sábado, 26 de novembro de 2011

2. The Smooth, Expanding Universe - Sean Carroll - Dark Matter, Dark Energy: The Dark Side of the Universe



As promised, this lecture begins the observation stage of the cycle. What do we see around us? The history of discovering the universe to be a large space expanding between galaxies (explained in the next lecture), thereby making more distant galaxies appear to be moving away faster, yet all being smoothly distributed, is all well put by Sean.

All that is, except for a somewhat desperate and comedic reference to dog years. This was in order to convert the age of the universe from 14 billion human years into 100 billion dog years, thereby equaling with the 100 billion stars in a typical galaxy, and the 100 billion galaxies in the universe. A bit of a stretch to say the least, but understandable in order to help a beginner.

The typical comparisons to the expanding universe as spots on a balloon and raisins in baking bread are all dissed. Sean gives appropriate enough reasons, but then turns around and use dog years? Plus these are both the demos used by Alex Filippenko, so maybe he is separating himself from his competitor?

An interesting setup for the next lecture is how Einstein's Theories predicted the expanding universe in 1915, yet when Hubble actually observed that happening in 1929, he did not present it as confirmation of Einstein, but as discovering recession velocity was proportional to distance.

I like the way concepts are being presented by Sean. It's accessible, appropriately paced, and does justice to the wonder of it all. Instead of making one want to walk away from the learned astronomer to gaze quietly at the stars before it's over (though one should certainly do that after viewing the entire lecture), the half hour goes by all too quickly to even think of it.

This lecture is going to be a fun one! We're going to go outside and we're going to look at the universe, virtually anyway. Viewers will stay inside and look at this DVD, Sean hopes! Yet we're going to take a look at what the universe looks like on the largest scales, and we're going to get good news. The universe looks pretty much the same everywhere. It's a dramatic, simplifying feature that our observable universe seems to have. So in fact, this lecture is going to cover a lot of ground. This would be a perfectly good course all by itself, this lecture, but the good news is that there's pretty pictures involved, so it's going to be a picturesque view of what the universe is made of, as far as what we can see.

Then in later lectures, we're going to take the evidence from what we see, and plug it into our theoretical notions to try to derive notions of what it actually is made of. So even though the universe looks the same everywhere, there is one thing that makes it not quite that simple, which is that it's getting bigger as a function of time. What that means is that different objects in the universe used to be closer together, and in the future they'll be further away. So we'll tell the story of how this was discovered and in the next lecture, what it all means in a deep down level.

It's very often that you'll hear people trying to explain to you the concept of the expanding universe by appealing to really bad analogies. So as a professional cosmologist, this gets Sean's dander up a little bit, when people use these analogies with the best of intentions to explain the idea of the expanding universe.

For example, they will have a balloon, put little dots on it, and blow it up. As it gets bigger, you see the dots moving away from each other. Then they go, "Aha, the dots moving away from each other, are just like galaxies moving away from each other in the expanding universe." That's correct in a sense, but you have to admit that when you see the balloon expanding, there's an inside to the balloon and an outside. Yet our universe is not like that! So the balloon analogy only really works if you look at the dots on the balloon and then imagine there is no such thing as the inside or outside of the balloon. It's possible to make that leap of imagination, but it's harder than just understanding what's going on in the first place.

Similarly, the other analogy that is very famously used is raisin bread. You start with a lump of raisin bread dough, with raisins inside. You put it in the oven and the dough expands, as perhaps you know. The raisins move away from each other and you say, "There you go, it's like the expanding universe!"

Yet again, you get a misconception from this analogy. That's because the raisin bread has an edge, a crust. It's also moving into something when it expands inside your oven. The universe, as far as we know, is all there is. When we say its expanding, it's not getting bigger into some preexisting space. What we mean is that the individual objects inside the universe are getting further apart.

Now how is that possible? How can you have the individual objects in the universe get further apart, even though it's not expanding into anything? That will be discussed in the next lecture when we explain how Einstein's General Theory of Relativity allows the space in between the objects to grow. Space-time itself is dynamical and can expand.

