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Okay. We’re gonna continue our discussion of the big bang theory today. Yes, definitely. And I wanted to continue discussing the microwave background radiation that was discovered by Penzias and Wilson when they were trying to set up microwave telephones. It turns out that this is a very important clue to the origin of the universe. First of all, it gave a temperature for the universe. We were able to realize that it was about 3 degrees instead of the originally estimated 5 degrees, but it had a temperature. It wasn’t zero. And what would’ve been even worse, I suppose, is if they’d found that it was 100 degrees because they couldn’t have explained that either. But it was comfortably close to what had been originally theorized. The problem with measuring this microwave background radiation is that only part of it was observable from the ground. In other words, the part that Penzias and Wilson were able to observe while they were doing their tests was only part of the total spectrum of that background radiation. But in order to determine what the exact temperature of the universe was and to determine whether the radiation was really a perfect black body radiation, astronomers wanted to ha ve much more accurate measurements and so they began sending up balloons into the high atmosphere to make measurements because some of the microwaves can’t get through the Earth’s atmosphere. Well, finally in the 1990s, a satellite was put into orbit -- the COBE satellite, as it was called, which actually is an acronym for the Cosmic Background Explorer satellite. Because that’s what it was. It was looking specifically at the microwave background from space where it could measure all the wavelengths with no problem. And once they got
those measurements, they realized that, yes, indeed, it was almost exactly a black body and the temperature was 2.726. Notice how accurately they got the temperature. And you can see the squares are the observations. The curve drawn through the squares is for a perfect black body at that temperature. So I think you can see that it fits quite well. It’s exactly a black body at that specific temperature. So now we had an extremely good temperature for the universe and we could start to look at even more detail. For example, this temperature was measured in all directions around the sky. The satellite could point in one particular direction and make all these measurements and get a temperature. And it could point in a different direction, make more measurements, and get another temperature. And so what they did was actually measure all around the sky to see if there was any difference. Because, you know, from the Earth it was pretty crude measurements. Maybe when you get up into space the temperature is different in different directions. And so that was tested and lo and behold, the temperature did vary depending upon which direction they looked. Now, there are several drawings here. I’ll show you one after the other. The first drawing at the top shows you the entire sky and it shows it in red and blue, depending upon whether the sky is a little hotter than that 2.726— that’s all the red — or a little cooler than the 2.726 — ‘cause that’s the average and that’s all in blue. And what you see is about half the sky is warmer than that average temperature and half the sky is cooler than that temperature. But you notice it’s not random. One direction in the universe seems to be slightly cooler, the other direction seems to be slightly warmer. Now, we’re talking about a difference in the third decimal point of that 2.726. In
actually plotted in galactic coordinates. So we can actually see the plain of the Milky Way. Then we make measurements of the Milky Way and subtract the Milky Way from this graph, so then we’re left with only a graph of the variations in temperature of the universe, ignoring the motion of the Milky Way and ignoring the heat generated by the Milky Way. And what you see is that now it’s kind of random. Little bits here and there are just a little bit warmer than little bits elsewhere. And now we’re talking about temperature differences that are out in the fifth or sixth decimal place. We’ve already subtracted the big variations. We’re now looking at the little tiny variations. And so what we see is that once you’ve gotten rid of the big variations, the little tiny variations are more or less random. There are slight differences in temperature of the universe in different directions. Well, it’s a good thing. It turns out that this was a very important discovery. If we had subtracted out the motion of the Milky Way and the temperature of the Milky Way, and the bottom graph had come out looking perfectly uniform, theoreticians would’ve been very unhappy. Because that would mean that when that radiation first became visible, the universe would’ve been perfectly uniform. Well, we know that it’s not. We know that there are clumps of matter i n galaxies and clusters of galaxies and clusters of clusters of galaxies, and that in-between them are the empty spaces. And so we know the universe is not perfectly uniform. It’s clumped. And so it’s kind of nice to see the clumping even in the background radiation, that there are little regions around the universe that are a little bit warmer than other regions. They have to be if the universe was not perfectly uniform. So this tells us something about the universe, the way it was at a particular time,
how non-uniform it was when that radiation was first given off. So we now have a lot of details about the background radiation that we didn’t have back in 1965 when Penzias and Wilson first announced the discovery, but it’s consistent. The numbers get better and better, but they still give us the same big bang conclusion. Now, there’s another thing we have to worry about as far as the big bang is concerned and this is the shape of space. The big bang theory requires general relativity theory to explain the big bang. General relativity, as you remember, has as a part of it that space is something that can be affected by the mass in it and that effect is to curve the space time itself. Now, I use that term “space time” because in general relativity, time is a dimension just like the spatial dimensions — up, down, and sideways; the three dimensions. Time is a fourth dimension. As far as the equations are concerned, time is equal with the other dimensions. And so we have to concern ourselves with the general curvature of space because there’s a lot of mass in it. If the universe were totally empty, then we would assume that if there was any space that it would be kind of flat. But you put mass in the universe, mass curves space, and so if you’ve got a lot of mass everywhere around the universe, what is the actual general shape of the universe as a result of that? Well, there are three possibilities. The first possibility is in this top drawing here and that is that space is flat. That’s possible. Now, what do I mean by “space is flat”? It means that the three directions, X, Y and Z, are exactly perpendicular and that lines running parallel through the universe never meet. It’s standard Euclidian geometry. Any triangle has 180 degrees of angles.
