so much better at seeing sources of light that are very faint. They can see things that are much, much farther away and therefore extend this curve way up to huge distances, quite close to the visible limit of the universe. So there's observational evidence that the universe is expanding. Well, the first thing to get straight about this is that you're not expanding. The Newton Institute isn't expanding. Cambridge isn't expanding. So what is expanding? Well, before you find the markers that take part in the expansion of the universe, you've got to go to the scale of great clusters of galaxies. They're the objects that mark and trace out the expansion of the universe. Things that are smaller, like galaxies and planets and people, are held together by other forces of nature that are stronger than the effect of the expansion. While the fact that the universe is expanding immediately means that its enormous size is bound up with its age, rushing ahead, we know that the expansion seems to have been going on for nearly 14 billion years. Remarkably, the Earth has been around for not much less than 4.6 billion years. formed. So our solar system has been around for really quite a large fraction of the whole time that the universe has apparently been in a state of expansion. Well, this great age has clearly been taken on board by others. I came across this little packet of German salt a month or so ago, and it had this wonderful little advertisement for itself on the side. This rock salt is over 200 million years old, formed through ancient geological processes in the German mountain ranges, best before April 2003. Well, the expansion of the universe allows us to turn the study of cosmology into a subject of physics as well as astronomy. So suppose we try to reconstruct the past history of the universe, measuring its expansion by some gauge of its size, the separation between those galaxies or the places where they would have been, against age in billions of years.

7:30 So here's the trajectory of its expansion, and we can start to piece together something of the biography of the universe. If we were to work backwards to when it was about a thousand times more contracted than the present, when it's about 300,000 years old, then the temperature of material in the universe will be about a thousand times hotter. If you take a large cavity of radiation and you decrease it in size, then the temperature of the radiation will go up inversely proportionally to the diameter of the cavity. So when it's about a thousand times smaller, the temperature is so hot that you can't have any atoms or molecules, no complicated structures of that sort. They're just beaten to pieces by the intensity of the radiation. So back here we have a state of dismembered atoms, of protons, of nuclei, of ions, of elementary particles. Gradually as the universe expands, it cools enough for simple atoms to form, simple molecules of hydrogen. And then by a complicated sequence of events, large regions of the expanding universe that are going a little slower than the average slow down, they condense, they separate off from the expansion, and form what we call galaxies. And within galaxies, complicated processes form stars, and ultimately planets, and ultimately people. If we were to look ahead into the far future beyond our 14 billion-year Spartan history, then things look rather bleak. The long-range forecast is not entirely optimistic. Eventually the sun will exhaust its nuclear fuel at first, it will expand dramatically, vaporizing all the planets like our own in the inner parts of the solar system, and ultimately it will just cool and shrink and die down to a size little more than that of the Earth, and just cool forever and ever. So we live in a rather propitious niche of cosmic history, not surprisingly,

10:00 after the stars have formed, but before they all die. So our view of the universe is slightly biased by having to live in this interval of time when there are stars and planets which allow atomic organisms to exist in reasonably temperate conditions on their surfaces. well that picture I think reinforces this issue of the connection between the size and the age of the universe and we might ask a rather straightforward question about the universe why is it so big why do we find the universe to be so well if we think about ourselves for a moment we can convince ourselves that we shouldn't be surprised by this we are rather exotic complexity. We're built of atoms which are heavier than helium and hydrogen gases, elements like carbon and nitrogen and oxygen and phosphorus. All these elements are made in the stars. They're made by a long sequence of chemical, of nuclear reactions that take billions of years to complete. They take the building blocks of hydrogen and helium from the Big bang from the early stage of the universe and turn them into elements which are biochemically useful. When the stars exhaust their fuel and explode and die, they disperse these elements like carbon throughout the universe. Sometimes even they get reprocessed through stars and do a second round of this activity. So we can appreciate that in order to have the building blocks of biochemistry, you have to have perhaps 10 billion years of time in which to make those building blocks. And because the universe is expanding, it must inevitably therefore be at least 10 billion light years in size. You might think we could get away with a universe that was just the size of our galaxy. There are 100 billion stars in our galaxy. It's a pretty good economy-sized universe. But have a universe that's the size of one galaxy, and it's little more than a month old. And you've barely got time to pay off your Visa credit card bill, let alone evolve within complexity. So the universe would have to be pretty much as big as it is just to support one lonely outpost of life.

12:30 This type of perspective tells us a number of other interesting things about the universe. its huge size necessary for the existence of life within it, but the darkness of the night sky, the general inhospitable appearance of the universe, is another necessary consequence of life-supporting conditions. Back in Newton's time, people used to worry about why the sky is dark at night. And the answer's got nothing to do with the sun, because if you look into a forest, you probably realize that everywhere your line of sight ends upon a tree. And you just see a phalanx of tree trunks. And people in Newton's day, like Halley in particular, who we know of through his comet, ask the question, why is it that if the universe is infinite, everywhere on the sky doesn't look like the surface of a star. Because if we look in any direction, we should eventually end up looking at the surface of a star, and the whole sky should look like the surface of the sun. So why is the sky dark at night? Well, the answer is provided by the expanding universe that what the expansion has done has to make the universe so large, it's degraded the energy in the universe and lowered its so that if today I was to click my fingers and turn every piece of matter in the universe into radiation and light, you wouldn't even notice, as long as it wasn't you, I wasn't turning into light, but all that would happen is that the temperature of the universe would rise from 3 degrees above absolute zero to about 10 degrees above absolute zero. There just isn't enough energy in the universe to make the sky dark. and the reason for that is that the universe has expanded so much it's so large and this again is one of our necessary conditions for life the other odd thing about the universe is that there's virtually nothing of it that the universe is pretty much just empty space if I was to take all the matter in the universe and smooth it out into an equal sea of atoms then there would be just one atom in every cubic meter of space. Now no physicist can make as good a vacuum as that in a laboratory on Earth

