The Standard Model in 90 minutes

[00:00:01]All right. Um, oh my days, my shirt is very dirty, but too bad. Who cares? Uh, okay.

[00:00:11]Hydrogen atom. Very familiar. As I said, the only thing I'm going to expect of you here in terms of knowledge is that an atom exists and it has a nucleus and orbiting electrons. Um, yeah. So, I'm I'm going to start by saying we're gonna we're gonna try and first off sort of derive in a way, but we can't really derive it without experiment and without uh actual results. So, um you're going to have to just trust me on a lot of what I say. Um so the the first thing here is that we can say there is an electron. It exists and it is a particle which can't be reduced.

[00:01:02]So we're going to call it a fundamental particle. And let's give it some sort of notation. Uh it's called an electron and it's got negative charge. So we'll call it E with a minus on top.

[00:01:14]Um simple enough. Then we have uh the nucleus. In this case of what I've drawn here, this is a simply just a hydrogen atom. Um so we have a proton and it's got positive charge. But we won't denote this as positive charge because particle physics convention is weird.

[00:01:38]uh for certain particles leptons only to my knowledge and in fact only half of the leptons we denote it as plus or minus up here actually no my bad there are specific particles like there's a delta plus and then there's even a delta plus plus is there yeah there is but that one has an incredibly short decay time so these two exist um the first the First questions we can ask really are can this be reduced?

[00:02:13]We find out that it can't be reduced. Uh because it it does decay. It can decay but only in really specific conditions namely when it's incredibly high energy.

[00:02:28]And yeah just a few things happen to be around it.

[00:02:34]um this can decay in many cases into a neutron and a posetron sorry plus um once again this is something that we can only really see from experiment and a lot of these things will be so I'm just not going to keep saying that um so a proton can decay if um yeah it can if it's got a lot of energy Um but if it doesn't have much energy then the probability of decay uh is well we believe it to be about zero uh for the decay of proton. Um and here's another interesting thing when you're considering the um what's it called?

[00:03:28]the decay of a uh t I think it's typically done with a neutron to proton and just a regular electron that's a p um there is a specific curve that is followed and can't quite remember the specific details about it but if I remember rightly there is a specific hard cutff point for the kinetic energy and the number of samples that we take. So if we take let's say 10 billion samples of sorry 10 billion events they're called uh and an event is just something that we observe in a collider uh or just in an experiment we can do I don't know uh do a a test to measure gravity a drop test and each time you drop it you get a new measurement for gravity And you'll probably come across some sort of distribution.

[00:04:41]And if you keep doing the distribution, you'll have sorry each of those things is an event. Each of those measurements you take is an event or set of measurements should I say. So here neutron goes to proton electron. And I can't remember what it is, but there's something about this number of events against kinetic energy graph which denotes the fact that there must be a third extra particle here.

[00:05:14]Um, and we ended up just calling that the nutrino.

[00:05:19]And after a lot more experiments, we discovered that there were more than just the electron and the electron neutrino. There's two more. of is the muon uh and the towel nutrina.

[00:05:34]Um sorry, the muon and the muon nutrino and the tow nutrino. Uh these two are significantly heavier which is why we see them less. Heavier things decay faster. I'll I'll get into that more a little bit later on. Um, I'm not too sure if I can explain the reasoning without a lot of maths and I do want to try and veer away from the the maths here because that just means it takes a lot longer. But yeah, I think in terms of this graph, it's because there is a cut off at some point. Um, which implies that there must be a third particle and then we just gave the third particle a name. Later on, we did a lot more experiments and we saw it coming up in different other pl other different places and we just called it the the nutrino.

[00:06:25]So up to now uh I can I think I can remove this now. Uh it's not particularly necessary. Um if we draw a part sorry if we draw a graph or a table should I say of the particles we have observed from these uh experiments up to now we have seen that there is an electron a new one and a sometimes it's called a tow but I'm pretty sure that's just blatantly incorrect and it is just called a towel. But I mean it doesn't particularly matter. Everyone understands you anyway.

[00:07:09]Um and then you yeah you've got the tow nutrino uh the nutrino and the electron neutrino.

[00:07:20]Um, I know there was a a guy in the I think it was the late 30s, I think it was about 1938 called Paul Dank who um he was messing about with an equation called the Klein Gordon equation which is a second order partial differential equation in both time and in space and he wanted to make that first order in both time and space.

[00:07:49]So he he did a lot of messing around and came up with a few things. Not I say came up with he I I would say discovered a few things. He discovered the Iraq matrices which link very much to spin. I'm sure many of you have heard of spin if not all of you.

[00:08:14]You know what? I'll try and explain that at some point here. Um, but I'll I'd like to get this down first.

[00:08:21]Yeah. Uh, he discovered that you could get an equation down in first order in space and time. Oh, why is my phone doing this? I don't like that.

[00:08:36]Uh, yeah. See why it's doing that? Sec.

[00:08:41]Yeah. partial slash minus n * s = z.

[00:08:48]This partial slash is interesting. It's basically a specific um the I mentioned the the gamma matric sorry the dat mat matrices earlier. Um am I getting them mixed up? No no power matrices are different. Yeah. So uh you've got uh gamma gamma not uh gamma 1 gamma 2 and gamma 3. Uh these are the uh a set of matrices for a clifford algebra. I can't remember what the name of it is but um satisfies this um and there's another one um oh yeah is the product over I of the gamma matrices equals oh this is tough. I can't remember what this equals. It might be the identity matrix.

[00:10:05]Um, so yeah, I think it's these two conditions.

[00:10:11]Um, and they form uh I believe it's the lead group of a specific group and it has something to do with spin. Yeah, I I didn't want to get into the maths too much of this. Um but yeah, he managed to make it first order in space and time.

[00:10:28]It's an x and a t. Just imagine a y and a z component as well.

[00:10:33]Um this partial slash here is the dotproduct between the first a vector of the first derivatives or um sorry the yeah it's a negative actually to do special relativity for that. Um yeah this partial slash is just this dot product here.

[00:10:56]Um, so this equation is now first order in space and time.

[00:11:02]And this is called the direct equation.

[00:11:04]I actually have a shirt for it. I think I might have worn it on my uh in one of my talks, but I'm not too sure. Um, and without going too much into detail, this predicts um negative probability densities. That might be the client Gordon. I'm not can never remember the difference between this. Sorry, which way round it is between the two? But basically this equation predicts uh yeah negative probability densities which doesn't particularly make sense.

[00:11:38]You can't have a negative 4% chance of a particle in a region. How will we make sense of that?

[00:11:46]So the way we make sense of it is by rean uh reanalogizing reanalogizing and saying that these aren't really uh negative probabilities for particles.

[00:12:04]These are new antiparticles. They're like the negative counterparts.

[00:12:12]So if if you go through the maths, you'll find that the charges are flipped. The when we get to quarks in a minute, the baron numbers are flipped and the spin. No, not spin.

[00:12:28]Um uh basically just a lot of different Oh, the um what's it called?

[00:12:36]The color is flipped for whites.

[00:12:41]Uh, so yeah. And now this is where the notation gets annoying. For these you've got the pluses and then for these you've got bars.

[00:12:53]I don't know why it's different. Um, when we get to the quarks they also have bars and when we get to the baronss they also have bars. No they don't. Sorry.

[00:13:04]Cuz barons um only one of them has an antiparticle and it's it's weird.

[00:13:10]So up to now I've kind of explained the these are called the lepttons.

[00:13:21]Yeah. Technically there is an interesting thing you can have with a hydrogen atom. Sorry. A sort of hydrogen atom which is um just a pro a regular proton and then either a muon or a towel. Let's go to the exotic.

