Osher Particle Physics Lecture 1 Transcript

Arthur Reed has been recording and transcribing the lectures with AI. 

He has made the transcripts available at the link below for anyone who is interested.

https://docs.google.com/document/d/1HJqcPaQh2JuHMYDCK3KoxaQ0VzhIZfSK-oxy8YssA7c/edit?tab=t.0#heading=h.ydp6798tb7uz

Also, mainstream press, right? So I guess that's how you guys heard of it. Um, and if you look at the headlines, they were really spectacular. They said these outrageous things, like giant lea for science, physics finds allusive partic ofles scene as key to the universe, right? And a few years after that, it was awarded the Nobel Prize, and so really a big splash. and so not only the headlines were impressive, if you actually look beyond the headlines, it would it took to discover the Hos on, it was also similarly impressive.

So here's a look at it in pictures, so this was something that wasn't discovered in a small basement lab in a university, like some big discoveries are, but it took a really international effort, so there's this international lab called the called CERN, so this is in Geneva on the border of Geneva and Switzerland. and they have a big collider there. They have a big collider there that's about 17 miles around, so it's like a racetrack. and the way to think about this is it's a massive, so this is the size of an international airport for scale, so it's really major endeavor. and the idea is that this is kind of like a racetrack where we send protons around going one direction and another group of protons go in the other, and you accelerate them to his high as energy as we can get them, and we make them collide at certain points along this ring. So for example, there's one collision point here, and at the collision point, we have big detectors. These things are like the size of apartment build, so these are little people for scale of complicated, basically like a 3D camera that that takes pictures of what happens when the proton okay? So this was what was needed to discover the Higgsos on. right? So, the picture is also there inressive.

If you look at what it took in numbers, similarly, it's an an incredible uh incredible numbers. So, this this effort was about 10,000 or more scientists, depending on how you count and engineers from 85, 85 different countries. We already said it enormous quite seven kilometer particle accelerator. The protons ruling essentially at the speed of light, so 99.9999 if you can see it there, as fast as we could get them to go, the speed of light, um and we didn't just collide a few protons. We we collided a billion protons per second, right? So we're these coll questions, a billion times the second, and we had to do that for two years in order to get enough data to make this discovery. Okay, so I took a lot of data, you can imagine this is expensive, okay? So should do this, it depending a bit how you cost, I how you cost it, it's about $10 billion dollars. So this doesn't include salaries of people, so that's just kind of construction and civil engineering and so forth. So, incredibly expensive, um again, these detectors are are massive things in the in themselves are kind of like cameras that are apartment building size, and they take pictures 40 million times per second. Okay, so they're taking pictures incredibly rapidly. That's one of the reasons why it is so expensive, still. Um, they generate an enormous amount of data, okay, so way more than Google and Facebook have to deal with. Okay, so they do 80 parzed percept because it per second, this is like 10 times the big library on camp. all the books. It's like 10 times that amount of data per second. Yeah. So it's it's you not a rid North data., this is another interesting number, okay? The salary of the people doing this, uh they're doing very similar things as you would do as a banker or an engineer in finance, is significantly smaller, okay? So people are making a lot less money doing this stuff.

And so this hopefully raises a bunch of questions, okay? The first question is, what the hell is the Higgsbows are we? okay? I everybody that's already been asked. Okay, the second question is, why do we have to go to such extremes to find it? Why are all these numbers so big and you know, why is it so expensive? Why do you need all this data? So on? And that's obvious question. Another one is why should even do this in the first place? If people aren't making any money, it's really hard to do, why you even do this, okay? And the fourth question is, okay, you you did all this work, you found it now one. okay? And so kind of the point of these lectures is to try to answer these questions, and we're gonna answer them at different levels of sophistication, right? So there's kind of surface answers you can give, then there's more deep deep answers, and so as we go along, hopefully that can hit on these many different times at different different levels of depth. looking for the sort of out and so, actually, this was kind of like a two stage act. and so so I actually so S has a rich history before that the LAC and before this big ring, it came about right after World War II, as it basically is a way to unify your, right, so to get it uh to get Germany and the rest of the countries that collaborate on scientific research in Russia and, you know, so forth. So that's kind of what the site was built in that in the 80s, there was a major upgrade where they built that big ring. okay, and that was the study some other particles that we'll talk about later in the course. and then that ring was upgraded to look for the hidds, right? And so the LHC is the upgrade is putting fancy magnets in the ring. And that was something that came later in in the Higgs was the main motivation for that for that second part. Okay, so this is kind of a big overview. There's these obvious questions and we're gonna try to figure figure out the answers to these, again, at different with different levels of sophistication.