15:00 by a vast margin. So there's hardly anything there. If we bunch the matter up a bit and instead of having it just as single atoms we group it into planets the size of the Earth then the density of the universe corresponds to finding a planet every 10 light years. If we join it up into stars, like the Sun, which are about a thousand times more massive than the Earth, then you'd have to go a thousand light-years, on average, before you found another star. And to find another galaxy with its hundred billion stars, you'd have to go ten million light-years. So you begin to see why extraterrestrial intelligence is so rare. The universe is a lonely place. there is a long, long distance between separate solar systems and star systems. If they were closer, the density of the universe would be vastly bigger, and it would expand more slowly, and its lifetime would be vastly shorter, too shorter for there to be any observers like ourselves. So we have a rather pessimistic verdict, really, that life-supporting universes like our own are big and old and dark and cold, and also fairly lonely. Well, we've talked about the universe today and some of its gross characteristics. Cosmologists are not content just to understand why the universe has particular properties today. They want to understand how it came to have those properties, why our universe is not like other universes that you could imagine. So cosmologists are interested in other universes, not just because they might occasionally wonder whether they exist, but they want to know why our universe has the very particular properties that it does. Because when you look at Einstein's theory, which enables you to understand and predict the properties of universes, our universe has all sorts of very odd properties. But if you were picking universes out of the hat, our universe would be one of these extremely unlikely events of the sort Robert mentioned in his introduction. Well, in order to understand why the universe is like it is today, the first game is to understand what it was like in the very distant past,

17:30 what it was like as close to its apparent beginning as we can push our theoretical understanding, because we suspect that there are the clues as to why the universe is as it is today. And the great discovery in this field was made by accident in 1965, the heat radiation predicted to be left over from the hot beginning of an expanding universe, the so-called Big Bang. It had been predicted to exist in 1948 and to have the spectrum of pure black-body heat radiation would get from looking at the inside of an oven or some uniformly heated equilibrium source of radiation. But in 1965, two radio astronomers working at the Bell Telephone Labs, a famous research institute in America, discovered this radiation serendipitously. And I always think this is rather remarkable that our telephone company really rather struggles to make my phone connect, telephone company discovers the secret to the origin of the universe, and still struggles to get your telephone to connect. Well, what's shown here is the intensity of the radiation versus the wavelength. The original observations were just down here somewhere, and Penzias and Wilson, who made the discovery, subsequently received a Nobel Prize in physics for that discovery. It took a long time before astronomers were able to create and launch a satellite which would map the whole spectrum of this radiation to confirm that it has this characteristic shape of heat radiation. The solid curve is a blackbody temperature of 2.7316 degrees absolute above absolute zero the boxes are the data points but the size of the boxes are by no means the error bars the error bars of these observations are 100 times smaller than the thickness of this theoretical curve so this is the most perfect black body heat spectrum ever observed in nature so it gives us a wonderful confirmation that the universe really was once extraordinarily hot and dense, hot enough and dense enough to relax that radiation into this pure heat form. So that radiation would have been sent on its way to us when the universe was about

20:00 100,000 to 200,000 years old. You can regard it as a photograph of the universe at that time. But we can do better than that if we take seriously our simple model of the expanding universe and we push it backwards one second old. This sounds completely bizarre. We imagine conditions must be extraordinarily peculiar, but not at all. Remember how low the density of matter is in the universe today. This involves squeezing it by a hundred or ten million times. And the density of matter in the universe, when it's one second old, it's just like the density of this table or this water here. Nothing peculiar or exotic. We understand this behavior. The temperature is sufficiently high, about a billion degrees, that the whole universe is predicted to act like a great nuclear reactor. And nuclear reactions take protons and neutrons and burn them into the very simplest elements. A proton plus neutron makes deuterium. Add another proton, we have helium-3. Add another neutron, we have helium-4. And lithium is the next. We can predict mathematically in enormous detail what the final abundances of these elements should be after the first two or three minutes of activity in the early universe. We know all the physics involved here. We know all the quantities. We can measure them in a laboratory. We have a nuclear reactor that is very quickly turned off, so the abundances stay the same because the universe is expanding and cooling. The predictions are remarkable. 22% by mass of the universe should be in the form of helium-4, 10 to the minus 3% by mass should be in the form of deuterium and helium-3, and about 10 minus 8% by mass in the form of lithium-7. These are precisely the abundances we see in the universe everywhere we look, in our galaxy and beyond. And these elements can't be made in these abundances by any other processes. So this is believed to be a remarkable confirmation that we know what we're doing back to when the universe was about one second to one minute old. That doesn't mean we understand everything that happened in the universe since then.