galaxy and it goes around a curve coming to you, how are you gonna know that it came around a curve? You’re gonna see the light and think it came in a straight line. How’re you gonna tell? They are actually ways to tell. And astronomers have tried to work them out theoretically and you can do it by looking at the distribution of objects in the universe. If you’ve got flat space — and it’s drawn there as flat — what you have is a random distribution of galaxies or whatever distribution you have, but the distribution is not affected by the curvature of space. It’s sort of not there. There’s no effect. If you have a positively curved universe, then if you start to measure the distribution of objects in the universe, that curvature will cause objects to appear more dense nearby. In other words, as you look out through the universe, if it’s positively curved, we’ll count more galaxies than we expect close by and fewer farther away even if they’re actually randomly distributed. So you might say it’s an optical effect. Because of the curvature, we see too many objects nearby and not enough far away. If we have the negative curvature of universe, what you’re going to see as you look out is that there will be an excess of objects far away and a deficiency nearby. So you can get a glimmer — maybe not a good idea of it, but a glimmer of the curvature of space by counting galaxies or objects. If you assume that they should go on forever, then maybe you can see what kind of curvature we have by the actual distribution. Now, that is complicated, of course, by the fact that the universe is expanding. And so as you look farther away, you’re looking back in time and so you expect the universe to look denser back in time because it was, and so you’ve gotta correct for that. But still you might be
able to pick out an effect from the curvature of space itself. So it’s something to concern yourself about because it could be important. Now, when astronomers began looking out through the universe, trying to measure these things and trying to measure the expansion rate, the red shifts, and everything else, they kept in mind that one of those things they had to worry about was this curvature problem. Well, now that we’ve been trying to measure this curvature for a long time, what we have decided — at least preliminarily based on the observations — is that as far as we can tell, it’s flat. We don’t see any effect from curvature, either positive or negative. As far as we can tell, it’s just standard old Euclidian geometry out there. The universe does not seem to be curved, one way or the other. And this could be cause for concern. Because the original idea was that relativity theory predicts a curvature of space because of mass in it, so a lot of theoreticians were kind of expecting — although they wanted to wait until the observations were in — they were kind of expecting a positively curved universe and they didn’t get it. The observations indicate that it’s flat. There’s no curvature. Now, what does this mean? You know, this requires a little bit of thought. If the universe is not curved by the mass in it, what does that say if you still want to accept general relativity theory as explaining what’s going on? What it means is that the universe has to be a wfully large. Because if it were a thing that expanded and wasn’t that big yet, we would expect a lot of curvature. But as the universe gets bigger and bigger and bigger, if you can think about being on the surface of the Earth, the Earth is pretty big. And so if you go out into a field and you are trying to measure something, the field looks pretty flat.