So Sean will not use any analogies whatsoever, and thinks the best way of understanding the expanding universe is to actually visualize the universe, the actual universe that we're in. Once you start conceptualizing it into some object inside something else, you get a false impression. As far as we know, our universe is all there is. There might be something outside, but we don't need to appeal to anything outside to understand what's going on. So lets just think about the universe.

Let's think of going outside, standing outside on a clear night where there are no clouds, and looking at the night sky. Furthermore, lets imagine you have perfect vision, so what that means is not only can you see things that are very faint and small, but also in all the wavelengths of the electromagnetic spectrum. In other words, you can see visible light, radio waves, and x-rays. We have perfect vision while standing outside looking at the universe. So what do we see?

Well there are some things that are obvious. You see the sun and the moon, which are fairly nearby as far as cosmology is concerned. You also see stars, and planets orbiting around the sun. These are all well and good, but the thing we'll focus on if we were standing outside on a clear night, is something called the Milky Way. This is a band of what looks like a cloud of milky whiteness, stretching from one edge of the horizon to the other edge, overhead. If you are able to look closely enough at it, you realize that this thing which looks like a cloud, is in fact made of stars.

The Milky Way is a huge collection of stars, and we can look at it better in the real world. We can have a satellite, so in fact NASA's COBE (Cosmic Background Explorer) satellite, took an image of the Milky Way which we see on screen. It looks like a picture of a galaxy you would see, taken by any other telescope. It looks like it's taken from the outside, yet we really live inside the Milky Way.

The trick is that it's a disk. So you imagine a disk of stars, all orbiting around each other, and we're located near one edge. So when we look inside, we see the center of the Milky Way as a concentration of stars, fewer in the opposite direction, less stars in other directions, and very few at the poles. We're embedded in a plate shaped collection of stars, and that is what we call the Milky Way Galaxy.

The Milky Way has about 100 billion stars in it. We don't know the exact number, and some stars are too faint for us to see, but 100 billion is a good order of magnitude estimate. Any such collection of stars, is called a galaxy. The important point here is that these stars are not fixed, sitting there in space, they are orbiting each other. So there's a pull, due to gravity from one star to every other star, so that this entire collection of 100 billion stars is orbiting under their mutual gravitational field.

So we could ask if that was the entire universe? Would it be possible to imagine a universe in which we had the Milky Way, a collections of 100 billion stars, with some planets inside, clouds of gas, and so forth, and nothing outside, just emptiness stretching forever and ever. Well it's a very plausible idea that's certainly worth taking seriously if we didn't know any better.

Just 100 years ago, that was in fact, the leading understanding of what the universe was like. This was the so-called island universe idea, that we lived in the Milky Way, this collection of stars orbiting around each other, yet there wasn't anything else. There wasn't anything outside the Milky Way.

However, astronomers did know there were different kinds of things inside the Milky Way. When we look at the sky with our perfect vision, we see stars which always just appear like points, no matter how much you zoom in or magnify them. There is no telescope on earth that can ever expand any star enough to make it look like a disk. It's always going to be point-like. Yet there were other objects that were not stars that you could definitely see did have an extent. These were called nebulae (plural of nebula), which look like fuzzy little patches of light in the telescope or on a photographic plate.

So 100 years ago, this was the hot topic in astrophysics. What are these fuzzy little patches called nebulae? Here's a picture of the Orion Nebula. This is a picture that they couldn't have 100 years ago. We have much better telescopes today. We see it's a very colorful and rich collection of gas and dust. In fact we know today that this is a star-forming region, a huge cloud of gas that is gradually collapsing under its mutual gravitational force, and will splinter off eventually to form individual stars.

So that is one kind of the many types of nebulae that exist. The Orion Nebula is right here in the Milky Way, with many other nebula just like it, also here in our galaxy. Here is another picture of a nebula, called the Andromeda Nebula. To a telescope of 100 years ago, this looked like a fuzzy patch, just like the Orion Nebula looked like to them. All these different nebulae you could see 100 years ago, had different shapes and sizes, yet all they were all still just fuzzy little patches. We knew they weren't stars, but didn't know what they were.

