Osher Particle Physics Lecture 2 Transcript

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That's what we want here. is really about. Okay, yeah, so maybe just a reminder about what we talked about last lecture and then I'll say where we left off. So the the whole point well, at the beginning of the last lecture we said that particle physics and in particular this example of discovering the Higgs was the Higgs boson was really hard to do. It was it was really expensive. It wasn't very profitable. and so the question is, number one, what is the Higgon? number two is it so difficult to why is it so difficult to find it? Why can't you just do it at a you know, a single university in the basement somewhere? given that it's so hard to do, why is it worth doing in the first place, and then finally, now that we've done it, now that we've found it, what are we gonna do? Okay? And so kind of the whole point of the lecture series is to try to answer those questions, and the first part of the first lecture was answering the Y question, right? And so the I think really the deep well we'll get other versions of the Y question later, but the deep reason is we see that there's this web of explanations, so things in our everyday lives can be explained in terms of laws of physics, and there are some kind of pattern of those explanations, and it looks like if you if you keep going deeper and deeper asking more and more why questions, we get the sense of unification, right? The number of answers or things that seem to be different are actually different manifestations of one underlying fact, right? And that the Higgsoson the discovery that H exposon is really at the front tiier of that picture. So the number of explanations keep getting smaller and smaller, the Higgs was one of the one of the missing pieces at the bottom, and the question now is how does that pattern continue? And it naively it just can't continue indefinitely, so something interesting has to happen. there. So I think that's really the wide question uh, you know, the real answer, but again, you'll see other answers later. Okay, to answer the other questions, we need to introduce two characters that will participate in a big drama that will be today's lecture, and these characters are the idea of space time, which we talked about and quantum mechanics, which we started to talk about. Okay, so there this a reminder of space time, the idea before Einstein was that physics are all about how things group in space and time, but those were kind of different things, right? You you could you could move in space and the time will kicking along. Okay, with Einstein, with this idea that there should be an upper limit to how fast things can move, then you can't talk about them separately anymore. They're they're connected, right? D different observers will see the same events in different points in space and time, right? And then we saw with this m this f goofy minus sign, you have you know hyperbolas instead of instead of circle that we're more familiar with. Okay, so on one hand, the one big part of the drama is space time, so so now fit physics is about what happens in space time. The second thing is where we left off talking about quantum mechanics. So this is this was um a much bigger departure from the physics that came before it. Things got much much more formal and we lost a lot of predicted power. So remember, before, you could predict everything if you had if you know where everything is in a certain time, you could predict everything in the future, what quant mechanics says is, now there's this new thing called the amplitude, which is related to the probability, so if you square it or multiply it by itself, you get something that distract the probability to find the particle somewhere in space and time. Okay? So we're all now we have to talk about probabilities, and it's much more formal, right? You're talking about this mathematical function that if you square it, you get you get probabilities. Okay? And so what we're gonna do today, well what I'm gonna first do is is uh finish the discussion of quantum meanics, so we kind of left off halfway through so I'll finish that and then we'll move to the second second half piece. Okay, so, and if you remember, um before quantads, we really couldn't understand almost anything, right? And there's a lot of there's a lot of detailed things that you could worry about, but the basic one is atoms, right? We don't understand uh, how Ads and why Adams exist. We have a good model for what they are, okay? So we think that there are nucleus where which has most of the mass, um, that's very small, and then an electron kind of orbiting it that has that makes up most of the volume of the atom um and they're opposite charged. So they're oppositely charged, there's a uh a force of electromagnetism. There's an embr square law that naïvely should keep it in an orbit. and, you know, that's a concrete prediction and the the physics sense that that should beustainable, it should you know, Adam should only lax that going into have a seconds or something. so it's obviously, obviously wrong, and the naive things to do are to say, um, you know, what you run what say, well, the model is wrong. not this picture, it's not just kind of as your system. or you can say the model's right, but the force is wrong, okay? And with what was so confusing is it trying to both the model was right and the force was right, what was different is the way the electron is allowed to move. okay? And that's where we're gonna pick up today's lecture. Okay, so that's basically what um yeah, I should have switched just slide in for it doing that? Okay, so we're again, we're we're still talking about quantum mechanics, um and this is this idea of the of the atom, and so just in these pictures that we're drawing, again, these these kind of one dimensional pictures, this is uh, this is space and this is time going in this direction. and and right here, we're just w worrying our quot mechanics, we're forgetting about relativity for the moment. Okay, and so again, this is the model and there's a there's an attractive force, we have the proton here and the electron here. And so what classical physics would tell you is gonna happen is the let let's take the proton just sitting still and just think about how the electron is moving. Okay, so the proton is just staying still so it's moving up and up in time. um and what classical physics predicts is that if you send it if an electron gets kind of captured by the proton or you start it in one of these orbits, like these planetary orbits, what will happen is that very quickly, so this is this is all happening in like 10 of the minus 10 seconds, the electron is kind of is gonna start oscillating. and there with very quickly, this its orbit will go will collapse to zero. Okay, so there'll be there'll be no size to the you know, remember, the the size of the atom is the distance away that the electron is from the proton and classical physics predicts that this, you know, it'll the the electron was a sit right on top of the proton. okay? and become clear that this wasn't quite So it it became clear as soon as as as soon as you tried to apply basically, as soon as Rutherford realized that this was the model. yeah. So what happens is the uh so why this isn't a problem for planets? is there's no way for the planet to lose energy? So the planets orbiting and it's really hard for the plan to lose energy, the gravitational force is so weak, that that's something that will come back to later. There's basically no gravitational radiation when the planet is is going around the sun. But here, the electric magnet is a force is pretty strong and so you can the electron can radiate photons. So if you give off light and we saw the last time that the predict is this continuous spectrum, and so that happens very quickly. Okay? And so so this is the problem. Again, you might say that that you should throw away the model or we should throw away the force, but really what happens is we talked about last time, quantum mechanics says you're not allowed to have these infinitely thin lines, right? There has to be some inherent thickness to the lines, and and that actually solves the problem. Okay, so the real solution is if you start with an electron forwarding orbiting the the proton, again, the proton is just gonna sit here. um and we we can get, we should put it in the thickness of the line, okay? And so it turns out that electromaticism is roughly correct, but if you put it in, very quickly the electron is gonna radiate and it's gonna get trapped into the lowest energy state. Okay, so it is gonna in some sense, it is gonna sit right on the electron, but it can't it can't sit on the electron with no thickness. And so this picture is roughly right, it's it's gonna it's gonna give off some light and it's gonna it's gonna end up here. Okay, but here it's a finite there's a finite withth. That's the whole point in Guine my can. This can't be arbitrarily small. and it turns out if you do this, this size here, the width of this line is exactly the size that you predict by the ad. Okay, so again, it's this is this this really counterintuitive thing, you would think the pro there's gotta be a problem with the model, right? or a problem with the force, but it's actually a problem with with the thickness of this line., so this is how this is how introducing a a thickness to the line solves a stability manner.? Okay, um Exactly, yeah, it's it's it's it's um you know, there's a couple of ways to think about it one is the probability of the movement, the other is the uncertainty principle. It if you know it's position very accurately, you don't know how fast it's moving. right? So it's kind of a trade off different than the specific she specific layers. which the frequency not continuous.. So so this is a simple this is like a hydrogen atom.. If you add more electrons, it gets more complicated. hydrogen electrons are in shells. Yeah, right. So so there it's true. Yeah. the electrons it's it's more complicated than this. it's like the ground stink. Okay, um okay, so this is one classance ofon mechanics. It predicts matter who Adam should be stable, okay, so we have to pig that's a big win. um but it also has other counterintuitive um things that will come up later in in the course as well. One is the minimum energy, okay, so here's a system that can have uh some energy, right? And so this is just like a ball and a stick, a pendulum or like a clock, a grandfather