[00:13:43]But the weird thing about this is first off towel has because it's incredibly massive. It has a very very short lifespan.

[00:13:56]Um and the electron because it's the smallest of these uh upper three laptops has the longest lifespan.

[00:14:06]Um in a sense this is why I was explaining earlier in a sense it is kind of like the proton with a massive uh decay um decay time.

[00:14:21]In fact, I believe we have put the protons decay period. Oh my days, I keep knocking the table. Uh I think we've put that around 800 years. It might be 800,000 years.

[00:14:37]But either way, the the decay period is insanely long. And I can't remember the one for a neutron. It might be like eight minutes or something and then everything else from there uh drops rapidly. Um like the third is like a few seconds to my knowledge.

[00:14:56]Um but yeah, and then the proton has hundreds of years at the very least to what I remember.

[00:15:02]>> Sorry, what are you measuring in? What?

[00:15:04]What? Like um you're saying a proton will decay like the halfife is a 800,000 years?

[00:15:11]>> Half life. Sorry, I was uh I forgot to say that.

[00:15:14]>> What does it decay into?

[00:15:17]>> What does it decay into? Was that >> Yeah. What does it What does a proton decay into?

[00:15:22]>> Um well, that's the thing. Technically, it doesn't decay. That's Well, that that's the thing. We have never measured it to decay before. So, because we have never measured it in a stable state to decay before. So >> wait, but if it if its half life is eight once every is 800,000 years, then like protons are decaying like all the time, right? That's pretty frequent for like a sufficiently large mass, right?

[00:15:50]>> Weird. Yeah. The weird thing is basically um the protons in for example an atom like this atom here it won't decay like sorry if we had to just a proton out on its own in the universe we predict that it won't decay because it's the most stable uh it's the most stable trio of quarks there Um, wait. Yeah. Well, it's the most stable barriion, should I say?

[00:16:24]>> Sorry. We predict it won't decay, but we also have a halfife for it. I'm I'm very confused.

[00:16:30]>> Yeah, the halflife is like uh how can I put this?

[00:16:37]It's like it it it's our current lower bound if that makes sense. It's us saying that like if it decays, we predict with high probability that the halflife is significantly greater than this. Does that make sense?

[00:16:54]>> Um, >> okay. So, it's do we even know that it decays? Like, is there evidence that we have in favor of it decaying?

[00:17:06]>> There is no evidence to my knowledge. Um there are uh sets of theories some of them um for example grand unifying theories GUS you might have heard of them um their purpose is to bring all of physics together um particularly particle physics but many of them to my knowledge maybe all of them bring relativity with that um but that Yeah, their purpose is to bring all of particle physics together. And some of those predict that like some of those theories say, well, maybe the proton doesn't decay at all. Some of them, some other ones say, well, the proton might decay, but it's halflife will be massive.

[00:18:02]Because in those cases, to my knowledge, I'm not I'm not this deep into physics yet. Um, but the grand unifying theories, the ones with massive half- livives must predict a more stable baron than the proton. Um, because the universe is always trying to get into its lowest energy state and the proton happens to have that lowest energy. So, it doesn't want to go any lower. Does that make sense?

[00:18:34]But we have no evidence at the moment to say that it will um it will go lower. Uh that the proton does decay.

[00:18:45]I I can't think of anything off the top of my head.

[00:18:49]>> Okay. So, this is just like a domain of pure speculation and nobody really knows what's going on.

[00:18:54]>> Yeah. Yeah. Um well, I wouldn't say it's pure speculation, but it is there there is decent amount of speculation. We don't know whether or not it does even have a halfife. So yeah, it's speculation in that regard. But the the bound that I gave was to say we have a we have enough evidence in or lack of evidence I guess to say that the proton has a halflife to where we can say that if it does have a halflife it must be this long.

[00:19:33]Um, >> I can imagine it would must like must it be like a lot more than that? Like I feel like if it was >> 800,000 years like we would >> I'm looking on Wikipedia and they say that the current experimental lower bound is 10 on the order of 10 to the 34 years.

[00:19:49]>> Yeah, that sounds more like what I would expect.

[00:19:52]>> I was way off work. I I must be working with um with something that my recent physics teacher has told me. Um cuz I I think I think the the number he gave was 800 years or something. But I Yeah, that was a mis misquote by me. My bad. Um yeah, it was yeah something 10^ the 34 years was massive huge bound because we have never seen it decay before. We have no evidence that it does. Uh, Suji, does that say does it give um a significance figure or does it just give the upper bound of the lower bound?

[00:20:30]>> It says 2.4* 10^ the 34.

[00:20:34]>> Okay, >> link to the Wikipedia page in the chat if you want to look at it.

[00:20:38]>> No worries. Thanks. But yeah, um I'll I might check it out afterwards, but I wouldn't quote me on that.

[00:20:45]>> I did have a question about that drawing you just erased, but >> Oh, sure. Go for it. Go for it. Was it the >> It was the You were showing the tow orbiting the proton, >> but the mass of the tow is almost twice as much as that of the protons. Would it be more like the other way or kind of like a somewhat binary?

[00:21:02]>> Um, I mean, yeah, I guess so. I guess I guess it would be a sort of binary. Um, >> so so you're implying this actually happens to like towel particles.

[00:21:11]>> No, I'm implying this actually happens.

[00:21:13]No, I'm saying that this could happen in theory.

[00:21:17]>> Okay.

[00:21:18]What does in theory mean philosophically?

[00:21:22]>> We we've never observed this, but >> someone on paper somewhere has come up with a model in which this is plausible.

[00:21:29]>> Maybe I I don't even know. I don't even know. This is um I I don't have any numbers for this. But I can imagine that if this were to form, even for the tiniest amount of time, it would really be the tiniest amount of time that it would last because the towel halfife is absolutely microscopic.

[00:21:50]And I really can't imagine that this even I think this would be shorter than the tow halfife itself, the halfife of this. But once again, please don't quote me. Um Oh, this should be minus. I got close up there. Oops.

[00:22:04]Um yeah, but yeah, this could in theory happen because like um how do I word this?

[00:22:19]Um actually, I can't I can't really think of a a specific reason as to why this would happen.

[00:22:28]To my knowledge, it could. Maybe there's someone out there disproving that, but to my knowledge, this is technically feasible. And same with new one, of course. Um, does anyone have any more questions? Cuz I think we could get on to the quarks, shall we?

[00:22:50]I'm going to take that as a no. All right, then.

[00:22:53]Um, so, uh, I'm going to rub this out. And it's going to be assumed now that for every particle in here, there will be a corresponding antiarticle in some antiarticle table.

[00:23:09]Um, all right.

[00:23:13]I forgot to set a timer, but that's okay. Uh, right. So, the proton exists, right? and so does the neutron. Um, I can't actually remember the reason that we decided to Oh, okay. So, there was a question um around the time that we discovered the protons and neutrons. Um, sorry, I've got hiccups.

[00:23:48]Why are these two attracted to each other? the neutron like at this scale with these masses. I believe we had estimates for masses around the time of this question, but at this scale with these masses, gravity should be minuscule. It should be completely negligible.

[00:24:06]Um, and if this is a neutral particle with zero charge, what on earth is keeping these two particles together?

[00:24:16]because first off, the force must be quite strong to be able to hold two absolutely tiny mass particles together.

[00:24:26]Um, yeah, inside an electron cloud.

[00:24:31]So, what is it? What what's going on here?

[00:24:36]There must be another thing going on.

[00:24:38]Um, well, there must be another property of the particles that we're missing.

[00:24:43]and the the property was the strong force. There's a there's a color charge.

