Thursday, March 18, 2010

Frontiers and Controversies in Astrophysics - Introduction by Charles Bailyn

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Professor Charles Bailyn: Some things about this course. This is a course for non-scientists. That portion of the enrollment policies is not a suggestion. I really don't want science majors in this class. If you are a science major, I'm going to notice because that's one of the things that appears on the class list; what your major is. So, don't take the course if you're a science major. Let me point out that freshmen don't have major, so it doesn't matter if you intend to be a science major if you're a freshman. If you are a science major I recommend Astro 210, which is being given this term. I have a little handout on all the different introductory astronomy courses at the front of the room if you're interested.

Let's see, it is also true that this course is kind of intended for non-science majors who have a certain basic high school level comfort with tenth-grade science and math. If you're extremely phobic about these kinds of things, I would say that Astronomy 120, while it has a similar level of math, has a somewhat shallower learning curve and a somewhat deeper safety net. So, if you're the kind of person who breaks into a sweat when somebody writes down an equal sign, check out 120. Let's see, but that's not the biggest difference between this class and 120. I think the biggest difference is what the class is trying to do. Astronomy 120 and also 110 and other courses in our department, and elsewhere in the university, are basically survey courses. Most introductory science courses are survey courses. They cover a fairly wide subject matter.

This is--isn't that, what this course is supposed to do is we're going to talk about three particular topics in very considerable detail. Enough detail so that by the end of our discussion you'll understand what's going on in current research in this topic. And by current, I don't mean this decade, I mean this week. Astronomy is currently in a stage of very rapid advancement, and one of the things that's happened every time I've taught this course in the past, is that at some point during the semester someone will publish some piece of research which changes some aspect of the curriculum. I'll come in waving some paper and everything will be changed, and I can't guarantee that of course, because I can't predict the future but it's happened every time in the past. So, we really are trying to get you all the way out to the frontiers of the subject.

I think this is actually a better approach for non-science majors, because after all, we live in the Internet age. If you want to find out a bunch of facts about some scientific topic you could go online and go to Wikipedia or wherever, look these facts up. That's not a big problem. The problem comes when there are two sets of facts which directly contradict each other. This happens quite frequently in scientific topics these days, particularly those with kind of political or moral overtones, and you get facts that directly contradict each other. What are you supposed to do about that? What I'm hoping is that by talking about situations in which the facts at the moment really aren't known yet, you can develop some skill in interpreting these kinds of contradictory facts for yourself. If you don't do that, then the only alternative is to listen to the experts argue with each other and vote for whoever argues the loudest or looks the best when they're doing it, or has a degree from Harvard or whatever it is. You guys can do better than that. So, the hope is that by practicing this kind of skill of evaluating science when the answer isn't fully understood, that you can develop skills that will stand you in good stead when you run into scientific controversies in a political context or a legal context, or just as ordinary citizens in the course of your lives.

It also happens that the three particular topics I think are of some real interest and importance in themselves. And I'll get to the three topics again in just a moment here. Let me point out that this kind of approach has a downside to it and this has been pointed out repeatedly on course evaluations. Because we're dealing with stuff which ultimately the answers are not yet understood there's no textbook. There can't be a textbook. We haven't figured out what to put in the textbooks yet. And the problem with that is that that makes the lectures very important because that's the only information you're going to get. There's a whole bunch of online readings and stuff but they tend to have a point of view, and so it's really the lectures that are the basis of the course. The problem with that is that I've chosen to give this course at the ungodly early hour of 9:30 in the morning, and you guys are going to have to show up and so here's the deal. I'll make a deal with you: Your job is to get to class by 9:30 in the morning. My job is to keep you awake once you're here, and so if we both succeed in cooperating in this sense we'll probably be okay. But seriously, if you're anticipating regular difficulties in getting to class this is not actually a great class to take because there's no backup in the form of a textbook.

All right, the particular topics that are under discussion, I've listed them here in green. The first of them are extra-solar planets, by which I mean planets around stars other than the Sun. It's well known that there are many, many of these planets. All you have to do is watch Star Trek or something like that and you'll find many, many examples and this has been a staple of science fiction for quite a long time. Oddly enough, until ten years ago, there was absolutely no evidence for this. We assumed that, because the stars are normal stars and there are many other stars--the Sun is a normal star and there are many other stars like the Sun that there must be many planets of the same kind as the planets in our own Solar System circling around all these other stars. But until 1995 there was not one bit of evidence to support that idea. Since 1995, this has become a huge growth industry and research, and we now know of literally hundreds of planets, all of them discovered in the last ten years. So, this is a situation in which, what ten years ago was science fiction, has become science fact and we're very rapidly trying to figure out exactly what kinds of planets these are, whether there are Earth-like planets out there, and that has some bearing on what the science fiction people refer to when they say as, "life as we know it." And so, that's currently one of the hottest topics in astronomy.

The next topic is going to be black holes, and this is a similar situation. Fifteen, twenty years ago black holes were sort of poised precariously on the boundary between theoretical physics and science fiction. A boundary that is more porous than you might believe. But again, in the past fifteen years or so this has been converted into a standard topic in observational astronomy. There are dozens, probably hundreds of objects we can point to in the sky and say, "yes those things are black holes." And so now, the current topic of research is do these things that we are pretty sure are black holes actually behave in the incredibly bizarre, science-fictiony manner that the theoretical physicists have been talking about for the past thirty or forty years. So, to what extent are these very exotic behaviors actually manifested in real life?

Finally, I want to talk a little bit about cosmology. Cosmology is the study of the Universe as a whole. That's too big a topic to go into in depth, so I've picked one piece of it. The piece I've picked is the existence, which was discovered in the late 1990s, of something called "dark energy." Dark energy is an all-pervading anti-gravity; it's a repulsive force that turns out to occupy essentially all of the Universe, and 75% or more of the entire mass energy of the Universe turns out to be in the form of this mysterious dark energy. The evidence for this comes largely, but not entirely, from observations of a certain kind of supernova. And so what I'm going to focus on is the observations of the supernovae and how they demonstrated that, in fact, all ordinary matter and energy and so forth is a tiny fraction of what's actually going on in the Universe, and what's really happening out there is something we totally don't begin to understand. So, that will be the third topic of the course.

These topics have something in common. All of them involve observing something that you can't actually see directly. We don't see these planets directly because they're too faint and too far away. We don't see black holes directly. By the definition of black hole you can't see these things directly. And of course, dark energy, by its very name, is also undetectable. So, how do we know that these things are there? The answer is we know that they're there because of their influence on other objects that we can see, and in particular, their gravitational influence on other objects that we can see. And so, what binds these three topics together, are first of all, the fact that the observational techniques to discover them are actually quite similar to each other. And second, that they all involve different manifestations of gravity. And so, we'll be talking in the first part of the course about Newtonian gravity. In the second part of the course when we get to black holes, that's relativistic gravity, general relativity, Newton's--Einstein's theory which supplanted Newton's theory. And then by the time we get to dark energy, it may not even be correctly described by Einstein's work, and we may be in the area of whole new kinds of physics that the theorists haven't even thought about yet. So, there will be a progression to more and more sophisticated theories of gravity underlying these observations.

There's another feature that these topics have in common, and that is that they can be understood in some detail without particularly sophisticated mathematics. Now, let me pause here and say some things about math. Astronomy is a mathematical topic. There will be math in this course, there ought to be math in any astronomy course or it isn't really an astronomy course, it's just a slide show. Now, the math in this course has been kept at a deliberately low level. That is to say, the kind of math we'll be doing is stuff you did in ninth and tenth grade. Introductory high school algebra, high school geometry, I think we take the sine of an angle a couple of times, but it's the one case it cancels out almost immediately, so don't let that scare you. It's the kind of thing that you all did on the math SATs and since you're all sitting in this room you must have done okay.

