 I'll go ahead and get started here. So, welcome everybody to the Science Circle. I do believe, and correct me if I'm wrong, Jess and Chantel, this is the beginning of the 2018-2019 year or season, depending on how you want to talk about it. So, welcome back everybody. That means talks will be happening regularly again and you can find the calendar on the website. I know that Jess put a new calendar in over the summer. So, presumably, that will tell you things, but I will leave it to her to put a URL in chat or anything like that if she wants to. I am Rob Knopp, many of you have seen me before because I've been talking in Second Life for probably over a decade now, certainly pushing a decade. And I am going to talk today about sterile neutrinos. Now, sterile neutrinos have been a hot topic in particle physics for like 20 years, something like that now. Over the summer when Jess asked me if I would give a talk at the beginning of September, I said, well, here, I'll talk about this. And the reason was, back in June, they were sort of in the news again for a little while because of the result that I'll talk about in a little bit. So, to do this, I'm going to start by talking about what neutrinos are in the first place and then why, well, eventually I'll get to why, why would they be sterile? I'll give you a hint. It's not because they use hand sanitizer. It's also not because they can't have kids, but there's a whole nother reason and we'll get to that in a little bit. But as with many of these things, the place to start is the standard model of particle physics, which this graphic which comes off of, it comes off of Wikimedia Commons and has been modified several times. In fact, it's sort of an old graphic at this point because they didn't used to have the Higgs boson on it. And this is, you know, and there's various different versions you can find, but there's at least one thing about this graphic that I'll talk about a bit later that I think is out of date. So the standard model of particle physics, this is all of the known fundamental particles in particle physics. By fundamental, what that means is that as best we know, you can't break them down into anything smaller and they don't have any substructure. So there's particles like protons and neutrons, which once upon a time were called elementary particles. But once the quark model proved to be so successful in describing the properties of lots and lots of fundamental particles, the standard model has now accepted that the quarks and the leptons and then these handful of bosons are the fundamental particles. And it divides the world into three or four categories depending on how you look at it. The quarks are the things that make up protons and neutrons, but protons and neutrons are just made up of up and down quarks. There's all kinds of other particles like protons and neutrons. None of them are long term stable. But, oh yeah, I'll come back to Alexander points out positrons. So I'll mention that in a moment. None of the other particles are long term stable, but you can make them in particle accelerators and we did that throughout much of the 20th century. The leptons are, well, the electron is the archetypical lepton. The electron is the same little thing that orbits around in atoms. And then there's two other kinds, the muon and the talon, which aren't stable. And then there's the neutrinos, which is the topic of today's talk. And the neutrinos are interesting particles. They're extremely low mass. They hardly ever interact with anything, which makes them very hard to detect. And that's why they were proposed sort of when Pauli was in extremes trying to figure out how things were working and said, well, I'll propose this thing we'll never be able to see. Then there's the bosons. The bosons are sometimes called the force carriers because if you think of the four forces, there's the strong force, the electromagnetic force, then the weak force and gravity notice isn't on here. In particle physics or in quantum field theory, those forces are described as an exchange of these bosons. And then finally there's the Higgs boson, which is the new one. Now as for the positron, where is that on here? The positron is actually the name for the anti-electron. Each one of, every one of these particles here also has a corresponding anti-particle. So there's an anti-up and an anti-down particle, sometimes called a U-bar because the way we do it is we draw a U and we draw a bar over it. So every one of these particles has an anti-particle, the U-bar or the D-bar. The anti-electron is called the positron because it was the first one discovered. It got a special name before we realized that it was just part of a general category. So it's the only one that has a special name, all the rest are anti what they are. And there are anti-neutrinos as well. The photon is its own anti-particle. So there's no such thing as an anti-photon. The changes to the quantum quantities that you do to turn a particle into its anti-particle doesn't change the photon. And then the gluon actually there are eight independent types of gluons. So it's a little more complicated than that. The Z-boson is its own anti-particle but there's both a plus and minus W, so one is the anti of the other. And we actually don't call it the W and the anti-W, we just call it the W plus and W minus, typically. And I don't think the Higgs boson has an anti-particle either. I think it's its own anti-particle. Nobody knows that I'm wrong about that, correct me, but I believe that is the case. So great, so this, everything that we know about almost is made up of this except there's a few little problems. Like for example, none of these really work for dark matter. None of these really work for dark energy, and dark energy even is a thing. And there's a few other anomalies that I'm going to talk about. So we know that there's stuff that isn't described by the standard model, but it's been very, very difficult to get a handle on the stuff that's not described by the standard model. So neutrinos themselves were proposed in 1930 by Pauli, Wolfgang Pauli. At the time they had this problem that nuclear beta decay, which is when you have a nucleus that's unstable and it kicks out an electron and leaves behind another nucleus. So what's happening underneath is that a neutron decays to a proton plus a electron. So the proton is positively charged, the electrons negatively charged, and then also kicks out, it turns out now we know an anti-neutrino of the electron type. But neutrinos, as I said, are extremely hard to detect. So early on they would just see, and so then the neutron, they didn't actually see it independently because it was inside the nucleus. They'd see the nucleus, they'd see the changed nucleus, which would have approximately the same mass, but would have changed its chemical species because it added a proton. And they'd see the electron coming out, okay, that's all well and good, but the electron was coming out all the time with different energies and different momenta. And it could not be explained by the loss of energy from the decay because it was always different and from the recoil of the nucleus. So there was this problem that there was energy and momentum missing. And in fact, people even toyed with the idea that, well, okay, maybe it turns out we're finding a violation of the principle of conservation of energy, that it's not a universal principle. So yeah, so Dave says, so to make a neutron star, you need neutrinos when the electrons collapse into protons in the nucleus. That's exactly right. So one of the signatures, so neutron stars are made in type 2 supernova or core collapse supernova. And it turns out that the neutrinos released by a type 2 supernova carry out much more energy