[00:24:50]Um getting to the point of being able to say this uh would require a lot more time and probably quite a bit of data to back it up. But basically the most in brilliant physicists of the I want to say 40s were able to discern that in the proton and neutron there were three particles and they were incredibly incredibly creative with these names. One of them had a positive charge, one of them had a negative charge.

[00:25:28]So they called them the up and the down.

[00:25:31]incred, as I say, incredibly creative.

[00:25:34]Um, they really, it doesn't get much more genius than this.

[00:25:39]Um, so yeah, and and the the force between these they called the strong force because it was very strong. Once again, incredibly creative.

[00:25:53]Um and that actually this will require a little bit of um a little bit more to be able to go further than this.

[00:26:07]So by this point physicists had discovered that the photon gamma um photon was uh a sort of transmitter of the electromagnetic force you know I mean maybe you've seen the diagram this is going to be very poor but then you've got like the Um, I think it's a little bit out of phase.

[00:26:40]Then you've got the Yeah, I really didn't draw that too well. These two are perpendicular to each other. This is the direction of travel. Um, I'm sure you can essentially imagine it.

[00:26:55]But yeah, the um whenever you moved um an electric charge through space, you would get this the the photon, the wiggles, should I say. Um, and they decided to essenti I don't want to say analogize, but they decided to look into it a little bit more and then discern that this must be the trans like the the thing that transmits force um between uh any two charged particles.

[00:27:36]And yeah, that is of course the case.

[00:27:39]That's relatively common knowledge. I wouldn't say household knowledge, but yeah. Um, I'm actually going to I don't like the wonkiness of this.

[00:27:50]So, the the question here is then given that we have another force beyond the electromagnetic force, we now have the strong force, right?

[00:28:03]Is there a mediator for that? Well, it kind of glues these together. So, let's call it the glue on given that we call this the photon.

[00:28:13]Uh there's probably a more scientific reason for calling it the glue on. Um might be something to do with Greek. I have no idea. But they decided to call it the glue one. Um and once again through more 3D magic they were able to discern that there are three color charges and a proton and a neutron individually are color neutral.

[00:28:37]basically meaning that if you um if you take the sorry actually I I should I should specify here color is not the same as color with light like if I were to say yellow here that's not close to the same as saying uh what is it 450 nmter light um it might be different to that, but that was just a guess. Um, that's different.

[00:29:13]Color is an analogy because you think you've got red, blue, and green, right?

[00:29:18]Uh, those tend to be the the three colors that make up the color wheel when you're doing um graphics design or whatever it may be. I'm not too familiar with uh color beyond that.

[00:29:34]This is more just there are three charges and they happen to follow a specific set of rules which can be analogized to color. This is actually an analogy.

[00:29:50]Does that make sense? Does anyone have questions about that?

[00:29:56]Is there like a set of all colors or like >> um there isn't? Well, but in a sense, yeah, there is um but there's more uh yeah, I don't really know how to describe it, but um there's a group SU3 um which acts on the um what I can't remember the name. the the color probability like the color wave function for each of these every every single um quantum value being color uh electric charge uh mass whatever it's all the wave function so the polar wave function let's call it s is acted on by an element in the group su3 three which is spe the group of special unitary matrices uh in >> is wait so is S a matrix >> uh size is a vector >> okay >> yeah S um S is a vector it's a in general it's a complex vector um yeah it's a complex vector with three components in it and together as a group these three components represent the color of the given quark.

[00:31:37]Um and SU3 tells you how to transform between those colors and it sorry an element of SU3 tells you how to trans and it can sorry and it transforms uh sorry oh my days I'm really kind of blanking a bit here. Um but it it can describe the interaction between two color charges um through this.

[00:32:16]Um you'll you might recognize this this for some given quark.

[00:32:27]Uh oh no no no uh this is just the uh trans pose I think I don't think it's the mission but if anyone knows correct me if I'm wrong uh it just does that I don't think there's any no I I want I want to say this also gives the complex conjugate so I don't know that the start um so yeah it gives the complex conjugate And then the transpose of s that's what sibar is.

[00:33:02]Um there are a few properties about cybar. Um sibar yeah it must be the trachondria because cy gives the magnitude of s. Um anyway if you recognize this this is the dra equation mentioned earlier.

[00:33:24]Um and basically well sorry this part here is the direct equation mentioned earlier. Uh but this for a given quark is the contribution that that quark makes to the color field.

[00:33:40]Um does that make sense as it is?

[00:33:50]Um, oh, I haven't really explained field. I haven't explained a field yet, have I? Actually, um, because it's not I don't think it's the same as a mathematical field, but I don't know anything about mathematical fields really. Um, yeah. Okay. So a field in the physics sense um let's consider a one-dimensional field only in space and magnitude. So let's call this the x and let's call let's not really give this an axis an axis label. Um yeah let's consider two particles in this field.

[00:34:39]Let's say one's here and one's here.

[00:34:43]Oh, you can't see that on the thing, can you from that? Ah, it's a little bit off. There we go. That'll do.

[00:34:53]Yeah. Let's say one's there and one's there.

[00:34:56]Um, and let's say that when there is a particle in this vicinity, the graph of let's call it let's call it the mass. Let's say the graph of mass looks like this.

[00:35:14]So, we could say this as maybe a ball.

[00:35:18]Uh, and we're looking in the x direction.

[00:35:21]Um, let's say the ball here on the right is wider, so it looks like this.

[00:35:31]And then the ball here on the left is a bit slimmer, so it looks like this.

[00:35:38]Um what you do when there's this overlap is you'll just add them together uh nice and simply. So it sort of comes out a bit like this. And you can rub this off.

[00:35:51]So this would sort of be the mass field in the x direction of two balls that we have. Uh I don't have any balls here on me. But if if I would pretend with my hands, uh this is the x direction. We'll have a ball here and then maybe this is in front and there's a ball behind. So we're measuring as we go along in each width delta x, how much of the how much of the mass of each ball in total is in that width delta x.

[00:36:29]Um and then we take the limit as delta approaches zero.

[00:36:34]And that's roughly what a field is.

[00:36:38]This should technically be mass density.

[00:36:42]This isn't mass. This is uh mass per meter cubed. Uh so this will be kilogram.

[00:36:51]Does that make sense?

[00:36:56]Okay.

[00:36:58]I'm going to take that as a general maybe.

[00:37:02]>> Makes sense. Not too sure. Go.

[00:37:11]All right.

[00:37:14]Um so yeah, that that's what that's what a field in physics roughly is.

[00:37:21]It um it'll tell you the density of some quantity in a given area.

[00:37:31]Um all right so this is the contribution of quark to the field.

[00:37:40]Um technically these both of these should be should have an x attached to them. Um and this x here actually contains time x y and z. It's more of a vector.

[00:37:57]Um, usually that's written as bold.

[00:38:01]I tend to denote it like this.

[00:38:06]Um, but yeah. Okay.

[00:38:09]SU3 is the group for which when you um if you take some SI and you act on SI by some matrix you get the same output for this no matter what.

[00:38:32]Um and you can kind of see that in the definition of an SU3 matrix. you have um yeah so for some matrix U u dagger u is the identity um U dagger meaning the transpose like this but for a matrix uh and then uh the conjugate don't ask me why it's denoted differently please um but yeah in general if you do this transformation onto some s any matrix in SU3 and to my knowledge in only a matrix in SU3 will do this um you get the same value out here which is why it's um it somewhat explains the uh transform sorry not explains but somewhat Yeah, it transforms between general uh color matrices.

[00:39:47]Well, that was a really poor explanation from me. Uh, and I apologize, but yeah, that's the that's like borderline uh quantum field theory, which I will admit is not my strongest suit. I'm only just getting into actually studying that, even though I've been meaning to for the last year or so.

[00:40:14]So, we we now have two quarks.