Having said that, I have discovered that saying that is misleading. And the reason it's misleading is cast your mind back to ninth grade; ninth grade math is hard. Remember? In particular, word problems are hard. You remember word problems. This is where you drive from here to Cleveland and you fill your tank up with gas, and the gas costs so much per gallon, and the question is what is your shoe size or something. [laughter] The way one approaches that is through a kind of common sense approach which involves the fact that many of us have been in a car, driving from City A to City B, perhaps not Cleveland, but somewhere else, and so you have a kind of intuition to fall back on. When you do math problems that are logically the same, but apply to astrophysical systems, for which you have absolutely no common sense to back you up, then you have to reason purely from the internal logic of the problem and that's hard to do. It's a skill that can be learned; it's a skill that's worth learning; it's a skill that I'm sure many of you already have to a large extent, but it isn't an easy thing. So, the fact that the level of the math is low doesn't mean that the problems are easy. We do have a lot of help mechanisms, which I'll describe perhaps on Thursday, to keep you up to speed if you start having trouble with these things.

So, I should say something about course requirements here. Let's see, we have sections in this class. The sections are not just problem solving sections, these are actually required. The fact that we're dealing in topics for which the answer isn't fully known means that one can actually have discussion sections unlike many science courses, so we're going to do that. And so, the structure of the course is like a history course. Two lectures a week plus required section, and so 10% of your grade comes from sections. A large fraction of that is just showing up, but there will also be something in terms of saying something intelligent once you get there. That's 10% of the course; 30% of the course is problem sets. We will hand these things out once a week. The first problem set will show up on Thursday, and if you have any question about whether this course is appropriate for you, the right thing to do is to look at that problem set and ask yourself is this reasonable. I will say that students on their evaluations have pointed out that it does--the course does get harder. It's not that the math gets more complicated, but the situations get more complicated. So, if you have serious trouble with the first problem set that's probably a warning sign. As I say, that will be handed out on Thursday. These things come about once a week; it's 30% of the grade. I'll say more about problem sets later on Thursday.

Thirty percent comes from two midterm exams. The way we do this is the one where you get the better score counts 20%. The one that you get the worst score counts 10%. So, that gives you a little bit of a break. And then there will be the Final exam, that's the last 30% of the class. There's also an optional paper. If you choose to do that, that will count 15% of your grade, and what it will do is it will de-weight whichever the worst of your 30% parts of your grade are back down to 15%. So, if you're a word person rather than a number person, you get this opportunity to augment your score and de-weight some other part of the class in which you may have done less well.

All of this stuff is on the classes server [Yale's online course tool]. I should say that the syllabus that I've put out here is just a direct copy off of what's on the classes server, so feel free to take that. But all the information, and actually more information is online. Let me pause now and ask whether there are questions about the course and the course procedures. Yes?

Student: This may be a silly question, but I saw on the web that right below the times listed for this course was a "to be determined" or some sort of notation that could indicate that there is another of this class at a different time?

Professor Charles Bailyn: No, no this class is going to meet now. I'll have to check and see what you were thinking of, but it may be that what that was referring to was section times, and actually this is something that I haven't mentioned. Sections are required. They're all going to be on Mondays. We're going to have a wide range of times, all of them on Mondays from 12:30 until I think 8:00 at night. But you do have to sign up for a section. Let me also say, I've mentioned here, I don't think this is--;actually, looking at the number of people here, I think we're going to be able to accommodate everyone, including juniors and seniors. But I did set it up in such a way that freshmen and sophomores get first crack. The way that's going to work is the online sectioning form opens up on Monday and juniors and seniors won't be allowed to officially register for the class until Tuesday. So, the freshmen and sophomores get to fill up the sections first. My guess is, again, looking at the number of people here today that we won't have any problem, and that if you're a junior or a senior you'll get in just fine. So, we'll be picking sections through what is now the standard online sectioning thing, which is going to open for business next Monday. I'll check the website and see if that's actually what you meant, but it may have been something else. Other questions?

Let me, in general, encourage you to ask questions. I know that that's hard to do in a big lecture setting, but we have an advantage over other courses, particularly science courses. We're not trying to prepare you for the astronomy part of the MCATs, so we don't have to cover a specific syllabus. We're not even trying to follow a textbook. And so we have a little more leeway than is ordinarily true to ask questions and go in weird directions, so please feel free to do that. I reserve the right to put a question off into the future or into discussion section or something, but do by all means ask. We have some freedom of action. Yes?

Student: Is it possible to take an early final?

Professor Charles Bailyn: An early final? Let me think about that. I prefer to avoid it because then I have to invent another final. The problem with that is trying to make them come out even. I will say this, that if I do an early final, I'm probably going to err on the side of making it hard. But it's very hard to make them come out even, but let me think about that. Other questions? Yes.

Student: In discussion sections, is it just going to be like discussing things or is it going to be working on the problem sets?

Professor Charles Bailyn: It's going to be some--So, the question is, "What are the discussions sections going to be like?" Are there going to be discussion of the problem sets or is it going to sort of general discussion of the course material? The answer is both. I think there will be both, in any given discussion section, there will probably both be an opportunity to talk about the previous problem set and to clarify things about the next problem set, and also some kind of activity that sort of extends and advances what we've been talking about in class. So, I'm hoping to do some of both. If we veer too much in either one direction that's probably not a good thing. There will be other ways of getting help as well, if you start to have trouble on the problem sets or in the course generally. I'll talk about those a little bit on Thursday. Yes sir?

Student: How are problem sets graded?

Professor Charles Bailyn: How are problem sets graded? Very carefully. Let's see, I think we'll probably--it'll probably be on a kind of zero to twenty-point schedule. But let me say this about the problem sets. There are going to be two kinds of things on the problem sets. One are kind of quantitative problems which have a right answer. Those are relatively easy to grade on some kind of a point scale; you give partial credit and so forth. But we will also--because this is a course that's not only about the specific of this topic but also about science in general, we're also going to have things that look kind of like essay questions on the problem sets. Those are a little harder to grade in this way, but we've got to grade them in the same way so that we can add the points up. And I'll talk a little bit more about how those are graded. I will say one thing; one thing that we do is we make sure that each problem or essay is graded by one T.A. or by myself, so that we don't have different people--so that if you're in a section it's not like your--all the problem sets for that section are all graded by your section leader and some other section leader grades all the other problems, because that leads to imbalances of various kinds. So, we assign each problem to a specific person for the whole class. It's basically a zero through twenty scale, although what that means varies depending on what kind of a problem it is. I'll say a little bit more about that.

I will also say there is a rather detailed lateness policy that's linked to the classes server, please read that. We're going to stick to it. And one of the features of that is that there will be answer sheets. Problem sets are typically due Thursday, there will be an answer sheet up the following Tuesday, so if you don't get it done by five days after it's due, you're toast because the answers are posted. Other questions?

Great, let's start. This is very cool. All right, this is going to be all kinds of fun. Planets, planets around other stars, but planets in general. So, let's start by talking a little bit about orbits, planetary orbits. You probably know some of this story, originally in the old days, people used to think that the Earth was the center of the Universe. So, the Earth was at the middle and planets went around them in circles. That's not much of a circle [drawing on overhead], but you know what I mean. And so, everything was circles around the Earth. And that's what planets did, where planets also included to their way of thinking, the Sun and the Moon as well, and so you had these circles around the Earth. This is what's called the geocentric model; Earth at the middle. It's associated with the name of a Greek astronomer named Ptolemy. The problem with this model is very simple. Namely, that if you actually go out and observe where the planets, and the Sun, and the Moon are night after night after night it doesn't work very well. So, this doesn't fit the observations. Doesn't fit observations.