We go. Okay, good. So so here's a lecture outline. um, so today I wanna talk about something called Newton Stream. um, and then in 20th century Revolution, and then we'll get get to these later. um, maybe something I should just had earlier, yeah, feel free to interrupt, you know, it's it's I think it's much nicer if we it's more of a conversation than just be droning on and on. but and it should be very informal as well. Okay? your background? Yeah, so that's a good it's a very good question.

So, I'm actually going to Caseburgh, so I grew up, um a couple miles south of here. I went to Baldwin Whiteall high school. Um, and then for college, I went to the University of Pittsburgh. I actually didn't get into CMU. That's okay. I had a lot of fun there. I was actually more interested in philosophy than physics. So I took physics in high school and, you know, it was something that is reasonably good at, but it wasn't something I thought was that interesting, you know, it was all about balls rolling down incline planes and movies and and so on. And I could see how it would be useful if you were gonna be an engineer, but but I really wasn't that I it wasn't that interested in it. and that was the same it when I started at Pitt as well. I was much more interested in philosophy, because there it seemed like the questions were obviously an important and it was only later that I realized and hopefully I could convey this in the lecture too, is that physics at the advanced level is more like philosophy, so often is trying to ask the same questions that philosophy does, but unlike philosophy, you can get answers in physics, whereas philosophy, it's kind of get the idea that sometimes it could be spinning its wheels, right? And so at first I was a philosophy major and then what I realized that I really switched to physics and and focus on on focus on particle physics. Then I went to University of Pennsylvania, so in Philadelphia for a PhD program. there I started to work on the science that we were gonna talk about here, so I worked at CERN, that the picture that you saw, and it's beautiful. If you look at Geneva, you you see pictures like this, um however, the cost of living is fantastically expensive in Geneva, so minimum wage is like $90,000. and that's not what you make as a grad student physics. So instead of making in Geneva, all the physicists live in the French side of the border in this place called Saint Genie, which is not very glamorous. It's more like Soviet kind of consteri construction. but it was it was a very fun experiment or experience and I got to work on the experiments that discovered the Hig, so that was a lot of fun. after that, I went to Chicago as a fellow and I was there for uh, you know, for about seven years and then I came back lucky enough to come back to to see him you. So I've been in faculty here for six years. That's really great., so look, did apologize to you for not as meeting I don't think I care. What's important is you forgave him.. I mean it's so hard to get to see him anymore. oh yeah. expensive. Okay, anyways, but I had fun at Pitt. I mean, I think Pitt is a better value too anyway. you didn't hear that from me. Okay, um so does that hopefully that ask the question a bit why am um okay, so, yeah, good, that was I kind of introduction, so let's get really dent in today's lecture.

So what I wanna what I wanna do today is really kind of two or three different things. The first is talking about something called Newton's Dream, okay? And this uh I'll explain what it means in a second, and then, you know once we have that in place, we'll be able to talk about some revolutions that happen in in the 20th century.

Okay, so there's a long history in a particle physics. you could really go back. You should think about physics in general, not just not just particle physics. So what's the idea of physics? Well, the idea of physics is really about explaining things, about explaining nature, and this, of course goes back to the ancients, right? So the ancients were explaining, you know, they come up with that'sations for things that they saw, but this really comes out, it can't came to life with Newton and to some extent with Galile before him. But he's the one that really started physics, and I would say started really the scientific outlook on on the world, and so his key ideas was that you really mathematics, so that's the key to describing nature. It's kind of the language that nature is written in, and he had this great work called the Principia that started this this whole thing off, and in order to do that, he actually developed a new branch of mathematics called calculus, and he explained he gave us loss of motion and he explained how quantitatively explained how gravity was. Okay? How and so in there is for this party is the most important physic is that's ever been, ever lived, um and but and this gets a lot of the tension, but I think probably the biggest advance of all is something called Newton's dream, and that's what I wanna try to explain to you uh, here.