[00:40:18]um we have an up quark and a down quark.

[00:40:23]Now question is given that we have an electron, a muon and a towel, sorry.

[00:40:31]Do we have three as we call them generations of quarks? God, I almost fell over. Um cuz here this is generation one. These uh lepttons are generation two and these uh tows a generation I think it's right to call these two as a collective towels wouldn't really make sense there.

[00:40:55]Um >> I mean you are just taking for granted that like the up and down quirk go in generation one, right? Is there some like >> underlying reason why we should assume there's an association between the up and down quirk and the electron and electron neutrino?

[00:41:09]>> Yeah, I I think there is I think there is that's a that's a really good question. Um so basically you remember how I said earlier that proton is the most stable um well I can't remember the word oh my days the most stable barriion um it it sorry I should put an equal sign there the proton this is not standard notation but you understand what I mean so I don't care the proton is made up of one up, one up and one down, right? And it is the lightest stable uh baron that exists.

[00:41:56]And that in a way sort of meshes with the fact that the electron is the lightest known lepton exists.

[00:42:05]And if there were to be let's say in this sorry in in this box just up here uh another clock let's call it I don't know uh up down top that's this one here for let's just call this one top for now. Um let let's say there was another a quark which was lighter than the heaviest one of these two which happens to be down quark.

[00:42:34]Then the proton wouldn't be the most stable and we wouldn't see it everywhere in nature. Instead we would see maybe up up top. Does that make sense?

[00:42:48]Um, I don't know if I understand why you're supposing that like lightness implies stability. It seems like you're making that equivalence, right? Or um, >> uh, yeah, I am that equivalence.

[00:43:00]I don't know how to explain if I'm being completely honest.

[00:43:07]>> Um, you could maybe make a connection with the fact that the lowest energy state is generally the most stable.

[00:43:12]That's a kind of a general fact in physics.

[00:43:15]>> Yeah. Yeah, I did actually say that earlier, didn't I? I completely forgot about that. Thanks. Um, yeah, but yeah, as a perfectly as Suji said, the lowest energy state in physics is typically the most stable and mass energy equivalent E= MC² as everyone knows it. Um, would mean would imply that the lowest energy is the most stable state.

[00:43:41]um that can be actually explained. I I say explained um but at the end of the day all of science is just an educated guess. Um but that can be understood through thing called the langium.

[00:43:59]Um this is going to be a slight detour.

[00:44:02]I'm really going to try not to go into too much detail there, but I know I am going to anyway. So, we got the thing called the action, which is that's a terrible integral. Oh my days. Um, d for x. This I'm really I'm going to redraw that integral. Don't like that.

[00:44:22]Um, this s is called the action. That works. The L is called the langium and dx just means integrate across t, x, y, and z.

[00:44:37]um without special relativity because that'll be uh accounted for in the lranian. Um the lranian itself L is equal to typically denoted as T minus V the kinetic energy minus the potential energy. Um and in the case of just a general lone quark, if you consider the potential energy, that will always be zero. The potential energy of the surroundings will roughly always be the same. So the only real variable here is the mass. And we want to minimize the action. We sorry we want to minimize the action uh which is denoted by a delta like this. So a very poor delta for me. That's better. That's how it should be drawn. Um so if we write a little subset symbol here. So uh this should really go outside for if we're being proper here. Um it's kind of like this. So if you were to consider the field graph again for the mass density which is actually denoted as row uh along some x-axis you would want to consider the var uh yeah this is variational calculus that you would want to consider the variance of v which is roughly proportional to uh the mass density here. You would want to consider it uh and minimize it in a way so that let's say this is what it looks like for a proton. That's borderline off the thingy. Let me pull a little closer.

[00:46:36]Actually, I could do that. There we go.

[00:46:41]because the integral of this area here gives you the total mass um for any higher mass barriion. A barriion by the way is just a system of three quarks. Um for any higher mass barriion it would look more like this.

[00:47:04]So the so this overall as you integrate over force space you get a higher value which means that we are not minimizing the action and therefore there is something we can do to minimize it further and in this case it would be to decay this particle down into a smaller one.

[00:47:27]Does that make sense?

[00:47:32]>> Makes sense to me.

[00:47:34]All right, I'm going to assume everyone else understood it then, unless anyone has any questions.

[00:47:43]But yeah, that's um probably the best I can do for a quick detour.

[00:47:51]Um and you can actually also use uh the lrangeian as I just showed you there to derive f= ma which shows that it is consistent with our previously known theories. Um all right so then there is yeah there's quite a bit more we can talk about here.

[00:48:13]So yeah, let's assume that there is a particle which mediates the force between these three.

[00:48:23]Um, and we are going to need in this case, God, I got hiccups again.

[00:48:30]We are going to need in this case for each of these three particles to have its own respective color charge.

[00:48:41]So, I'm going to label them arbitrarily, red, green, and blue. Uh, you can actually label these any way round and it will be exactly the same. Uh, S3. Let's go. That's not a three. That's a three. Um, yeah. So given that we want the net polar charge of the uh of the pro proton here to be zero.

[00:49:14]What we would want is for the color charges of the mediating particles to also net to zero.

[00:49:28]Um so first off this is a rather important fact. Red plus green plus blue equals zero.

[00:49:39]>> And remind me these are elements of uh su3.

[00:49:44]>> These are on by elements of su3 but these in general are vectors.

[00:49:49]>> Okay.

[00:49:51]Of what dimension?

[00:49:53]>> Three.

[00:49:54]>> Okay. Uh >> do we know the values of them? Like are we okay? Sweet.

[00:50:00]>> Uh well we kind of uh we set them by convention.

[00:50:04]>> Right. Right. Right. Gotcha.

[00:50:06]>> Uh I think this is one way you can write it. But I can imagine there are actually infinitely many ways you can write it.

[00:50:16]Um as long as you act on these three with the same vector in SU3, you'll always get zero. since I made uh a general matrix with yeah finite determinant zero push it to zero. Um yeah that looks right to me.

[00:50:34]So yeah that's um that's one property of these and that's the main main one that we need. The other one is that uh anti- red plus anti- green plus anti- blue equals zero. And uh let's use red as our example.

[00:51:00]Red plus anti- red also equals zero. Uh you can actually just rearrange this here to say that red is equal to the negative of anti- red. So here you'll just put negative and positive instead.

[00:51:14]Um, this also presupposes the existence of an anti- red, but that will make sense in a second.

[00:51:24]So the weird thing about these is how do these actually attract each other?

[00:51:32]Because in what sense does it make sense to say that blue attracts green and green attracts red, but red repels blue?

[00:51:40]It just it doesn't really make a lot of sense. So what we do is we say that the the gluons between them have a pair of color charges.

[00:51:54]Um yeah, sorry. I just want to make sure that I'm not messing anything up here. I don't think I am.

[00:52:07]All right. So, um yeah, we'll have this one here. We want it to attack uh attract the blue charge and we also want it to attack the I think this should be anti- green. I I feel like I'm doing something wrong, but it might also just be the fact that the diagram is uh misleading in of itself. But we'll have in general for some chat for some quarks, we'll have uh a blue anti green, a red, an anti- red green or green anti- red as it's usually written. Uh that was Oh, wrong way around. Sorry. uh red anti- green and a blue anti- red for uh some quarks.

[00:53:04]Uh either this or their inver inverses.

[00:53:07]So uh yeah, blue anti- green, red anti-blue, green anti- red.

[00:53:16]And then as you can see, if you add all these up, they sum to zero. Um, I mean, you can actually kind of see that in the fact that you've got green, blue, red, and red, anti- green, anti-blue. Both of these sum to zero. Or you can see them via this. The reds cancel, the greens cancel, and so the blues.

