sábado, 26 de novembro de 2011

7. Atoms and Particles - Sean Carroll - Dark Matter, Dark Energy: The Dark Side of the Universe

This was another great lecture that cleared up a lot of personal confusion I had in the subject. Once again, particle physics is now my favorite topic! Sean also cleared up his promised use of small cycles to go over and over material in order to make it really sink in. Alternating between the experimental, observational lectures and the theoretical lectures is exactly what he meant, as we have been doing since the start. Lecture two's observations of a smooth universe led to two lectures on theories of curvature and expansion in a smooth universe. Observations of a lumpy universe then led to its theory. And now the observations of particle physics will lead to theories of the universe and ultimately composition of dark matter and dark energy. The larger cycles of knowing how we got here, why we believe in our theories, and speculations are yet to be fleshed out.

The clear presentations of fermions and bosons really sets the stage for the rest of the lecture. Sean tells the great story of how professor Bose, the namesake of bosons, had to get Einstein's recommendation in order to have his mistake turned discovery published. Unlike fermions, bosons actually prefer to pile on top of each other, although the story is not exactly clear on how the mistake implies this!

The atomic force fields and their associated carrier particles are presented nicely. Although the name of the force carried by the pion that holds the neutrons and protons together is not explicitly stated. Maybe a version of the strong force carried by the gluon?

Concluding with Feynman diagrams, one wonders if they were included more due to Sean's Caltech office being formerly occupied by their famous namesake, or if we will use them later in the course. Either is fine, but I do hope its the latter.

In this lecture we take another turn of the hermeneutic circle that describes how science is done, going from experiments and observations, to theorizing, back to experiments and observations, back to theorizing, and so forth. In lecture 2 we looked at the universe and saw that it was smooth, more or less the same everywhere, big, filled with galaxies, and getting bigger. Then in lectures 3 and 4, we thought about that. We asked how we could fit that into a picture of a theory of the universe, and talked about General Relativity and the expansion of space as described by the Friedmann equation, the smooth expansion of space that could have a curvature all of its own.

Now in the last few lectures, we talked about observations again. We looked at the universe and we took seriously the fact that its not perfectly smooth. There are lumps in the universe, there are galaxies and clusters of galaxies. These imply that we can measure the amount of matter in the universe, and we find that it's much more than can be accounted for, we think, by ordinary matter.

So now we're going to go back to the theorizing again, and start thinking about what it could be. If there is dark matter out there, if there is more matter in the universe than can be accounted for by ordinary stuff, what candidates can we come up with for what the dark matter might be? So to start in this lecture, we'll have to think about what kinds of particles may exist, full stop. We'll classify the kinds of particles you can find in nature.

The next lecture will examine in detail the kinds of particles that actually do exist, that we know of so far. The Standard Model of Particle Physics, tells us enough to explain all the data that we have about particle physics experiments here on earth. Only then can we sensibly start talking about what new kinds of particles we might invent to be the dark matter.

So first thinking about ordinary matter in the universe, we want to think about the particles that we have, which arrange themselves into atoms. These were Democritus' word for the indivisible particles of which everything is made. Sadly, in the 19th century, scientists jumped the gun, and gave the word to atoms to something which are not quite indivisible, yet are collections of particles that form the basic building blocks of chemical elements.

We've already mentioned a little bit about what an atom really is, so let's review very quickly the structure of an atom, since we're going to dive into the center of that atom and figure out what it's really made of. Atoms consist of atomic nuclei surrounded by electrons. So electrons are very light elementary particles that as far as we know, or even in the context of our best theories, are indivisible. No one has a good model for how an electron can have stuff inside of it. We think it's a fundamental particle of nature, at least in our observable part of the universe.

These electrons are orbiting around a nucleus, which is much heavier than the electrons themselves. Almost all of the mass in ordinary matter, comes from the nucleus, not from the electrons. The atomic nucleus is a combination of protons and neutrons, which are both heavy particles and have about the same mass of some 2000 times the mass of the electron.