The truth is that the Andromeda Nebula is actually the Andromeda Galaxy. The Andromeda nebula is its own collection of 100 billion stars, orbiting under their mutual gravitational attraction. In other words, the Andromeda Nebula is just like the Milky Way. It is not inside the Milky Way, but is a separate collection well outside the Milky Way. So we do not live in an island universe, but a universe that is filled with other galaxies just like ours.

So how do we know that? This is something that was first figured out by Edwin Hubble, a remarkable figure in his own right. It took Hubble quite awhile to find himself as an academic, growing up more famed by his athletic prowess than anything else. He was a high school track champion, he played for the University of Chicago basketball team when they won the national championship, which they're not likely to repeat ever again! He was a Rhodes Scholar, so went to Oxford and studied law for awhile, then Spanish for awhile. He came back to the US and actually worked as a high school basketball coach, as well as a lawyer!

Eventually he realized his true calling was astronomy, so he got a degree, a Ph.D. in astronomy, and went to California in order to go to the Mt. Wilson Observatory, which at the time was the world's leading astronomical observatory. They had just built a huge new telescope, the 100 inch Hooker Telescope. The 100 inches refers to the diameter of the mirror used to collect light. So you had a large mirror collecting light which could see distant stars and galaxies with a better perception than you ever had before.

So what Hubble did was to look at things that looked like nebulae, little fuzzy patches. First, he was able to resolve some of these patches into individual stars. Not everywhere in the patch, not in their centers, but at the edges of some of these these nebulae, he could see that it was not just gas and dust, but there were individual stars there, and a lot of them!

That was certainly suggestive that these were not in fact just clouds of gas here in our galaxy, but were individual collections all by themselves. Yet he still couldn't be sure. It could just be that there were a few stars, but still relatively close and inside our galaxy. How do you know how big the Andromeda Galaxy is? You can't count all the 100 billion stars!

The answer is that Hubble was able to measure the distance to the Andromeda Nebula. He was able to figure out that the distance between us and Andromeda was such that given the stars he observed, there must be "billions and billions" as Carl Sagan would say, of stars in that nebula.

So how do you do that? You use a technique called "standard candles." This is a very simple idea. Imagine that you have some object at a certain distance away, like a candle, and you can see that it has a certain brightness. Then someone takes that object and they move it, twice as far away. If you're in a dark room and all you see is the object getting further away, once it's twice as far away, it will seem dimmer to you. In fact, if it's exactly twice as far away, it will only have 1/4 of the original brightness. There is an inverse square law, so as something gets further away, it looks dimmer. That makes perfect sense to us.

The problem is that if you don't know the intrinsic brightness of the candle to begin with, you can't figure out how far away it is. So the difference between a candle and a standard candle, is that the latter is something whose intrinsic brightness is known. If you know how bright something would be, if it were a fixed distance from you, and you know how bright it appears to you, then you can calculate how far away it must be to make that distance and brightness make sense.

So one of the major projects in astrophysics and cosmology 100 years ago, and still today, is to find standard candles and measure the distances to things. As you're standing outside just looking at stars in the universe, indeed you see all these stars but have no idea off the top of your head, how far away they are! So astronomers had to build up what they called the cosmic distance ladder, in which the most important technique is the use of standard candles.

Hubble used standard candles called cepheid variable stars. This is a type of star that pulsates, getting bigger and smaller. Yet the "standard candleness" is not absolute, so that cepheid variable are not all exactly the same brightness, but they also don't all have exactly the same period of oscillation.

By 1908, an astronomer at Harvard named Henrietta Levitt, though women were not even allowed to be called astronomers at the time, made one of the crucial discoveries in all of astronomy. There is a relationship between how bright the intrinsic brightness of the cepheid variable, and its period of variation. So even though you don't know its intrinsic brightness just from the fact that it is a cepheid variable, if you can measure its period, then suddenly you do know how bright it really is.

So Levitt calibrated this relationship, which taught us if we saw a certain period, then it must have a certain intrinsic brightness. Hubble went to his Hooker telescope, the 100 inch at Mt. Wilson, and he discovered cepheid variable stars in the Andromeda galaxy, as well as in other galaxies. He noticed that these variable stars, given their periods, were much dimmer than the cepheid variables in our galaxy. So he could work out how far away they were, and he realized that Andromeda was a galaxy all by itself, comparable in size to the Milky Way.