Okay, and so I'm gonna I'm gonna do it by these these kind of crappy cartoons. um, and so so what I'm gonna explain by a scientific explanation is this era, okay? And so what what I mean by this is that if you have something, some concept s or something in the world that's explained by something else, I'm gonna draw this arrow between the two. okay?

Um, and so what Newton did, again, in this famous work, the Principia, is he explained planetary motion. So if you look up in the skies, you see these things that kind of look like stars, but they move in it very differently. We know as their planets. He explain how and why they move in terms of the force of gravity. Okay? So that's what I mean by these explanation rows? Um, and famously he also piled he was the same the same force of gravity that keeps planets in orbit, also explains things on earth, right? So projectiles or how things fall on earth is explained, it can explain these things that are very different, right? This looks like it's something you only see at night and it's like almost like a star. These are like apples falling down. right? So things two things that are naively, totally different from one another, actually have a common explanation in terms of this force of gravity. okay? And he did another thing too, the ties also. again, totally different the ties look something like planets, they look nothing like apples, but he but he showed how that these could be explained also by this fourthram. Okay? And so Newton was was famous not only because he explained he could explain these things, but it's kind of the first time that we see that these very diverse phenomena planets tides, projectiles have kind of a common explanation. There's some kind of unification of their behavior. Right? And so when he says in the in the in in the prefest in the preference to this this famous work, is that just some you know, quoting here basically he says that he would he wishes he could derive the rest of the phenomena of nature, so that means everything else. So he will only explained a couple things, right tides, motions, planets. There's all this other stuff around us, and he says that he it says wish that he could and he suspects there there's many reasons to suspect that they can be depend on certain forces. So basically his idea is everything around this, not just these three things that might have some ex common explanations. Okay, that's kind of h that's what I mean by his dream.? He wasn't able to do that. He was only able to to kind of connect pieces, but his dream and and his kind of intuition was that maybe everything could be explained in this way as well. Okay, and so that that's what I mean byreme, basically the idea is to understand all of nature in terms of simpler simpler sensations.

so that's kind of the goal. physics and and really it's science, and in fact, you can summarize all the science from Newton until the 20th century as in making this dream come true. Okay, so we we've realized this dream, okay? And so what's interesting is we've again, the history of science since since then is connecting you know, drawing a much more arrows, right? And whoop, what's interesting that we we see is a certain pattern to these arrows, okay? So there's many different phenomena you can imagine. They all almost so basically everything has an explanation, okay? And you can ask deeper questions, so what's the explanation of the explanation, and what we see is that there is this kind of overall convergence, as you as you go to deeper, you ask why more and more often or you go to deeper, deeper explanations. One thing is you always find an explanation, but the other thing is there's this idea of convergence, right? There's fewer and fewer explanations as you go farther down. in this in this kind of web of scientific explanations.

Okay, so so an example might be, so something at the at the high level, you know, some obvious fact about our our world is like the length of the year. Okay, so you might go to know what's why does length of the year is what it is? Well, we know that as a way as a planetary motion, and of course, Newton famously explain this in terms of students claws or loss of gravity, which we now understand in terms of relativity in general activity. Okay, another example is the weather, okay? So again, very important to our everyday life, right? you know, something awful around us, we we' now we explain this in terms of pressure fronts, and so the meteorologists will talk in terms of eyes and lows and how they're moving. these pressure fronts we know are just huge collections of molecules and molecules we now understand in terms of chemistry. chemistry is understood in terms of the smaller pieces that that participate in the chemical reaction, so atoms and electrons, these as we're gonna talk about later are understood as being parts of a quantum theory and what we call the standard mod. Okay, so some high level thing, weather comes down to, you know, is explained by some basic same thing. gross features of life, right? So if you wanna talk about kind of land speeds of animals or sizes of animals, um there's some there's, you know, we understand them and in terms of evolution, that in terms of DNA, which is a molecule and then you're back down. down. Okay, so there's there's this uh again, this notion basically everything around us is connected in some way in this web, and the web hasn't there's a directionality to it. the the number of explanations are getting smaller, as you're going down.