[00:53:41]Um, yeah. So, in general, that makes sense.

[00:53:47]So, we have a glue on. The question now is how many gluons do we have?

[00:53:55]Uh this question uh oh I just bit my cheek the other day and it really hurts stuff. Um so the question is how many glueons do we actually have? Because I mean I've just demonstrated that this at least six, right? But um I mean this on its own won't really seem like a coherent thing to just impose.

[00:54:30]But deriving it requires more skill than I have. So I'm just going to say this.

[00:54:37]If you take the lead group of SU3 with uh cell su3, it has a magnitude of eight.

[00:54:52]There are and and this means that there are eight gluons.

[00:54:58]The other two gluons, if I'm remembering correctly, are Yes, I know. One over <unk>2 seems like it's coming out nowhere. Uh, red anti- red plus green anti- green.

[00:55:16]I think that's right.

[00:55:18]Um, I mean, in general, I guess you can shift it around uh and it won't particularly make a difference. So, you've just got to pick the right pair of these two final blue ones. Uh, and the other one is one over<unk> six.

[00:55:39]Um, I think I think it's red uh red anti- red plus green anti- green minus two blue anti- blue.

[00:55:55]very very strange. I'm aware. I don't fully understand it myself, but I know that this is true. And there are a clue on.

[00:56:03]Um maybe someone can provide an insight into why this is, but I personally cannot.

[00:56:15]>> So like you're saying there's eight different types of gluons. Do they each have like different names or >> they don't have they don't have different names? No. Um to my knowledge they are um they are represented by the galman matrices um which are just lambda sub i where i ranges from 1 to 8 um and these are by definition the matrices in the lee algebra of su3.

[00:56:55]But beyond that, I I can't really say a whole. Um, yeah. I mean, I think you just call them like if if you want to write them down individually, you'll define what you want your G1, G2, G3, and whatever to be. Um, but I don't really think they ever come up in equations as like the Galman matrices on their own.

[00:57:21]Uh, so you never really have to.

[00:57:25]Um, yeah.

[00:57:29]Does that make sense? Does that answer your question? I'm not uh I think I might have >> Yeah, I think so.

[00:57:34]>> I I think so. Um, I just asked if they had names and I guess the answer is no, except you can enumerate them. Um, >> oh yeah, that was >> say again those two values on the screen are are what exactly? like those are just two of the gluons or those are the final glue on.

[00:57:50]>> Um in general with every other glue on it you'll have some color one and then some antique color too.

[00:58:00]>> So we say that a gluon has a color, right? This isn't the glueon itself.

[00:58:04]This is the color of the gluon.

[00:58:07]>> Uh this is the color charge.

[00:58:13]This is the anal uh the analogy kind of thing. Um how do I actually explain this? So you remember the the three vectors I gave you earlier which were representing the different colors, right?

[00:58:29]>> Um >> yeah, >> I think I gave you like one zero negative one and so on.

[00:58:36]Um, basically a glue one has um like a pair of these colors. So it'll have red and anti-blue and you just if if I put anti-blue in front there, this will just sum up their matrices. I don't know what it would be. Maybe like this this this.

[00:58:58]So you get what? Two1.

[00:59:01]And that's this is the actual color puller.

[00:59:07]This is the charge the color charge of that blue one. This is just what we call the color charge because it's easier to write things in something that we understand rather than just abstract vectors everywhere.

[00:59:22]>> Wait, so you're saying you're saying that the is the plus operator here and like the multiplication operator like the same operator?

[00:59:29]>> Yeah. Yeah. Yeah. Okay, I didn't realize that.

[00:59:34]>> Once again, once again, really do not quote me on this, but I'm pretty sure this is how it works. Um, as I say, this is this is getting into quantum field theory again, which is once again not my uh expertise.

[00:59:50]Um so yeah the these two as written may be wrong but they are close to what I can think of as sorry as the final two galman matrices the final two gluons since um as I imposed earlier kind of arbitrarily there must be eight gluons um and then these happen to be the missing two you can show that through the gal man matrix.

[01:00:21]Um, also I realized I was wrong just then. My bad. I've been lying to you.

[01:00:27]Um, the matrices, uh, the vectors I just showed there, they aren't the colors.

[01:00:33]These are the colors.

[01:00:37]>> Um, are are color charge and color synonymous? You've been saying both of those terms.

[01:00:45]>> Color charge and color are roughly synonymous. Yeah.

[01:00:49]Um color is like I guess it's just a specific set of values of the color charge but the color charge is like everything. So like color would be red blue green anti- red anti- blue anti- green but then color charge would be like red anti- green or just red if that makes sense. Does that makes does that make sense?

[01:01:10]>> What is their type? The type of of color is a vector of length three. And the type of color charge is also a length three vector.

[01:01:23]>> Um yeah, I I do think so. But >> okay.

[01:01:27]>> Yeah. Uh yes, I think I'm right. I'm I'm going to I'm going to stop there though because I I'm I'm getting way out of my depth. Well, I'm Yeah.

[01:01:41]Um right. So there are three colors red, blue and green and they make up quarks and through test not tests sorry through um experiment uh after test after you know um I think the first was found in a thing called the synatron and I'm not going to get into how that works but the next lightest particle here is the strange quark.

[01:02:11]Now the strange quark uh was measured uh you may have heard of a quantity called strangeness.

[01:02:22]It it represents absolutely nothing. It just tells you how many strange quarks there are in some given um some given math. Uh not mass sorry barriion. And it's called a strange quark because when we were measuring these baronss, they had a they had strange values for their mass which were a bit larger than the regular values. Um, and I do believe this, uh, the strange crack is what allowed us to discern that that the proton and the neutron weren't the fundamental particles and that there was something more fundamental being the quarks.

[01:03:07]Um, because, you know, we could see that there was a particle P and it had a mass of, let's say, one unit and there was a particle Q and it had a mass of two. But every other value of P and Q was the same.

[01:03:25]So we um assigned uh a strangeness value of one or negative one depending on um whether or not I was a particle or antiparticle um to say this particle is strange and this one isn't. So yeah, strangeness exists as a quantity.

[01:03:50]But it's about as relevant as saying is particle. It it doesn't particularly mean anything beyond the particle. So there there is something weird about this barriion. Um yeah. Does that make sense?

[01:04:13]>> Yep.

[01:04:14]>> Yeah. I was going to say I'll take that as a Yep. All right then. Um and then after plenty plenty more experiment we discovered that there was uh equivalency of the top quark and then this fueled further the idea that there was indeed a third generation and we discovered the top and the bottom quarks.

[01:04:36]Um, so up, down, uh, up, down, strange, charm, top, bottom.

[01:04:46]Um, these used to be called, I can't remember what top used to be called, but the bottom charm used to be called the be the bottom quack used to be called the beauty quack.

[01:04:58]Um, yeah. Uh, now that I've gotten most of this down, I'm going to go for these two, final two. Um, well, there's also one more harder box for that now because I think this appropriate timing.

[01:05:19]Um, also the electron was discovered long this here was even relatively theorized.

[01:05:29]Um, all right. So these two particles here are the uh I'm going to give them a name already. W plus or minus and zed.

[01:05:40]Uh sometimes it's got uh uh zero up at the top z. That's just to denote the fact that it has no charge. Um w plus or minus in the same sense that the electron has a plus or minus.

[01:05:56]Um but we need to denote both here because um there is not really a way to say that one is the antiparticle of the other.

[01:06:09]It's just they both exist.

[01:06:12]Uh I think that should hopefully make a little bit more sense in a little bit.

[01:06:17]So the here here's a question. If the proton sorry uh I'm going to try to avoid the question from the proton decay. If the neutron can turn into a proton and an electron I'm going to ignore the nutrino for a moment.