clock swinging back and forth. and it can have potential energy if it's if it's displaced from its minimum or if it's swinging, it also has kinetic energy. Okay? And so now you can ask classically, what's the minimum of the energy of the system? Well, the minimum is like a broken clock, right? So the broken clock, this thing is at the lowest point, right, and it's not moving. So it's just sitting at the bottom, not moving. That would be the lowest possible point, and we would say the energy has zero, zero energy at that point. But you see, the problem here is we're saying two things, we're saying it's located at the zero, so it's position is well known at the zero, and it's not moving. and it's the end that's not allowed in quant mechanics. You can say one or the other, you can't have both at the same time. So in so classically you can have zero energy in in quantum mechanics, you can't exactly be at this minimum position.? Because that again, this would be like an infinitely thin line if it's if you know where it is and how it's moving, in the quantum world, if in this, you know, if this ball was small enough, we' quant a mechanism important, there's some un there's either an uncertainty in in a position where it actually is, where there's an uncertainty and how it's moving. So the lowest energy of the system can't be zero., you can think of it as as the thickest of the line, that you dryer, or you can think of it is there some in inherent jiggle to a ball at the bottom end. the clock at the at the bottom number. It occurred to last week is what. Yeah, exactly. Exactly. So, right. Yep. I. Okay, so this is another funny thing. Now that the there's there's a non non zero minimum to the energy. This will come up, so it'll come up later. Okay, so up some other consequences of of quantum mechanics. So before we had this idea that, well, there were some things constantly that looked likeaves, right, like light looks like a wave, a sound looks like a wave, and, you know, things that look like particles. and the question is which one is more fundamental? what quant mechanic says says everything is a particle, okay, but they're quantum particles, right so the particles are a quantum mechanics. What are these particles? Well, particles are things that can have mass, though that we talked about, but classicalophysics, that's still there. and they could have something called spin, okay, so this is this is a deep thing that I think we really don't understand the deepest level yet, but you can kind of think of it as uh as like the earth spinning, okay? So so the earth there's energy in how or angular momentum and how it's moving, right? how it rotates around its axis. Okay, so you can think of that as of a you can think of that as the analogy of the particles. So so particles can have a mass just like the earth could have a mass. and particles can kind of be spinning about their their axis. Now, the spinning is not right, they're not actually spinning, but they behave as if they're spinning. okay? And the value that they can have is quantized, so that's one of the reasons we call it quantum channics. In some units, this spin can be zero, so that means it's not spinning, or it could be a half or it can be one, three half so. it could be whatever you want, but it has to be a half integ. It could be seven half, 11 half. 13 Okay, and they could have other properties as well, things like charge, okay? So that's a problem? Um, another bizarre thing with Juan with Kan mechanics is the notion of identity, okay? Um, and so this is a little confusing. um, but if you so this is now classically, let's say we have two particles and we're gonna have them interact, okay, so we're gonna shoot them together, they're gonna interact and come out at different at at a later time. And so this is kind of like a collider experiment. We shoot them in at one time, they collide, and we see where they are at a different time. Now, classically, we can label these particles, because we know at every g at every point in time where particle one is, because these lines are infinitely thin, right? So we can say, ah, yeah, this is partle one, it interacted here and then particle one came out there. and same for particle two. Okay, but with Quan mechanics because they're inf because they're they can't be the lines aren't infinitely thin, there's overlap, okay? And so that means if we do this experiment, theider experiment, so let's say, again, we're starting with two particles, they're shooting it shooting in at some time and we're gonna measure them at a later time, because there's some thickness to to these to these paths, we actually don't know, we we can't tell even a principle whether this one, you know, what we we started with this particle one and let it up here, or if it's the one that ended up here. Okay, again, because of the thickness of the lines's question. Yeah, these have the same charge. If they had different charges, you would know. Same with spin. So they have to have the same if they have the same char and spin, they're otherwise identical. you can't you can't follow them. Yeah, this is a subtle point. It's that, you know, when when these when these areas overlap, you don't know which is which. Okay? Yeah, so so if they have different masses, then you can tell. Okay, and so the point is, at at these that we can't in principle tell which is which at these later times. Now, the physics no, because we can't in principle tell, that means the physics has to give us the same answer if if we switch the labels. Right? Um, and okay, so yeah, so identical particles must be treated as as if we can switch the labels. And this has this has uh a funny consequence. So, because identical particles are indistinguishable, again, meaning we can't we can't trace the trajectories through, uh the physics has to be independent, but remember, the physics is the probability that depends on the square of this amplitude. Okay? So if there's two particles, whatever the amplitude is, when you square it, it has to be invariant if you if you strip the li flop the labels so that you particles. Okay, so if I you know, if you calculate if you label one as P1, the other is P2 and square it, you have the equal, the case when you call the other one P2 and the other one P1. So this is the statement that the physics is the same, the amplitude squared is the same, but that means the amplitude itself, you have two options. It can pick up a minus sign or or cannot pick up the minus sign. Because when you square it, the minus sign is gonna give you a plus. Okay, again, this is kind of a subtlety. It looks like kind of a loophole, right? You would think the wave function has to be symmetric, but it can also be antiymmmetric with a minus sign, because when you square it, that was satisfied the equ question. Okay, again, it looks like this kind of irrelevant text of detail, but what we call is part particles when so there's two knowledge, two types of particles in nature. There's the particles when you flip them, if they're identical and you flip them, you get the plus sign. or the particles where you get the minus sound. So the if you flip them and you get the plus sign, we call those boszons, okay, so that's a hicks boson, boson means you get the plus sign when you do those flipping. and there's another the other particles are called fermons, that we get the minus sign. Okay, so again, two fundamental types of particles, the fermions, pick up this minus sign and bosons is plus on. Again, this looks like a kind of like a detail that's just coming from the fact that when you square those wave functions, you have to get the same answer. Okay, question. Fur me on Fermy Yeah, En Rico for me. Yeah, Bo B. Yeah, he's he's one of the first really famous Indian physicists. Okay, and so, this partially explains this classical dichotomy, so classically, you had these things that look like particles and looks like waves. Now we're saying everything is a particle, but they're quantum particles, but there's two type of quantum particles. There's boszans and fermions, and that explains the classical buality, right? So big collections, if you have macroscopic collections of particles that are firmions, okay, so uh protons, electrons, or fermons, those things behave classically like particles. If on the other hand, you have big collections of bosons, so things like photons are a boson, those macroscopic collections of photons behave like classical waves, like light waves. Okay, so we can see, so here you're starting to see this duality, right? that this um things that look totally different classically are actually described by the same who similar things. They're all particles, but there is this funny minus sign. Some of them have the minus line one there's signs. So okay, this this looks like it's irrelevant. It's just this mathematical thing that if you squared at the minus sign goes away, but it allows two types of things and these two types of things are exactly explain particles and waves classically. Okay, um good, so that's kind of all I wanted to say about quant quant mechanics. Again, there there is you know, there we get like three years of quant mechanics courses to be people to do actual calculations of stuff, but it's really justong through these basic basic ambience. Okay, and so now one obvious question is why don't we notice these strange effects in our everyday life, right? It sure looks like this have a well defined position, momentum, and it doesn't look like you have this idea of time dilation, the things slowing down if you move very quickly. Um, and the main reason is just a numerical a numerical reason. For relativity, it's that these funny things only really kick in when you're moving close to the speed of light. And the speed of light is a big number, okay? It's like half a billion miles per hour. Same with Quantum mechanics. We have these funny effects when the thickness of the lines is noticeable, right? But the thickness of the lines in some, you know, everyday units is tiny. It's like 10 of the minus, you know, 30 Again, it doesn't really matter what what these units are practically for like baseballs and bricks, the lines are essentially infinitely thin, okay? But if you really do very precise things with small objects like at the atomic level, then this thickness of the line starts to matter. Okay, so it's it's it's it's an accident of the numeric values that set the thickness of the line or the upper speed limit. Okay, so if you know, so humans, if you know, if I if I move as fast as I can go, which is like 500 miles per hour, if I do this for 80 years, I will gain about a millisecond in my life, okay? So not very practical. right? Um, similarly, if if I can tell my p if I know exactly where I am to the size of an atom, that's what I know I ever you know, then there's an uncertainty on how fast I'm moving and then uncertainty is completely negligible, right? 