Okay, so just a few a few things to point out. One is not all the connections have been made, okay? So, you know, it's not like we have explanations for absolutely everything. Um, but not all the areros are worth connecting. That's another thing. So the cases where we haven't made the connection, it's it's not because we think there's some mysterious thing happening there. It's just it's not practical that do that, right? So, particularly for weather, right, the meteorologists don't worry about quantum mechanics when they predict the weather, they talk about the pressure fronts, and in order to predict the weather, it's much it's it's much more effective to do that, right? So they don't bother making the connection to the lower level lower level physics for what they want to do, okay? And it but it's not that it's not possible to make that connection. It's just it's not worth it, but we're not we don't think we'll learn anything by doing that. Okay, the other thing that I've said before is that there is this, it seems like there's this direction or this convergence of explanations. okay? And what I want to stress here is this is this is begins with I think it's science we do a bad job of this. This is a fact, this is a scientific fact about nature that we've that we've discovered, okay? And it's probably the most important thing that we've discovered in science. if if we really think about it, um it didn't have to be this way, so, you know, we went out and we tried to connect these to draw these arrows and this is the pattern that emerged, right? We see that these arrows look like this, and this is something, again, that nature is kind of telling us that arrows of explanation look like this, okay? And so what do I mean it was a fact, it didn't have to be this way. I it could have been different, right? It could it could have looked like this. question, yeah. Where is the big Bang fit? So the big bang is that the bottom here. That is the bottom. I'm convincing when we get there. Okay, yeah. Okay, so it it didn't have to look like this, right? It could the arrows could have looked more like this, right? You could have had instead of convergence, you could have diversions. You could have asked the question and you would get an answer, and then you ask, well, what what's the next question? behind that? and you get two different answers. Right? Or is the contingent on multiple things, question? actually relatively they been, you can look at it that way too. And it started, and that's how it spanded out. You're working backwards, so that'spective that's very relevant… so so certainly in terms of in terms of how the matter moved, it looks more like this. But I think in terms of explanations, right, there's fewer there's fewer relevant things in the right. the world now is much more complicated than it was in the Big Bang. in many ways. So you talking extrude like, what I would call theational forces, like, say, will of God or, you know, something that science cannot explain, yeah. Yeah, yeah, so disregard this. Right, right, okay, so so it could have been this way, another way it could have been is this, right? You could have had overall conversions, and then there could have been some phenomena that that looked like maybe they were related to each other, but totally disconnected from the rest of the system. So this could be like the will of God, are you gonna imagine? And there were times when we thought this was the case. every time we thought this was the case, we we ended up making an arrow.. Again, this is this is observed this is an observation, right? So we we're connecting arrows and we're seeing, the way we think of it now, this never happens. right? There's always an arrow in or out. and connects to the bigger the biggest picture. Where do you put the independent things like electricity, magnetism and does the same thing, but but the arrows are totally different. Those would be around if you know. somewhere at this level. We we'll talk more about that. Okay, another way it could have been is like this. okay? you could have conversion, divergence to the bottom, and this is really like the will of the, right? You get to the bottom, and then you ask, why is this this way? oh, it's because that there's a big arrow that goes back here. okay? Again, there were pies when we thought this was the only arrow to draw, okay? And in fact, one of the things that makes the Higgs so exciting is there's mysteries associated with it that are that we will get to later in in the lectures here, is the Higgs is down here, okay? It's it's it explains things, explains many things above it, and you can ask questions about the Higgs, okay? So it it's at the same, what so exciting is at the same time, it's inevitable, okay? It has to be it's the explanation for some other layer, but you can ask a question about the Higgs and the answer seems impossible, okay? So we have this particle this inevitable on one hand and impossible in the other impossible meaning it looks like this is the only arrow to draw. okay, and scientists don't like drawing this arrow. um and so one of the explanations for how the pigs is possible is that this arrow is the right arrow to draw. Okay. um, but again, we we think that's it's probably a minority opinion, um, but we don't know this could be the