[01:06:38]How can this just happen?

[01:06:40]What what there must be some sort of force which is pushing this to happen. There must be well like you can't just say that something in existence happens without something making it happen if that makes sense. Um I guess contingency you could say. Um I've been drawing on the wall. Whoops.

[01:07:05]Um so yeah something must be making this happen. There must be another force mediating this interaction.

[01:07:17]Um I will actually begin drawing Fineman diagrams now. Um I think a little bit after the discovery of these qu uh Ozans sorry um Fineman began drawing his very famous diagrams and they are really good. So this is going to be the time axis uh sorry the space axis and this is going to be the time axis. This just tells you the position of something.

[01:07:44]This tells you how long it's been.

[01:07:48]Now, uh, ignore the fact that I've drawn this weirdly, uh, just kind of space.

[01:07:55]You're going to have to ignore the specifics.

[01:08:00]Don't think of these as having like being actual axes with one, two, 3 nometers, 1, two, 3 seconds. Don't think of it like that. Think of it as just a rough guide.

[01:08:14]So let's say I have particle. Let's say it's a a proton and it's moving and there's another proton here.

[01:08:26]I want to now draw a diagram to show that when these get near each other, they deflect because that's what happens, right? Uh because they've got the same charge, they will begin to repel each other. Um so how can I show now that this is going to happen?

[01:08:50]So okay I'll start by denoting the first proton and the second proton with arrows representing the direction they're traveling in. Funky arrow but it's fine.

[01:09:03]And now we know that there must be a force, sorry, a photon mediating this interaction.

[01:09:11]So it's going to go up like this and it's going to have to uh interact with this proton pushing it that way, right?

[01:09:21]And we also know that momentum must be conserved and this photon has momentum.

[01:09:29]So, as this proton emits this photon, it gets a little kick to the left, pushing it up this way.

[01:09:43]Very standard uh diagram, I feel.

[01:09:48]Um, but this may be your first time seeing it or any variation of it. Does this make sense to everyone? Do we have any questions?

[01:10:01]I should also put a gamma here to say that this is a photon and an arrow to show its direction. The arrow is not in the right place, but it doesn't matter.

[01:10:12]I'm going to take that with no questions.

[01:10:15]Now I'm going to rub out this little proton diagram and I'm going to draw another one to show that this neutron is turning into a proton, an electron, and an antiutrino.

[01:10:38]Uh yes, it turns into an antiutrino.

[01:10:41]um that gets into conserved quantities.

[01:10:43]I might get into those a little bit later. So this is a neutron and it's moving and then suddenly bursts off into a proton and another particle.

[01:10:59]But there must be but this particle here must be mediating this force because as we established earlier there is a force which is causing this to happen.

[01:11:13]Now as in the uh proton photon example I gave I'm just going to draw that.

[01:11:25]This can just come out of a particle. It doesn't have to come into the particle.

[01:11:30]It can exit the particle um at at what is called a vertex.

[01:11:37]Um so yeah, this might look a little strange, but it can do this.

[01:11:44]Let's call this particle here W. And we know that it has some charge which must be negative due to charge conservation, right?

[01:11:57]So now this here goes into electron and an anti-electron neutrino.

[01:12:06]Uh this is yes I am just going to assert this for now. Uh I probably will the whole time. Um but this is generally what a neutron to proton electron antiutrino diagram looks like.

[01:12:23]um maybe draw on a bit differently, but this is it.

[01:12:28]Does anyone have any questions about this yet?

[01:12:36]All right.

[01:12:38]Um also, you can just shout out some questions. I don't particularly mind.

[01:12:44]So, this equation in of itself isn't incorrect. I would say it's misinformed.

[01:12:52]If you were to write this out more properly, more fully, not necessarily more properly, more fully is definitely the right uh term for that, you would say neutron goes to proton and a w minus and then that goes to a proton and electron and then antiutrino.

[01:13:14]So this in general is how you would posit a theory to say that um you know we assume that there is a particle mediating the force.

[01:13:27]So then these are the properties it must have. it must have negative charge and it must decay into these two particles.

[01:13:34]And then you would tell the experimentalists go out and look for this particle or send me some data so I can analyze it and look for this particle uh in your data and then it is kind of proven beyond a reasonable doubt as it is put that this particle does indeed exist in the data and it does show up.

[01:14:01]Um, in fact, I'll quickly take a little detour for about 20 seconds here to explain beyond a reasonable doubt.

[01:14:10]But for actually, no. Does this make sense to everyone now?

[01:14:15]I've kind of been talking at you for a while. Uh, does anyone have any questions?

[01:14:22]>> I've seen fman diagrams before. I'm pretty comfortable with this, but anybody else feel free to speak up.

[01:14:32]Um, I'll take that as no questions then.

[01:14:38]Um, all right.

[01:14:40]So, yeah, if I um swap, do you remember what I said I was going to explain about 20 seconds ago?

[01:14:50]I remember. Never mind. It's okay.

[01:14:52]Beyond a reasonable doubt. So how do particle physicists decide? Like there must be some threshold for which the data says we now believe this.

[01:15:09]Like if if any evidence comes up against this, like how likely are we to um No, sorry.

[01:15:24]Given what we have seen in the data, how likely is it that the theory posited is true?

[01:15:34]How likely is it that this is actually the case or that this is able to explain reality in a sufficient manner? And this is five sigma.

[01:15:48]Five sigma for discovery. Uh four sigma for um it might be four or three. I can't remember. I think it's four. Um like five sigma for discovery, four sigma really put a bit of effort into trying to figure out if it's true.

[01:16:08]Um right, five, what does five sigma actually mean?

[01:16:15]The way that you think about this, well not even the way that you think about this, just exactly what it means really.

[01:16:22]I draw this quite wide is if you consider some normal distribution uh let's call this variable V and let's call this uh I'm I'm not going to label it against the axis actually.

[01:16:40]Um actually no I should I'll call it T.

[01:16:45]Don't know why, but let's call this V and T. Uh maybe there's something more standard standard you'll label this with, but who knows? Um me, I would say everyone knows this, but maybe not. Um a normal distribution is denoted by the mean and the variance.

[01:17:08]Variance denoted by sigma and the mean by mu.

[01:17:12]Let's set the mean here equal to zero because it's not particularly important.

[01:17:22]Basically, what this means is if you uh the peak should be at zero, but I drew it kind of wonky. Um what five sigma and four sigma mean is if you take if you go four standard deviations away from the center of the distribution which in this case will be zero.

[01:17:48]How likely is it that um there will sorry how likely is it that there is a value greater than this?

[01:18:01]Um and in the case of uh five sigma this happens to be about 1 in 3 million.

[01:18:14]And what that what that means in terms of the actual physics is if you were to have found something if you were to say that a theory is true to five sigma or greater the probability that that theory doesn't actually describe reality accurately is about 1 in 3 million. We can never of course reach 100% accuracy. That's kind of uh ludicrous to say that yes, I know my theory is 100% definitely accurate and there's nothing to say otherwise. That's wrong every time.

[01:18:54]Um even f= ma could be wrong. It could be f= 1.00003 ma. um you know there's nothing well there is a lot to say that it isn't but it could it could be the case um and five sigma says that there is a one in three million chance that I'm wrong this so I am correct beyond a reasonable doubt I think that makes sense uh I think I explained this bit a bit poorly but uh if anyone has Any questions? Uh, just ask.

[01:19:38]Once again, I will take that as no. All right.

[01:19:41]Um, and the final two particles I want to try and explain on this diagram are ZN not and mystery particle up here that everyone knows the name of, but I'm going to not say it for a little while.

[01:19:58]H um and actually I think I've got about 10 minutes left before um my 90 minutes are up.