So, they said, all right well maybe that doesn't work all that well, so what we'll do is instead of imagining that the planets are on circles around the Earth, we'll imagine that there are circles on circles around the Earth, and the planets go on those. So, you add a kind of extra circle here, so the circle goes around the Earth and the planet goes around on that circle. These circles were called epicycles. So, add epicycles. And what happened is they would add an epicycle and then they'd go out and observe some more, and in particular, the Arab astronomers a thousand years ago. A thousand years ago the center of all science was in the Arab countries; they gave us all their--all our star names by the way are in Arabic, so are mathematical techniques such as algebra; it all comes from the Arabs. They knew what they were doing back then when the Europeans were kind of in squalor. And they made these great observations, and every time they made more observations it turned out it didn't fit. So, they had to add more epicycles. So then, they added one here, and one here, and so on until you had circles, and circles, and circles, and circles in order to explain the observations. So, add epicycles repeatedly. And this is kind of unsatisfying because it's not a good thing where every time you get more or better observations you have to revise and extend your theory.

That's not such a great theory. In fact, the word epicycles has now become a kind of a swear word in the scientific community, meaning a sort of theory that has become so complex it's just ridiculous and you don't want to believe it anymore. So, someone will come up with some really seemingly sophisticated but very complicated theory and if you don't like that you just go that's just epicycles, forget about it. So, this has become a little bit of a swear word, and it was unsatisfactory at the time. Now, let me pause for a moment and confess that the story I've just told you, which is the standard story about Ptolemaic epicycles is, well, it has what I think Colbert would refer to as "truthiness." It's a commonly told story that people like to believe, but if you talk to the historians of science this isn't actually how it happened. And, in fact, this idea of circles on circles, on circles that isn't the way epicycles worked, they had circles and they did get more complicated every time they fit the observations, but not by adding more and more circles. They would move the circles side to side, they would have things going at variable speeds around the circle, all sorts of things but this little picture that I've just drawn here has a kind of "truthiness" to it. I would say that this is a general issue with the way scientists describe how science works.

We tell these nice anecdotes and we put them in the textbooks too; in the little bars that go down the side of the textbook, where you get the head and shoulder shot of the famous dead white male scientist and so forth. And then we tell these stories. And the historians of science hate this because it isn't actually what happened. Nevertheless, we persist in telling these stories, and I've been thinking about why that is. I think the way to think about this is what these stories are, are fables. And like any fable, the point is not that the story is true. The point is that it vividly illustrates a moral, which tells you how to behave or how not to behave and they're useful for that reason. You'll recall the famous fable of the ant and the grasshopper. Grasshopper sings and plays and dances all summer long. The ant is very industrious, piles up food, doesn't have any fun. But then in the winter, the grasshopper starves and the ant does fine. If an entomologist were to come along and say but that's not how ants and grasshoppers behave, you would correctly say that he's missed the whole point. And the point is that it's just a nice story which illustrates certain kinds of behaviors and whether they're good or bad. So, here's what I'm going to do; I'm going to tell these stories, but I'm going to label them fables and I'm going to point out the morals explicitly. And the optional paper is going to be: go and take any one of these things and find out what really happened and comment somewhat on the implications of the real story for science.

I should say that the biggest of these fables is probably the one about Galileo and the Catholic Church, where the Catholic Church oppresses the pioneering scientist and the scientist stands firm against this huge impersonal bureaucracy, and the establishment trying to squelch them and so forth. The truth of that is actually very subtle and very interesting and I can't go into it now, among other things because I'm not a historian of science, I'm not the best person to talk about it, but check that out sometime.

Anyway, for this particular--this is the fable of the Ptolemaic epicycles and the moral is that simple theories are better. And you particularly don't like theories which get more and more complicated, the better and better your data become. I should say that the word simple in there turns out to have a technical meaning if you take a statistics course. What I mean by simple is something that has relatively few free parameters. I'll just leave that at that. You can go talk to the statisticians about it. So, if your theory is getting overwhelmed by epicycles, then you'd better go out and come up with some other better theory. And so, people tried to do that, and the first step along the way was, of course, Copernicus.

Copernicus, as you probably recall, decides that the geocentric model is wrong, things ought to be heliocentric; the Sun in the middle. So, you put the Sun in the middle and everything, including the Earth, goes in circles around the Sun. This was revolutionary, and in fact, the title of the book he published was De Revolutionibus Orbium Coelestium, which means "of the revolutions" in the sense of "revolving of the celestial spheres." The use of that word revolution is one of the things that pushed the word revolution to its current meaning, meaning overthrowing authority in some ways. Originally, it just meant to revolve but this was so revolutionary that people started to use the word in the other way. This wasn't actually as great a theory as you might think, because it still needed epicycles. Not as big, not as many, but it didn't get rid of the problem with epicycles. And that didn't work itself out until a generation or two later when Kepler came along.

Kepler was a famous astronomer and he had in his possession, because he stole them, the best naked-eye results that had ever been obtained of the motions of the planets, in particular, Mars. He described these motions in Three Laws of Planetary Motion. You can look them all up in a textbook. In other kinds of courses we would have you memorize these things; I'm not going to do that. The key point here is that these are not circles; they're ellipses around the Sun. That, it turns out, gives you a model for planetary orbits which, when you take better and better data, doesn't change. They're still ellipses; you don't need little ellipses on top of these ellipses to explain everything that's going on. So, this now has excellent descriptive power. It really describes what's going on, and when you make further observations, it still describes what's going on. It does not have any explanatory power in the sense that if you say, "why ellipses?" Kepler had no idea. That's just the way God made it. So, it's not in any particular way an explanation. For the explanation you have to wait another generation or two until we get Newton.

Newton writes down three laws of his own, but these are now three laws of motion, not planetary motion in particular. And again, one could write these down and memorize them and learn them, and that would be a good thing. Let me write down one of them, the Second Law, looks like this: F = ma, force equals mass times acceleration. And I write this one down simply to point out that that equation is the entire intellectual content of Introductory Physics for physics majors. If you go take Physics 180 this is all that they do and they spend the whole time. It turns out you don't actually want acceleration, that doesn't tell you what you want to know. What you want to know is the trajectory, where the object is as a function of time. Those of you who have taken some calculus may recall that if you take the acceleration, and you take an integral twice, you'd come up with the position as a function of time. So here's what--so in the next thirty seconds I'm going to explain Physics 180 to you. You substitute in some kind of a force, you divide by mass, you take two integrals, and that gives you the trajectory of the thing. That's all you need to know. Technically, of course, it's quite hard, but conceptually pretty straight-forward.

One of the things that Newton did with this equation was he took a particular force, namely the force of gravity, which he also wrote down a Law of Gravity. That tells you for any given situation what the force due to gravity is, substituted it in here, and figured out what the motions of the planets ought to be. And it turns out that he could derive Kepler's Laws. He derives Kepler's Laws. Very nice. Now, of course, in order to do this he has to invent calculus, so it takes a little while. He was a great genius but even so, inventing calculus from scratch, not something you want to attempt at home. And that was basically the start of both modern science and modern mathematics.

So, this marks the start of science in the following sense--that Newton has to make a couple assumptions along the way, sort of deep assumptions about how the world works. One is that the Universe is governed by laws, and in fact, by universal laws. What I mean by universal, in this sense, is that they apply everywhere; that the same law of gravity that resulted in the top of my pen falling to the floor over there also is responsible for the orbits of the planets and the motions of the stars. This was a new idea. It's very familiar to us by now, but the idea that the planets ought to behave according to the same rules as stuff down here on Earth was a whole new concept. The other piece of the new concept is that these laws are mathematical in nature. This is why science is hard, because it's hard for human beings. I think it's something to do with the way our brains are wired, to accept that this is true. It's very easy to imagine a world in which that's not true. Go read any fantasy novel. Any fantasy novel has a situation where the hero or the villain, by virtue of their strength of character influences the events around them. So that is a rule governed by laws, perhaps, that are not mathematical in nature, but depend on the moral character of the individuals involved. Every human culture has such stories including our own. It's very hard to get away from it, and the idea that there's just this sort of mathematical structure and that your moral stature has no bearing on what's going to happen is kind of hard to accept. Fortunately, people turn out to be pretty good at math, so we can actually solve these problems and move forward. These two ideas were revolutionary and they are the basis pretty much of all science.