10 of the minus 25, 26 miles per hour. Okay? So this is the reason why we didn't notice these things right away? It's also a reason why these things are not intuitive, okay? Costco physics is more or less intuitive, because well, this is not philosophy. I think it's because classical physics mattered for your survival, okay? If a if a tiger was, you know, in the bush, it was gonna come at you, you need you need to know, okay, how r roughly how fast is hit moving, how fast can I move, how far away am I and so on? These types of effects could be in depending on the values, they could be important for that, but in practice they're not, right? If you know where the tiger is to one to the length of an atom, it's not gonna change whether or not you survive, right? So knowing about quantum mechanics or relativity does not did not help our forefathers survive. and but classical physics, I think, really did, and so there's some intuition that we have that's imprinted on us, probably from evolution about classical physics, that we should not expect to carry over to these realms that are so far from our everyday experience. Okay? So I think, yeah, you know, what you're in yeah, another thing is there there's in in the press, there's a lot of stuff written about quantum mechanics. a lot of it is crazy, and it's because it's very int not intuitive. and the people that try to make it intuitive, um can can get that shit beyond beyond the truth.. I think the reality is it's just not intuitive because our intuitions are not built in a in in a world that's governed uh that we quant mechanics that's relevant to our survival. Okay? um yeah, maybe that's all I wanna say about this. The the other thing I should say is there's no disagreement at all about the formulas of quantum mechanics and about the predictions that it makes. There is a big disagreement about how we should interpret quantum mechanics. So what is, you know, which of the equations actually tell us for this class, it's actually not that relevant, um, but it is something where where there isn't consensus yet on, you know, among the physicists about what the equations are actually telling us. Okay? And so if people are interested in that, I'm happy to talk about it, maybe off uh after class, I think there is I think there is a clear answer to the physics is telling us that the right answer, but some of my colleagues are not, uh they're not with it yet yet to realize they're right answer. Okay, um, but I think that's all I want to say about quantityans. Okay, um right, so so what I I just wanna say something again about about Newton's dreams, so we had this idea that about the explanations were converging, we hit a wall in the beginning of the 20th century, and we have these new revolutions, these things where we're changing the physics that came before it. uh quantum mechanics much more so than relativity. but these revolutions are particular nature, right? The previous theories were not completely rejected. So it wasn't that well, what you were doing before was just crazy, it was wrong. They are approximations that are very good, right? We still teach them to in to freshmen, right? because they work in our everyday lives, they' they're the right way to think about it. um but they're they break down and certain contexts and there's a way to extend there's a way to map onto the previous theories um, these new ideas, relatively aut mechanics. Okay, one of the things that's interesting um is that progress in being able to describe a larger domain, we see comes with a real significant loss in productivity. So before, you get before relativity, you could say things happen at the same time. Now that's kind of, you know, there's no well defined meaning at the same time. Before you could predict what happens, if you know everything, you predict what happens. Now you if you know everything, it's the amplitude, you can only predict probabilities. Okay, so this is an interesting feature. This actually continues even even as we make more progress, there's less and less uh there's lots of less stuff we can say, and so I don't don't know what else to say about that. Um the other thing is there is this idea of unification, so there's things that we thought were different, that we see are actually different phases of the same thing. okay? So with relativity, space and time are actually, you know, related, you could trade one for the other, they're not completely different things. I didn't talk about this this much, but energy and mass, right, famously equals MC squared. That connection happens with relativity before they were thought to be totally different things. Electric electricity and magnetism didn't talk about this, either these forces are different classically with relativity, one observer will see an electric force and another observer will see it the same thing as the magnetic force. And so again, unification, um and we're not gonna talk about here until maybe the very end, but gravity is also shown to be really related to space time itself. Okay, quantum mechanics does this even more, so waves and particles, again, these things these entities that look totally different are actually described all by quantum particles, and it's just it's funny minus sign that distinguishes them. Um and but even in the high level with quantum mechanics, we can now really unify chemistry in physics. right? So the chemists were we're seeing these spectra, these fingerprints of atoms, making these wonderful progress. We' physicists predicted that atoms shouldn't exist, with quantum mechanics, physics can now predict that atoms exist, and they can explain these these magic numbers that come from uh the spectra of light when you burn certain down. Okay, um good. So now we're really getting to uh to electric here. Okay, and so now the obvious next step is now we have to combine these ideas. Okay? And so what's interesting here is that um that it looks impossible, okay? Right? And so again, this is just a reminder, I think I can I can skip this, um but yeah, so so with relativity, you need the different observers will will think of particle or some of that happens on this on this line or on this on these hvertelos, and we have we't mind about it, but we also have energy and mass of equal squared. Okay, quant mechanics, we just we just went through that so I I can skip. I could skip this, but n maybe I'll just highlight, okay, we have this amplitude, that's the only thing we're allowed to talk about. and what the theory actually tells us is how these amplitudes evolve in time. okay, so if I give you the ampltitude at one time, the theory tells you how it goes to different times, and you can convert these amplitudes into probabilities by squaring them. And that was the big takeaway. and we said determinism is gone, you can only predict probabilities, and we have these finite thicknesses to the lines. Okay, um good. So now let's let us talk about combining relativity required mechanics. Um, and so this is interesting, again, kind of philosophically, because the first 25 years of the 20th century were giving these revolutions, so coming up with them, the second 75 years was trying to put them together. So it turns out it was much harder to put them together than it was to come up with them in the first place, right, which is interesting, and and I think part of the reason is the first getting the revolutions, you really needed to be a radical, right? You needed to say, look, I understand the physics that happened before, and I'm gonna change it, right? It's not right. These things gotta change these details. It turns out that right answer as we'll see of combining them is being super super conservative. Okay, but of course, they didn't know that at the time. the whole generation w was taught by their, you know, the previous generation where the right answer was being radical, right? And so they were like, okay, yeah, the so we're gonna try to put together quantum mechanics relativity. It's not gonna work, as we'll see. And oh, no problem. We just need to throw everything away, come up with new ideas, more revolution. And it turns out the answer is to be is it gotta be radically conservative, so it's really take the principles of space time and clim mechanics super, super seriously, and what happens is it doesn't it basically doesn't work anywhere. You try to do something, it's impossible. and it's only these extreme edge cases where where it works, just barely works. so I'll I'll try to motivate that here. So essentially it doesn't cannot combine them, except for these isolated extreme points, uh, you know, where certain numbers are infinite, right, or or what you'll see it. And that that's predicting that the world must look like this, right? And lo and behold, one of the amazing things is that is exactly the world we see. So we see this funny thing of all these different particles, and basically that actually the only way it had they could be to combine Qant mechan's relativity. Okay, so that's gonna be the upshot of today's lecture, and I'm gonna try to motivate uh what I just say there. Okay, so it looks to be impossible, so why is it impossible? Okay, what's the problem? Why can't we do it? Well, basically they they speak two basic different languages. Remember, quantum mechanics is saying, if you know the thing the amplitude at this time, here's how it changes in time. relativity, the whole point is time isn't not big of a deal. If you're moving, you you're gonna different observers are gonna disagree at the time. There's no notion of simultaneity, right? So, how do you even talk about the initial condition of a final condition? okay? And so that's that's the problem, right? in quantum mechanics, time has a special role, it's a fundamental role, like the fundamental equations have time in it. and relativity, the whole idea is time isn't special. So so that seems to be a contradiction, um again, it turns out it's just very barely possible to put these these together, um and this really determines the way that that the world can work. I if if it satisfies the principles of quantic cancer relivity, putting