than the light of the explosion. Most of the energy actually comes out in a neutrino burst. So yes, tremendous numbers of neutrinos are produced when you create a neutron star in the collapse of a supernova. And one of the very few sources of neutrinos that we've ever seen outside our solar system. So we've certainly seen the sun in neutrinos and we see them from nuclear reactors all the time. A supernova 1987a, which was a core collapse supernova that happened in the Large Magellanic Cloud, a companion to our own galaxy. And that's when you do the inverse of this reaction. Well, it's not exactly inverse, but you get proton plus electron goes to neutron plus neutrino, not anti-neutrino. So that definitely happens in a neutron star. Well, so here's what it is, is that the energy is not just in the mass of the things, it's also in how they're packed together. So in a neutron star, what happens is the gravitational forces get so strong that it becomes energetically favorable to combine the electrons and protons to make neutrons. That would not normally be the case. In fact, a neutron all by itself lasts something like 10 or 20 minutes before it decays into a proton and then an electron and an anti-neutrino. But in the environment of a neutron star, the gravity gets so strong it changes the parameters of all of this and eventually that becomes more energetically favorable. So that happens. So anyway, scientists were toying with the idea of saying maybe conservation of energy and momentum isn't right. It's a poly feeling maybe desperate. This is from a letter he wrote in 1930 proposed that there's this new particle which he called the neutron. This is before we'd actually discovered the neutron itself, so it got the name first. He was proposing, we now call it the neutrino, and he thought, you know, there's two problems. First of all, why haven't we seen it? And if we haven't seen it, then it's a particle that we'll never be able to detect, he thought. And he said, you know, sort of a terrible thing to do to propose a particle you'll never be able to detect. Although, you know, I guess we do that kind of stuff all the time nowadays, but back then that was it. And notice he says discussing every path to salvation. That gives you a sense of how much angst was associated with the notion that we might have to toss out conservation of energy and momentum. Those were core principles and still are today core principles in all of our physical theories. And so it was nice that we had them. Yeah, well, so slow moving neutrons clad with urinating atoms. That's how you make things go boom. And they proposed these things that they weren't discovered for a few decades after that 26 years, I guess I don't know if that counts as a few decades, it's between two and three, depends what a few is. But by the time they were discovered, sort of nobody was surprised because they fix so many problems and they worked well enough that everybody pretty much accepted the at least probably have to be real. But of course, I mean, it's sort of like string theory, which I would bet if I had to bet now actually isn't a theory of physics. But it's been around and lots of people think it's real, but we have yet to come up with any actual experimental confirmation. So we needed the experimental mental confirmation here was here it was 1956. And we've detected lots and lots of neutrinos since then. One of the most important places neutrinos exist and certainly the biggest producer of neutrinos in our solar system is the sun. The sun is powered by nuclear fusion and there's various detailed processes. You may have heard of the CNO chain or the proton proton chain and I've hidden all of those inside this little foamy looking thing. But the basic idea is that you start with four protons and there might be catalysts that go along for the ride and get temporarily changed partway through like in the CNO cycle. But you start with four protons stuff happens out the other side you end up with an alpha particle. That's this alpha here but it's really a helium nucleus has two protons and two neutrons protons each have a charge of plus ones. This helium nucleus only has a charge of plus twos we've lost two charges well so two positrons anti electrons come out plus two electron neutrinos come out. There's a conserved quantity called electron number which electrons have an electron number of one and positrons have an electron number of negative one. So that being a conserved quantity if it really is a conserved quantity and you have negative two electron number here and you had none. There's got to be something else it turns out well that's the neutrinos these two neutrinos each have electron number one. So the sun is doing this absolutely all the time it's converting if I remember correctly something like four billion kilograms of mass into energy every second. I did this calculation on my modern physics class yesterday. I think I remember the answer it's something like that huge amounts of mass by equals mc squared is converted to energy every second in the sun but don't worry about it. The sun has a lot of mass it's going to keep burning for a few more billion years, but all of those produce neutrinos so the sun is producing neutrinos all the time. And John Bacall is a physicist who did a lot of calculations about solar structure and nuclear production of energy and the sun and can predict how many neutrinos we really ought to see given the production in the sun. And in 1964 John Bacall and then Ray Davis and Ray Davis eventually got the Nobel Prize for this. Detected solar neutrinos by filling up a giant tank with cleaning fluid basically you start with Clorox not Clorox chlorine Clorox is something else you start with chlorine very very very rarely occasionally when a neutrino hits the chlorine. Most of the vast majority of neutrinos just go through the tank and never interact with anything but rarely one of the neutrinos will hit a chlorine, interact with it, kick out an electron and leave behind argon which is a noble gas and won't interact with anything. So basically what they did is they filled up this big tank with helium. They put it in a mine so that no nuclear reactors nearby would mess up the signal they're trying to measure the signal from the sun and they let it run for a little while. And when all is done they go and see how much argon is there and then that tells you how many neutrinos they were detected and they detected neutrinos from the sun it was great but they detected too few of them. According to the calculations there should have been three times as many neutrinos as they actually detected. So this was called the solar neutrino problem and it wasn't formally solved for something like 40 years 30 years after that 30 or 40 years after that we didn't solve the solar neutrino problem. There's this problem that we had very good nuclear physics models that did a very good job of not only predicting the sun's structure and the sun's output but also things like the lifetimes of other stars which when you look at star clusters we saw that they matched exactly what you would expect. So we thought these models are very good but they're predicting more neutrinos than we actually see so something is wrong. And you know possibilities include something is wrong with our solar models. Another possibility is something is going on with neutrinos that we don't know about. There's always the possibility it's some sort of experimental systematic but that was not the case here. This was a very robust result. And so when it was solved well there were neutrino observatories built to check the solution and one of them was this thing the sub-variant neutrino observatory. There was also Kamiakanda and super Kamiakanda in Japan and they figured