hero. Okay, um good, and so so what I want to stress is that we can really, in our everyday world, okay, things that we see around us, the sun, even more esoteric things like radioactivity, um you can weapons, that kind of thing? This could all be explained, right? Everything that basically matters to everybody here, have be explained in terms of simple principles. physical principle. It's part of this web, and we know how it fits in. There are things that that we don't yet know, but they're very, very esoteric, or they're at the bottom here. okay, we haven't we haven't made all the connections, and what's fascinating is this pattern can't continue. You can't keep having fewer and fewer explanations. at some point you get one explanation. right? And again, this, you know, it's on one hand, it's telling us we're on the right track, probably. um and it's very philosophical, right? That this is something like it would be a you could imagine being like a god, right? One one answer, okay? And again, this is something that we've discovered. We're not imposing this on on the science that we're doing. Okay, um, good. So so part of physics is entering interesting because it's probing these deep these deepest levels. So we're at the frontier and particle physics, we're trying to make connections that have yet to be made, and we're trying to see how far this conversion is actually actually goes. um and again, there's hints that that we're approaching the final explanation. and again, part of this lecture series is gonna be to make that make that case to you. um and what I wanna emphasize is the the principles actually get simpler, okay? Unfortunately, the mathematics does not the mathematics gets a lot more complicated. um and what and we often don't talk about this, these type of subjects that that I'm not try to talk to you. It's lecturearies to the general public, because it it requires very, very advanc mathematics to make calculations and new proofs. okay? If you don't care about making calculation of doing proofs, if you just care about the physical principles, it concepts the ideas behind it, it's actually not that complicated, okay? So what I'm gonna try to do here is really focus on the principles and ignore the mathematics. And so there's gonna be no proofs, they're not gonna do any calculations, if you know, if that's a uh it's hard to do that, right? So a lot of this stuff here, we don't even cover in graduate school. so it's like postgraduate school, um and that's mainly because the mathematics, not because of the physical principles. Okay, um but one of the again, there's fewer and fewer moving parts, there's fewer and fewer explanations as you get deeper. and deep down, this is really the why particle physicists do what they're doing, right? We don't really care about the Hicks bos on. We care about it because part of the picture at at the frontier. and we want to understand the frontier. Okay, so this is kind of on first partial answer for why people look for the Hos, why do we care what the exposed on? Because it's a crucial part of the this front here? Uh, it's not that there's gonna be some, you know, fancy electrical devices made of the Higgs bosons. It's more of a philosophical or even kind of a religious idea of trying to understand how how this structure continues. Okay, so this is one kind of surface level of why the h expos on is why it's worth finding the hos. even though we don't know what it is yet. I mean, it's a part of this part of this p picture of the deepest level. Okay? Questions. I maybe I shouldn't. Uh, are you saying that that's sort of the end all because, you know, this issue that it has a fine idea sort of?. You know, it doesn't have to because it could was it Xeno's paragraph? It what paradox? half half half? originally we thought Adam were the smallest and air broken up in small. How do we know that the boson is the smallest and there could be more. and that people building. So that's not. So as you so so one of the answers to are we doing if we have the Higgs? there's an obvious question you can ask, why is the Higgs oz on, have the properties it ducks? And there we have it's that era that goes all the way back to the top. So we have no explanation for that. So the Higgs is like at the bottom right now. and, you know, we want explain, you know, why why isn't why why does this dot is what it is? and we we don't know the era to connect yet. What I'm what I'm gonna try to show you at the end is we have very good ideas for what the what the next connection is. um, they're kind of too good to believe these ideas. um, and they don't seem to be correct. okay? Um, so it's and the radical departures. Okay, so so we're gonna see, again, I'm kind of getting ahead of myself. The Higgs is something that was put in to fix the theory in a way that we'll talk about in a way that's more concrete in a couple of lectures. And it was a kind of a small modification to explain why the H exist of properties it is, you need to make a radical departure, so radical meaning things like there has to be extra dimensions, okay? or there has to be another form of antimatter, or there has to be this arrow that connects all the way back to the top. Okay? So we think the hicks is special because its arrow it the arrow that explains it can't be this