[01:20:11]So right ZN Z is a weird one. Um it kind of I mean it pops out in the maths. It is a real particle. It has been um what's it called? It has been shown to exist and to my knowledge it has a mass of about 90 jev.

[01:20:34]Um it might be like 89 or something. Um actually you know what I'll explain Jev a little bit. Uh that's well Jev or giga electron volts is a unit of measurement of energy.

[01:20:52]Um it is the amount of energy gained by an electron as it is accelerated through one volt of potential difference and then giga is* 10 9. An electron volt is absolutely tiny. Um, this has a mass to my sorry actually really interesting thing here. I'm not going to explain it because um uh I don't really know how to but we can't actually measure the the masses of these three.

[01:21:36]Um they are incredibly small. We can put rough bounds on them, but we in the same sense that we can put uh an a lower bound on this, we can only put upper bounds on these three. I think we've got some lower bounds, but they don't particularly like have a lot of whacking behind them. The sum of the masses of these three is around about 0.6 6 electron volts as the upper bound and I think the lower bound is 0.12 but if I'm right that's to about 3 sigma so it's not incredibly confident but it is still quite confident um but yeah these three are absolutely tiny um even the electron has a mass of I want to say 311 mega electron volts It might be 0.9.

[01:22:41]Uh yeah, maybe someone knows that other than me. Um but yeah, bigger electron volt on this scale is quite large.

[01:22:54]Uh in in fact, it's very large. I would say the top qua I want to say uh sorry I know that this is definitely the heaviest particle on here by far.

[01:23:06]Uh it has a mass of about 140 gel electron volts which is just insane.

[01:23:15]This thing is tiny in comparison.

[01:23:18]Um photon and gluon have no mass by the way. Uh they I I don't really want to go into that but that does mean that they move at the speed of light. Obviously with photon being light technically saying the speed of light is um logical with a photon because it is light.

[01:23:42]So from now on I'm going to say speed of gluon um right znot um or the z bzon I'm going to denote it with just a z knot.

[01:23:58]Um, this is a weird one. This denotes neutral channels as the um I don't actually know a lot about the Z Bzon on its own. But if I'm right, the top quark it, if it wants to go to an up quark, it will do that via Z knot.

[01:24:22]Yeah, I prefer ZN KN.

[01:24:25]Um the zero means it has no charge.

[01:24:30]Um and it can decay into many things but it tends to decay into um particle antiparticle pairs.

[01:24:43]Um and it sometimes likes to decay into if I'm right four photons but it might also be two. Once again don't quote me.

[01:24:53]Um, and sometimes it'll also decay into uh gluons.

[01:25:00]Um, I don't think it ever decays into an odd number of particles.

[01:25:09]I think that would be silly, but I can't say why.

[01:25:14]Um, because I don't know. But yeah, so this is the best of my knowledge in terms of uh the Z part, the Z bzon. Bzon. Yeah, Bzon. Um and with this that does come a rather funny quirk I think. Um, you can have a top particle into an up and a Z knot and then that will then further decay into an up and another up and an anti-up.

[01:25:51]Well, these two will have a lot of energy because conservation of energy of course and this is a tiny particle with an incredibly small mass. And this is a massive one which uh is probably on the order of hundreds the mass of the upquack.

[01:26:10]Oh my days, my hiccups are back.

[01:26:12]So these two will have an insane amount of kinetic energy. Um, and I'm not sure a Z knot would really decay into an up and an anti-up. It would probably decay into charm, anti- charm. Um, but yeah, that does then mean in theory that these the uh this up and this anti-up can uh sort of they can annihilate. You know, I'm sure you've heard of antiparticle annihilation before.

[01:26:46]So then you'll be left with one very high energy up part up quark um and you'll be left with uh two photons or maybe four or two gluons or whatever.

[01:27:00]Um it's a it's a very very interesting particle and to my to my knowledge not a whole lot known about it and there is something called the Z prime uh bzon. I'm not sure if it's denoted with prime or with a star. Can't remember off the top of my head. Um there's also um a a photon prime. I don't know what it's called.

[01:27:30]This one I'm not too sure about actually. Don't know why I've mentioned it, but I feel like it exists, but yeah, these are theoretical particles. We don't know if they exist yet. Everything on here has been proven to significantly sigma. Um, yeah. Does anyone have any questions? I may have just rubbed off someone's question.

[01:27:56]I'm going to take that as a no, but feel free to shout out still.

[01:28:01]Um, right. The final particle then that I will uh explain um is of course the Higs Bzon.

[01:28:14]Um there's a lot of speculation around whether this is the only Higbos and it's is very weird. It has a mass but it's also the the particle which gives other particles mass which it I'm not sure how accurate it is to actually say that it's the mediator of the field which is the mass field.

[01:28:52]So as in in the same sense that the gluon is the mediator of the colar field, the higs bzon is the mediator of the mass field. Um and through a process called spontaneous symmetry breaking uh you can um demonstrate that uh a particle interacting with the Higs field the part the field of this particle will in a sense gain mass.

[01:29:28]Um, I think I think that's the best way I can explain it without getting into too much detail.

[01:29:34]It's very very very strange.

[01:29:38]Not strange, but um complicated.

[01:29:43]Uh, in fact, just is straight up quantum field theory. The rest of it I could I tried to get around quantum field theory as best I could, but I can't explain this without it.

[01:29:54]Um, I actually didn't explain these two fully. I'll go into a little bit more detail about those. Um, they mediate the weak force. That's what it's called. Uh, I mean, I showed you in fineman diagrams earlier. In fact, just because I want to draw another one, I'm going to um to draw the Z.

[01:30:19]Um, let's show a This is a particle with a top quack in it. Um, oh, actually, oh yeah, I'll explain that in a minute. Let's just say that this is a top quack on its own. Um, it lets off a Z blow on.

[01:30:41]Um, there you go. Z. And it fires off into an up.

[01:30:50]This then here could fire off into uh yeah ant up.

[01:31:03]This is not correct. This should be this.

[01:31:07]Um this actually says that the upwork is going backwards in time which doesn't make sense. Um, I think I've drawn the diagram the wrong way around.

[01:31:22]Yeah, I I have.

[01:31:25]And you can just switch these convention. Uh, I think I think this is the typical convention, but having the X and the T either way around doesn't particularly matter.

[01:31:37]Um, yeah, I just wanted to draw a di Z on it.

[01:31:44]So, I've done that.

[01:31:48]All right.

[01:31:49]I think that is the end of my 90 minutes of roundabouts.

[01:31:54]>> That's 92.

[01:31:56]>> 92. I don't know. No, I've gone over.

[01:31:58]Whatever shall they do? Um, >> anyone have any questions?

[01:32:08]I guess one thing I was just kind of thinking about regarding the Higs boson is that I feel like it's commonly described as the thing that gives particles mass. And while that is true, it was originally conceived as just the mechanism for electro symmetry breaking and it was kind of that other kind of aspect of it was kind of added on later.

[01:32:28]>> Um the what what was that? You said you mentioned something about electric symmetry breaking. It was what about it?

[01:32:37]Sorry.

[01:32:38]>> So I was saying the Higs field was originally introduced as just a mechanism to do electroeak symmetry breaking >> and then it was later that they realized oh we can actually use the same thing to give particles mass >> like the other particles because it gave the Z and W particles mass and then they realized oh we could actually use this for everything else too.

[01:32:58]>> Ah yes that is correct. That is correct.

[01:33:03]Um, it will seem >> I feel like it's just kind of like >> Yeah, >> I don't know if this is the right way to say it, but I feel like it's almost doing the Higsfield a disservice by just saying it makes things have mass when originally it was just intended to be the mechanism for electro weeks symmetry breaking.