The protons are positively charged and the neutrons are neutral, so you can balance a positively charged center you can get from a collection of protons in the nucleus, with a negative electric charge you get from the electrons surrounding the nucleus, so that most atoms are electrically neutral. Most ordinary matter such as a table or us, has a very tiny, practically zero, electrical charge. There could be some stray fluctuations, but basically in bulk, ordinary matter is electrically neutral.

So in those protons and neutrons, which create most of the mass in ordinary matter, it turns out that they themselves do have constituents. Protons and neutrons are by themselves not elementary particles, but are made of smaller particles called quarks. This is only something that was worked out in the 1960s and 70s, and now it is very firmly established that there are quarks inside protons and neutrons, and it turns out there are two kinds of quarks that you need to explain how to make both protons and neutrons. They're imaginatively labeled up quarks and down quarks.

The up quarks have an electrical charge of +2/3, while the down quarks have a charge of -1/3. Both protons and neutrons have three quarks each, so you can more or less guess how it's going to go. The proton, which has a charge +1, is going to have two up quarks and one down quark. The neutron, which is neutral, is going to have one up quark with a charge +2/3, and two down quarks with a charge -1/3 each. So the neutron will have a net zero charge, while the proton is +1.

It's very nice and convenient, but not an accident that the charge of the proton is exactly minus the charge of the electron. So that's the basic structure that we have for atoms, which we've already talked about. You can take these protons, neutrons, and electrons, and arrange them in all the different combinations that fit, according to the laws of physics, and you get the entire periodic table, with which you can do all the chemistry and all the other sciences other than physics.

However it's not the end of the story. We need to tell why protons, neutrons, and electrons, or if you like, up quarks, down quarks, and electrons, arrange themselves in those particular combinations, rather than some other combinations. As we know, the reason why particles stick together is due to some force of nature. So on one hand, you have matter particles in nature, you have electrons and quarks, stuff that makes up stuff, but then there's also the forces of nature, the things that hold those particles together in the nucleus or in the atom.

The most obvious force we have of course, is gravity, the one we've been talking about already. Yet let's put that to the side for the moment. In the atom, the important force is the electromagnetic force. Again, about 200 years ago, you wouldn't even have used that word, but would have separately talked about the electricity and magnetism. These are two separate phenomena.

Yet in the 19th century, a series of two physicists working hard, culminating in the work of James Clerk Maxwell, managed to unify our understanding of electricity and magnetism, so that physicists now talk about a single force called electromagnetism. In fact, this unification of electricity and magnetism, is precisely analogous to the way that Einstein unified space and time together into spacetime. So just as the time that clicks off on a clock will depend on how you move through space, whether or not you observe a certain field to be electric or magnetic, also depends on how you move through space!

This unification of electricity and magnetism into electromagnetism, was the inspiration for Einstein's theory of relativity. So it's the electromagnetic force which takes charged particles and makes them match up. Oppositely charged particles attract each other, particles with the same charge will repel each other, and that's the rule of electromagnetism.

The way that such forces are carried in nature, is by fields. Yet there's an interesting thing that happens due to quantum mechanics. This is the replacement for the classical mechanics of Isaac Newton, that physicists developed by the 1920s. Quantum mechanics is a very rich and complicated subject, not anything we'll really give due justice in this course, and requires an entire set of lectures all by its own.

One of its features is that if you start with a field pervading the universe, like the electromagnetic field, and you look at it carefully, what you see is that you can resolve it into individual particles. This is the relationship between the electromagnetic field that we know about and Maxwell talks about, and the individual photons that are the particles that carry radiation.

Photons are the excitations, the individual bundles of electromagnetic energy, that quantum mechanics predicts. Yet that's only part of the story. What quantum mechanics applies to fields, works for everything in the universe! According to our current understanding of nature, the universe is made of fields, which when quantized, appear to us as particles. Not only is there an electromagnetic field that appears to us as photons, there is an electron field that appears to us as an electron. There is a gravitational field that appears to us as gravitons, as we'll discuss later.