the big bang. And so some of the predictions — I’ll just show you an example of some of ‘em. On this overhead, it shows the present and on the left scale is the scale of the universe or the size of it. Now, we don’t know the size, but we know that if it’s expanding it’s getting bigger. In the past if it was smaller -- because if it’s expanding out it had to be smaller — we can calculate what size it would’ve been with various assumptions or what size it will be with various assumptions. So if we have an empty universe — in other words, perfectly flat with no mass in it — we can calculate that the universe would expand uniformly forever. Nothing to stop it. It’s just gonna keep expanding. At least that’s our simple idea. If you have mass in it but there’s not enough mass in it, then you’re going to have the universe expanding, the gravity of the mass pulling back kind of slowing the expansion a little bit, and so you have Case A where the universe is getting bigger but at a slightly slower rate. And so Case A means that the universe will continue expanding forever, but that the expansion will weaken essentially. Case B is that the universe is flat and that there’s almost enough gravity but not quite enough. So that the universe continues to expand and it’s slowing down, but it never quite stops. Almost enough mass, not quite. But the universe would look pretty flat under that circumstance. Or, if things were going a different way, if there was plenty of mass in the universe to stop the expansion, if the gravity was strong enough that as things were going out and came to a stop, then it might s tart to fall back in. And so Case C shows that it would reach a maximum size and then begin to shrink again and finally collapse down to zero size. So
these are different assumptions based on what’s out there. And so astronomers have spent 30 or 40 years measuring the speeds of things to try to see which case is the actual case. And the way you can do it is you notice that A, B and C have different starting points also. Well, we can look back into time by looking out into space. We can see how fast galaxies are moving apart 10 billion years ago, we can see how fast galaxies are moving apart 5 billion years ago, and we can see how fast galaxies were moving apart a billion years ago just by looking at different distances out in the universe and seeing what their red shifts are. So we can kind of get an estimate of which one of these cases seems to be the actual one by looking back in time — because, of course, we can’t look forward into time. Be nice to be able to see what’s gonna happen in the future, but we do have the opportunity to see what happened in the past by just looking at different distances. And so we can estimate whether it’s A, B or C from those measurements. The problem is — and we’ll get to it in a little bit more detail later — none of these cases work. When we actually measure the speeds of galaxies at different distances from us, we come up with what we would have to call — in this overhead — Case D. And Case D is if this graph went out above the empty universe. In other words, the universe is actually speeding up rather than slowing down. Sounds backwards because mass should be slowing it down. But the most recent observations don’t back up any of these three possibilities. They back up the counterintuitive one, the one where the mass doesn’t seem to be doing anything of use, and the universe is actually speeding up faster than if it were empty. So your best laid plans, as far as proving one theory or another, can
started, it was extremely hot because all the matter and energy were all in one spot, and so that was a pretty hot place. And then it began to expand a nd cool off, and it’s been cooling off ever since. The expansion of the universe is the basis for the whole model. If the universe were not observed to be expanding, we would not have a big bang. We would have a steady state in the universe or some othe r model to explain it. So the first basis for the big bang theory is the observations that the universe is expanding. The second basis is the cosmic background radiation, the microwave radiation that I just talked about being observed and measured very a ccurately. Where did it come from? How did this radiation get there? It’s just the leftover temperature from the hot bang. The universe was extremely hot. As it began to expand, everything gets red shifted — which means it cools off. And as it continues to expand, it continues to cool off. And so after 14 billion years, it has cooled down to a temperature of 2.726, more or less. And so that is another leg under the big bang theory. Now, what I haven’t talked about yet is nucleosynthesis of light elements. I haven’t even hinted at that. Well, it turns out that we can even explain the makeup of the universe with the big bang. In other words, we have hydrogen, helium, and other elements, all the elements on the periodic table, floating around in space. But what we know from observation is that hydrogen is by far the most common element, almost 70 percent. Helium is the next most common, over 26, 27, 28 percent. Depends on where you look. It’s always over 25 percent. And then all the rest of the elements are very small amounts. We’re all of a sudden down to 2 percent for everything else.
We can explain that with the big bang. If you’ve got a universe that is extremely hot, it would be so hot that you wouldn’t even have elements. If you take atoms and you heat ‘em up, the electrons escape. You get ionized gas. If you heat those ionized particles up too much, the nuclei break apart. If you continue to heat ‘em up — and now we’re talking theoretically ‘cause nobody’s ever done it — you get to a point where even the nuclei, the protons and neutrons, can’t exist as protons and neutrons. And so they break apart. What do they break apart into? Well, it turns out that protons and neutrons and other nuclear particles are made of smaller particles called quarks. There are different kinds of quarks and these little particles are what make up protons and neutrons and other particles. And so if we propose that this thing was very, very hot and very, very dense, we also have to propose that there weren’t any real elements as such in that hot, dense material. It was, if nothing else, just energy. Because, as you know, you can take matter and turn it into energy. You can take protons and collide ‘em and get energy out because you’re changing some of the mass into energy. So mass can be turned into energy. So you can look at mass as condensed energy. And so if you go back up the temperature scale far enough, you go back to a point where the particles couldn’t exist. It was too hot and they would’ve b een just pure energy. So the universe probably started as pure energy, at some extremely high, almost unimaginable, temperature. As it began to expand and cool down, particles would have condensed out of the energy and those particles would’ve been quarks. Because those are the basic building blocks of all the rest of the material.