In fact we now know that we live in a local group of galaxies, with the Milky Way and Andromeda being the two largest galaxies in the group, with many smaller galaxies as satellites of the two. So Hubble established the first important fact about our universe, namely that it is big. In fact, we now know that in our observable universe, there are about 100 billion galaxies that we can observe. That's a convenient number, and in fact 100 billion is basically the only number you need to remember in terms of how big the universe is.

This is because there are about 100 billion stars in a typical galaxy, and about 100 billion galaxies in the observable universe. The age of the universe is about 14 billion years, yet even that works out to be very close to 100 billion dog-years! One ordinary human year is just 7 dog-years, so 14 billion times 7 is very close to 100 billion, which is the number for the scale of the universe in different units.

Here is a picture from the Hubble Space Telescope, named after Hubble which is an orbiting satellite built by NASA. This particular picture is called the Hubble Ultra Deep Field. All they did was take the telescope and point it to the most blank area in the sky they could find, where they didn't know of anything in the field of view, but they let it sit there and collect a large number of photons over a long period of time, and then so to speak, they developed the image.

What we see in this picture is a lot of galaxies, almost every little dot here is a galaxy all by itself, with literally billions of stars in it. So Edwin Hubble was the one to figure out that the universe is big. That not only do we have a galaxy with 100 billion stars, but that galaxy is not unique. It's one of 100 billion galaxies spread throughout the universe. So that's a nice picture of what the universe is made of. It's not an island, not just the Milky Way galaxy surrounded by nothingness. There's a collection of galaxies spread out.

Yet don't get complacent, because the universe is not just staying there, but it's getting bigger. This is the second important fact about the universe, after the fact that it's big. The second fact is that it's getting bigger, and this is also discovered by Hubble.

He was not the first to get onto some idea like this, in fact. An astronomer named Vesto Slipher noticed that galaxies that he observed tended to be redshifted, from the light that came from them. So what does that mean? When we have atoms giving off light, it is very frequently the case that the light it gives off in a certain kind of atom, is always at the same frequency. The wavelength that you have of light, will be determined by what kind of atom is giving it off.

So if you look at an atom that's giving off this light, you know what wavelength the light should have. Yet when he looked at distant galaxies, he noticed that all the wavelengths of light he was observing were stretched. We'll go into this in more detail later, but basically you go from a short wavelength blue photon (particle of light), to a longer wavelength red photon. Slipher found that this was happening over and over again in the galaxies he observed.

Now the phenomenon in the shift of the wavelength of light, was well known as the Doppler effect. This was the thing that makes the pitch of noise change as the object goes by you. You start with something coming toward you, and it goes by. The very high-pitched noise you hear when it's coming toward you, will convert to a low-pitched noise as it goes away from you.

That's just because the waves of sound coming toward you are compressed, while those going away from you are elongated or lengthened. So you get a blueshift when something is coming toward you, something is squeezed to shorter wavelengths, while something going away from you will have a redshift.

So Slipher looked at all these galaxies and saw they were all redshifted. In other words, all these galaxies seemed to be moving away from us. So that's half-way to saying that the universe is expanding, and all the galaxies are moving away from us. Yet it's not quite all the way. It was Hubble who figured out the rest of the story, because he knew how to measure the distances to galaxies.

So Hubble went with his collaborator Milton Humason, and compared the distances to galaxies that he had measured, to the redshifts that Slipher had measured, and found a fascinating result. The apparent velocity that the galaxy would have to have, moving away from you to explain its redshift, was strongly correlated with the distance. The correlation is that the further away an object is, the faster its moving away from you. So that is what you need to be able to say that the universe is expanding.

So instead of a bunch of galaxies exploding away in some primeval explosion, if we imagine that the whole universe is just getting bigger, if the space in between all the galaxies is expanding, then you will see close-by galaxies move away gradually, while far-away galaxies will be zooming away at high speeds, since there's more space in between to do the expanding. That was what Hubble discovered.