22:30 We understand the gross expansion in considerable detail, but we don't know all the technicalities, the weather, if you like, of how galaxies and stars form. So just as fluid mechanicsists understand the general principles of how fluid aerodynamics behave, that doesn't mean they can predict the weather in detail tomorrow because of the sheer complexity of all the events concerned. And so it is with the universe. we understand, back to one second, in pretty great detail, the overall pattern of events. We're clearly using the right sort of expanding universe theory. And it encourages us to press back into that first second to see how much farther we can go in the past. If we try to go earlier than a billionth of a second, we encounter temperatures that are higher than those in particle accelerators on Earth. and that's one of the reasons that cosmology is an interesting subject for physicists you can think out the consequences of theories of high energy physics, work out the astronomical consequences, test the theories without spending 60 million pounds on building a particle accelerator instead you spend it on a telescope so far we've talked about only one sort of expanding universe, but there are different varieties of expanding universe. Here's our picture again with distance against size. Here was the expanding universe. You are here about 14 or 15 billion years after the start. But there were two sorts of expanding universe. There's this rather agoraphobic sort that starts expanding and just keeps on going forever. But there's a more claustrophobic sort of expanding universe that is decelerating so that eventually the expansion stops, and it reverses into contraction, and it heads back to a big crunch in the future. And in between, there's a sort of British compromise universe, the so-called critical universe, that just does the smallest amount of work needed to keep on expanding forever. Well, the British Compromised Universe is remarkable, not just because it seems to be a one-in-a-million universe,

25:00 but our universe is tantalizingly close to this critical divide. I'll tell you a funny little story about the British Compromised Universe. Many years ago, I was invited to go and give a talk about cosmology to Mrs. Thatcher and some members of her cabinet. And like all these things, you had to go and do a little mini-rehearsal the week before to make sure you weren't going to say anything that was sort of controversial or offensive. And so I just had to talk for five minutes, and I mentioned this British Compromise Universe. And the cabinet advisor, who was a very serious man who didn't quite see the joke about this, to me afterwards and he said when you come to talk to the prime minister and he said when you mention the british universe can you be much more upbeat about it it's just the sort of thing the prime minister likes to hear about well you can see again there's something interestingly uh human-centered about these universes we shouldn't be surprised to find ourselves very close to this divide, because universes that try to race the way up here expand so fast that galaxies never get a chance to form. Materials are whipped away from other material before it can separate off and form great islands like the Milky Way. So we couldn't exist in universes that expand as fast up here. Similarly, if you're rather too closed, you'll hit a crunch before there's a chance to make any stars in galaxies. So again, you shouldn't be surprised the claustrophobic universes. However, we still like to have some explanation as to why it is that our universe has found itself along this trajectory, and it's not one of these other universes. Because after all, if you were just to wiggle the starting conditions a little bit, it's very difficult to stay on this trajectory for a long, long time before peeling off. And to stay on it, or close to it, for as long as we've been around, requires the initial starting speed of the expansion to be fine-tuned to 1 in 10 followed by 75 zeros. So that seems a rather unlikely state of affairs. Well, in about 1980, a new cosmological theory came on the scene

27:30 that was an attempt to understand why our universe was very close to that special divide and also to try to understand why it was that our universe expanded at the same rate in every direction unlike other universes of which we can conceive, and why the universe did contain irregularities like galaxies. So why wasn't it perfectly smooth? Why wasn't it lumpier than it's found to be? The lumpiness of the universe is on the average about one in 100,000 everywhere you look. So why is it this number and not another one? Well, the inflation of the universe is a complicated piece of mathematics, the sort of thing that programs here have been devoted to in the past, but the idea is very simple. If we go back to our picture of universes expanding in size against time, you've probably noticed that when I've drawn them, they all sort of curve away in this direction, whether the universes are going to expand forever or whether they're going to crunch in the future. of is that all that happens to universes after they come into being is that gravity tries to slow them down. So gravity is putting on the brakes, and this curvature of this line is just the slowing or the deceleration of the expansion. Well, the inflationary universe is a suggestion that for some tiny insolute of cosmic history close to the beginning of the expansion, the universe underwent a bout of accelerated expansion. And there are elementary particles, which theorists have inferred to exist in their theories, which would ensure that this happened. So once these particles appear, there is a short period before they decay where their effect is rather like having repulsive gravity. These particles exert tensions upon one another, negative pressures, which causes the expansion to accelerate. Soon afterwards, these particles will just decay away into ordinary sorts of material, and the universe will keep on decelerating and expanding as before. You can see the general effect of this is to make the universe bigger