out in right around 2000, 2000 plus or minus a few years. They came up with measurements that convinced us that yes what's happening is the electron neutrinos produced in the sun are being turned into something else. I think Kamiakanda used something like chlorine. I don't remember anymore but the Sudbury neutrino observatory this is a big old tank. You can see a person here to give you a sense of the size of this. This is a big old tank of heavy water. Heavy water is water where one of the hydrogens on the H2O molecule is replaced by a deuterium molecule. And heavy water has a higher cross section or a higher chance of interacting with a neutrino than regular water. And so that's why they used it. And I think when I don't think the Sudbury neutrino observatory is running anymore but when it was I think they actually had a substantial fraction of the world supply of heavy water. At least it had been isolated. So if you go into the ocean this heavy water absolutely all over the place mixed in but it's a tiny fraction mixed in. So you have to if you want to isolate it that takes some effort. There's also a tiny fraction of heavy water mixed into the ice sheets and there are modern. Yeah, they may have sold it off now. I don't know what happened to it. But there are modern neutrino observatories that stick scintillators just photo tubes detectors down into the ice sheets and Antarctica looking for neutrinos that interact with the ice. And that will include some deuterium down there in the ice as well. We haven't sheaved it all out. So, so this what they did is they looked for neutrinos. Now, as we said before, there are three types of neutrinos three generations there's the electron neutrino the muon neutrino and the town neutrino. And all three of them exist but the electron neutrino is the only one that is produced in the sun. And then if you want to detect these neutrinos there's different ways you can do it there's different things that happen. The chlorine argon experiment was only sensitive to electron neutrinos. Well, so there's various things and here's some of the jargon terms of the charged current and the neutral current just because of what comes out on the other side. So one of them was in heavy water of a neutrino hit a deuterium nucleus. So that's a proton and a neutron stuck together. It gets split apart. But yeah, thanks for one gives a information about super comma conda super cameo conda, which was in Japan still is in Japan could split the deuter on into two protons and then also kicks out an electron. And the neutrino is absorbed in the process. There's also one where any kind of neutrino can split apart a deuter on, but the neutron stays in neutron so that new neutrino still stays there and then there's also just if there's an electron. The neutrino can bounce off of it and some energy is released in that now all of these processes hardly ever happen. The vast majority of neutrinos that go through these gigantic detectors hard to just go through them and don't interact. And that's why you need these gigantic detectors so that the small fraction of neutrinos that actually interact are enough that you'll be able to get some signal to measure. But here's the deal with this is notice this is sensitive to electron neutrinos. These are sensitive to all kinds of neutrinos. And so that was important. And so when you put the snow and the cameo conda results together. And this is so 2001 2002 2001 is the discovery paper about this and this is a complicated plot. So what I really want you to notice is that this here is the notice the subscript e on the Greek letter five there. So this is flux or amount of neutrino of electron neutrinos coming through. And then this here is the amount of mu in town neutrinos coming through and the colored bands are different experiments or different subsets of experiments. What the data is consistent with. So if you just start with a charged current, that's this red band here and that is equivalent to what the chlorine argon detector was finding. You get this value what the actual value is not all that important, but you get this value. But what's important about this value is that it's only one third of what's predicted from the sun. But then when you add the green from elastic scattering and the blue from the charged current bands together. Well, this doesn't tell you much. It's like, well, the fluxes could be anywhere between here and here. But if the blue band has to be right and the red band has to be right, then you know in between they've got to be somewhere here. And what's great about this is that if you take this number, this number is about twice this number. So that when you add all three together, you get three times this number. And now you're getting the right number of neutrinos that you expect from the sun. But the problem is the sun is producing electron neutrinos. You are detecting electron muon and tau neutrinos. Well, this is a property or a thing. It's a thing called neutrino oscillation. It was a proposed solution that Kamiakanda and Snow were built to look for that neutrinos. They thought maybe changed their identity as they're flying through space. They're produced as electron neutrinos. But in between the sun and the earth, some of them spontaneously turn into other types of neutrinos. If that was the case, then we should have seen enough muon and tau neutrinos coming from the sun to make up for the missing electron neutrinos. And that is in fact exactly what we saw. So, and that sounds a little weird. It's like, okay, so they turn into other neutrinos. Why would that happen? Well, this is where one weighs one hand, one's hand, and one says quantum mechanics. This kind of stuff can happen in quantum mechanics. So, quantum mechanics is named after quantum, as in quantized, as in finite steps of things. So if you're familiar with orbitals and atoms at all, there's only specific energy levels that electrons and atoms can have. It's not just any old energy level, but it's quantized, comes in steps. So there's lots of things that comes in steps, including identities of particles or quantized steps, in a sense. Now, however, there's this issue that if you look at things different way, the steps might be different. So the steps of individual... This even happens in atoms in a way that it's not so obvious. There's three electrons in a lithium atom. Two of them are in the lowest orbital and one of them is in an excited orbital. Great, but you might say which two electrons are in the ground and which is in the excited, and that turns out to be a meaningless question. Because each one of the electrons is, in a quantum sense, kind of in both the ground and the first excited orbital. This is weird, right? That you don't have one energy level and one electron is there, but all three electrons are kind of in the energy level. So if you wanted to pick out, yeah, all electrons are blue, and that's right. Protons, as you saw on my earlier slide, protons are red, neutrons are orange, and electrons are blue. That's correct. Yeah, well, it's based on probability, but here's the thing is that there's probability there that if you try to say, where is the electron right now, it's probabilistic as to where it's found. But of the three electrons, what Mike is saying, all electrons are blue, electrons are indistinguishable particles. So that means you even, in principle, cannot tell one electron apart from another. And so if you've got three electrons and they're all together in this orbital, it's not even meaningful to say which electron is in which orbital. So you get these mixtures of states and quantum mechanics. And so the weird thing that happens with neutrinos is that there's different ways you can slice the bread. There's three different