So the particle that carries the force of electromagnetism, is called the photon. If you like, you can think of the reason why an electron is bound to an atomic nucleus, as the fact that this nucleus and that electron are exchanging photons back and forth, which carries a force that glues the negatively charged electrons to the positively charged protons in the atomic nucleus.

The same thing happens with all the other forces of nature. It's the same kind of story over and over again. The next obvious force we need to explain is why protons and neutrons are bound together in the nucleus, or for that matter, why quarks are bound together inside the protons and neutrons. The individual protons and neutrons by the way, are collectively known as nucleons. Protons and neutrons are so similar that sometimes it's useful to label them with a single thing. We call them nucleons and they're the things which make up the nucleus.

So what keeps those quarks together in the nucleons, is a new force of nature, not the electromagnetic force. It's a different force which again, very unimaginatively has been labeled the strong nuclear force. This is what binds together individual quarks inside protons and neutrons. So if there's a force, there's a force field. If there's a force field, there are particles. The particles associated with the strong nuclear force, are called gluons, which actually is a pretty good name when you think of it! They are gluing together the individual quarks inside the protons and neutrons.

So in the next lecture we'll be a lot more systematic with all the different forces of nature and the particles that are associated with them. For this lecture, what is more important to us is just to understand the basic distinction that exists in all of particle physics between on the one hand, matter particles, and on the other hand, force particles. These two kinds of particles account for everything we can observe in nature.

There are even theorems in quantum field theory that say these are the only possibilities. Those theorems wouldn't work if space were two-dimensional for example, but in the world in which we actually live where space is three-dimensional, those are the only two kinds of particles we can have, matter particles and force particles.

Matter particles are named fermions, after Enrico Fermi, who is the physicist who has the most stuff named after him of all time! There are particles, fermions, there is an interaction, the Fermi interaction, there is a laboratory outside Chicago called Fermilab, there is a unit of length called the fermi, etc. He was a very influential physicist, both as a theorist and as experimenter. Fermi was the person in charge of the first self-sustained nuclear chain reaction that humans put together as part of the initial phases of the Manhattan project.

Yet before that he was a theorist thinking about what kind of particles that can exist in nature, and Fermions are named after Fermi. Fermions are the matter particles in nature. The characteristic feature that is important to us know, is that matter particles take up space. That means if we have two fermions we cannot take two identical fermions, two electrons lets say, and put them in exactly the same place, exactly the same quantum state of matter.

You take a bunch of electrons and you can only squeeze them so close to each other. Electrons being matter particles, being fermions, take up a certain amount of space. That is a good thing. It's very good that matter particles take up space! That's why a table doesn't collapse! It's made of atoms, which are made of electrons in their outer shells, which makes them able to be packed together only so close. The atoms take up space, and that's why the table is solid.

If electrons were not fermions, were not matter particles that took up space, there would be nothing to prevent the table from collapsing. This principle that electrons cannot be put in the same place, that no matter particles can be in the same location, is called the Pauli exclusion principle, after Wolfgang Pauli, another physicist. It just says that no two particles can be in the exact same place, doing the exact same thing, at exactly the same time.

Quarks are also matter particles, so when you put three quarks together, you form protons and neutrons, which are also matter particles. The fact that you can't put protons or neutrons too close together, because they take up space, is not really relevant to our everyday lives, because the electrons take up more space. So most of the space being taken up in an ordinary table or in us, is due to the electrons taking up space. Yet in principle at least, so do the protons and neutrons.

In contrast to this we have bosons, which are the force carrying particles of nature. The important thing about force carrying particles is that they can pile on top of each other. You can go from individual particles to coherent classical excitations of the field. That's the reason why, in the context of force fields, physicists were confused for hundreds of years as to whether or not light for example, was particles or waves. We now understand in the context of quantum mechanics, that it's both. The fact is, that light is a set of particles, but are force particles. So they are bosons and can pile up on top of each other to make a wave.