these together is something called quantum fuel theory, so that's like the relativistic version of quantum mechanics. um and the idea, again, is it basically doesn't work, okay? Uh, and it your but if you insist that it must work, it dramatically restricts with any possible theory can look like. And so that's what I'm gonna kind of talk about, um today. And so what are the consequences? Well, the first consequence is dramatic. You have to have antimatter, you have to have anti particles. Okay? This is this is this is shocking and unexpected, especially because we didn't know about antiarticles before they tried doing this. It doubles all the you know, predicts that every single particles there should be another partle that that's in the universe. and it also makes the vacuum or makes nothing interesting, and I'll say what that means in it later. It says there's a key rule of spin, okay? So remember, before spin had to be quantized, that was part of the quantum and quantum mechanics. Um, now, not only does the spin not only can you talk about spin, in some sense you have to talk about spin and particle that are the half end your ones, they have to be fermions, particles that are the integer ones have to be bosons. Okay, so that comes out by finding these, and also dramatically limits a number of particles we can have. Okay, there's also major constraints on the types of interactions that are allowed, um and I'll I'll show this I'll show this in a second. Okay, so again, you try to do this, you try to do it in some gen general way, right? So here we're not even looking at what the world looks like. We're just saying, how do I come up with a theory that has quantum mechanics and relativity?, and it says, it cannot work unless you put in antimatter, right? So, the basically people did this, they put it together and they said, oh, this theory is predicting antimatter, we don't see anti matter. So the thing so it's impossible. So we need revolution, right? Or if you said, um, if you ignore the antimatter one, it says, oh, these particles can only you can only have a certain number of particles where it looks naively like we have other particles. So they said, oh, that's we need more revolution, right? And so what we're gonna see is, instead, if you take these ex very, very seriously, it's making predictions on what the world should look like. Okay, so shortly after this, we see that antipartles were in need were indeed discovered. Okay, so I wanna talk first about this anti matter, so why do we need antimatter in if you combine quant mechanics and relativ? Okay, this comes back to causality, okay, so causality is something we don't really talk about. It's it's a fancy word for saying, what happens next? should only depend on what has happened before. right? It might not depend on it, but it shouldn't depend on something that's happened in the future. Right? So so an example is, if somebody dies from a gunshot, the gun should the gun should have been fired before the person dies. Right? That just it's it's super basic. it's obvious, um and it's kind of a prerequisite to science, right? If you don't have that, you can't even do science. So we we basically almost never talked about it. We just assume that you have present. if the consequences have to come after their process. Okay, so let's think about causality in relativity. So so not with quantum mechanics, just with relativity. um so so remember, things are moving in space and time. um and things can't go faster than the speed of light. okay? So let's say this is the A is the point in space time where our gun goes off, and it kills uh or injures, I guess, this person at B. Right? And remember, where the person a B gets shot or where the bullet enters, is observer dependent, right? So this one observer will think it happened here at different moving observer will disagree on the position, but they will agree on its happening somewhere in this hyper. different different basically this event can happen anywhere on the red line, depending on how the observer's moving. Okay, and and this is good, because, well, it's bad for the person that dies, but it's it's good that for causality, right? Because all the moving observers, they agree that B happens at a later time than A, right? All these all these times for B are after they come later than A. Soosality, okay. in relatively. Okay. Um, but imagine that you could shoot the bullet faster than the speed of light. Okay, if you could shoot bullet faster than the speed of light, then what would happen, so relatatively says you can't do this, but if you could uh, one observer would say, okay, the gun goes off here and B dies there, but now a different moving observer thinks that they lie somewhere on this hyperbola. Right? And the problem here is a lot of these observers think B is happening before a. Okay, it's on a problem and with relativity because you can't go fast on this vehic, right? Um, but if you could, causality would be violated. Okay, so what what happens in quantum me again? So now we're gonna do this game, we're gonna put it in quantum mechanics and remember, now we have some finite thickness, all right? And so that means if you if you really, really zoom in on this, like at the entire level or below, there's always some thickness here to this line, right? And so that means there's always some chance it's usually very small, but there's some chance that that the particle looks as if it's going faster than this beautifully. So there there's some probability for the particle to get out here. Right? Because the line can't be, you know, it can't be infinitely thin at this point. Okay, so that means, um and if you put mechanics, there's there is if you shoot Adam or it's if you if you don't shoot bullets, but let's say you shoot protons, there's some probability for this to happen. Okay, so to go from uh from A to B where that's that's we say it's out of the light code of fashion as speed of light. Okay, this looks like a disaster because a different observer is gonna see it's gonna see, you know, be getting hit before A goes off. Right? And so the only way um right, so different observer is gonna see this, right? And again, this looks like a problem because it looks like there's current or it looks like there's pro positive charge kind of moving backwards in time. Right? And that's that's that's not good for cazality. Okay, so the only well, a a necessary condition, this isn't sufficient, but the the only potential way out is if this observer, so back up. we're shooting a proton from A to B. So all the observers agree that there's less that after the process, there's less charge at A, and A has some charge, including a proton, and loses the proton, so it loses some charge, and B gets more charge. after it gets hit. Okay, so the only way to have causality is for is for this observer to say, no, no, no. it's not that something came from A to B, but's something came from B and went to A. Okay, so again, this this isn't this isn't a proof that it works, but it's necessary. It can this is a necessary condition. If we need causality, and observer that lets down here in needs to interpret this as something going from the A. okay, but they they both agree that B got more positive, and A got less positive. So, whatever is coming from whatever this observer thinks is coming from B to A has to have the opposite charges as the particle that the other observers think is going from A to B. Okay, this isn't this doesn't prove this is just a a necessary condition. It doesn't prove that that caality is okay. If you do the calculations, it turns out causality is okay, um and the only way it's okay is cause this observer w won't see something once he proton going backwards in time, they'll see an anti proton going forwards in time. Okay, and so again, this cartoon doesn't prove it, but you see that it has to be if you want the arrow to go this way, because the charge is going that way, the current is going that way, you need the opposite charge of the particle. And is this still a theory or is this proven? So this is all theoretical. Now you can say is so this makes a prediction. every single particle that that has a charge should there should be another particle that has the exact same mass and opposite charge. So there has to be in a positive electron. theory far? So this is the third this is the 30s. just after quant mechanics comes comes around, and at the time they didn't nobody knew positive charges, but people started doing experiments with um with balloons looking at cosmobeys in in in either on mountains or in in hot air balloons, and they saw articles that looked exactly like electrons, but with the wrong charge. So it came, you know, very close, almost a year, a year after it was predicted, even less, it was discovered.s been around about 90 years, but it's still not proven to be five, we now there's an articles. Every particle that we've discovered, we've discovered an anti particle. Yep. But when it was when it was predicted, that there we didn't know about them, and so a lot of theorists said, oh, there's gotta be wrong, because they're we don't know about any we don't know about anti particles, uh, but they were later discovered. What's that? anti particles. in some way to have the same mass. They have to have the same mass and they have to have the same spin. is, so I think the real way to say it is if if you're in this situation where where where the proton gets out of the lightone, it looks like it's moving faster the speed of light, then that there's actually no well defined statement that that was a proton. Some observers will see that as a proton, other observers will see it as an anti proton. But it's only in that it's only in this regime when you're out here, when you're here, everybody agrees that the particle is an a proton or an anti proton, out here, the process happens out here, there's an ambiguity, and an observedependent ambiguity. some probably is. Yeah, you everything is problem.. Yeah. Okay, so again, shocking. This predicts every single particle has to have an antiarticle and now know that that that that's true. All right? So if you try to put the other quantum mechanics and relativity without antiparticles, you can't you don't haveality and theory just doesn't work. Okay, so only in the world that where there is antimatter, that doesn't work. Okay? yeah, that's what I say here. Okay, and so this actually has big consequences on nothing or on the vacuum, okay? So empty space. Okay, so what