kinds of neutrinos. We know that. Although we're going to talk about sterile neutrinos as a possible fourth or more later, but for now there's three kinds of neutrinos. But there's two ways you can slice the loaf. If you slice the loaf by type of neutrino, well, you get electron, muon, and tau neutrino. If you slice the loaf by mass of neutrino, you get what we very imaginatively call the lightest neutrino and the heaviest neutrino and the one in between. But the slices are not the same. It is not correct to say that the electron neutrino is the lightest neutrino. It is like slicing a bread horizontally versus vertically. Any little piece of bread that you slice horizontally isn't in a single vertical slice. So this is two conceptual ways of slicing up neutrino dumb. So what that means is that when you produce an electron neutrino, it's not a lightest neutrino. It is a quantum mixture of the lightest, the medium, and the heaviest neutrino. And that's kind of wacky. And so then, as somebody mentioned probabilistically, what that means is as time goes by, the probability that if you measure the type of neutrino, you'll get an electron neutrino goes down. And the probability that some muon or tau goes up. And so once you get far enough away into a state that we'd say is no longer coherent with how the electron was produced, you end up with a probability that maybe is a third, although it depends on details, of any of the three types of neutrino. So it's wacky. So that means that an electron neutrino is a mix of new one, new two, and new three. Also vice versa. If somehow you have a new one, and these are the things that fly through space, neutrinos of given mass, if you have one of those and then you measure what type of neutrino you're going to get, it's going to be random, whether you get an electron, a muon, or a tau on. And the same with new two and new three. So this is the core of neutrino oscillations. We say that they change their type, and okay, that's not a bad way to say it, but it's maybe more accurate to say that the neutrinos are produced as electron neutrinos, but then they fly through space as one of the masses of neutrinos, and it's random which one they fly through space as. And that then when we detect them, each neutrino, it's random which type of neutrino we're going to detect. And the probabilities depend on how far the neutrino has gone. Just, there's probabilities that have to do with how far away is it from the process that produced the neutrino. If it's very close, it's still going to be an electron neutrino. As it gets farther and farther away, eventually the neutrino oscillation phenomenon rears its scary head and you have different types of neutrinos. So if we wanted to summarize this, what happens with neutrinos in the sun, you could say they are produced as electron neutrinos. They're produced with definite flavor because this is the first interaction in the proton-proton chain. So two protons come together, make a deuteron which we'll later combine with other things to make the helium nucleus. You get a positron that kicks out, it will almost certainly find an electron very quickly in ILA and produce energy, which is great because that helps the sun shine. And it produces this electron neutrino and because neutrinos hardly ever interact with anything, the vast majority of them just come flying out from the center of the sun into space. But that's the electron neutrino is produced. As it flies through space, it's actually not the electron neutrino that flies through space, it's going to be one of new one, new two or new three, one of the definite mass neutrinos that flies through space. So an electron neutrino is produced, but then to fly through space, and this has to do for reasons of conservation of energy and stuff like that, it's a much better approximation to say that, oh, it's one of the definite mass states, and it will be random. When you produce an electron neutrino, it's random which definite mass state you get. They don't carry any charge, they're all neutral particles, so there's no electric charge. If you are worried about lepton number, this does represent a non-conservation of lepton number, which makes me a little scared, but if you don't know what lepton number is, you don't have to worry about it, it's great. So they're called the electron neutrino, so there's three different types of neutrino because processes like this one where you produce an anti-electron or you eat an electron or you eat a positron will produce the electron type of neutrino. If you do processes with muons, you'll produce a muon type of neutrino, and processes with tauons, you'll produce a tauon type of neutrino. And so there's different types of neutrinos get produced in different processes, and then on the other end, you may remember a few slides back. Let's see if I can go back to it. The reaction here where you take a neutrino and produce an electron, that will only work with an electron neutrino. So you have one of the other types of neutrinos, it won't work. You produce a muon but not an electron. So if you collide a proton with a neutron, lots of things can happen. Maybe one of the most common is you just stick and you have a deuteron, but it's possible that, that's almost certainly what's going to happen if you collide a proton with a neutron, they'll just stick. But there are other things that's possible that could happen. You could have two protons come out as well as an electron and an anti-neutrino. They have approximately the same mass. Neutrons actually have slightly more mass than protons. The things that propagate through space have definite mass. So the neutrinos produced as an electron neutrino, but then as it propagates through space, it becomes either a new one, new two, or new three. But then when we detect it, it's going to, well we detect it, it turns it into a type of neutrino again. Yeah, okay, so that's an interesting question. Do electrons turn into 1000 mu? As far as we can tell, that mixing doesn't happen. There's no evidence that electrons and muons and tauts actually turn into each other unless you have the catalyst of turning, you know, taking the electron, colliding it with something, making a neutrino, then it, the neutrino could oscillate and then it could turn into a muon later when it collides with something else. So indirectly you can do that. But directly I don't think electrons just spontaneously turn into muons the way electrons or the way neutrinos do. Right, so this is what happened with neutrinos. They start with a definite flavor. But then they fly through space with an indefinite flavor and a definite mass. But then when we detect them, they have to have a definite flavor again. So the solar neutrino problem, the essence was electron neutrinos were produced. But then the things flying through space had indefinite flavors. So when we measured the flavor only a third of the time did we get electron neutrinos. And that solved the solar neutrino problem. Okay, so can they be called dark matter? I would say no because we detect all these things. And dark matter we don't detect. Now we'd like to detect dark matter. And it turns out that dark matter, the cosmological dark matter seems to have processes very much like or processes properties very much like neutrinos. But there's not enough neutrinos in the universe to make up the amount of dark matter we need. At least we think. And I'll come back to that in a little bit. So while dark matter particles would be like neutrinos, they're not these flavored neutrinos that we know about. Now there's one other concept I want to throw in and that's helicity. So helicity has to do with how a neutrino spins. And actually any old particle can do this. Photons have helicity because photons