He didn't call it that though. The plot we see is Hubble's original plot of the data. He plotted the distance on the x-axis and velocity on the y-axis. It kind of looks like a noisy plot with a scattering of points. Yet Hubble was a genius, so he drew a straight line through it and turned out to be correct.

The next plot is a much more modern version that looks like the points are much more closely aligned with a straight line, which is true, but also the size over which it's now measuring distances and velocities has grown enormously. So we really do have very strong evidence that the universe is expanding.

If you look at this plot and think about what its telling you, you realize that even though the universe is expanding, even though all the galaxies are moving away from us, it is not that we are in the center of the universe. We see nearby galaxies moving away, and further away galaxies moving away even faster. Yet someone in that middle galaxy, the one in between, would see us moving away in one direction, and the distant galaxy moving away in the other direction.

In other words, in this collection, every galaxy sees every other galaxy moving away from it, and the further they are, the faster they are moving away. There's no special point to this. Every galaxy is moving away from every other galaxy. It's the whole universe that is expanding all at once.

So Hubble had an equation. We'll actually show this equation! Occasionally in this course we'll see an equation, though we won't use them. It's important not just to mention that equations exist, but to actually look at them and show what they're saying. So here's an equation:

v = Hd

Velocity equals H times the distance. H is a constant, a number, which we now call Hubble's constant. So this equation is just telling us that the velocity of a distant galaxy is some fixed number once and for all, times the distance to that galaxy. So the further away the galaxy is, the faster it's moving away.

We say once and for all, because in our universe today, every galaxy obeys this law. Yet the Hubble constant is really better to be called the Hubble parameter, since it's telling us how fast the universe is expanding. In the past, the universe was expanding much more quickly. So what we call the Hubble constant, was a much bigger number in the early universe.

It turns out that measuring the actual value of the Hubble constant is much harder than you might think. It's been something that cosmologists and astronomers have been struggling with for decades, yet they think they've finally pinned it down. Wendy Freedman of Carnegie Observatories and her collaborators, have measured the value of the Hubble constant, and the answer they got is 72 km/sec/Mpc.

So what does that mean, km/sec/Mpc? It's telling us that the Hubble constant converts from distances to velocities, so 72 km/sec/Mpc, means that one galaxy, one Mpc (megaparsec) away, will be seen to be moving 72 km/sec away from you. If it's 2 Mpc away, It will be moving 144 km/sec away from you.

So what is a Mpc? It's a million parsecs, where a parsec is about 3 light years. In other words, a parsec is about 30 trillion km, a very big distance. An Mpc is a typical distance to a fairly nearby galaxy. So this number, the Hubble constant, 72 km/sec/Mpc, measured by Wendy Freedman in the 1990s, is basically setting the scale for the universe. It sets the time it takes for the universe to expand, and sets the distances to different galaxies. So the fact that we've figures out what this number is, is a big step forward in our understanding in the scale and size of the universe.

Now that we know that distant galaxies have this relationship, the Hubble law, their apparent velocities we observe are proportional to their distances, it become much easier to map out the universe. Measuring distances to galaxies is hard. You can't find cephied variables in very distant galaxies, they're just too faint. Measuring redshifts is easy, so we can use the redshifts, the velocity measurements, as a stand-in for distances. You know that the bigger the velocity, the further something away is.

Now we see a plot that is a picture of where galaxies are in the universe, created by a survey called the SDSS (Sloan Digital Sky Survey). We live at the center of this picture, and we see two cones going out in either direction. That's just because there was a northern hemisphere survey and a southern hemisphere survey. It costs money to collect every one of these data points, so they didn't observe the whole sky, they just observed parts of it.

Every one of the little dots, almost too small to be seen individually, represents a separate galaxy. So this is hundreds of thousands of galaxies, spread throughout the universe. We see two important lessons here. One is that the universe is basically the same everywhere. There's no dramatic difference between one side of the sky and the other, or from place to place in that universe.

If you took a big sphere of space that was sufficiently big, megaparsecs across, and took the number of galaxies in that sphere, another sphere in a completely different part of the universe that was just as big, would have basically the same number of galaxies. This is the crucial simplifying feature that makes it possible to study our universe in a systematic way. It's more or less the same.