30:00 than it would have otherwise have been, to sort of make a surge in the expansion and dramatically increase the size. Here's another way of saying the same thing. Switch yourself in the universe today, and if you were to look out with better and better and ultimately perfect telescopes, there's a limit as to how far you can see. And that's the distance that light has had time to travel since the expansion began. It's about 14 or or 15 million light years, 10 to the 27 centimeters. And we call that the visible universe. It's not all the universe there is. The universe could be infinite in extent, but it's all the universe that we can see. A remarkable property of it is that that radiation, that heat radiation I showed you earlier, has got the same temperature all around the sky to an accuracy of one part in 100,000. so the universe is very similar from place to place it's expanding at the same rate in every direction looks the same, north, south, east and west now in the conventional picture of the expanding universe that's impossible to understand because if we take the universe backwards in time we squeeze it back to some very early time we can ask well how big was it a split second, 10 to the minus 35 a second old. And in the conventional theory, it is so big that there has not been time for light to travel from one part of the universe to another. And so there's no way in which it could be smoothed out. There isn't time for smoothing processes to iron out irregularities and explain why the universe is so smooth everywhere you look today. What the inflationary expansion can do for you Because it accelerates the expansion, it can grow our whole visible universe from a region that's much, much smaller than the conventional picture. So small that light signals do have time to travel from one side to the other. And so our whole visible universe is just the expanded image of a tiny elementary state where everything is kept smooth and regular, just up to little statistical fluctuations.

32:30 And this accelerated expansion makes sure the universe becomes very large and stays very, very close to that critical divide for billions and billions of years. It predicts that we should be within one part in a million of that critical divide. It doesn't say on which side we lie. So that means really, in effect, astronomers will never know on which side of the divide we lie. We'll never have a direct astronomical observation that can measure to an accuracy of one in a million which side of the divide we lie. Well, at first it was thought that would be the only test of a theory like this, just whether we really were pretty close to that divide. But in the early 1980s, particularly at a meeting that was held here in Cambridge, a great gathering of theoretical cosmologists, worked out in some detail that there were other remarkable consequences of this picture. So this tiny little domain, this little embryonic region that's going to expand and eventually become all the visible universe we see today, will have tiny fluctuations in it. There will be little differences in temperature and density required by quantum theory and intrinsic randomness. And when it's expanded and inflated, then they become large. They become significant irregularities in the universe. Perhaps they're the irregularities that eventually turn into galaxies and clusters and stars. Well, if they are, on the way, they leave little imprints of differing temperature in that radiation that we saw earlier. So if we look around the sky, we ought to find that the temperature is slightly different in one direction to what it is in another at a level of about a few parts in 100,000. This is an artificial sky map made recently at the South Pole by this balloon experiment which flies a radiometer high in the Earth's atmosphere to make very accurate observations of the temperature of that radiation from the Big Bang. And the sky map has been put on the Antarctic sky here so that if you had radio-sensitive eyes, this is what you would see. I should say, incidentally, when your television doesn't work

35:00 and you get that nasty sort of white noise on it, a very significant fraction of that noise is this microwave background universe from the Big Bang. The changes in color here are probably about 10 to 20 micro-Calvin in amplitude. So the point here is that we can create, we can produce quite detailed maps of what the temperature distribution is on the sky of this radiation today. So if we can make very detailed predictions as to what this theory of inflation predicts about these maps, we can compare and test the theory. Now, flying balloons from Antarctica is okay. You can get very accurate observations, but you only see a very small part of the sky. Antarctica is good because it's very, very dry. Also, the ozone hole is a wonderful thing for doing radio astronomy through. So you have your graduate students back at base using their aerosols while you're observing through the hull. But you really need to go into space to test this theory with very great precision. And at this very moment, there is a NASA telescope taking observations to make this critical test, the so-called MAP telescope, whose results will be announced all over the newspapers, I suspect, next January and February. And then in 2007, there's a European mission to follow up in even more detail. And what I'm showing here is the size of the fluctuations in temperature, if you like, the difference in the color contours on the previous map, plotted against angular size on the sky. So if you were to measure the temperature over here and then go one degree cross on the sky, what would be the difference that you would see in the temperature if you then do that on all the one degree separations all over the sky and take the average? And the key statement here is all over the sky. The satellite enables you to do this all over the sky. You have a huge number of observations. Therefore, the statistical errors become very, very small. And what I've plotted on this picture is typical theoretical prediction of this inflationary theory here. It's rather particular. Here are the angular separations on the sky. the perspective, this angular size, corresponds to about the size of the full moon on the sky.

37:30 So we're looking at very, very small fluctuations because they're the size of fluctuation that will turn into galaxies. So that was where you will see the lumps and bumps that will eventually turn into galaxies. Up here, the prediction is perfectly straight line on larger scales, and we already see that, so that's not very interesting. But what's interesting is whether you can predict and confirm this very detailed oscillatory structure. And plotted on this picture already are the observations from the ground, in particular the ones from the South Pole. And you can see things are really looking very promising indeed. But the size of these miles are the errors of the observations down here. The action is very poor. But you can see there really is a very good case that this theory is going to be confirmed. Small variants of the theory, little details about how you make galaxies, will make the curve slightly differently placed, slight different peak, but the general shape should be the same. As would the measurements of the spectrum, what the space observations will ultimately do is reduce the size of these arrow bars so that they are much thinner than the thickness of that line. escape for the theoretical predictions. So this is very exciting. We have a way of directly testing whether this type of event happened very close to the beginning of the universe. Well, as people thought more about that theory, they realized that there are all sorts of other exotic consequences of it. We thought about one tiny little domain which is going to have a for a while and turn into the region that we see and inhabit. But it was then realized that, well, things are really rather more complicated than that. In particular, geography is a much more complicated subject than you ever thought. Because back at that early moment, there were all sorts of other little domains in the universe which might even be infinite in size. And they may have slightly different conditions. they will have different amounts of this inflation that will last for slightly different times. It's rather like having a great foam of bubbles, which you heat up and all the bubbles get bigger,