have angular momentum. Maybe easier, photons maybe harder to think about because they're moving the speed of light but think about an electron. If the electron has angular momentum and so if you look at this, you notice that it's spinning around such that if you hold your right hand up and you curl your fingers along the direction of spin, your thumb points to the left. Whereas this one, if you hold up your right hand and point your curl your fingers along the direction of the spin, your thumb points to the right. So that's just the direction of the spin. When you have a particle that is flying through space, its helicity is how does the direction of spin compare to the direction of motion? So a right-handed particle, yeah, it's basically that same kind of right hand for the cross-particative vectors, basically the same thing. So if you have a right-handed particle, it means it's a particle whose direction of spin, when you turn it into an angular momentum vector using the right-hand rule, your thumb points in the same direction as the direction of motion. A left-handed particle, if you use the right-hand rule, your thumb points in the opposite direction or use your left hand and you curl your fingers around the direction of the spin, you'll notice your thumb is pointing in the direction of motion. So there's two different kinds of helicity. This is important for photons. This is actually, photon polarization is the helicity of photons. And because photons move at the speed of light, nobody can ever pass a photon. So helicity is always the same for a given photon. Well, so neutrinos early on, when we first talked about neutrinos, we treated them as if they were massless. And indeed, we probably thought they were massless, so helicity was fine. But there's a little issue nowadays. Neutrinos aren't massless. You wouldn't get neutrino oscillations if neutrinos didn't have mass. So now we know that neutrinos are massive particles. This throws a bit of a wrench into this. And here's the deal. Yeah, that's our point out the problem here. If we try and slow down a neutrino so that it's moving very slow, they're extremely hard to detect. They have very little energy at that point. So we haven't actually detected any neutrinos that aren't moving almost the speed of light. Right, they should be there, but we've never detected them. So, yeah. Yeah, I mean, we can always... I mean, so here's... there's neutrinos left over from the big bang that should have slowed down a whole lot, but we have not seen them because they're just too low energy and we're not able to detect them. All right, so symmetry breaking. Here's the thing. All neutrinos have left-handed helicity. Most of the laws of physics are symmetric with respect to doing a mirror image, right? So take your right hand, take a mirror image of it, you get your left hand. Most of the laws of physics, it doesn't matter whether you're dealing with a right-handed or left-handed particle, they behave the same. But the weak force, which neutrinos and electrons interact under, violates the symmetry. Why are they like that? Wow, that's a hard question. Because they seem to be that way. There may be something in it. If you look at the Yang-Mills theory of the electric weak interaction that says they have to be this way, but I suspect this is a case where, well, we know that they're this way and so we're going to create a theory that works with that. It's sort of an observational fact that this happens. Why would it be this way? I don't know that there's a good answer to that question. But anyway, so the weak force, sometimes you take a mirror image and you get different answers, which is a little bizarre, but it happens. And neutrinos are the strongest example of this in that all neutrinos have left-handed helicity, all anti-neutrinos have right-handed helicity. So you go from a particle to an anti-particle, while the electric charge doesn't change, the left-hand number does, and the helicity of the particle changes as you go from a neutrino to an anti-neutrino, but this now brings up a problem. Given that neutrinos are massive, it is possible to go faster than one. You can't go faster than light. Decisionally should charge interactions as they are opposed to each other. Well, it's not a charge per se. It's just if the neutrinos hardly interact with each other and they don't interact via the electromagnetic force, they do interact via the weak force, and because the weak force does violate parity, meaning it's not mirror-symmetric, you could say that's a manifestation of the helicity interacting. Yeah, so you would certainly get their fermions, so you would get the same kinds of things if you managed to have some sort of states like an atom. I don't know how you get a neutrino to stick next to another neutrino or an atom, but with electrons, the opposite spins, you can put two into one orbital because they have opposite spins. The same sort of statistics would apply to neutrinos if you could get neutrinos into ground states like that. We've just never done that. But yeah, that same sort of thing would happen. And is this a clue? Maybe. Maybe this is a clue. I don't know that anybody has worked out exactly how this works, but it does, you know, it is a symmetry breaking between antimatter and matter particles of some sort. So I would be surprised if it wasn't somehow related, but that's not an answered question. So yeah, it's probably a clue. Anyway, because neutrinos are not going the speed of light, only massless particles go the speed of light, so you can never pass a photon. But you can pass a neutrino if you get going fast enough. So if in this guy's frame of reference, the neutrino is moving to the right instead of to the left. And so it has the opposite, yeah, they all have beards, goatees really. So it has opposite helicity, which then begs the question, where are the right-handed neutrinos and where are the left-handed anti-neutrinos? We don't see them. Are they out there? Let's just leave that as a question for now that we will come back to in a little bit. There's actually several other experimental... Oh, you can't send anything fast in the speed of light if it's massive. It would take an infinite amount of energy to accelerate it to the speed of light if it's massive. And so unless there's some physics beyond the physics we know and there's tachyons, but as far as we understand, there's no way to do that. So there's several anomalies in neutrino experiments that are much more subtle. Yes, here's the problem. If we theoretically do it, then we have to have a theory that handles doing that. And our theory that we have right now doesn't handle crossing the speed of light. So that's a hard question to answer because we don't really have a good theory. There is theory out there for particles that are always faster than the speed of light, and those are tachyons, and there's no evidence they actually exist, but there's theory for that, but there's no theory for something that crosses the speed of light. So anyway, these anomalies are not obvious things. They're just, huh, there's too many or too few neutrinos out there. So neutrino oscillations explain the fact that there were too few electron neutrinos seen from the Sun, but there's still some left over too few or too many neutrinos in some experiments that you can't explain with that. There's four that I'll mention briefly. One is called the gallium anomaly, one is the reactor anomaly, and then there's these two experiments that look at the same sort of thing, LSND and Miniboon, and Miniboon was the one that put out the paper over the summer that had people paying attention. So the first one, the gallium anomaly. There are neutrino detectors that use gallium stuff, I don't remember the details, but