So then Newton's laws get elaborated on for several centuries. By the end of the nineteenth century things are starting to come apart a little bit. There are now problems that show up with Newtonian physics. It's been a big success on the whole but there are now problems. And in the early twentieth century what happens is two new laws of physics are invented. These are the given the names quantum mechanics and general relativity. And the situation with these is they don't overturn Newton's laws, they extend them. It turns out that in the kinds of situations that Newton was looking at, both quantum mechanics and general relativity, reduced down to Newton's law. So, you have a situation where here are Newton's laws, Ns Laws, of which Kepler's laws are a tiny subset. And then general relativity; I'm drawing a kind of Venn diagram here, is here, relativity, occupying Newton's laws but that's some other stuff. Quantum mechanics looks kind of like this; extends in a different direction. Let me make these axes-specific. I don't like Venn diagrams when they don't tell you what you're actually plotting. This is mass, so heavy things are when relativity kicks in. This is size, and so small things are when quantum mechanics kicks in.

But you can see the problem. We've got two big theories. You really want those theories to be encompassed by one yet bigger theory. And that is the current goal of theoretical physics, to try and find the one great theory that encompasses both quantum mechanics and general relativity, which contradict each other in various awkward ways, particularly in this region up here. This is called the Theory of Everything, or TOE. And the best current guess as to what kind of a theory that will be is that it will be some kind of string theory. I won't go into string theories now, you can go read many popular books on this; it's very exciting. There is currently no string theory that really works out all that well but the people who are studying this kind of thing like to believe that that's going to work out sometime in the future. This is good.

We've gone about forty minutes from the start of science to the Theory of Everything, so we're done. Everything else is a detail and so the whole rest of the course is filling in details. The first of which--so let's start on the details. The first of which, I want to go back and catch one of Kepler's Laws. And I want to write down the Newtonian Modification of Kepler's Third Law. That is an equation that looks like this:

a3 = GMP2/4 π2

We're going to circle this in red. This is something you're going to want to memorize. This, it turns out to be, a basis of a large fraction of what we're going to do in this course. So, let me explain the symbols; a is the semi-major axis of an elliptical orbit. Remember these orbits are going to be ellipses; here's an ellipse. The long side is the major axis; the short side is the minor axis. Half the major axis is the semi-major axis, so this is a right here. P is the orbital period, how long it takes the planet or whatever orbiting object you've got to go around one orbit. M is the total mass of the two things in orbit around each other, of the orbiting bodies. And the existence of that M is why this is Newton's modification. In Kepler's law, it was always planets going around the Sun, so the mass was always the same; the mass was that of the Sun and so it cancelled out. In general, you can use the same equation to deal with things orbiting the Earth or things orbiting the Moon as long as you put in the right mass there. G is a constant of nature, the gravitational constant, and it equals some value depending on what units you use. And we'll come back to that later. Four is 4, π is this obscure number from elementary mathematics 3.14159 whatever the heck it is. And you can punch it in on your calculator or whatever. So, you can use this equation to find things out.

Now, these numbers tend to be awkward to work with. The mass of the Sun is some huge number of kilograms, G is a very awkward number, π is always a mess. But let me show you a trick. Consider the Earth's orbit around the Sun. The semi-major axis of the Earth's orbit is a very common unit in astronomy, and it's called an Astronomical Unit. It's a unit of length, or AU. The mass of the Sun, mass of the Earth plus the Sun is mostly the mass of the Sun; of Sun, is called the solar mass obviously, and it's given this symbol M with a little circle with a dot inside, that's the symbol for the Sun. What's the orbital period of the Earth? A year, thank you very much. Period of Earth--one year. That's what a year means; it takes a year for the Earth to go around the Sun. So, it must be the case that one Astronomical Unit cubed, is equal to G times the mass of the Sun, times one year squared, that's P2 over π2.

Now, let me show you a trick. Take the general equation, it's a useful trick, and divide by the specific equation. So a3 = P2GM/ π2 and we're going to divide that by 1 AU3 equals one year squared, G mass of the Sun over 4π 2. We can do this because these two things are equal so we're dividing both sides of the equation by the same amount. G cancels, 4π 2 cancels; that's very nice. We end up with a over 1 AU3 equals P over one year squared, M over the solar mass. This is just saying that quantity is a in units of an Astronomical Unit. This quantity is P in units of a year. If this is two years then this number will come out to 2, and this is M in units of the mass of the Sun. So, you can say a3 = P2M, providing you're dealing in units of the mass of the Sun, units of one year, and units of an AU. So, this is now much easier to work with. You've got rid of all kinds of terrible things, so let me give you the first numerical example of the course. This will be the last thing we do today, namely, the orbit of Jupiter.

Turns out the distance from Jupiter to the Sun is about five times the distance of the Earth to the Sun. So, a of Jupiter is approximately five times a, a of Earth; a of Earth you'll recall is this 1 AU so this is about 5 AU. So, how does this equation work out? You get 53 equals P2M, M is the mass of the Sun, 1 solar mass. And since Jupiter is going around the Sun that's equal to 1. So, you have 53, 5 times 5 is 25, 25 times 5 is 125, so you end up with 125 equals P2, so you can answer the question now. What is the orbital period of Jupiter in years? Obviously, that's going to equal the square root of 125. Here's another trick. What's the square root of 125? Quickly? Good, more decimals? You could type it into your calculator though and find out, but let me make a suggestion. Don't take the square root of 125; take the square root of 121 instead. What's the square root of 121? 11. Much easier, right? And notice this, a of Jupiter is approximately five, so 53 is approximately 125, and it's just as good to say 121 is equal to the square root--the square of the period, and P equals 11 years. That's the orbital period of Jupiter.

All right, so now, I'm aware that many of you are shopping the course today and may not be back for future lectures. And so, I want for those people who have decided against this that they'll do something far more worthwhile with their time, I want to leave you with something you can carry through your life from your brief experience with Astronomy 160. And that is the following piece of advice: Don't take the square root of 125, take the square root of 121. It's much easier. This is what the business people call thinking outside the box. Don't do the stupid hard thing. Do the thing that is just as good but requires some thought first in order to make it easy. So, I will leave you with that, the rest of you I'll see you on Thursday morning.


Professor Bailyn introduces the course and discusses the course material and requirements. The three major topics that the course will cover are (1) exoplanets--planets around stars other than the Sun, (2) black holes--stars whose gravitational pull is so strong that even their own light rays cannot escape, and (3) cosmology--the study of the Universe as a whole. Class proper begins with a discussion on planetary orbits. A brief history of astronomy is also given and its major contributors over the centuries are introduced: Ptolemy, Galileo, Copernicus, Kepler, and Newton.


Professor Bailyn introduces the course and discusses the course material and requirements. The three major topics that the course will cover are (1) exoplanets--planets around stars other than the Sun, (2) black holes--stars whose gravitational pull is so strong that even their own light rays cannot escape, and (3) cosmology--the study of the Universe as a whole. Class proper begins with a discussion on planetary orbits. A brief history of astronomy is also given and its major contributors over the centuries are introduced: Ptolemy, Galileo, Copernicus, Kepler, and Newton.