40:00 and you'll create an enlarged foam. Some of those bubbles will be large enough to live long enough for stars and galaxies to form. Others will not. Some may by now even be collapsing back to their own big crunch. So for all practical purposes, these are other universes. These regions beyond our visible horizon can have very different conditions, different density, different expansion rates. And in fact, it turns out that the processes that create the inflation can even create different strengths for the forces of nature and different numbers of forces of nature in these different domains of inflation. So you might have a region where there is only a gravitational force, not the forces of electromagnetism, radioactivity, nuclear force, and gravity, which there is in our region. So it had always been an idea of rather pessimistic philosophers that there was no reason to believe that our universe was the same beyond our visible horizon. It clearly could be completely different in many respects. But this is the first time there has been a positive reason to suspect that that's the case. But the result of inflation occurring in regions which have quite wide variation is to produce this foam, so-called chaotic inflation. Well, soon after this was realized, that geography is a rather messy business, Andrei Linde and Alex Vilenkin realized that not only is geography more complicated than you thought, And that once this inflationary process occurs to produce these little bubbles, it's almost inevitable that it creates within those bubbles the conditions for further inflation to occur. So any one of these bubbles will then produce many, many more inflated regions of different shapes and sizes, different patterns of forces and so forth. And those bubbles in turn will create yet more bubbles. So it's like a never-ending process, so-called eternal inflation. And we have to see ourselves as inhabiting just one of the large bubble-like universe regions in this process,

42:30 old enough for stars and galaxies and life to develop. The process seems to require no end. It's not known whether it really needs to have a beginning. Well, this is rather unusual, rather exotic. You have no way of knowing whether we can test that theory, except very indirectly, as to whether the sorts of theory which can do that give fluctuations of a special sort that we can see in that background radiation. but inflation is something that's imagined to occur when the universe is about 10 to the minus 35 of a second odd so after it's been expanding for sort of a split second suppose you were really wanting to go even further back in time what's the ultimate scale of size or of time to which you could try to apply your physical understanding of the universe Well, remarkably, there is a basic smallest length in our study of the universe that's given to us by the nature of the universe and its laws. If you take three of the constants of nature, big G, which we usually call Newton's constant, he never wrote it down, he was just interested in proportionalities, that big G is the strength of gravity, Planck's constant, H, which tells us something about the quantum nature of the world, and the velocity of light, C, which tells us about its relativistic characteristics. Now, there is one and only one way in which you can combine those three fundamental constants of nature, multiplying two and dividing by the cube of the other and taking the square root, and you get a length. And this is the length on which the universe thinks, if you like, 10 to the minus 33 of a centimetre times 4.1. It's fantastically small, unimaginably small, perhaps, we'll see at the moment. But if you want to know what's the way in which the universe thinks about itself, centimetres are units we've created because they're pretty much just the size of the end of your finger. and so whenever we talk about astronomy we end up with enormous numbers that the universe is 10 to the 27 centimetres in size clearly centimetres are not the units

45:00 to be using but even if we use the universe's units these Planck lengths its size today is 10 to the 60 of those Planck lengths and that's what we mean by saying that the universe is it's 10 to the 60 Planck times in size. When we get to this scale, when we follow the universe back to 10 to the minus 43 of a second, we have to understand the nature of physics, the nature of space on this dimension. And that is where quantum mechanics and gravitation collide, and one has to understand how these two great influences and forces of nature combine. And one of the programs at the so-called M-theory, is a program to try to do that. Let me try and give you an idea of what the Planck length is like. I call this the origami of the universe. But suppose you have a piece of paper, like A4 paper, and if you try and fold it in half, I think if you can fold it in half more than seven times, I'll give you ten pounds. So folding things in half dramatically reduces their size. Now, if you could fold this piece of paper in half 30 times, quite a lot of times you won't be able to do it. It's not unimaginable. Then it would have the size of just a single atom. If you kept on going and you folded the piece of paper in half 47 times, you would be at the size of the atomic nucleus, a single proton. on. If you could fold it in half 114 times, you would be at the plank length. So if you're a secretary or administrator, you know that that means that you want a sheet of sort of A110 paper corresponds to the plank length in size. If we doubled this piece of paper we would be up to the size of the visible universe 10 to 60 Planck lengths and 15 billion light years so the whole scale of physical reality from the size of the visible universe to this Planck scale of quantum gravity