does it mean to study empty space? Okay, usually this is you kind of a silly question, so you if you wanna know what's in a certain region, you just like look to see what's in like, is there anything in the in the closet you look in the closet, right? And so nothing there's nothing special, this doesn't get hard until you go to really small regions. When you go to really small regions, quantum mechanics kicks in, and what happens is, well, let's take a before quantum mechanics. Bore quantum mechanics, let's say you want you wanted to see what having in a really, really small reasons. There's a lot of science fiction about this, um, like uh Jules Ver had these things of building tiny robots, right so you build this tiny robot and maybe you can chain them together, like the little robots build even tinier robots, and they report back to you, and so you can you know, there's no limit to this, right? So you could build super tiny robots that in the magic school bus, right, we're going through your the body and reporting back. So before bond mechanics, that's fine, you can do this. You could go a little robots, and there would be no problem. With quantum mechanics, what happens is when you get to atomic distances, the uncertainty principle kicks in, okay? And with what that's saying is if you know that yourre searching this this small region, if you if you know you're Delta X is really small, because of the uncertainty principle, the Delta P needs to be big. The satisfy that to make a line have a have sewn the thickness that it needs, and that means that as you get smaller and smaller, the amount of energy or the amount of like velocity momentum that the particles have or energy that the particles have is getting bigger and bigger. Okay, so to actually probe really small distances with quantum mechanics, you need something that has a lot of energy. So you can think about this as light, too. the wavelength of light is as the wavelength is smaller, the energy and the length gets bigger. That's exactly that the snack on mechanic. idea. Okay, so with on mechan, so this is why these accelerators need to be so big, right? Because we're trying to study what's happening at these really small distance scale scales in order to do that, the protons eat very high energies. because there's just inverse relationship. Okay, and so what happened? So so that's just with quant mechanics. So now let's put let let's put quantan, so we're studying small regions, we need big energies. And now let's put in relativity, okay? Now the problem is uh, eventually you put in so much you're going to so small energies that you need or so small distances that you need so big energies, that that this that this number becomes like twice the electron mass. Okay, once it's twice the electron mass, you now have enough energy in a little region to create a part of one in aniparticle. Okay, so in some sense, you thought there was nothing there, in order to check if there's nothing there, you put in all this handy, but that energy at some point, it's enough to create a part of one anti particle. Okay, and this is new with relativity before relativity, you you only had electrons, so you had to conserve charge, and you can't make you can't make two electrons because then that's that's that's not conserving charge, but now you you have you always have this you have to have this partner that can conserve charge. okay? And so what this means is, so when you do this, there's there, you know, there's no loss in physics preventing this to happen, or you can conserve energy, you could serve charge. So quantum mechanically, there's some probability for this to happen. Remember, it's just probability is um, but it it can happen. You have to conserve spin, yes.us Yeah, exactly. So that there spins will be coral if you know, if one spinning this way, the other't want to be spinning, like that. Okay, and so this is a this radically changes what we think of empty space as being, right? So before this, we thought empty space is just as nothing in it, right? Now there's nothing in it, nothing in it nothing in it until you get to the distance scales that are set by the mass of the electron, now there's like the C of electrons in and anti electrons coming in and out of existence, right? It's probabilistic. So if you if you look, maybe sometimes you'll see the electron with some energy, sometimes you'll see it with a little bit bit more, sometimes it spin look like that, sometimes it'll look like that. So it changes every time you look, but it's it's a rich, but it is rich structure there and of course, as you go to even smaller businesses, there's heavier part of both says, we'll see, and you could create those part and particle particles. look go, but you in really close you see much more ber structure that level. that's a good way to put it. so empty space has this rich structure of particles, anti particles, um kind of figure that as like popping in and out of existence. Okay? So the so so again, the simple act act of looking creates something, and you should think that there's no sense in which the vacuum that means at something with nothing in it is empty. It's it's only empty at distance scales bigger than the top than like the electronic. Does that have anything to do? I was amazed, but I look at too final theory, very basic level, and they talk about dark energy and dark manner We'll come back to that. Yes. So, maybe it does. We we don't know, because when you talk about the stuff in the vacuum right. from what I read that the actual Adams is 5% of math. so there's a direct relationship with dark energy. So you so we we'll come back to that at the very end and we'll talk about that. That's one of the big mysteries. okay, so often you hear people say, in these public talks, work on this big collider apartment in Geneva Switzerland, and it's like a big microscope. and I think that sounds good, but then you think, like, what the hell are they talking about, microscope? What are they looking at? or are they looking at like a piece of hair or something? Um and so really the answer is it is like a microscope, and what we're looking at is the vacuum, okay? We're looking at the vacuum, and that's not a stupid thing to do because of quantum mechanics and relativity, the vacuum is this interesting place. Okay, the vacuum is interesting. There's things coming in our existence, and so with these microscopes are doing is they're studying the vacuum.ing the vacuum by desc sending in these particles put very high, uh high en. Okay, and here's this just a card cartoon of that, so at some distance scills, you start creating electrons, if you go to even smaller distance scales, you'll create heavier particles, like a muon, we'll come back to. Okay, so the other thing I should say is this is super, super advanced stuff, right? This is beyond grad school in in in many cases. So it if things aren't aren't obvious, that's it's all but is super, super nice. Okay, there's other there's other implications. okay? So so if you just have pawn mechanics, we said you can accommodate an you can accommodate spin. You can describe it if you want, you kind of take it or leave it. if you want to do it, they have to be half integers. Okay, um also, you can have basically any interactions, you can have these particles interact in and crazy ways and basically what we do to refreshment or not freshmen, but juniors is we tell them about quant mechanics, and then we give them all kind of different react interactions. We say, okay, solve this interaction, not solve that interaction. and and, you know, that's what they do. Okay, um that's with pawn mechanics. You try to add relativity and you see with spins, you have to tough it first of you have to talk about spin. Okay? Second, there's a connection between integer, spin and bosons and half the Negers and farmons. okay? If you tried to do it the other way, it wouldn't work. You you would either not have relativity or you'd have violations of causality. The other thing is, you can't have any spins you want. There there's you go from an infinite number to only five, okay? You can have spin zero, one half, one, three half two. Okay? So you can't have a spin 112 or 11? You're only allowed five options., not only that, you're only allowed to have one of these. These, you can have as kind of as many as you want. You can only have eight of these, and you can only have one of these. Okay, so okay, you it's like these these these extreme points in in all the space of all possible theories that are allowed. Everything else, you try to put in spin five particle, it can't be fun mechanical and relativistic. Just just those numbers, is that the speed that Yeah, you could think of it as the speed. in some units, some units. Okay, interactions. So first is, you have to conserve charge, okay? All interactions are local, so they have they have to have an point in space time, and there's only a finite number of interaction. There's only three. Okay, there's a case where four boszons come together and a point, there's a case where three of them that come together, and there's a case when two fermons and a boson come together. Right? So again, you go from an infinite number of potential interactions to three, right? These are the only possible ones. Okay, so you can see how hard this would be if you if if you were if you didn't have the radically conservative or this very ulra conservative mindset, if you said, I just wanna put together on activity and you weren't prejudiced about these are the only interactions you can have. You would think it's just impossible. right? You would think, okay, fully impossible, and it's only when you take the mindset that I'm gonna only look at things with these have to be work, you see that almost everything is impossible, except these radical restrictions, um, and you cannot use that to your advantage. You can say, look, I'm predicting the world must look like this. these things from experiment this this is all theoreical this is all mathematical consistency, root theory or whatever, early. I mean, it's really just if you try to put if you try to you need causality, you need things you can't look like they're going faster to speed of light unless you have antimatter. Yeah. Yeah, and then the o the other big one is the probabilities can't get bigger than one. So, for some of these things, you get if in it probabilities. Okay, um, and so again, this at this point, you're just this is the basic framework of any possible theory, right? So it's