So the concept of bosons was invented in 1922 by Satyendra Nath Bose, an Indian physicist. Bose was actually literally giving a lecture to some of his students about a well-known problem in statistical mechanics. This was the fact that when you took a bunch of particles and added up the different ways they could combine, you didn't get the right answer! In the 1920s this was considered to be a real problem, so he was trying to explain it to his students. Yet by mistake, he solved the problem! This was because he had goofed, and made an error which is easy to understand.

Imagine you have two boxes and two balls. You try to ask the different ways you can put them into these two boxes? basically there's four different ways. If you have a red ball and a blue ball, they could both be in the left box, both in the right box, the ref could be in the left and the blue on the right, or the blue on the left and red on the right. So these are four different possibilities.

So according to conventional statistics, if we said we knew nothing about where the balls are, what is the chance that both balls are in the left-hand box? It would be one in four. Yet during his lecture, Bose made a mistake, and considered three possibilities. Both balls in the left, both in the right, or one ball each. He didn't distinguish between the two balls being in the two different boxes. He assigned a probability of 1/3 to each of these possibilities, and miraculously he derived a formula that was in agreement with observation!

So he realized that somehow, fundamental particles of the Bose kind, must be indistinguishable. It must not matter whether the particles are here and here, or vice verse. It counts as the same kind of thing. He realized that is you make that assumption, suddenly everything fits together. You can see what the consequences of that assumption are. He's saying there are two particles on the left, two on the right, one particle each, are three possibilities that should actually be weighted equally. So now if you ask what the chance is that the two particles are on the left, you used to think it was a 25% chance, yet now you think it's a 33% chance, a one in three chance.

When particles obey Bose's behavior, they're more likely to be in the same place, than if they behave like ordinary, classical particles. Bosons not only can pile up on top of each other, they like to pile up on each other. This fundamental insight is in charge of things like lasers and a whole bunch of technological applications. So when Bose realized this in 1922, he became very excited and realized he had just figured out a resolution to a long-lasting problem. So he wrote a paper and submitted it to a journal, only to have them laugh at him for doing so! They said, "What do you mean? You've made a mistake! We're not going to publish this, you're mistake!"

No one understood that by making a certain assumption, he was able to explain a long-standing problem. So in despair he sent his paper to Einstein, who did understand what was going on, and Einstein used his influence to get Bose's paper published. The statistics that come out of it are known as Bose-Einstein statistics.

So photons are one such example of bosons. They can pile on top of each other, such as when they make a classical electric or magnetic field, or an electromagnetic wave. Gluons are also bosons, so can pile up on top of each other inside the nucleons to bind the quarks together. So we then get something that is working very nicely as a system. We have matter particles that take up space, that give things extent throughout space, and we have force particles that bind them together. It's good for us that we have both kinds of particles, otherwise the world we know would be a very different place.

So there is another feature of bosons that distinguishes them from fermions, and a lot of times if you hear on street corners where people talk about bosons and fermions, this is the language they will use, which is that they have different kinds of spin. It turns out that every elementary particle has an intrinsic spin, just like the spin of a top or a spinning coin, except that for every kind of particle, that spin never changes. It's a fixed amount that is never going to become some different amount. A top can speed up or slow down, yet an electron is always spinning just as fast.

You can measure the amount of spin in a certain fundamental unit of spin, which for historical reasons, always assigns a spin of 1/2 to the electron. So you can have particles that have a spin of zero without any spin at all, or a spin of 1/2, 3/2, etc. It turns out that all bosons have an integer amount of spin. In other words a boson will have either zero spin, or be spin 1, or spin 2, 3 or 4, etc. Whereas all fermions, all matter particles, will have spin given by an integer plus 1/2. So a spin 1/2 particle can be a fermion, spin 3/2 or 5/2, all will be fermions, matter particles.