47:30 corresponds to 204 doublings of this single piece of paper well what happens if you try to understand the universe at this Planck time much publicity about ideas then, trying to understand how the universe came into being, if it did or not, whether it had always been there, whether it's perhaps the relic of some previous phase of contraction that turns into expansion, whether perhaps it didn't once expand at all and then suddenly began to, whether it always expanded in some eternal way, or whether suddenly began, because the universe came into being, for some reason we don't understand. So there are other interesting aspects of the nature of theories that try to come to grips with events around the Planck time. The first is that when you try to make sense of theories about that time, you inevitably discover that the universe really wants to have more dimensions of space than the three that we're familiar with. If you write down physical theories of particle physics and gravity and you try to join quantum theory to gravity in worlds with three dimensions it just doesn't work you get infinite answers to questions that ought to have finite answers the theories are not well defined whereas if you have rather more than three dimensions you have ten dimensions the theories are beautifully posed and have remarkable properties. And so for a long time now, physicists all over the world have worked rather hard on trying to understand the details of theories with extra dimensions, and whether indeed our universe has more dimensions of space than three, and if it does, where are the other dimensions? Well, the first thing I'm going to say about this is, if you go back to the late 18th century, the famous philosopher Immanuel Kant was the first person who realized that there's a deep connection between Newton's famous inverse square law of gravity, which he conceived just down the road, and the number of dimensions of space. So Kant showed that the fact that in physics, when we study, for example, electricity, magnetism, gravitation, we see these inverse square laws. The forces fall off like one over the distance squared.

50:00 This is a consequence of space having three dimensions. So the square is just the number of dimensions minus one. If we lived in a ten-dimensional space, we would see inverse ninth power laws all over physics. So we can then take seriously for a moment. Let's suppose we live in a universe which has any number of dimensions of space and even of time, and important of all, all these dimensions are pretty much the same. It's a rather democratic type of universe. Then we are here. We're in a world with three dimensions, with one dimension of time. And as we start to contemplate and calculate what would happen if we lived in universes with other dimensions, the results are really rather pessimistic. If you have more than three dimensions, many planets. So there are no forces which bind things together to make molecules or atoms or planets or stars. And similarly, if you try to have rather many dimensions of time, you have similar problems. If you try to have lots of dimensions of space and lots of dimensions of time, this green region up here, things become very peculiar. It's to predict the future from the present. So the future doesn't depend on the present. And so you don't have a situation where something like evolution by natural selection, where living things could exist and persist in a stable way. If you try to have just two dimensions of space, or one, then things are too simple to make anything that's complex a memory that's complex, or to have even a force of gravitation. So there's something very special about worlds with three dimensions of space and one of time. As far as we can see, living observers couldn't exist in any other combination of dimensions of space and time. So if our one time and three dimensions are something that happen at random in this inflationary process, or perhaps they're allowed to pick different values in some ultimate theory, then we have to find ourselves in a three-space and one-time universe. Well, these theories of extra dimensions don't, in fact, envisage, because of reasons for that sort,

52:30 that all these dimensions are pretty much the same. We clearly live in a universe where three dimensions of space have got very large. And one way in which that might be is that when the universe begins expanding its size against time, as our picture again, at first, all the dimensions expand. But then perhaps in some process, most of them become static. They're held and they don't expand. They remain fantastically small. But three of them continue to expand and inflate, and we end up living in those. what is it that stops these dimensions expanding? By the way of phrasing it, what is it that allows these three to keep on expanding and become vastly bigger than the others? It's as though a process of inflation might just have acted upon these three dimensions and not upon the others. Another favorite line of attack on this problem, much studied here at the moment is that some of the forces nuclear forces, radioactivity, electricity and magnetism are confined in their influence to just three dimensions and it's only gravity that acts in all the dimensions of space so we live on this surface as it were this three-dimensional surface sometimes called a brain or a brain world as a generalization of membranes, gravity acts in all the dimensions, and this gives us a way of understanding why it's so much weaker than the other forces. So these are conjectural ideas. They're worked upon in enormous detail by huge numbers of people. In the years to come, we hope we might have some observational predictions of theories of that sort. Another thing I want to say about them is that they change your attitude nature. You see, if the real universe contains nine or ten dimensions or more, then the true constants of nature are defined in that total number of dimensions. And the things that we measure in the laboratory, the charge on the electron, Planck's constant, the strength of gravity, these are just three-dimensional shadows of the true constants, and there's no reason for

55:00 them to be constant at all. In fact, in these theories, if the extra dimensions were not still, were not static, but were to be slowly expanding, we would observe that immediately because our constants of nature would change at the same rate. So an interesting probe of extra dimensions is to carry out high-precision observations of the constancy of our constants of nature. And here's a favorite one. It controls the atoms and molecules and explains why everything has sort of the consistency it does. It's called the fine structure constant, or alpha, and it's made out of the charge on the electron, Planck's constant, and the speed of light. And it's a number, roughly one divided by 137. One of the great goals of physics, fundamental theory, is to explain that value. Why does it have that value? Well, in the last few years, a group of us have been using some of the world's best astronomical telescopes, like the Keck, to test the constancy of the fine structure constant over a period of 13 billion years. And using astronomy, you can get a test which is probably about 500 times more sensitive than any laboratory experiment could ever achieve. So what we do is to really measure the separation of spectral lines in light that leaves a distant quasar 13 billion light years away. Quite close to the quasar, there are clouds of dust where some of this light is absorbed quantum mechanically by some of the atomic species. And what we want to do is to compare the atomic physics, the separation of the spectral lines in these absorption spectra in the clouds with those we measure on Earth. And so in this way, we're really able to tell, was the fine structure constant the same 13 billion years ago to what it is today? And the results are rather tantalizing. I received lots of publicity. This is on the front page of the New York I think some months ago, to read more about it I have a book coming out about the constants of nature in September which this is a little part of the story. But what's being shown here is the look-back time in the universe from