to detect solar neutrinos for measuring the solar neutrino problem. Well, one of the things they did to calibrate is they stuck a radioactive source inside the detector and they knew the radioactivity of the source so they knew exactly how many neutrinos were out so they could figure out, just make sure that the detector is detecting the number they're supposed to. So this is a calibration thing, but when they calibrate it and when they, you know, it's possible there's still a calibration error, but when they calibrate it, they're still seeing a few, too few neutrinos. So if you zoom in on this plot, you'll notice that the airbar's got a little swallowed here in my resizing of the image, I apologize for that, but you notice there's four points here from these two experiments and then this red band is the average of those four points and this ratio is the ratio of the number of neutrinos they see from the calibration source to the number they should have seen and so they're only seeing 85% as many neutrinos as they onto have. Now there's a 5% uncertainty on that, which means the, this is what we would call a three sigma result because the value is three times the uncertainty away from the expected value. So that's a marginal detection. I mean, if you're in ecology or social science, that's the strongest effect you've ever seen because it's a p-value of less than 0.1. But if you're a particle physicist, that's a marginal detection that you don't get excited about because you get random three sigma events all the time. But it's there and it seems to be fairly robust that it's staying there. So it's not something that you'd necessarily get all upset about, but it is something you might scratch your head about a little bit saying, huh, this warrants further investigation. So this is saying too few electron neutrinos are being detected for the ones produced by these radioactive sources and these are embedded inside the detector. So you don't have the distance between the Earth and the Sun or even lots of neutrino experiments are done with nuclear reactors. The kilometers between a nuclear reactor and a neutrino detector to have the standard neutrino oscillations happen. So this is something else if it's real. There's also the reactor anomaly and this is when you do really short baseline experiments from nuclear reactors. You put your detector 30 meters away instead of kilometers away and so that's what this horizontal axis is distance from the reactor. You see we go as low as 10 meters. This is about 100 meters. When you get out to 1,000 meters, well, ignore the blue line for now, but the red line is what you should get from the neutrino oscillations that solve the solar neutrino problem. And they're grayed out here, but out here notice the weight of the points is all below except for this one. The weight of all the points is below the red line. And again, it's not a hugely significant result. You could say it's just a random experimental fluctuation. It's a 2.5 sigma result. So that's not that huge, but it's there. And again, it's one of these things that makes you scratch your head and think maybe we should look a little harder and see what's going on. So then we get to the experiments which really were, I mean part of their purpose was to look for these kinds of things. The liquid-sensitator neutrino detector or LSND, it's a gigantic tank where they fill it with mineral oil and some other goop stuff that will shine when the right interactions happen with neutrinos in it. And then you see there's a little guy here and there's all these photo tubes around the edge of the tank that are there to detect the dim flashes of light that happen. And they point a beam of neutrinos at this. They make the beam of neutrinos with a particle accelerator and in this case it was mu neutrinos. So they had a process that produced a bunch of muons that would decay and that would send mu neutrinos out. And then they measure mu and electron neutrinos and they discover more electron neutrinos than they should have seen. So it looks like some of the mu neutrinos turned into the electron neutrinos, but once again, it's only 30 meters. It's not long enough for the standard neutrino oscillations that you get explaining the solar neutrino problem. So they have a little bit of an excess. And then, and so this has been around since, what, this has been around for two decades now, I think, the LSND. And there's been various different experiments that have or have failed or have not did in confirming this result. There's other things. So it was considered an anomaly, but it was less than five-sigma. It wasn't a real good detection. And so then another experiment, Miniboon was put together to try and be more symmetric. And so Miniboon is actually at Fermilab near Chicago. It was to be more sensitive. You see, here's a person here. And once again, it's a tank full of stuff that will blow when the right particle interactions have been surrounded by photo tubes. That's what these little yellow spots represent. Looking for the light from this. And their first results seem to not be confirming the LSND result, which suggested, all right, it's some anomaly, some experimental error issue going on. But just this summer, they published more results with more statistics and they do have a detection of an excess of electron neutrinos in a beam of mu neutrinos. And when you put the LSND and Miniboon results together, you get a significance of 6.1 sigma. Now there's this number, 5 sigma is the threshold in particle physics where people start to say, okay, maybe you've actually really detected something. Now we have had 5 sigma anomalies before that go away. So you haven't always detected something, but that's where you really start to take it seriously. And now we have that as of this summer. We have a 6 sigma detection of this neutrino anomaly where we have too many electron neutrinos in a mu neutrino beam. And if you put these together with the other marginal deficits of electron neutrinos, it starts to suggest that there's some additional oscillation going on between electron and mu on neutrinos that is not the standard oscillation that's part of the solar neutrino problem. Because again, the baselines are just way too short. These oscillations are happening way too fast for the standard solar neutrino problem. Well, one suggestion is that there's a fourth kind of neutrino or even more, there might be two or three more kinds of neutrinos that are sterile neutrinos. What does this mean? Well, here are standard flavored neutrinos. So electron, mu, and tau, those are the three flavors of neutrinos. So next time you're at the ice cream store, you'd say I'd like to have some muon ice cream on a cone and see what they give you. Those are the flavors. They all interact with the weak force and they have this helicity we talked about before. Flavored neutrinos have left-handed, helicity, anti-neutrinos are right-handed. And there's reasons to be sure that there's no more than three flavors of neutrinos. Different kinds of experiments. This is actually something that, I remember back when I was in college in 1989, was around when they, somewhere around there is where they discovered the Z-boson. And the lifetime of the Z-boson would be different if there were different numbers of flavored neutrinos out there that are consistent only with three. Also, it turns out that the number of flavored neutrinos would influence the ratio of elements produced in the Big Bang. That is also consistent with three. And now we also have cosmic microwave background things. So we're really sure there's no more than three flavored neutrinos out there. So if there's another neutrino, it would have to be a sterile neutrino. What does that mean? What that means