For our purposes, it's much more important to keep in mind that fermions take up space, and bosons pile on top of each other. That's what makes them matter particles and force particles respectively. Yet it's also true, due to something called the "spin statistics connection," that if you know something to be a force particle, you know that it's spin will be an integer. If you know it's a matter particle, it will be an integer plus 1/2. You'll hear people talking in that language, so we just thought to mention it.

So those are the two basic kinds of particles that we can get in nature. Matter particles, or fermions, and bose particles that carry forces in nature. Yet there are also anti-particles. There is something called anti-matter. The way it works is subtly different for bosons and fermions. Ordinary matter particles like electrons or quarks, all have their own specific kind of anti-particle. So you have the electron which is charge -1 and a certain mass, the anti-particle will always have exactly the same mass, but the opposite charge.

So the electron has charge -1, spin 1/2, and a certain mass. The anti-electron (positron) has a charge of +1, the same spin of 1/2, and the same mass. Everything is the same, except that the charges of the particles go to minus what they used to be. So the anti-electron, which was the first anti-particle ever discovered, is usually called the positron, which plays an important part in the early universe.

Yet every fermion has its own anti-particle. So you have an up quark, and a down quark. You also have an anti up quark, and an anti down quark, and so forth. For bosons the situation is a little bit different. Some bosons can be their own anti-particle, like the photon. The gluons come in a set of 8, within which you have a bunch of particles and their corresponding anti-particles. So it's a little more complicated, but also it doesn't matter as much, because it's the matter particles, the fermions, that take up space and could run into each other.

When matter particles and anti-matter particles run into each other, they annihilate. So you take an electron and a positron, bring them together, and they will turn into photons, or energy. That is why we know very well that anti-matter plays very little role in our current universe, which is full of stuff. Yet even though it's a very dilute place, in the past it was actually quite densely packed. If there were a lot of anti-matter in the universe, it would have annihilated with the ordinary matter a long time ago. In the early universe, particles were bumping into each other all the time, and when that occurs, they create photons, energy in the form of photons.

We believe that in the early universe there were a lot of anti-particles and a lot of ordinary particles. What happened was that almost all of them annihilated. Yet for some reason, there was a slight imbalance. Somehow in the early universe, there was slightly more matter than anti-matter. What we see today, all the ordinary particles we see today, are the residue, the left-over, slight asymmetry between the amount of matter and anti-matter. We don't know why and it's a mystery in current physics. We have plenty of theories to try to explain it, yet are not sure which is correct. There's an ongoing research program and we'll be alluding to it in future lectures occasionally, yet don't have time to get into any details on the specifics.

So we'll just have to believe Sean that there's not a lot of anti-matter in the universe. The anti-matter in the universe is certainly not the dark matter, since it's not dark. It runs into ordinary matter and shines very brightly. That's not what we want for dark matter to be. So now we have some knowledge of what exists and what can exist. We have matter particles (fermions), force particles (bosons), and they each have their own kinds of anti-particles.

Now let's go back into the atom and see what we have. Remember that we have a nucleus with electrons going around. The electrons are matter particles, fermions, and so are the nucleons, the protons and neutrons that make up the atomic nucleus. They are bound to the electrons by the exchange of photons, of those particular force particles, back and forth. If you dive into the individual protons and neutrons, you see three quarks in each one, and they are bound together by gluons going back and forth between the different particles.

You can then ask what is making the protons and neutrons stick together in the nucleus? There are different ways to answer this question actually, depending on how you want to think about what is going on. One simple way of answering it is to think about pions, which are a different kind of particle, made of quarks. A pion is an example of a meson, which is made of one quark and one anti-quark bound together. The exchange of pions between protons and neutrons provides the binding between them.

So the pion is a boson, with one quark and one anti-quark in it. The individual spin of +1/2 and -1/2 add up to zero, because they're pointing in opposite directions. So the pion is a boson of spin 0, and it's a force particle. They can bind protons and neutrons together in atomic nuclei. That's one way of thinking about what is going on, inside the nucleus.