57:30 where we're gathering our light in billions of years. Here is the shift apparently in the value of the fine structure constant between its value in the clouds far away and in a laboratory today. If there's no difference, if the fine structure constant never changed, the observation should lie along this dotted line. Each of these points represents 10 observations, so there's about 150 observations here taken by a number of the world's leading observers and reduced to try to understand what is the apparent value of the fine structure constant. And the worrying thing about these observations, which have gone on for several years now, is that they persistently seem to want to tell us that the fine structure constant was very slightly different, about seven parts in a million different, smaller, at the redshift where these clouds were absorbing their light. So this is an archival situation. we need to work even harder to discover whether there is some environmental effect in the quasar which mimics this effect all the time doesn't look very likely present statistically this is a fantastically significant result it's seven sigma statistical significance if you're a statistician so that's not the cause of the concern it's whether there is another effect creating the same thing The last thing to say about that is that there is another very simple-sounding laboratory experiment that has a deep Newtonian connection, so I want to mention it. And that is if you build theories which can try to accommodate that type of change in the fine structure constant, which some of us have done, then they make another very definite observationally testable prediction. And that is, you remember Galileo supposedly dropping cannonballs and stones off the Tower of Pisa, claiming that they reached the ground at the same time. The true form of this experiment is to take different masses, drop them in vacuum, and they should reach the ground at the same time. Everything will fall at the same acceleration under gravity. And that is tested to fantastic accuracy by experimentalists.

1:00:00 part in a thousand billion, one in 10 to the 12. If these astronomical observations are correct, and there really is a change in the fine structure constant at the level observed, we predict that there will also be a change in this free fall result. Different objects will not fall at the same acceleration. There will be a relative difference of one part in 10 to the 13, back to 10 smaller than current observations, but well within the reach of space-based observations that will occur in the next three or four years. They will ultimately reach a sensitivity of 10 minus 18. So this is an example of how, while exotic physics about extra dimensions has consequences for the constants of nature, we can test it astronomically. It then has other consequences for laboratory experiments and space experiments about gravity. It's a network of interconnections that you try to test by observation. Now, the last thing I want to tell you is about something that's a mystery that we don't know the answer to, and it's called the cosmological constant. And it has a surprising and little-known Newtonian connection. The cosmological constant is textbooks and talks about cosmology is usually painted as something that Einstein predicted he didn't like, to explain it away and then ultimately ignore it, said it was the biggest mistake he ever made in his life. What it was was the prediction that there's another piece to the law of gravity, that it's not just this inverse square law you learn about at school where you take two masses and as you move them farther apart, the force between them falls like the square of the distance, but that there is another piece. And that piece increases with their separation. Now, what's the Newtonian connection? Well, one of the great problems that Newton solved was he showed that if you took this law of gravity, his famous inverse square law, then if you take a sphere with a particular mass, you can treat it gravitationally as though it's a point of zero size having the same mass. So gravitationally, it behaves in the same way. And remarkably, that's not something that's true of any law of gravity.

1:02:30 that it was true of a law where the force is inversely proportional to the square, like his law. And he also showed that it happened to be true for a law where the force was proportional to the separation. But he thought that wasn't very interesting, so he threw it away. But the most general law where that's true is the sum of the two. Now, until quite recently, astronomers had assumed, and particle physicists had assumed, that this term doesn't exist. The law of gravity doesn't have this component. But observations taken with the Hubble Space Telescope and from the ground have managed to see far enough of the expansion of the universe to show that this term does seem to exist. That if you observe supernovae close to the edge of the visible universe, that their expansion is not decelerating like things are locally. It's accelerating. This is exactly what happens when this term is present. So here is our universe again, here's our size-against-time picture, universes that are expanding, that we thought were going to go crunch, or just keep expanding in some rather uninteresting way. If this new cosmological constant term exists, then suddenly they start to accelerate again. And we seem to be living about here. quite soon after the acceleration has resumed. Now, this means that this cosmological constant has a rather particular value. Nobody knows quite why it has the value that it is observed to have. Because if you work out what the value is from the expanding supernovae, and from other observations as well, they're not the sole evidence, You get a value which in our CGS units is about 10 to the minus 54. But if you're a particle physicist and you hadn't seen the real universe at all, so you lived in your dungeon down in the Newton Institute cellars, then if you came out and said there is a cosmological constant and I know how to predict its value, the value you would predict would be wrong by about a factor of 10 to the 120. Clearly, something is being missed here. Particle physicists always perhaps rather hope that the answer might be zero,

1:05:00 that there would be no evidence for a cosmological constant, because there might always be some deep principle that told you it had to be exactly zero that you might have missed. And so this number might be multiplied by zero. But the fact that it's a very particular value is very mysterious. The value sounds very, very small, and it is, was just 10 times bigger, we wouldn't exist. Again, as we counted earlier, if the value was 10 times bigger, this acceleration would have begun before any of the stars and galaxies could have formed. And once it begins, they're not able to form. So it's a rather fine-grained, a mysterious situation. First of all, what's the origin of this cosmological constant? does it have this very peculiar value? And are we just lucky that it's a value that just enables galaxies and stars to form and allow us to be on the scene to listen to lectures about it? Thank you. Thank you. I'd now like to throw the floor over there, yes. A question about the correlation of the angle length scale and 5. How close, I assume the hospital has always had a lot of three parameters to make a difference to work nicely. How close are the observations that we do in our family's experience with this contract that we can find that? Sure. So some have already been ruled out. I say there's a rather robust prediction that back here, the reason this curve comes in which go way down here, which tells you where it starts. Now, you should really envisage the predictions as being a number of these sorts of curves, roughly the same sort of shape, quite close to each other. And why there are different curves is because there are other parameters which are uncertain, like exactly what the expansion of the universe, what the rate is by a factor of two, or how much dark matter there is, and so forth.