kind of mathematical trick. It has to be some deep new thing, okay? And that's what that's kind of the whole purpose of this last of here is is to get get to that point correct behind my impression as an experimental physical chemist is that we were doing pretty damn well when we got down to electrons protons, neutrons which decayed with electrons and protons. and the life of magnet force. seems like and then there then all of a sudden there was different kinds of muons and bogans and whatever. And I don't see that you see it. You've seen seems to have gotten more comp, I' we'll get there. I'll get here. I will get there. so I'm not way off on that. No, no. Yeah, that's a good lead to 20th century evolution. Okay, so new stream, that's again, the big picture, that's why we get up and do what we do, okay, it's not because the salary it's not not because we care what the expose on, because we wouldn't understand this picture. Okay? um, and I said that realizing Newton' dream was what happened from New time until the beginning of the 20th century, but actually at the beginning of the 20th century, the picture was confusing. It looked like you had this general conversence, okay, but then it looked like we hit a wall. okay? We hit a wall and there were there were these isolated regions, we call them chemistry, physics, biology, these days we could kind of explain well, you know, a lot among themselves, but they look like they were disconnected from one another. okay? And again, a lot of people, um that this was a a very confusing time, um and you have these crazy enrightrospect, crazy seeming quotes, okay? So this is Albert Michlson, okay, saying there's there there was famous physicist the University of Chicago. says there's nothing new to be discovered in physics, okay? This is the time when they can't explain how why atoms exist, okay? The obvious thing you can't explain how anything about atoms and he's making this crazy statement, okay? again, he's a great physicist, so what is how what what's going on here? okay? And the I I think the the way to read the statement is Michaelson didn't think of physics as this whole picture. He thought of physics is this isolated level. He thought there was this isolated web of explanations that just did not connect the chemistry, right? And so in that sense, he was correct, right? If this is physics of like balls rolling down, inclined planes and springs, he was right, you know, we basically had everything. We could explain, oh that stuff. Of course, chemists had their own thing, right? They were burning things and looking at the light that came out of it. They were understanding that there were atoms, and that was great for chemistry, they were able to make tremendous progress. Ph physicists had no idea why it was happening.? And similarly biology, it looked like they were you know, some matter was animated, it could move, it could do things. Physics said, no exclamation for that, okay? And so we really were at this wall and it was through two major revolutions in in physics that happened in 20th century that allowed us to break through this war. Okay, so to answer your question, the idea, you know, everything is great, you have atoms, you have electragic forces, that was kind of true here, but in order to break through this wall, you have to go beyond this and that's forces, this other stuff on this. How many of these structures exist? Is there one, or is it 500,000? I think to well, the first order it depends on the questions you're asking, right? Um, but a good way to think about it is at a university, all the departments kind of have things that talk have thatations is that roughly talk among themselves. Of course, there's crossalk between them, but if you're gonna ask a you know, a a question in chemistry, you're gonna want an answer from a chemist, right? Of course, we now know that you it well, we'll see you later that you can explain this in terms of physics, but it's it's hard to do that, right? It's it's much better to, you know, s these explanations do clump, but at this time, it looked like they were totally disconnected, okay? Now when we go through the revolutions, we see that we can break through this wall, but there still is clumping, even though there's kind of loose connections between clumps, and those clumps are roughly a good way to think about them is they're the level of the departments and universities. Okay, good, so in order to break through this wall okay, so now we're at the point in the story where we have this wall, there's an engineing this right, we have this converting, but we hit this wall, and to get past this wall we need revolutions and physics. Okay, and so that's what the next uh next few slides are about. um but before we get to before I talk about the revolutions and physics, I'm gonna tell you about what physics was like before the revolution. And so what what's Newton's physics all about, and then I'll explain how it's changed by the by the revolutions. Okay, and so the point is the kind of the only thing that you really need to know about physics is it's about what happens in space and time. okay? So there's there's there's three dimensional space, okay, and there's time. Right? And so the physics tells you how things move in space and time, right? That's basically it. there's