And of course we have gravity, the most obvious force in all of nature. Quantum field theory tells us that if we quantize gravity, we will decompose the gravitational field into particles. We have not succeeded in doing this yet, and don't yet understand how to think about gravity on a quantum mechanical context. Someday we hope to be able to do so, and we think it's a very robust prediction of the framework of quantum mechanics itself, that when we finally do understand how it works, it will involve gravitons, individual particle-like excitations of the gravitational field. So we believe that gravitons exist, even though we don't currently know how to describe them in any full way.

So given the set of particles that we have, we can start thinking about what those particles do. In particle physics language, we talk about the interactions between different kinds of particles that can bump into each other, annihilate, create things, emit different particles, and absorb different particles. We have a language of describing these processes of interactions called Feynman diagrams.

Richard Feynman of course, was the famous physicist at Caltech, where Sean currently resides. He was sufficiently famous that Sean now sits at the same desk which he used, which means that tourists will occasionally come to Sean's office to look at Feynman's desk! They won't look at Sean's desk which he has had at various places around the US, but Feynman's desk is famous enough.

The thing that Feynman did that was most obvious to the life of a working physicist was to invent the concept of Feynman diagrams. It seems like a fairly trivial idea. You just draw little cartoons of what particles can do. In fact, to a working physicist, each one of these little diagrams is associated with a number that lets us calculate the likelihood that a given process is going to happen. So we're not going to talk about any of that in any detail, as there's a lot of math involved, etc. It's not a lot of fun and requires years of graduate education to figure it all out.

We'll just use these little diagrams to remind us of which interactions can happen. So we see one example of a Feynman diagram where an electron moves from left to right, which at some point emits a photon. So the fact that this is an allowed Feynman diagram is telling us that electrons can emit photons. The reason why, as we'll discuss a little bit more in the next lecture, is that an electron has an electrical charge. The things that photons respond to and interact with, is the electrical charge itself. So for electrically charged particles, they can emit and absorb photons. This Feynman diagram is an example of an electron interacting with a photon.

Then there are certain rules about how you can manipulate Feynman diagrams. There are rules that say if a certain diagram exists, and describes an allowed process, then you know for sure that another specific kind of diagram can exist. For example, if you have a diagram where a bunch of particles come in, interact and then go out again, there will be a new diagram which is also allowed, which you can get by taking one of the particles that came out, and move it to the other side, so that instead of going out, it came in.

So our diagram has the electron coming in, which spits out a photon and then goes away, still as an electron. We can take that photon and move it over to the other side. So there must be a diagram describing the absorption of a photon by an electron, a diagram that has an electron and photon coming together, joining, and then going off as a single electron. Indeed, this happens. So we have a different kind of Feynman diagram that describes a different example of the electromagnetic interaction at work.

Finally, we can also do this, yet not with the photon, but the outgoing electron as well. So we had an example where the electron comes in, spits off a photon and goes away as an electron. What if we moved the outgoing electron to the initial state? Then we would have two particles coming in and going out as a photon. However the rule says that when you take a fermion, or something that has an antiparticle, and move it from one side to the other, you need to exchange particles and anti-particles. For the photon, that didn't matter since a photon is its own anti-particle. Yet when you move an electron from one side of the Feynman diagram to the other, you need to exchange it with a positron, the anti-electron.

So the fact that there is a diagram where the electron comes in, spits off a photon and goes off as an electron, this implies that there's another diagram where a positron comes in, hits an electron, and they go off together as a photon. In other words, it must be the case that an electron and positron can annihilate into photons, just as we predicted. The fact that an electron can spit off a photon, implies that it must be able to annihilate. Of course this is seen in the data, being consistent with the physics that we observe.

So these are just a few simple examples of how we can understand the interactions of elementary particles in terms of Feynman diagrams. In the next lecture we'll be more systematic. We'll tell of all the elementary particles discovered in the laboratory, and all the interactions they have. The point will be to say that none of them can be the dark matter, so we need to invent more particles to explain that part of the universe.

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