1:07:30 appeals about this project and why huge sums of money have been spent on satellites is because the observations by mapping out a very particular line will be able to tell you those unknown things as well. So we want to tell the difference between this line and one that doesn't have such a high peak, one that comes down here and is a bit lower. So the height of this peak, the location of this peak, for example, depends on the total density of the universe. So determining this curve with fantastic precision is really the secret to evaluating all the parameters of the universe's structure, like its age. Well, what's happening is that you're making so many observations, okay, that instead of having data points, you will in effect have a continuous curve. So the experimental results will be a continuous curve rather than several points here. There are just so many of them. there really shouldn't be any escape for a theory. I mean, it will be confronted really with observations of every wavelength taken continuously. And it will move cosmology into being subject like particle physics where you're doing very high precision observations so instead of worrying about whether the expansion of the universe and its age is uncertain by a factor of two, you'll know in one percent. Yes, you have to see a different... Here we go. There are theoretical predictions here from a theory that we worked out that's the simplest way of incorporating this idea into, say, general relativity. And what it predicts, interestingly, is that, if we have some chalk, that if we were to plot

1:10:00 alpha against time then in that first 300,000 years of the universe's history when it's dominated by radiation it won't change but then it will increase which is what the observations see logarithmically in time and then when this cosmological constant takes over the observation, takes over the expansion of the universe, it will become constant again. So there is an interval of cosmic history in which the fine structure constant is predicted to increase logarithmically with time. So this fits these observations reasonably, but what we would like to do actually is to have many more observations around the redshift of about a half and 0.7, changeover is expected to occur. So it's just there's just not enough data yet to make a critical test. So you can fit this theory. It fits very nicely. If we were to put it on this picture, it would sort of go through here. Just like that. There's one free parameter in it. If you fit it to the best fit on this picture, that's what gives you the 10 to the minus 13 prediction on the weak equivalence principle free fall experiment. So that's the idea there. It's to test whether this fit really is correct by working out other consequences of it. So we might hope in the next year that observations would half the error bars on these points. So I say there are 10 observations pinned in each of these points. There's a large amount of data. but it's rather early days that's right, that's a very good question that's true Well, the question that he's saying, he's saying, doesn't the universe expand faster than the speed of light during inflation? And indeed it does. One of the surprising things about cosmology is that the universe does at different epochs, both during inflation and even when there's no inflation near the beginning, it expands faster than the speed of light.

1:12:30 At first, you might think, well, didn't Einstein tell us that nothing can go faster than the speed of light? What Einstein said was that no information can be transmitted faster than the speed of light. Now, the expansion of the universe doesn't involve anyone sending any information from A to B. If you think of the expansion of the universe as... Imagine you have a two-dimensional universe, so it's just a disk. And as it expands, what that means is that our disk is sort of getting bigger. It's getting fatter, right? Well, there's no signal being sent from here to here. So if we tried to sit on the boundary here, and we sent a little light signal around the edge of our circular universe, as it expanded, it would sort of get left behind. We could send our signal here at the speed of light, but the universe is able to expand much faster than the speed of light. Because think about it, all we're doing is somebody is putting an A here and saying, right, that's one point, and putting a B here and saying, right, that's another point. We'll measure this distance, we'll come back later and measure it again, and say, well, A's moved away from B faster than the speed of light. So what? You know, you've just chosen to mark that point and that point. Nobody sent a signal from A to B. Nothing's happened faster than the speed of flight. So that's perfectly allowed. You just mustn't send signals faster than the speed of flight. Another little example like this. Suppose you have a line of men. So if people did national service here, they will probably have had this sort of experience. You have lots of soldiers. You were to put them in a line. Okay. and they're going to number, you know, they're going to shout out their number, one, two, three, four, all the way down the line. And you give them each a little earpiece, and you say, well, when you receive my little impulse, my signal, so when your bleeper goes, shout out your number. And with fancy electronics, we could arrange that each of them's going to receive their signal and shout out their number, so that if we were listening to what was happening,

1:15:00 numbering would go down this line faster than the speed of light there's no reason why that can't happen no information would be transferred none of the soldiers knows anything about any of the others he doesn't know he's in the line even he doesn't know anybody else is going to call out a number but the numbering could proceed down the line faster than the speed of light because number two is not shouting out two because he's heard number one and so on and that's what the expanding flight. It can go as fast as you like, but you mustn't send information faster than the speed of flight. Okay, I think I'm going to have to stop there. John Barrow is one of the only people I know who could see me in the title of, Are You Surprised? I think several of us will have been at what we've heard today, so I'd like to have a sec. Thank you. Thank you.