[01:33:19]>> Yeah, I think the uh the more interesting uh story behind the Higsfield is that uh Peter Higs wasn't even the first guy to find it. Um, I think it was >> Is there somebody's law that says that everything that's like every mathematical thing that's named after somebody is not named after the right person?

[01:33:40]>> Uh, yeah. Yeah, I think I've heard of that somewhere. It's sort of like the Oiler thing. Um, everything's named after the guy who found it after Oiler. But yeah, um, I know one of the guys called Engles died a few weeks ago. Rest in peace him. Um, I think it was called Frank Engles or something like that. Um, he was the guy alongside someone else who discovered the Higsfield before Hicks did. Um, well, I say discovered, I mean more um described the Hicksfield before he did.

[01:34:16]Um he just to my knowledge um rediscover like redescribed it a few years later and went into a bit more detail and then like kind of pushed for it a bit. Um but the first two guys did in a sense discover it first.

[01:34:36]So yeah that is something which is uh quite interesting I do think.

[01:34:42]Um does anyone else have any more comments or questions?

[01:34:47]Uh, I think there's more I can go into detail in as well.

[01:34:51]Like I mentioned that you can't just have a quark on its own.

[01:34:58]And I am going to I'm I'm going to let someone try and figure that out while I wait for some more questions.

[01:35:06]Uh, if anyone has any ideas as to why Quark can't just exist on its own.

[01:35:16]Um, while I'm while we're here, I will actually write down the separations of the um of this chart here. Uh, it's very, very messy. That's been left up there for about an hour now. So, right, I'm going to like thicken up the borders here a little bit for each individual section.

[01:35:43]Right. Uh, and then this the Right.

[01:35:50]Yeah, I feel like that's relatively well bordered. Um, it probably could have been done a bit better, but so this section here, this is the ozones and this section here is the firmians.

[01:36:12]Um, I actually did mention earlier that I was I might have gone into spin.

[01:36:20]Um, I actually don't think I managed I managed not to mention it for 90 minutes. That's incredible. Well, about 70 really. Um but these have uh spin uh n for uh integer n. And these have spin uh plus or minus 1/2, but typically that's just said spin 1/2 uh as to reference the magnitude. Um, someone quote me on this if I'm wrong.

[01:36:59]Uh, sorry, not quote me. Uh, tell me this if I'm wrong, but the spin values on each of these are 0 0 1 1 0.

[01:37:13]Um, I I might be wrong.

[01:37:15]>> I'm looking at the diagram right now and they uh everything like the gluon everything in that column. I don't know why I mentioned the glue one, but they're all spin one and is the only spin zero.

[01:37:26]>> Ah, right. Yeah, that's right. I was I'm an empty. Yeah. One, one, one, one, zero. Um, I'm not going to try and explain spin. I'm really not. Um, no, I really want to.

[01:37:44]>> Okay. Um, right.

[01:37:49]Yeah, fine. and I'll explain spin. So spin 1/2 in fact I'll I'll explain spin one first because that's that's the one everyone's famille it has an orientation you can tell me which direction it is facing like if I let's say I've got a 2D particle that has spin one, right? This is the particle here. These are all the directions in a circle.

[01:38:29]It can be facing this way or this way or whatever direction you want. And you can tell me which direction it's spinning in. Sorry, not spinning in. It is looking in. Either way, this is an analogy. This isn't an actual explanation. An actual explanation would probably take about 3 hours, and I'm not here for that today.

[01:38:50]um at least three hours by me because I'd probably have to reerive 80% of it on the spot. Um a spin one sorry a spin zero particle being something like the Higs you can't maybe maybe I'm wrong on this but the way I'm going to analogize it is you can't really tell me which direction it's facing. But you can tell me which direction it's moving in, but you can't tell me the direction that it is facing.

[01:39:21]Um, yeah, it's I guess you could say it's facing in all directions at all times or it just doesn't have a direction. It has no spin. It has spin zero.

[01:39:34]And for a spin 1/2 particle, it's somewhere in the middle. And by somewhere in the middle, I mean you can tell me which direction it's facing.

[01:39:44]But it also has another component on that being uh I'm I'm going to call it a zero one. Basically, every time it does a full rotation, you add one to this and then if it's at one, it'll go back to zero. So every time it does a full rotation, you flip the bit.

[01:40:07]Um yeah, this is SU2.

[01:40:14]That's the spin matrix. Uh not matrix, sorry. Spin group basically. Um I believe there is another group.

[01:40:27]It's not SO31. That's all group. Um, but basically the reason without getting into any group theory here is that this is the double cover of SO3.

[01:40:46]Um, I think I guess isomeorphic would be the right thing there. Uh, I pi one I want to say two swappy might have a bit more experience in this. If B is in here, she might be able to say something on this.

[01:41:02]I don't know. Um, but yeah, because SU2 covers for sorry, for every element of SU2, there is two elements in SU3.

[01:41:17]>> I think it's the other way around.

[01:41:20]>> Yeah, I was about to say this feels like the wrong way around. Um, let me talk to that, man.

[01:41:30]I've never touched these groups. I don't know anything about them.

[01:41:33]>> Yeah, that's fine.

[01:41:37]>> One of the ways around it. It doesn't particularly matter. Uh for one of these is uh the double cover of the other. I >> It's SU of two is double cover of SO3.

[01:41:49]>> Yeah. Yeah. What I was saying. Okay, good. Thanks. Um Yeah. Okay. because it's the double cover of episode 3. It's sort of got this. This is my incorrect analogy for it. Vast oversimplification, but that is the case.

[01:42:09]Um, and in a particle which we experience in general life, it has spin zero, not spin one. I explained it the wrong way, I think. Um, no, not really, actually. Cuz like you can't really tell me which direction this is, this board, let's call it, is facing because like that requires you to choose arbitrarily which direction it's Yeah, I mean, you could say it's facing this way, but that's relative to a specific thing. It doesn't have an inherent direction.

[01:42:51]Um yeah uh this is actually also the reason that the magnetic field exists um as a separate and away thing to the electric field. Um yeah that's very cool. I think I think I've done a half decent job explaining it here. Um, right.

[01:43:18]One last thing then.

[01:43:21]I'm I'll ask Suji directly cuz I feel like you might have the best shot at this. Why do you think blacks can't be on their own?

[01:43:33]Um, so I know that the the one general thing that I've seen people say is that if you try to add energy to separate two corks, two bound corks, it'll just end up creating more quarks.

[01:43:46]>> Yeah, >> I I remember it's been a while since I've thought about just like a single lone cork.

[01:43:53]I do know that it's it's related to the fact that gluons themselves have charge and so the strong force ends up kind of becoming stronger as things get further away which kind of pulls everything together >> kind of things I've heard.

[01:44:09]Yeah, that is that is in a sense well that sorry that is correct and in a in a way that's kind of the reason but the more fundamental reason I mentioned it for about half a second maybe an hour and a half ago now maybe not an hour and a half but about an hour ago um when you have any given particle such a a proton for example it will have a net charge of sorry a net color charge of zero right but quarks and gluons in inherently do have a nonzero color charge so them being on their own isn't stable >> then where do you get that principle of everything needs to be color neutral >> um you get it from don't quote me on this actually no yeah do quote me on this do I'm pretty sure this is correct uh you get that from the QCD lrangeian remember the thing I mentioned earlier the action um and langian um you do get that from the QCD lranian it's called confir that I have not looked at the QCD lrangeian so >> that's completely fine >> I have to run but thank you for the talk um cut the recording You can as well if you haven't already.

[01:45:40]>> What's that?

[01:45:41]>> Thank you.

[01:45:41]>> Yeah. Yeah.