Class Notes - Lecture 1 [PDF]

Professor Bailyn's guide to Extrasolar Planet Websites

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New Planet Could be Earth-Like - Astrophysics - Charles Bailyn Yale

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Professor Charles Bailyn: Just in time for our last class, we get this in yesterday's New York Times, and all over the rest of the media. "New Planet Could Be Earth-like." You know, every time they get a new planet, it's always Earth-like, but this one might really be true. It was found by the standard Doppler shift method, which you guys all remember, and turns out to be the lowest mass planet that's been discovered in that particular way.

And so, as a kind of final farewell calculation, I thought we'd check the New York Times' numbers on this. You can go back and read the article for yourself. The information given there is that the orbital period is about 13 days. The distance between the planet and its star – that's the semi-major axis – is given as 7 million miles. These are, of course, not the world's best set of units. The distance to the system is 20 light-years. That's really close. Somebody's quoted in the article as saying, you know, we could go there. Not so much. And I looked up the apparent magnitude of this star, which turns out to be about 10.5.

And so, what can we do with information of this kind? Well, let's first put this into some kind of sane set of units, here. Thirteen days is--let's see. Three days is--3.5 days would be 1% of a year. So, this is, like, 3 x 10-2 of a year. Seven million miles. That's something like 10 million kilometers, 107 kilometers, which is 1010 meters. So, that's something like 7 x 10-2 Astronomical Units. And you know right away what to do with that, or, at least, you will if you go back in your notes for a few months.

This is in good units to use a3 = P2 M. M, then, shows up in solar masses. So let's figure out the mass of this star. Let's see, (7 x 10-2)3 / (3 x 10-2)2. That'll be the mass in solar masses.

7 x 7 = 50, times 7 is 350, times 10-6 over 10 x 10-4 [(350 x 10-8) / (10 x 10-4)]. That's 35 x 10-2.
.35, which is 1/3. Okay? So, this star is 1/3 of the mass of Sun--perfectly respectable mass for a star to be.
And then--let's see. Let's do something else. It's 20 light-years away. Twenty light years, that's something like 6 parsecs. So, it's really nearby, as these things go. Not that you would want to take a spaceship and go there or anything, but it is one of the closer stars. And then, we can do this thing. We can figure out the absolute magnitude of this star. I've written down the apparent magnitude. So, that's that equation. Let's see.
5 log (6/10). Let's call that 2 x 3 x 10-1, yeah? That's 6/10 - five.

And then, you know, this thing about logs, if you multiply them inside the bracket, you can add them outside the bracket. So, this is log of 2, plus log of 3, plus log of 10-1. Log of 10-1 is -1, and the other two, I happen to know. The log of 2 is .3. The log of 3 is .5. Minus one, that's 5 x -.2 = -1. And so, 10.5 minus the absolute magnitude would be -1.

Let's see. How's this going to work? This has to go over there. That has to come over here. Absolute magnitude, 11.5. Now, you may remember that the Sun has a magnitude--an absolute magnitude of around 5. So, this is much, much fainter than the Sun. That's good, because it's less massive than the Sun, and low mass stars get faint really quickly. How much fainter? Well, we know how to do that, right?

Let's see, that looks--in the easiest format, it looks like this: Mstar - Msun = bstar / bsun. This a minus sign out here in front? Yes. So, that's 10-2/5 (11.5 - 5), which is equal to 10(-2/5)(6.5). All right, what are we going to do about that?

6.5 over –
65/5 = 13. So, this is 10-1.3 x 2.
2.6. You could work it out.

And that, in turn, is equal to--remember, this is bstar / bsun, brightness of the star over brightness of the Sun. That's 100.4 x 10-3; 3+; 3 + .4; - 2.6 and that's – oh, I don't know, what, 2.5 at a guess, times 10-3. A tiny fraction of the brightness of the Sun. Less than 1% as bright as the Sun.

And this is the importance of the discovery. Because it's in a 13-day orbit. It's really quite close to the star. We figured out how close. It's 7%. The distance of the Earth to the Sun is this planet from its star. But the star is much fainter too. And so, if you do the little calculation, which is quite straightforward to do – we won't do it here – of how much energy this planet receives from its star, compared to the amount of energy that the Earth receives from the Sun, you get almost exactly the same answer. So, here is a planet whose surface temperature is likely to be quite similar to that of Earth. Here is a planet where liquid water could exist.
Now, we don't actually know that much about this planet except for its mass. It's five times the mass of the Sun--sorry, five times the mass of the Earth. That could be either a big Earth or a small Neptune, and those are quite different objects. And we don't really know what category, from that point of view, it's in. It seems unlikely that it would be a big Earth, because this is a low-mass star. It's also, as it turns out, a low-metallicity star. So, it's got only 1/3 the stuff of the Sun, and it's got less than 1/2 the frequency of heavy materials as the Sun. And so, it's hard to imagine it could build up a rocky planet five times bigger than the Earth, but you never know. Stranger things than that have happened, and will probably happen again, in astronomy. So, you don't know what will happen with this one.

There's rumors going around, I should say, that there are even more entertaining planets going to be announced in the next few weeks, so, keep your eye on the newspapers. There may, in fact, be more to come. Okay, so that's the last calculation, here. You just never know when these things will show up in the newspaper. Okay.

What we're going to do on Monday and Tuesday, we're going to do this double strength section--sorry? Monday and Wednesday. Thank you. We decided not to do the Tuesday one. We've got you guys all sectioned. I think there was an email yesterday, which told you what section you're in. If you have any problems with that, you know, make sure we know about it in advance. And later, well, probably Saturday, or so, I will post three pages of instructions. You don't have to read them particularly carefully, but I would like you to download them and print them and to bring them with you to the class.

Let me take you through the first page of this. Here we go. Cosmology: The Game. And let me just take you through the sequence of play, so you know approximately what will happen. So, at the start of the game, everybody gets a role. You can be a junior or a senior scientist at one of several competing scientific institutions, or a member of the review committee that decides which projects to do. Each of the competing institution then proposes a project and a funding request. The senior scientist has to present the case. The review committee then gets to decide. And so, you can't do all of them. You can only do some of them. So, the review committee decides what projects to approve and they give either partial or a full funding, and then, they report why they have made the decisions they make. And then, we tell you what the results of that scientific exploration is.

So, you know, you go out and you try and find more supernovae and we tell you that--I don't know what happens. Magically, all the supernovae have disappeared, or they're all way, way, way too bright, or whatever it is that the answer turns out to be. And then, you know a little bit more about the Universe.
At that point, the review committee, which is made up of aging pundits, all die off. The senior scientists are promoted to the review committee. The junior scientists are promoted to senior scientists, and the review committee are reborn as junior scientists, or something like that. And so, we sort of cycle through all the roles. And you keep going through these cycles until you figure out what the dark matter and what the dark energy is. And then, at the end, we will sort of debrief, and decide what the key moment of discovery was, and award a suitable simulation of the Nobel Prize. It was M&Ms last year, but we'll see.

So, that's approximately what's going to happen. And the key thing is what kind of projects can you propose? And the other two pages of this handout are going to be a list of potential projects that you can propose. You can also propose anything else you can think of, and we will invent results on the spot for any other kinds of projects that get approved as well. But I figured it would be a good idea for you to have, at least, a range of possibilities of things you might consider proposing, and why.

So, that will be posted on Saturday. My experience is that in just under two hours, you can figure out all the secrets of the Universe in this particular--well, of a Universe that I design, which is, you know, not as sophisticated, perhaps, as the real Universe will turn out to be. Okay, procedural questions on any of that? Yes?