is it has no flavor and it does not interact via the weak force. I mean, that sounds like super dark matter at that point. It doesn't even have to interact via the weak force. Yeah, well, vanilla is a flavor, right? I think vanilla gets a bad rap. This is more just like a slushie with no syrup in it. Just a shaved ice, right? I mean, what's the point? So the idea would be you have these flavorless sterile neutrinos. They don't interact via the weak force, so it's really hard to see them. But if the flavor states in the mass states are like slicing bread in different directions, you can produce a flavored neutrino like an electron neutrino, and there's some probability, probably a small probability, that it will oscillate into the flavorless neutrino, and then there's a probability that the flavorless neutrino will oscillate back to a mu neutrino through the mass state. So there'll be four neutrinos, four different masses, three flavors, and a flavorless flavor. That sounds like an oxymoron. It is an oxymoron. And they can oscillate back and forth. So the only way you interact with these flavorless neutrinos is via gravity, because everything massive, anything with energy, interacts via gravity. But the flavorless neutrinos would not interact through the weak force, but because flavor neutrinos could oscillate into them, you would see an effect because of that. So this sort of thing could explain these anomalies. I'm going to show you a technical plot here. All right, what the heck does all of this mean? The oscillation amplitude, this is basically saying if you have an electron neutrino and another type of neutrino, this flavorless neutrino, this is related to the probability that the oscillation actually happens over some time period. And so it peaks out at one, and it goes all the way, this is a logarithm plot, so it goes all the way down. So you'll see, I mean, basically the filled-in regions is where the data is consistent with these parameters. So, yes, there's probability all the way up to one, but also a lot of the probability spends some time down here at less than 1%. So this is, actually, it's not really a probability, it's an amplitude, but whatever, at low numbers. The vertical axis, this is kind of a weird axis. What this is is the difference in mass between the electron neutrino and the other neutrino squared. And the electron neutrino is very, very light, a lot less than we use electron volts as a unit of mass. If you don't know what that means, don't worry about it, just the electron neutrino has a mass a lot less than one electron volt. But notice here, a lot of the probability, I mean, it even goes up to like 10 electron volts. But a lot of the probability is around, sorry, that would be 100 electron volts. That's 10 electron volts because you take a square root, right, so it's 100 electron volts square. Here, this would be like 3 electron volts, this would be one electron volt. It only goes down to something like, and if you take the square, well, the square goes down to like 10 to the minus 2. This is still way too big for direct electron muon oscillations. The delta M squared value is much smaller for the standard oscillations that we already know about. Now again, these are marginal detections, right? It's at 6 sigma right now that this is even happening. And then this says, right, if it's happening, this is the realm where we might have this thing related to the probability and thing that tells us about the mass. And because the electron neutrino is so light, you can take a square root of this number and get the mass of this other neutrino, right? Meaning if it turns out that this is the right spot on this diagram, that would be one electron volt sterile neutrino, right, which is a lot for a neutrino. It's very small mass for every other particle we know about. The electron itself has a mass in these units of half a million electron volts, right? So that gives you a sense that neutrinos are really low mass. But this would be very massive for a neutrino. So this is what the data shows. There remain tensions, though. So even if, so this isn't a case where, hey, we just have to confirm this and we have it, there's still some problems with the picture. And among that, cosmology actually sets constraints on this nowadays. The cosmic microwave background, because it's a sensitive probe of stuff that happened in the early universe, would show, would be different if there were sterile neutrino species out there. Now, this is a paper from 2006 by Scott Dottelson who said that there's the current limits from the cosmic microwave background limit it to a massive 0.25 EV, right? So if you go back in the previous page, that would limit it to like here and below or something like that. Okay, well, there's still some data there. But it turns out that if the neutrinos, if there's more than one, and they have some sort of interaction between themselves, we could actually get around that limit. But this does provide tension. And there's even within these measurements, there's some tension where they don't all quite just nicely line up together, which suggests that there may be more than one sterile neutrino out there, if in fact sterile neutrinos are the answer. And there may be another solution to this. In fact, one possible solution is that it really still is. And there are some, you can find people who will argue the problem is, is that you don't have the data or the numbers that go into your calculations calibrated, right? The anomalies are really just anomalies and how well you understand gallium, for example, that you've just overestimated how many you should have seen. And okay, that's fine. So that's still a possibility, although given that a few different types of experiments are all showing in anomaly, maybe that's not so likely anymore, but each experiment has a very low significance. It's only when you put them together that they have a significant, but I would say that we see anomalies like this a lot. You may have remembered a year or two ago, there's a suggestion of a new particle called the Large Adrenaline Collider and then it kind of went away. You take more data and it's not confirmed. This is a case where Miniboon was the one that I think a lot of people were expecting Miniboon would just not confirm the LSND result and then it would go away. Well, it seems to be confirming it. So maybe there's something there. Maybe there's something there. So what does all of this mean? What are the implications of a sterile neutrino? Well, the first thing, we don't know at all, but something is going on. It may be that something is imprecise theoretical parameters. We don't understand Gallium well enough or unidentified systematic error. There's something going on in the experiments that we didn't take into account. Okay, something is happening. It may turn out to be boring, but it may, if it's real, if these effects are real, it is physics beyond the standard model because the standard model of particle physics is not predicting the results properly. So if the results are real, it is something. Maybe a sterile neutrino, maybe something else. A sterile neutrino is one decent idea that seems to help explain it. And here's why this is important. I was talking to Chantal about this a little bit an hour before the talk. High energy, fundamental particle physics is in a bit of a doldrums right now. It was really exciting to be a fundamental physicist in the 20th century. If it was the first half of the 20th century or especially the first third, there was this kind of horrible thing that happened between 1935 and 1945 in the 20th century. But leaving that aside, they were figuring out quantum mechanics, a whole new theory of the fundamental nature of reality that was a completely