there's complic you know, there's equations to explain that we high school students. how you know, how things move how you calculate how things movements based in time, but the whole point of physics is explaining how they move in space of time. So I'm gonna do it with these kind of simple diagrams, so there's gonna be just one dimension of space, and so this is like, how far you already from the wall, right? And then the time is gonna be going going up. Okay, so part of the so something like a particle or a person just sitting there and not moving in this what we call a space time diagram would just be a straight line. It has it has the same um the same position as time goes on. just stays there, just a straight line up. Okay, so that's one way that's one way uh particles or people or objects, baseballs can move. Uh, another way is that they have a constant velocity. Okay, so if you're moving at a constant velocity away from the wall, then as time goes on, you're gonna move you're gonna move a little bit over. if you're moving this way as time goes on, you're gonna you're gonna go go like that. Right? And this is this is a constant velocity, okay, so the line it's a straight line, not moving is kind of like a concept velocity zero, so you also have a straight line. And one of the things that Newton said is this is the natural way things move., so things want to move in straight lines. They either not moving or some constant velocity, um but things can also bend, okay? So you so I should so this is this slope here, is like the velocity, it's like speed, how how fast something's moving. I Another thing that we found useful, again, this is kind of empirical, something that we learned at the equations from the equations is there's another quantity you can calculate, which is that the speed, times the mass, okay? That's we call that the momentum. not so important, but that's a relevant one of the things Newton taught us is that's an important quantity. How fast something's moving and if something is more massive, that counts for more in terms of momentum, okay? then he also taught us that things could bend, which so this is the natural way to move, constant velocity or cost, but you could also bend, okay? And if you bend, there has to be a force supply. Okay, so constant motion or or or constant velocity, straight lines, that's the natural thing. If you want to do something unnatural, you have to put a force on it. Okay? And so he and then this is where it gets mathematical. So if you know how big the force is, you can calculate how much the curve bends, and this is why imp momentum important, so that so the change in momentum, which is the mass times the slope here, that's the thing that's related to the force. So, just so it's not the space time, it space time pass. that's three items we item.. But the mass doesn't change in space and time. So the mass is like, you know, every part of it has some number or every, you know, object has some number that its mass, and physics, you know, what you know that mass, then you wanna know how it moves in space and time. And Newton says, everything's straight lines, except when you have a force and then you can have bending. Okay? eventually will have masses no longer constant. So we're gonna get, we're gonna get that. So then so not only that, he taught us how to calculate these forces. These aren't important these equations, but this is just, you know, I'm not bullshitting here at news, not bullshitting. he gave us equations. He said, this said, this is how you you know, these are numbers you stick in here, and couple of these numbers are. You get calculate the forest and you can see how much things bend. so this is like the forest of gravity, Another example is electragnetism, and so if you have two charged objects, there's another force, and again, you can calculate and get put numbers in here, and you can calculate how big this force is, and that tells us how the particle is bend. Okay, so this is really all the physics is about, how how do you how do you move in space and time straight line? Except there's a forest? We know how to calculate the forces the forces often depend on the dis the the inverse square of the distance. and we say these are inverse square logs.? So basically, if you have two two particles, that's what this bar is and how far apart they are, and then there's the masses. A or the charges? Hey, you copy at the forces, and now you can see how things bend. Okay, so the other thing that's important is if you know everything happening at one time, you can calculate all the forces and you could predict what's gonna happen at a later time. And that's physics before the revolution. Things moving space time, masses, forces, you and you you could do these calculations. Okay? um and this is what I say here. So, in principle, you can predict that, if you know all you know everything at one time, you can predict everything at later times. Okay, so that's physics before the revolution, nominated two revolutions, the first revolution is relativity, okay? So this was a revolution, uh that was caused by one one person, right? was Albert Einstein, but it was really one guy thinking very hard about space and time and how things move the change, how we think of the physics, okay? Again, this is a very