Student: So, the Universe that we're looking at isn't going to be like the actual Universe as an exercise?
Professor Charles Bailyn: Who knows? Since I don't know what the actual Universe is, it would be a little hard to give you the actual Universe as an exercise. What I have done is I have invented a Universe, which is consistent with everything we know now, and has many more answers than we know now. I would be very, very fortunate, indeed, if that turned out to have anything to do with the real Universe. So, I wish it were true that I had those kinds of powers. But it's possible. That's the key. Other questions?

Okay. So, last time, we ended on kind of an optimistic note. I had written down this plot, which was a plot of Ωλ versus Ωm, going from 0 to 1 and beyond. And I put down--I showed you the plot of three lines on this plot, which is the lines indicated by different kinds of cosmological observations. So, the supernovae, which we've talked about a lot, force you to be on a line something like that in the plot. So, this is where the supernovae observation kind of forces you to be.

And then, the observations of the Cosmic Microwave Background force the sum of these two quantities to be one. And so, you end up with something that looks like that from the Cosmic Microwave Background. And then, by comparing simulations of the growth of clustering to the actual clusters of galaxies that we observe in the Universe, there turns out to be a third line, and it looks like this. So, this comes from clustering. Is that legible? Close enough.

Okay. And so, the great thing about this was, if you will recall, that there were three different lines on a two-dimensional graph, and they all cross at the same point. And this constitutes a test of the theory, because it is not necessarily true that if you put down three lines at random in a two-dimensional space that they will all cross at the same point. And so, the fact that they do makes you think that something about how we understand what's going on is going pretty much right. Because there's no reason for these things to cross at a point. We predict that they do because you know they're all measuring the same Universe but in different ways. And so, the fact that they do lend some credence to this whole wonderful set of stories.

But there's another way of looking at this plot, which is to look at what these axes are. What are we actually plotting on this plot? This Ω that shows up is the ratio of the density of something to the critical density of the Universe. So, this axis is, effectively, the density of the dark matter. And this axis, here, is the density of the dark energy. So, what we are plotting in this wonderful plot where everything works out so nicely is the density of something we don't know anything about versus the density of some other thing that we don't know anything about. And so, in a certain sense, the fact that we're working--regardless of where the lines are, the fact that we've got these two axes means we don't have any idea what's going on.

So, that's perhaps the more pessimistic view. And, you know, thinking about this, you get a kind of faint odor of epicycles. Remember epicycles? Epicycles, I talked about in the very first class, your very first lecture of this class. This is the business back in the Middle Ages, where they thought the Earth was still the center of the Universe, and they were trying to figure out what was going on with the orbits of the planets. And they discovered that a single circle for each planet didn't do the job. It didn't concord with what the observations were.

So, they said, all right, well, you know, the Earth's the center of the Universe, and we know everything has to be a circle. So, we'll put circles on top of circles. And then, they were able to match the observations. But then, the observations got better and they had to have ever more complicated circles on top of circles. So, let me--so, that was the story of epicycles back in the Middle Ages. And then, of course, what it turned out is that the idea that the Earth was the center of the Universe, and the idea that everything goes in circles is just wrong. And as soon as you abandon those two ideas, and have the idea that the planets go in ellipses around the Sun, all of a sudden, everything gets much simpler and it's all explained.

So, what's happening in cosmology now? We're observing the motions of galaxies and of objects within galaxies, like supernovae that we can see. And the first thing we found out is that the rotation of galaxies and other indicators of matter aren't in accord with what we expect, so we invent dark matter to explain the internal motions of galaxies and galaxy clusters.

We then discover that the external motion, the motion of these things through the Universe, also doesn't accord with what we would have expected, so we invent dark energy in order to explain that. So, we've now, in the past twenty-five years, invented two different, but completely imaginary, as far as we know, concepts, to fill 96% of the Universe with, to figure out what's going on with the fact that the motions we observe are not the motions we expect.

How many more? You know, let's go out and measure some more things, then maybe we'll need dark something else. And dark something else after that. And maybe it needs to change with time. And maybe it needs to magically appear halfway through the history of the Universe, or something like that. Who knows? You know, if you keep inventing these things, of course, you can explain anything you like, just in exactly the same way that if you have enough epicycles, you can have a model with the Earth at the center of the Universe that explains all the motions of the planets you see. If you get to just keep inventing words here, of course, you can explain the Universe.

And, you know, what would have happened if this line didn't come across? Supposing that line had been out there. What would you have done? What you would have said is, well, of course, we don't understand dark energy. So, we've just proved that dark energy varies with time, or varies spatially, or becomes opaque at large distances, or some other quality. And then, we would have rewritten this graph so that they do cross. That's not very compelling.

And indeed, it has gotten sufficiently embarrassing that there is now just beginning to be a feeling that maybe what's going on is we need new laws of physics. Maybe we're at a moment like the end of the sixteenth century, or the end of the nineteenth century, where the current basic ideas that we base our theories of the Universe on are about to be radically transformed. That's possible.

It's also possible that we'll wake up three years from now and see in the newspaper that someone has discovered what the dark matter is. And that three years after that, we will wake up and read in the newspaper that some scientists have developed a good string theory that entirely predicts exactly how the dark energy is going to behave.

I think, in general, it's always a good idea to bet on standard physics, rather than revolutionary, new ideas. But, if you keep at it for a quarter of a century, as we have, in looking for the dark matter, and keep finding nothing, you got to start to wonder.

And indeed, there was a radical theory, proposed a few years back, about the dark matter in particular, that there is no dark matter. It's just, we don't understand the laws of gravity. And so, you know, we had to modify the laws of gravity for very high gravitational fields. That turned out to be relativity. And they suggested that you also need to modify the laws of gravity for very low gravitational fields--the kinds of things you feel at the edge of a galaxy, from the galaxy. And they figured out how you would have to do that in order to explain the orbits of galaxies without using any dark matter. This is called MOND, for Modified Newtonian Dynamics. And I don't think that--it's become clear that that particular theory probably isn't going to go anywhere, for various reasons. It doesn't seem to be self-consistent. But nevertheless, this was seriously proposed.

It was also, I have to say, a little philosophically dubious, because if you want a new theory of gravity, you don't want to go back to Newton and start over again. You probably want to start with relativity and move on. But they made it consistent with relativity. They worked out all the stuff and it seemed to work okay, except, it turns out, it disagrees with observations, also.

But it was a real attempt to imagine that these things might really turn out to be epicycles. And if there isn't progress in finding out what's going on, I think we're going to see more of that as time goes on. And it may be that in fifty years, these things will look like what we think about people who thought that the Earth was the center of the Universe. So, we'll see.

Now, there is one additional thing that we know about the Universe. In addition to, you know, these three lines, which are kind of the basic information that we currently have. And that is--so, here's another fact about the Universe, kind of an obvious one. The fact is that we exist. Otherwise, we wouldn't be having this conversation, right? And what does that tell you about the Universe? It tells you the fact that life exists, and in particular, what we grandiosely refer to as intelligent life, exists.

Let's see. What do you require the Universe to have if life is going to exist? It needs a couple of things. We can get into a whole argument about life as we know it, and whether you can make it out of silicon instead of out of carbon, or whether you can have life made entirely out of neutrons on the surface of a neutron star, or something like that. But no matter how you slice it, it's got to have some complexity to it. You've got to have a lot of moving parts one way or another. You have to have information flowing back and forth. You can't make a living creature out of nothing but helium atoms.

Helium, you may remember from chemistry, is a noble gas. It doesn't interact. It can't form structures. And if you had nothing but helium, there would certainly be no life because there would just be a bunch of helium atoms that don't interact with each other. If you made the Universe entirely out of WIMPs, Weakly Interacting Massive Particles, that just, kind of, fly past each other and don't pay any attention to each other, you're not going to have anything like life, because there's no complexity.