different way of looking at reality. It was huge. And it was really exciting to be part of that. But even after we'd established quantum mechanics and had figured out, hey, look, we should build cyclotrons and we can detect new particles, we were finding new particles all the time. And we even found kinds of particles that we didn't expect, like the muon. Nobody expected to detect muons, and then there they are. And then we detected strange particles which nowadays we would say are particles that have a strange quirk in them. But at the time there was just like, this is something that doesn't fit with everything else. We're going to give it a new name. It's strange. We're calling it strange. Up through the 60s, people were detecting new particles all the time. And there were very different ideas and theories about how to make these fit together, and they kind of got modified and wormed around. And then eventually in the 60s and 70s, they coalesced on the standard model of particle physics. And a lot of this came out of the quirk model which Mare Calmon is famous for and got his Nobel Prize for this. So the quirk model and the standard model of particle physics are all this stuff that we have seen. Down to that the handful of stuff that I showed you on the first slide. So we've had the standard model and there were a few leftover particles that we still hadn't detected like the Zebo's on which I think was detected in the late 80s and the top quirk which was detected either in the late 80s or early 90s, something like that. And then after that the only thing left was that our understanding of the weak force predicted this thing called the Higgs boson that we had not seen and not seen and not seen and then we did. So finally we have now detected his Higgs boson I don't know four years ago, whenever that was, five years ago. But what's sad is we haven't seen anything that's not predicted by the standard model and in the heroic age of particle physics all the time we were seeing these things that we didn't know why they were there and they didn't fit our models and we had to come up with new models. So now particle physics doesn't really have any strong good there's anomalies that hang out like dark matter and dark energy and maybe the sterile neutrino thing but we don't have any really good solid things that have been leading us to new theories and so at some level particle theorists are bumping around in the dark and it gets to the point now where lots of physicists think that fundamental particle theory has gone badly off the rails. String theorists have been working for decades and have not produced a testable prediction nor do we have the right kinds of anomalies that string theory has been able to explain and so a lot of fundamental particle theory is now disconnected from experiment and that's kind of unfortunate. So if the sterile neutrino effect is real this would be important to particle physics because it is something beyond the standard model that would allow us to really sink our teeth into it and try and figure out what's going on here. When the LHC was first turned on if you go back and you find some old recordings of me giving talks I predicted that dark matter particles were the lightest supersymmetric particle and that they'd be found at the LHC. Well, fast forward to today the LHC has not found this thing called supersymmetry. I don't think it's completely ruled out but it's starting to look very unlikely and so the thing that I would have bet on is the most likely candidate for the dark matter particle it doesn't look like it exists or at least it hasn't been found even though I thought it would be. So that was one kind of physics beyond the standard model which would have pointed towards string theory that we didn't find and so there's this doldrums we're just not finding stuff so this would be important if it's real. Now, me being a cosmologist also the question is can sterile neutrinos make up the dark matter? Well, probably not unfortunately they're not massive enough for them to be enough of them to make up the dark matter. If there was it would look very different in the cosmic microwave background. So, maybe maybe with some complicatedness you can make a few sterile neutrinos into dark matter but I'm not sure I bet on that right now. So, I will stop there and I know that some questions went by that I didn't answer while I was talking so if there's some questions you still want me to answer ask again now. Okay, let's see. Question. Part of neutrinos energy for practical application what is the energy density? Yeah, okay. So, the energy density in neutrinos from the sun is a lot lower than the energy density of photons from the sun. Almost all of the sun's energy comes out as photons. So, there's not a lot of energy there but even more the practical problems is really, really hard to absorb a neutrino. When we build neutrino detectors they tend to be gigantic tanks or gigantic blocks of detectors which detect tiny fraction of the neutrinos going through. So, from a practical point of view, harnessing the energy from neutrinos is extremely difficult. So, I don't think we're likely to do that. The photons not too hard, right? You put out something opaque and it absorbs all the photons. SR asked a question, can you tell me, due to mass condensation, is there every possible subatomic particle in a black hole? I can't tell you that. I can speculate so I will feel free to speculate wildly. I would guess that, yes, near the core of the black hole where quantum gravity matters and we don't understand how it works. Every possible subatomic particle probably does at least flash in and out of existence there but to really say that with any confidence we'd have to have a working theory of quantum gravity that would allow us to talk coherently about what goes on at the core of a black hole and we don't have such a theory. So, that's more of an, I don't know how do we not make a small black hole on study? Oh, we'd love to. It's just, it's hard. Well, okay, it's hard and it's dangerous. So, if we were able to make a small black hole and we dropped it and it fell through the earth to the center of the earth, everybody would become sad very fast. There were ideas that the large hadronic collider was going to make little black holes that would fall to the center of the earth and destroy everything. Those ideas were not ever held as very probable by any actual physicist, but people who like to get afraid of every new technology thought that would happen. It didn't. Guess what? We turned them on and the earth is still here, so we're cool. That LA, she probably does produce things called quantum black holes, but they're not really exactly the same as a regular black hole and they are extremely unstable. They last a tiny fraction of a second. So, they're not quite the same thing. Now, I would love to have a, I don't know, a mountain mass that we could nest down into a little tiny, tiny pin sized black hole to play with and do things, but again, I'd probably drop it and go through my hand and destroy me or something, so I'm kind of an oaf that way. But yeah, pulsar, we do study pulsars. We don't have one that we can fly to. That would be nice too, but we do look at pulsars in space and we have learned things about general relativity from looking at pulsars. My gravitational waves, which were directly detected a few years ago, were directly detected in a binary pulsar system a couple decades ago. So, yes, that is something we could do. All right, well, thank you all. I'm going to wander off net. Do we know, is there a talk next week and do we know who it is, Jess or Chantal, do you know? All right, well, thank you all and I will see you all again at some point. Have a good day, everybody.