it's it's how any possible universe that is relativically a quantum mechanical have to look. It has to obey these these const strengths. Okay, so now what I wanna do is shift and talk about what are what our worlds actually made. okay? And so you can see here, again, you can kind of turn this into into an advantage, right? This is radically restricting what a possible universe can look like, and what we're gonna see is our universe is is very particular, but in a way that exactly agrees with this. right? And so that's again, it's a big sign that we're that we're on the right track. Okay, so so what is our actual world made of, so that so the the theory that that is quantum mechanical and relivistic that we think applies in our universe would call a standard model? It's kind of a a bad name for this standard, but um, basically it describes, you know, that you know, all the stuff in the in the in the universe or in the world, right? And so we know that everything is made of atoms. We already said atoms that, you know, nuclei and and electrons, um so this before, the electrons are negative charged, they're responsible for the volume of of atoms, or or it's everyday materials. These are thought to be fundamental, right, so these are in our fundamental, you know, these are a quant particle in our fundamental theory. The nucleus is positively charged, it's responsible for all the mass of the atom basically all the mass, it was no quite early that the nucleus nuclei themselves are not fundamental. They're made of protons and neutrons. We now know that we now know that these are also not fundamental. These are composite things made of particles that we call quarks. and that's just a funny name for a quantive particle that makes up the neutrons of protons. Okay, and these quarks are now thought to be the fundamental particles. Basically, the fundamental theory has can describe all of the like the period table, has electrons, and it has these corks that come together to form protons and nucle neutrons that come together to form nucleac., so this is all the stuff that's in the world, um and again, large collection of these matter particles ha behave like fermions, so that means that the electrons and quarks because they behave like part things in the periodR table behave like classically like particles, they' their fermions. Okay? So here's okay, so that's one part, so one part of the describing the world is what's in it, the other part is how does it interact? and how these particles interact with each other? Well there's there's uh a number of forces. I mean, there's now four four forces that we know about. The first is gravity. Okay, this has been known, you know, since antiquities, so basically forever, um it has an inverse square law, famously, and it's always attractive. okay? And what we're gonna see is it it's we'll see that this is probably at the end of the class is super weak in in some way compared to the other forces. So it's totally irrelevant for atomic sub atomic physics. Okay, we have electric magnetism, right? This again, was known uh to the ancients. It also has an inverse square law, so it kind of looks maybe a little similar. However, if you look at more detail, there's a lot of differences, so it's either attractive or repulsive, depending on the charges. um and this is the thing that that we know holds, uh electrons and ads. Okay, the other question, what's the relationship between the electro part of the magnetic, a Russian. I think the simplest way to think about it is it's observer dependent. One moving the one moving observer will think something is electragnet is just electric, another observer will think it's just magnetic. And in general, you'll think it's some combination that you. Okay, so we've more recently we've discovered two other forces. One, we called a strong interaction. So this is the thing that's responsible for holding corks together to make neutrons and protons. Okay, so so we we knew that there had to be a a force the electric force wasn't strong enough. There's a stronger force, we call it strong interaction. It was discovered in the 1900s. It was only really relevant at these short distances. It does not have a sim relationship, so it's it's very complicated, there's no inverse square law, there's no simple thing that you can say. It's also very important to everyday life because it holds together in the nucleus, right? And so this is responsible for like all of the mass um in the periodic table comes from this force. Okay, but it looks nothing like the other two. Okay, and then then there's the fourth force, what we call it, weak interaction. um this was discovered really just before the turn of the 20th century. it also looks nothing like the others. It looks totally different. It's responsible for radioactive decay. Okay, this force is also important to ourday lives. It heats the sun and it heats the earth as well, actually. Okay? So, one thing I wanna I wanna stress is these we have these four forces, naively, they look totally different from one another, and they're all important to us. right? They're all important to our existence. Okay, and that's what I, uh say here. Okay, um right, so okay, so so now I' I was gonna back up and say what do we actually do with the standard model? Okay, so, uh it's described in terms of this this on field theory. um, and again, the particular version of this was really developed through the second half of the 20th century, much of it happened in the 60s and 70s, but it it continued even even beyond that, I would say. um the thing that that I want kind of stress, you know, most of this has been it on cartoons and, you know, kind of the concepts, but there there is serious science behind this. This is the most accurate theory we've ever had, you know, in all of science, um it it can describe interactions down to distance skills as ten of the minus 19 meters, so way smaller than a nucleus, um, you know, a hundred times smaller than a proton. um and is as we'll see this as accurate and described accurate and precise description of basically all what we can do in the lab. Okay? I'll maybe I'll show you that. in in another lecture. Okay, and so so what what actually does it do? Well, again, physics is all about how things move in space and time, right? But now we're thinking about space time, what we have a lot of mechanics, so we have to draw these thick lines, right? We have to draw all these these like the wedges instead of fit lines. And so one of the things that you can imagine doing is having on this collider like experiment where I'm gonna collide two electrons and see what happens. Okay, so the theory will predict what's gonna happen or what should happen when you do this, so again you say what the initial condition is at one time and you predict what happens at a later time. and so the first thing that happens, for some reason we switch space and time. This is like the big the hardest thing in a quant mechanics. So now, from now on, I'm gonna draw space on the X axis in time on the space on the Y axis and time on the X axis. I don't know why we do that. doesn't matter, okay, and so the key the key is that the way that we do this is using something using these kind of stick figure diagrams, and this is really due to richer finding. I think there was a question about him last lecture. And soinement basically taught us is how to calculate the probability for this type of thing to happen. And what you do is you draw a you draw a stick figure of how this, you know, what is one way that this process can happen. Okay, so this is that in this way the electron comes here, there's a local interaction with a photon that comes and hits this other electron, okay? And this is one possible way you can do it, and he taught us you' basically draw these thick figure diagrams and there's a prescription to, you know, these correspond to a number. It's a complex number, but that that's more detail, but just the theory tells us, you know, for each of these stick figure diagrams, what's the number associated with it, um, again, these these these diagrams are all have to be simply connected, so they have, you know, things are happening. Nothing's happening in a distance, right? They have to be it have to be connected. Um, and what you do is you add all of them together. okay? So, you know, this is just one way that it can happen. Another way is the electric could come down here, in a little farther, and then it meant the phototon. So that's a different slightly different stick figure you can draw. There's number associated with that, and you add up all of the possible ways, all the possible ways that are consistent with this with these thick lines. Okay, so you kind of move this around as much as you can. each of those is a number, you sum up the numbers. Okay, again, this is only we teach in in like, grad grad school, how how to do this kind of thing. Okay, and then that once you sum up those numbers, it gives you uh it gives you the infiture. Okay? And uh okay, and so from now on, instead of drawing this complicated thing of, you know, there's these read there's these red regions that are consistent with quantum mechanics, and I'm gonna sum all of them up. We're just gonna draw out this one thing finger, so there's just one example, and this is what we call five mid diagram. So we say, you know, this is what happens the electron, you know, exchange the photon with the other electron really what we mean is there's an infant number of ways that this could have happened, each one has a small probability where we're summing or each one makes a small contribution to the amplitude. We're summing them all up, consistent with quantum mechanics to get the amplputage. Okay, but you can kind of just think you just draw something that can happen and the theory tells you how to compute the amplitude from this. Okay, question. people used to say that if you went to a a lecture you went by Richard findman, it would be perfectly clear and you understood all of it until you walked out and tried to distract the anybody. That's the signalk. You haven't left yet. Are we here? Yeah, okay, so yeah. can you performer design you very. Can you tell us how you measure these things with the collider at the certain thing? that what you're seeing to to verify this I' having trouble that. So that's gotta be another electric theory. Yeah, so I mean, basically what happens is these big colliders, they're like cameras, so they take they take um really complicated pictures and the