It probably also needs some time to evolve. It took a while. If you start--there's this wonderful experiment where you take a whole bunch of stuff that was supposed to be in the oceans of the early Earth. And you put it in an atmosphere of carbon dioxide, and you keep sending electricity through it, simulating lightening strikes. If you keep at that for long enough, you can make things that seem like some of the simpler amino acids. So, you just keep flashing lightening at the ocean and you hope that you eventually--you build up life. Maybe yes, maybe no. But, certainly it takes a long time.

And once you have somehow, magically, out of this process of self-replicating viruses or something like that, then, you got to stick around for a few billion years while evolution takes hold and makes bigger and bigger and more and more complex structures. So, you have to have a certain amount of time to allow this process to go forward.

So, for example, supposing it were true that Ωλ, that's the density of the dark energy, instead of being around .7, was greater than 100. So, the whole Universe is being pushed apart by this stuff, and there's hundreds of times more of it than there is in the current Universe. You're not going to form any structure. We looked at the formation of structure last time. You just push the Universe apart really fast, and you never get galaxies, or stars, or anything like that, because there's too much dark energy to let them congeal. So, push Universe apart--no structure. So, that would be a Universe that's very unlikely to have any kind of complexity and any kind of life, because you just take all these individual particles and push them far away from each other.

Supposing it were true that the density of matter is significantly less than 10-2. So, instead of having 1/3 of the critical density, it has less than 1% of the critical density. Then, you've got nothing to form the structures with. And so, the same thing happens. Also, no structure.

On the other hand, if the matter density is way up in the thousands or the millions in this kind of scale, then everything collapses right away back into a black hole. And again, there isn't a lot of structure in a black hole. It's one single point in the center of the event horizon.

So, we have no way of knowing what these numbers should be. But what we do know is that we are fortunate that they happen to be in the relatively narrow range, because if they weren't, we wouldn't exist. This turns out to be true of most of the constants of nature.

For example, here's another example: the Schwarzschild radius. Remember the Schwarzschild radius? The event horizon of a black hole, given by 2GM / c2. Now, supposing you lived in a Universe in which G, the constant of gravity, was substantially bigger than it is in our Universe. If G were bigger. And supposing you--in that same Universe, c, the speed of light, were a good deal smaller than it is in our Universe. Just some other--pick some other values out of a hat such that this is true. Then, the Schwarzschild radius associated with any given mass would be bigger, because both G is bigger, c is bigger, and then, for the same amount of mass, you get a big Schwarzschild radius.

So, now, think about what happens if the Schwarzschild radius is bigger than the radius of a white dwarf. Then, you never get white dwarfs from neutron stars. All stars evolve when they run out of nuclear fuel straight into black holes. All stars end as black holes.

And the consequence of that is that the carbon that is made in stars is never dispersed into the Universe, and you never end up with planets. Because the next generation of stars is still made out of pure hydrogen and helium, just like the first generation of stars was. And you never end up with enough heavy elements--with any heavy elements. And so, you can't form planets. So, no carbon, or anything other than hydrogen and helium. And you're not going to make life out of hydrogen gas and helium.

Now, carbon of course, this fabulous substance, does all this wonderful chemistry. It forms rings. Does all this great stuff. That's why organic chemistry, which is the chemistry of carbon, is more complicated than the whole rest of all the other elements--chemistry of all the other elements put together. And so, the properties of carbon are very, very important for allowing complex structures to exist. So, properties of carbon.
And it turns out that if you vary--would disappear, or not be able to support these complex chains and complex carbon chemistry, would disappear if the constants of nature, and in particular, something called the fine structure constant, was even slightly different. It also turns out you couldn't make the carbon in the first place, because there's a property of the way the energy levels work in an atom that allows the reaction of three helium atoms to fuse into a carbon atom, to occur fast enough for that reaction to actually take place by a substantial amount. So, it wouldn't take much messing around with the constants of nature to make carbon either not exist, or have different kinds of properties. You know, if carbon turns out to be just like iron, and it just kind of sits there, you're, again, going to have some trouble creating any kind of complex life.

So, we have this odd situation, in which it appears that drastic, really quite drastic, fine-tuning of natural constants is a pre-requisite for life. So, not any set of constants will do. In fact, if you picked a random bunch of numbers for all these constants, almost certainly, that would be a Universe with no complexity in it at all.
And this gives rise to a set of ideas called, generally, the Anthropic Principle, which is kind of the idea that the fact that life exists, and people, in particular, is important for understanding physics--for understanding basic physics. And the way I've just stated that, you know, that seems kind of obvious, right? Of course, it has to be true that the Universe is such that we can exist, because we know we exist, and we're the ones who are studying the Universe. And so, just in that form, it's not very interesting. But the implications of it lead you in a wide variety of different philosophical directions.

So, the question is: why do all these constants, G, c, λ, what have you, have the values they do? Okay. So, as I said, there are a wide variety of different kinds of categories of answers to this.

One is that it's just a big accident. You know, whatever it was that set these numbers happened to pick a set of numbers that allowed life to exist, and there's nothing to talk about because it's just a complete accident. And it could just as easily have picked out some other numbers. And even though most sets of numbers don't allow for the existence of life, the one that's--the set of numbers that were somehow determined by whatever mechanism determined, just kind of by accident, produced a set of numbers that allows complexity to exist. Not very satisfying approach because, among other things, if that's true, your thinking stops dead right at that point. If you can attribute everything to accident, you know, you just go on with your life.

Another, sort of the opposite of this, is to say it happened on purpose. Life was created, if you want to use that term, or the constants of nature that allow life to exist, are created on purpose. And there is an obvious religious sub-category here, where you say that there is a Creator, a god of some kind, who did this on purpose. So, this leads to various kinds of religious explanations. But in more general terms--and it doesn't have to be religious. This is what's called the Strong Anthropic Principle, which says that for some reason, be it religion or anything else, that the Universe must have life, or have the set of constants that allows life to exist.
You know, one of the things that the physicists are trying to do is to figure out why these numbers have the values they do. Maybe, it turns out that if you finally work out the final theory of physics and everything, that will tell you what these numbers have to be. And there's only one choice that you can't choose randomly from these numbers, that there's some theory that underlies, that requires you to pick certain numbers, and that those numbers in turn require the existence of life. And whether or not you attribute that to religious causes, it doesn't make a difference to the sort of structure of this kind of argument, that there's only way you could have made the Universe.

Somebody phrased this, it might have been Einstein, I don't remember, phrased it as: the question is, did God have a choice? Could you have made a self-consistent Universe with some other set of numbers? Maybe not.
But the version--the approach to this, which is getting the most attention at the moment by the kinds of people who think about these things, is the concept of the multiverse. Universe is one Universe. Multiverse is many. So, the idea is that there are many Universes with different sets of constants, sets of numbers. Numbers and laws.

Well, if that's true, then, things are pretty straightforward. If you've got 100 jillion Universes out there, and each one has different set of laws, a different manifestation of the laws of nature, then, it's not surprising that the one we live in happens to be conducive for our existence, because there's a whole bunch of other ones out there that there are no people in. And naturally, we exist in the one case where we can.

You know how this works. It's like going out into a parking lot, and you see a license plate out in the parking lot. And the license plate is 308 BJ6, or something like that. And you say, gosh, what a coincidence. Out of all the license plates in the Universe, that one happens to be sitting right in front of my office. But, of course, if it was any other license plate, you would have said the same thing. And so, that's actually not surprising.
So, similarly, if you have a whole lot of cars--of Universes in the world, if you have--there are a whole lot of cars in the world, right? There's billions of cars in the world. What are the odds that you get into the one you own? Well, pretty high, right? Because you're doing it on purpose. Similarly, if there's lots and lots of different Universes, each one with a different set of physics, what are the odds that we exist in one that allows us to exist? Pretty high.