The second feature is that it's not exactly the same. When you look closely at this image, you see there is structure there. There are little holes where there are almost no galaxies, and are concentrations where there are more galaxies. Those are clusters and superclusters of galaxies.

The evolution of the universe at early times from being almost perfectly smooth, to being the slightly non-smooth, lumpy distribution we see in this picture, is a fascinating story that cosmologists are just beginning to unravel right now. The universe is pretty smooth on large scales right now, in the past it was even smoother, so we're trying to understand how we got here from there.

So that's the picture that we have of the universe. It's quite a nice picture, but it's also quite provocative. To put it into context, we'll say the basics again. The universe is big, not just one compact collection of stars, but it spreads out as far as we can see. It's getting bigger as the space in between galaxies is growing. This manifests itself as the idea that every galaxy we see, appears to be moving away from us. Hubble's law tells us that the further away it is, the faster it appears to be receding.

It is smooth on large scales, so we can treat the universe locally in basically the same way that we treat the universe far away. The same average density, the same number of galaxies, the same basic properties of the universe, should apply here as well as somewhere very far away.

Then we can start thinking about what that means. If the universe is getting bigger now, that means that in the past it was smaller. We can imagine taking the current state of the universe and asking what it was like? Where did we come from? So if things were smaller, they were denser, closer together, with more things in every cubic light year and every cubic megaparsec.

If that keeps going, if you can extrapolate that back and things became very densely packed, very hot as things bump together, they heat up. If you keep going, you get to the Big Bang. You get to a point where the density is infinitely large. Where everything is on top of everything else. That would be a naive extrapolation from the fact that we're expanding now, you go backwards and what do you find, but that everything is on top of everything else.

It's perfectly reasonable to say we shouldn't be so naive. There might be some change in velocity of expansion, a change in the expansion rate. Maybe it started out not expanding? Maybe the universe was static and only slowly began to grow? So what we need is a theory. It's not enough to make the observations right now that the universe it expanding. We need a theoretical understanding of how it should expand in the presence of different kinds of stuff.

So that theoretical understanding is given to us by Einstein's theory of General Relativity, invented about 1915. The expansion of the universe was finally discovered by Hubble in 1929. So physicists had about 14 years to play around and try to figure out what should happen, according to General Relativity. What they figured out, will be he subject of the next lecture and the one after that. This is that the expansion of the universe depends on what is inside.

So in other words, after this picture of what the universe is like, we're drawn back to the questions of dark matter and dark energy. We have claimed in the introductory lecture that 95% of the universe is dark matter and dark energy. Dark matter is some kind of heavy, massive, slowly moving particle with a local gravitational field. Dark energy is something that is smoothly spread out, and is something that persists. It doesn't go away as the universe expands.

So given those ingredients, given the theoretical understanding of space and time that General Relativity provides, we can ask the question of what the universe looked like in the past. Was there a Big Bang? What will happen to the universe in the future? Will it expand forever or will it contract?

Now these are not trivial questions. When Einstein invented General Relativity, someone started saying very quickly thereafter that if space-time were expanding according to his theory, there should be something called the redshift. There should be a lengthening of the wavelength of photons. Yet not everyone believed it. Einstein himself was very skeptical about this effect.

So when Hubble found that the universe was expanding, found that distant galaxies obeyed this relationship, and had a velocity proportional to their distance, he never spoke about that phenomenon in terms of General Relativity. Hubble never said, "I discovered the expansion of the universe that people working with General Relativity had predicted." He always talked about just what he observed. He was a really good observer, and didn't want to make predictions or judgments on the basis of theories.

So Hubble never said he had discovered the expansion of the universe, but that he discovered that distant galaxies were moving at a velocity that was proportional to their distance. He also kept saying he deserved the Nobel Prize for discovering this, yet he never did. In his time, the Nobel Prize all the time, which is as it should be!

The next lecture will talk about Einstein and his General Theory of Relativity, for which he also never won the Nobel Prize. Yet it forms the basis for our understanding of space and time, so will let us make sense of this picture of an expanding universe.

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