pictures can tell us what particles are present and the images. And the theory tells us how often we should see certain particles. right? So basically we have a prediction for which pictures, which types of pictures we can see, and what what what's the relative bringing between them? And we just measure those. we taped the pictures and we see the you know, the number of nuons we see is that agree with the predicted number of muons. So the cameras actually capturing the existence of the police? Yeah, very roughly. example would it show on Right, so for this example, it would say it would say if you so if you start here with a well defined beam, right, and you ask, what's the probability that one electron comes out at this spot and one electric comes out, this spot, you get an answer. okay? And then usually what we do is we we act we we change this, so we say, okay, now what happens if they come out here, here, here, here, here, here. You get different probabilities. And then we measure how you know, we measure how many electrons do we see here? how many do we see here, here, here, here, here. And so there's a curve, there's an observed distribution of electrons and then there's the predicted one from these probabilities. with the show that No, the gamma we we can't see. Okay, um, good. Right, so so now, the idea of these forces, again, the constantly there are like these long range things, right? There's gravitational force from the earth uh, you know, or from the sun on the earth, or from one charge on another, uh what we see with with pont field theory is there's no long range forces. all the interactions are local. So for everything that we thought was a force, so this is the case of the electromagnetic force, it's really a point like interaction with a force carrier, which is the photon. And so for every force, there's a particle that makes the interaction local. So it looks like that there's a there's a I guess if these are both electrons there are repulsion between these two electrons, but that appulsion happens not at a distance, it happens from exchanging a photon. Okay, so the theory says there's a connection between each of the forces and a new particle or associated particle in the theory. And so for every force, there has to be a particle that conveys the force. Okay, and this is the example for electrom magnetism. And that through space behind. That's through space space, exactly the that's. Okay, so again, these forces that large distance skills look totally different from one another, right? So the ancients who got some of them, the other ones, we didn't discovered those my century, now we see in this theory, they actually all look similar. They come from these stick figure diagrams, and the details that change are what are the force carriers, so that the gravitational interaction would be an electron coming on and it's interacting with the graviton that goes and interacts with something else. Whereas an electromagnetic interaction would look basically the same thing, except this is a photon instead of a gravaton. Okay, and similar for the other one. So the strong interaction, there is another particle called a gluon, um that holds together, uh or that that conveys a strong interaction. The weak interaction is a little complicated that you actually need to we don't know there's two particles. There's one that looks like a photon, we call it the Z particle or the z boson that's that's heavier, this is like um or it's very heavy, this is a like a hundred times as heavy as a as a proton. And there's another one that ha that has a charge called the W boson. Okay, and so, um, so what we see is that the well, what the theory tells us is that the forces, all the force particles have to be bosons. Okay, and there's a different one for each for each force. um and again, large collections of these behave like classical waves. electromatic the gravities that they behave like uh like waves. Okay, and similarly to the electronic quarts, these force carriers are thought to be fundamental. So those are fundamental partles in our in our theory. Okay, and you can see they all have this there's all interaction and it's an interaction is one of the allowed pipes, right? We said the electrons have to be fermions because they're matter particles, so they have to behave constantly like particles. So these things are fermons and the only interaction that's allowed that's consistent with quant activity one of the three possibilities was two fermions and a boson coming together, and that's exactly what all these stick figures are. So these are bosons, these are fermions, so this is one of the allowed partments. by stress. It has to be this way. if you wanted a quanticantivity, this was the only way to happen. Okay, so something I snuck in here actually was this uh so this actually, this electron doesn't just admit or it doesn't just interact with the W particle, it changes into the new particle, called a neutrino. Okay, so these neutrinos are so they are another hy ofatter particle that's needed to describe the weak interaction. These were really forced on us by experiment. Okay, so we you know start studying the weak interaction. um there's a long history of this, but we see that it looks like energy's not conserved.? So again, one of one of the one of the things that you know, what of the approaches you could take is, oh yeah, we just need revolution, right? Okay, so now who cares about energy information? We's thrown away, but it turns out you can explain that the apparent nonener conservation by adding a new particle that carries away energy, and we now know that this particle does exist. It's called the nutrina. So, this is like a partner to an electron, so the electron turns into into a neutrino when it experiences this weak form of the week interaction. It has it has one of the reasons why it's so hard to see is it has no charge, so it doesn't experience the the electromagnetic interaction. It doesn't experience a strong interaction, and it has almost no mass. And so it's it's kind of like a ghostl like particle and again, it was invented just to make up to make the formulas work out, the energy conservation work out. Later we we've actually observed it in experiments, and we see that these things they actually exists some time ago I took a one of theseosher classes of talking about the events. and the offic presenter uh said that at the time of the Big Bang, the only thing around was a cork, glue, plasma., if corks at glue o are fundamental, where do the electrons come from? Because they're supposed to be fundamental. Yeah, so probably what they meant I think the electrons were okay, but anyways, what so so what could happen is the cores can come together and give you a Z? So there's there's an interaction where we have core Cork Z. and then there's the interaction where that Z can turn into electrons. So if you just have corks, you could create electrons. I think in the big Bang, probably in that corkoom of plasma, there probably was electrons around, too, but I'm not an expert on that. But if you just have porks, you can get electric so, you know, we we just collide corks at the LHC.times we produce elect electrons. So how does the world fuck for me? F fundamental A fundam is the creator destroy, right? No, no, that's not what it means here. So, in this context, it means fundamental means it's one there's no substructure to those particles in the theory. You can create them and destroy them, but they themselves are the basic building marks of the theory. Yeah, they have no substructure. that's that's what. Yeah, that's a good point. So and it's weird because a fundamental particle can turn into two other fundamental particles. speed is a chemist, we first figured out that matter in general can be described by atoms. and then we found more fundamentally that there were electrons and protons and neutrons. Yeah, narrowing down the number of fundamental enginines that you need. But now you physicize a buck, exactly. So we'll see. so that's what I'm gonna get to next, actually. So we need this firm, this again, this this uh neutrino is forced on us by experiment, so it's another thing that we' adding to the list of particles, and it we believe it is fundamental as well. Okay, so so this is how this state amount we often draw, you know, we can we can do this thing of like what the pure I cable for the standard model, you would think it's this, okay? So you have um to describe atoms, you need electron and to describe nuclei, and you need nuclei to describe those, you need corks, and there's two types of corks, there's an enough cork and a down cork. Okay? So if you have up up down, that's a proton, if you have down down, up, that's an a neutron., not important. There's just two types of quartz, and then there's this other particle neutrino that's forced on us by by weak interaction, radioactive the kids. Okay, so you would think this would be enough for the matter particles to describe everything, and then we have the of course, the forces between the matter, that is described by interactions, and each of those has a particle. um and here they are. So there's the the photon, there's two for the weak interaction, there's a glue on, there's also a graviton that I'm not gonna describe because it's so weak. so you would think that would be everything. okay? However, when we actually go out and look, so the other thing is, these because they're matter, they have to be fermons and they're spin a half, we've measured their spins, and that's consistent with the fact the requirement that fermions have to be half in ajured spins. These things uh need to be bozons and we measured um their spins are now are one. So half in it or so uh integer spin. Again, consistent with the combination of onivity, uh, but if you go on and look, this is not all that you see, for reasons we have uh, before I get there, um the other thing I should say is there's there's mathematics, of course, behind all of this, um, that's that's beautiful, also very complicated, um, but it's again, you can make predictions. Okay, but what I wanna stress is when we go out and look, we don not only see this, we see copies of the matter particles. Okay, we we call these generations of particles. So we see we see a heavier version of the electron that's called the muon, and we've been talking about that a couple times already. um and there's a yet heavier version that's a we call the T towel particle. And so again, we we have no idea why these things exist. We know they