But the question is, "Where do all these Universes come from?" And so, how do you generate many different Universes? Why wouldn't you be satisfied with just having the one you've got? And so, again, there are a number of different sub-categories, here. There's the one in which you look beyond the cosmic horizon.
Now, the cosmic horizon--you know, if the Universe is 13.7 billion years old, we can't see anything more than 13.7 billion light years away. And, in fact, the further away we look--we look back in time, so, we certainly don't know anything about what something 13--what about something 15 billion light years away is doing now. And so, you can imagine that there are kind of slow changes in the constants and laws of nature, and that by the time you're 100 billion light years away from us, that part of the Universe, which is causally disconnected from our own, has some other kind of physics that is going on. And so, you postulate an infinite Universe of which we can only detect ever, in principle, a tiny fraction. And over there, somewhere, there's another set of constants going on. And so, there's another set of physics far away that we know nothing about. So that's one option.

Another option is other dimensions. Those of you who have read any of the popular accounts of string theory may be aware that one of the problems, or perhaps, advantages--well, the computer scientists call these features, of string theory, is that you require either nine or ten, or eleven, or perhaps twenty-six spatial dimensions, in order to make it work out. Then, they do this clever thing where they say, of course, we live in a three-dimensional Universe, but it's really a ten-dimensional Universe with seven dimensions rolled up so tight you can't see them. Kind of a dubious proposition, but it works out--it actually works out quite well, mathematically.

But you could imagine that you're in a two-dimensional Universe. And here's your Universe, but it's embedded inside some additional spatial dimension. There could be another two-dimensional Universe down here, and you would have no way of interacting with it. And so, you can imagine that these extra dimensions that are being postulated allow the existence of many different three-dimensional Universes, kind of, next to each other, spread out in these higher dimensions. And perhaps they don't all have to be three-dimensional Universes. They can be other kinds. I mean, that's another crucial number, right--is how many spatial dimensions your Universe has. And so, one could imagine that these kinds of extra dimensions, talked about quite seriously by the strength theorists, allow the existence of many different Universes with different physical laws to choose from.

There's also a kind of evolutionary argument. This is presented in a popular book by a guy named Lee Smolin, which is a wonderful book. I want you to read it. His thought is that each time--and this came up, I think, earlier in the class. Each time you make a black hole inside the event horizon, a new Universe forms. So, that's one way of doing this. So, new Universes form from old ones, from black holes, or whatever.
And supposing you postulate that each daughter Universe has slightly different parameters, but only slightly different, from its parent, in the way that each of us has genetic material that's closely related, but not identical to that of each of our parents. Well, what happens? You, then, favor--in the idea that you may come out of black holes-- you favor Universes that produce lots of black holes.

And so, there's a kind of survival of the fittest--not just for organisms, but for whole Universes. If you're the kind of Universe that produces lots of black holes, you're going to have lots of children. Then, after this goes on for a long time, most of the Universes in the multiverse will be the kinds of Universes that produce lots of black holes.

How do you make black holes? You make the most black holes by producing lots and lots and lots of stars. Stars are complex objects. This is the kind of Universe that you're likely to end up with life in. And so Smolin's argument is that because of this survival of the fittest for Universes as a whole, you're almost guaranteed that any particular Universe you pick out is the kind of Universe that will produce lots of black holes, and therefore, lots of complexity, and therefore, will support life. And there are various other versions of this same kind of thing.

And this is an attempt to, kind of, use the biological arguments for how you get complexity on a cosmological scale. There's a difference, of course. In the case of biology, we get to go back and look at the fossil record, and we also understand genetics, so that we know how the small modifications are created. I mean, you need a set of physical laws, here, that tell you how different one Universe is from its parents. And of course, that is not something we have any understanding of, or knowledge of.

And this whole multiverse concept is now getting a lot of attention from the people who worry about the philosophy of physics. And one of the arguments that people get into over this kind of thing, which is kind of an interesting one--people spend a lot of time that--people worry about this spend a lot of time worrying about, is this science? Smolin, by the way, thinks it is. He thinks that his idea of these black holes makes a testable prediction--namely, that the current Universe should be one that produces the most number of black holes of any possible Universe. So, if you imagine changing the constants of nature and doing a big simulation of what the Universe would look like with that, then any other set of constants of nature would produce fewer black holes than this Universe does.

I think that's actually problematic, because most stars in our Universe don't produce black holes. So, you can think, well, tweak it up so that they all make black holes. He then argues that that same tweak changes star formation in such a way that you actually get fewer stars to work with in the first place. Maybe so.
Other people argue that this is totally not science, because as soon as you are invoking Universes other than our own, you've left the realm of science, by definition. Because, what is the definition of science? It's studying our own Universe in ways that you can actually test. And, by definition, if you're talking about another Universe, it can't be tested. So, this isn't science.

Other people say, well, look. Supposing you have some kind of a theory which predicts things in our own Universe, which you can observe, and also, the same theory predicts things about the multiverse, which you can't observe. If you observe the things in our Universe that you can predict correctly, then, that gives you some confidence that the rest of the theory might also be right. And so, this is a sort of intermediate case, where it's mostly science, perhaps.

I have to say, I, personally, think it's the wrong question. Because both sides of this argument presuppose the idea that if it's science, that's good, and that if it isn't science, you shouldn't be talking about it. Right? I think that's a problematic point of view. Just between you, me, and the video camera back there, it's just not true that things that aren't science aren't worth thinking about. There's plenty of things that are worth thinking about that aren't science. And my own personal view of this argument is that this is one of them--that this really isn't science. But I don't care if it's science or not, because it's still pretty interesting.

And I think we should also keep in mind that the border of what science is and isn't has evolved rather quickly over the past 100 years, and this ought to be apparent from what we've talked about in this course. Twenty years ago, talking about planets around other stars was complete science fiction. They did it on Star Trek, but not in the scientific journals. And this has, now, as we saw from the example this morning, changed really, very dramatically.

Forty years ago, the idea that you would have black holes to actually look at, that you could pour gas into them to see what happens, was equally unscientific. A hundred years ago, the idea that you could say anything scientific about the Universe as a whole was completely preposterous. That was part of philosophy, not part of science. And yet, over time, all of these things have been kind of assimilated into science, and there's no reason to think that the kinds of philosophical musings about the multiverse might not also, in some way that we can't currently understand, be pulled into science.

And so, this whole argument over whether this is science or not might be overtaken by events. And events are, after all, moving pretty rapidly these days. This is a golden age of astrophysics because of the instruments we have, the techniques we've developed, the theories we have. You know, historians of science a thousand years from now will say, the beginning of the twenty-first century, that's when it was all discovered. And so, it's kind of a privilege for me to play some small role in this, and to have the opportunity to talk to you guys about it.

And so, I would say, whether or not you've learned anything interesting about astrophysics, and whether or not you've learned anything useful about the way science works, if you've acquired even a fraction of the enthusiasm that I feel for this enterprise, then, I think our time together has been more or less worthwhile. And so, that's all I have to say. Thank you for your attention, and we will meet next week.
[end of transcript] April 26, 2007

About this lecture on Astrophysics by Professor Bailyn

Professor Bailyn begins the class with a discussion of a recent New York Times article about the discovery of a new, earth-like planet. He then discusses concepts such as epicycles, dark energy and dark matter; imaginary ideas invented to explain 96% of the universe. The Anthropic Principle is introduced and the possibility of the multiverse is addressed. Finally, biological arguments are put forth for how complexity occurs on a cosmological scale. The lecture and course conclude with a discussion on the fine differences between science and philosophy.


Class Notes - Lecture 24 [PDF]
Final Exam Preparation Handout [PDF]

Problem sets/Reading assignment:

Section Activity 3: Cosmology Game [PDF]

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