because the universe was still expanding. And so what you would have is the end of fusion reactions because the temperature would get too low for fusion reactions to occur. So once the fusion reactions began, they could only go on for a finite amount of time before this expanding universe cooled enough that the next stage of fusion could not occur. And you can actually calculate the temperature — at least using nuclear physics — the temperature at which quarks would turn into protons, and then protons would begin to combine into deuterium and light helium and heavy helium, and you can calculate how the temperature would be dropping during these fusion reactions and you can actually determine how much of the hydrogen would have turned into helium before the temperature dropped below 4 million degrees. Because remember, below 4 million degrees, no fusion reactions. And it turns out when you do the calculations about 25 percent of the universe should have turned into helium before the temperature quit or it got too low. And that’s just what we see out in the universe. We see 70 percent hydrogen and a little bit more than 25 percent helium. Now, why do we see more than 25 percent helium? Because helium fusion has been going on ever since at a slower rate inside stars. But the basic constituents of the universe right after the big bang was about 25 percent helium and 75 percent hydrogen. And I say “about” because there was a little bit of lithium and beryllium and boron that would also have been forming at that same time. So you’ve got mostly hydrogen, mostly helium, a little bit of light helium because some of it would’ve not finished turning into regular helium, a little bit of deuterium. And you can do calculations as to how much of each of these elements should have been
formed at the various temperatures before the temperature got too low, and that narrows down what the conditions were in the early universe. Because if we can observe the percentages of those elements in the present universe and can look at our models and say, “Okay. Which one of these big bang models actually gives us the right percentages?”, then we have an idea of which model fits the data the best. They all fit the 25 percent helium. That happens with a lot of different possible models. But the model is much more sensitive when you measure how much deuterium or how much lithium or how much beryllium. So you can kind of narrow it down by looking at those lighter elements and seeing what percentage of those is still floating around in the universe. So the element abundances also agree with this hot big bang. Now, the last one here, formation of galaxies and large-scale structure. Remember I mentioned that theoreticians were very happy that the cosmic background radiation showed that when the universe first gave off this radiation, it wasn’t exactly uniform. Because if the universe had exploded perfectly uniformly so that all the matter was coming out perfectly smoothly, then there would be no way for galaxies to form. Because galaxies forming would require non-uniformity of the matter. If you get a clump of material here, that means it’s got more gravity and so it begins to attract more material. And so you needed to have some clumps here and there around the universe or you never would’ve gotten bigger clumps. A bigger clumps has to come from a smaller clump. And so if everything was perfectly uniform, it would still be perfectly uniform. We would have a universe of atoms that were perfectly smooth, spreading out into the — whatever it’s spreading out into. It’s not spreading into anything that we know of. It’s just
opaqueness of gas, occurs from electrons. The electrons are flying around loose and they are what the photons bump into. Well, if you can get rid of the electrons, then space is much more empty and photons can go through. Well, the way to get rid of the electrons is to have them all attached to nuclei — in other words, normal atoms. Well, as the universe continued to cool, it was opaque, opaque, opaque, until it reached about 3,000 degrees. So it went from, you know, a quadrillion degrees all the way down to millions where fusion occurred, and then down to 3,000 degrees. And at 3,000 degrees, hydrogen can hang on to electrons. And so as soon as it crossed that temperature range, the electrons were captured by all the hydrogen nuclei. And since that’s most of the universe, all of a sudden the universe cleared. It’s like the fog suddenly cleared and all the photons that had been flying around, bumping into everything, suddenly could travel anywhere they wanted. So that moment of transparency, when the photons suddenly took off, is what we are actually looking at when we look at this background radiation. We are seeing the photons when they left. When the universe became transparent, all the photons started heading out. Those photons have been getting red shifted ever since, traveling across the universe as the universe expands. And so this background radiation is actually what the universe looked like when the universe had dropped to about 3,000 degrees. And by calculating how long it would take for the universe to drop to that temperature, it turns out it was about 300,000 years after the bang. The universe suddenly cleared. So we can actually see through the universe back to the age when it was 300, years old, but we can’t see any farther because it was opaque. So it’s kind of like seeing
the wall. We see the background radiation. We cannot see any farther toward the beginning of it because there was nothing to see. Okay. We’ll continue this tomorrow.