they each come with their own neutrino. Okay, so there's like a neutrino when when the so the muon can participate in the weak interaction, when it does, it turns into a muon type ofitrino, an arino that's different from the one with the electron turns into. Okay, again, these all these these have no almost no mass and no charge. and similarly, the corks comment through there's three generations of quarse as well. And we have no idea why. there's some pattern, so these are heavier. and so the only difference between the muon and the electron we think is it's mass, the electron is the muon's a heavier version of the electron. the towel is heavier still. The nutrios is it's not clear because their masses are so small, but it is true for the corks as well. So these these are like heavier versions of particles that make up the neutron proton. These things are they were discovered in the 60s and 70s, so they have crazy names, because, you know, physicists are they probably taking drugs, so this is the charming cord, this is the strange core, this is the truth cork and the beauty core. but these are just names they're just names, right? We often now call this the top and the bottom cork instead, but yeah, there's nothing like charmed about thisarm work orr strange. Well, there is something strange about strange. there're just you could just because of his names. and again, we have really have no idea why why this is These we think are all fundamental. Yeah, these are all fundamental and they all have anti particles of course. yeah. Okay, and then if you look at the in the details, there's actually eight different so these have a charge, there's eight different types of charge here. This one is a plus in a minus charge. There's only one of these and there's only one. Okay, so again, it's this weird thing, right? but much of the pattern is forced by us by just the the principles of relativity quantum mechanics. and so it predicts that we don't you shouldn't see any spin three partles. We don't see anything. um and this corresponds between spin and firoposon and the types of interactions that we see. Okay, and so here here are the masses of these particles. um and so again, this is we don't really know what the make of this. These are like inputs to the theory. right? So the theory needs to know what the NASes are at the these the numbers, where we think they are, um nobody knows what they make of these. So there is these patterns that that the within so this is like the first generation, so the electron in the up and down core, um you know, here the the lepon is lighter than the other two. Lepton is is like a derived from the Greek for light, um and that that's why it is the the electronism smaller mass. That's true, and the other generation so the muon is lighter than the charm the strangeork by not that much. Same thing with the towel. Here, the upcork is the first generation of the upcork is lighter, the second generation, and a third, the the cork and the upper position is heavier. you know, maybe these this is telling us something, we we don't understand now. um the this is all like the proton mass, okay, so the charm is about the proton mass. Some particles are really heavy. The top cork is just 200 times the mass of the proton. uh on the other hand, theotrios are have a tiny mass. so we know we now know that their masses are nonzero, but they're like 10 of the minus 11. proton masses. So they're kind of qualitatively different from the other particles. We don't understand that. most of the force carriers or the photon and the gluater NASus, so they have zero mass. uh but for theak interaction, they have a mass that's like 100 times the proton mass. Okay, so okay, don't really understand this. only works you see in our uh up and down, everything else is like theoretical. No, we've observed all these now… Of course I I mean I should put an abstract on un scene. You you can't you can't observe a pork directly, but we infer their existence. Yeah, yeah. are heavier approach on that I thought of them as So they they yeah, they're point like. We think they're point like, um, but their mass is bigger than the mass the approach.. What what's the meaning generation? So generation is just um it's just these groupings. So we know that there's a sense in which this nutrient, no goes with this muon and this strange core or this charm wants to go with that strange core. So we just say that that this is the second generation um and this is the first. but it doesn't refer to a time difference? No, no, no, no. No. Are all the Nitrinos admitted by the sun electron neutrinos is it I'll get a question. The first order that if they're all electron neutrinos, there's fine print there. then. Yeah, there's a lot of fun. It's very interesting, but it's um okay. good enough, yeah. The first order they are all electrons. Oh part of the problem is, with mute with nutrinos an electron nutrino can turn into a mut on nutrino, even an empty space. So that's part of the uh Okay, so again, these these numbers are inputs to the theory. There there's something that you have to go out and measure with the numbers are. Once you know what the numbers are, then you have a theory that's predictive. okay? um and yeah, so maybe this is telling us something, right? you know, the history of chemistry, you put the P table together before you knew Guant mechanics, which you really need to understand what the structure and so so a lot of people were getting, you know, you were doing basically numerology with with the elements to try to infer something deeper happening. and that happens in particle physics, too, so people play with these numbers and they play with these patterns to see if, you know, maybe's telling us something deeper, and there's no consensus on that at this point. Okay, um let's see. um okay, so yeah, so in the last couple minutes, what I wanna say is, um going back to the interactions, okay? So not only so we see these forces are totally different on long scales. when you go to small distance scales where in when pond field theory is important, they' characterized by the same kind of thick figure diagrams with just some detail are different, right? The which partle carries the force is different. If you actually look at so what the theory says is for each of these each of these vertexes, vertices, there is a number associated with it, and that number tells you how big the amplitude is. Okay? And so for the electragnetic interaction, this number is like one over 100., okay, these are also inputs to the theory, by the way. um for theak interaction or for the strong interaction, it's like one over 10. Okay, so in some sense, this interaction is strong because this number is big. It's it's stronger than electragnetism. Okay, so that's what we said. It's stronger. um the weak numbers is about one over 50, so we see, not only are they described by the same basic language, right? These thick figures, but even kind of quantitatively, the numbers are similar. You know, it's it's one over 100, one0, one over 10. okay? um and again, these are directly related to the strengths of the interaction. These are all sympathy theories. That's what I say here. um again, this is another answer to why we care about small business scales. We care about small business skills because this is the first time we're seeing these four these very important forces all behave very similarly. They're described by the same language, um and the and in fact, the fact that they look different to us is actually, um it's a long distance illusion, okay? If you go to small distances, the forces are almost identical. the distance the differences are just these numeric differences, one over 100 verses, one over 50, and it's still it's it's those diff details with those differences project out the long distances that make them look to us so different. right? And so um again, I I just don't have time to explain uh some of these distances, but basically what happens is uh, the showing force are strong because it number is bigger, it's 10 times bigger than, let's say, the electromagnetism. The weak force is weak, not because this number is so big or is so small, it's actually bigger than it electromagnet interaction, but if this forced carrier has a big mass, right? So the mass of this particle is like 100 times the proton mass, where this is the photon is massless, and it's the mass of this particle at long distances makes the weak force look totally different. So the weak force is only on small scales because this has a big mass. If you go to small scales where the mass of this part was is irrelevant, or if you go to energies that are heavier than the than the mass of this part particle, then these forces are basically identical, apart from like a factor or two. Okay, the strong force, again, when you are at small distances, uh smaller than the distance of the proton, it looks very similar to the other forces on long distances, it looks more complicated, and this has to do with, um it has to do with these quantum fluctations in the vacuum that if if people are interested in the detail, I'm happy to talk about. I'happy to talk about lot more. this question you get from I mean, the gamas a photo? Yes. And uh electron electron interroduction is electromagnet. Can you the one over ourired law from the Okay, so this is the reason we been gloified. This is the more sophisticated version of the Y answer. We build colliders because we wanna go to small distance scales, we wanna go to small distance scales because the forces all behave the same way in these small distance scales. So we think that you know, there's this unification of the forces, potentially that's happening and that's happening at small at small businessills, not a big distance scale. Okay, so this is why colliders are are so important. Okay, so so that's and nutshell is the standard model. um again, it took its kind of its modern form in the 60s and 700. That's that's when we really predicted that there should be these weak force carriers that are very massive. That was an unusual thing, uh, but that happened in in the 60s and 70s. And again, it makes very precise in and highly accurate predictions where we're not covering that hardly at all on this in this class. and and it's but you know, it can do things there's certain questions that you can that it gives answers to that are incredibly precise, that we could actually measure with the same precision, and they agree

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