complicated subject. You can give you know university, we give a whole lecture on this. um and most of the lectures is trying to go through algebra and f figureuring out how to do a lot of algebra. The concepts are actually pretty simple, okay? So I'm gonna try to explain uh the idea inmerat. Okay? and they're but there actually was also a notion of relativity in Newton's in Newton's physics, okay? So so the idea of relativity was already there, Einstein just changed it. Okay, so I wanna I wanna talk and and you're actually familiar with this notion at all too, okay? And so so that's what I'm gonna talk about, um, before talking about we're talking about what I Einstein did, so already in the physics that came before, there was a notion of relativity, and this actually came goes back to Galileo. In fact. And so the idea is if this is what space plan looks like to some observer, okay? So somebody's sitting at rest, okay, that's not moving, and there's another there's another let's say, person moving away from them with a constant velocity, physics to this observer looks like this, right? There's a constant straight line.. But you can imagine another observer, okay? another observer that's moving this direction. Okay, so I have an observer that's moving with the same speed as the rel observer here. okay? And to this observer, to the observer that's moving, they see a different space and time pictureure, and in that space and time picture, the red observer is just standing still. because this velocity is the same as the velocity that they' moving. Okay, and so this notion relivity is, you can you could either think about physics from this point of view where the observers at rest and the red the red guys moving to the right, or you can think about physics in this point of view, where the observers moving along with the red guy. Okay? The details are different, right? So here it looks like there's a velocity, it looks like there's a big momentum. Here, there's no velocity for the red guy, there's no momentum. Okay, so the details change, but the idea is that all the predictions you would make in this picture is the same as in this picture. Okay, so that's what we mean by relative. And I send you're familiar with this, think about what happens when you're on an airplane, okay? You're on an airplane, you're pouring a beverage, right? You don't account for the velocity of the plane and you pour the beverage, right? You're moving on the p but the plane, you know, if somebody on the ground, the plane is whizzing around, you know, 500 miles an hour, a passenger sitting on the plane, it totally ignores that ph velocity. It's they pour the drink just like they're on on earth. So what's happening is to somebody at the airport, this plane is whizzing along, and it looks like, you know, they're pouring the drink and the drink is moving 500 miles an hour and the cup is moving and it catches up and so everything's happening, you know, here, going in some crazy speed. But of course it's much more simple to just think about the person on the plane. The person on the plane is moving with the same velocity as the plane and to them, they're just pouring they're just pouring the trick is normal. Okay? So basically, if if your reference frame is moving and the constant velocity, you can describe physics in that frame or a frame where it's standing still. Okay? And one of the things that we teach you know, so one question is, if physics is this simple, it's statistical about moving things, why do why are the why do you have like semester long courses? Most of the course is getting students to figure out you can do it in this ring. So we give them a complicated problem, it's very hard to solve in this frame, and one of the things that they need to figure out is, oh, I should go to this frame and it's much simpler. Okay? So this is a trick that was known, it's used all the time, this is what high school students do all the time. It makes problems easier, and again, you have some intuitive, I understanding of this as well. Okay? So that's all we mean by relativity. You can you could look at the same thing from different points of view. Okay? Okay, so another example, this one will be more important later, is now, if I have some so now I'm running, so okay, so I have to be an observer that's running, and there's something that's moving with respect to this observer. okay, so you can think of this as like, maybe a quarterback that's running in this direction and then he throws the ball in that direction. And so in this moving frame, this has some velocity, or you can imagine it you have like an airplane that's shooting that that's dropped that's flying this way very fast, and then it shoots a rocket this way. and so so there's a speed with respect to that the airplane of the rocket. okay? um and and again, this is kind of intuitive. This is again, this is the observer from the airplane, an observer at rest sees the rocket come out with a much higher speed, right? The speed relative to the ground is the speed that the airplanees traveling plus the speed of the rocket with respect to the airplane. And so get another notion of relativity. If you' if you're if you're not moving and the airplane's moving and it shoots are moving rocket, the rocket looks like it's moving even faster, drops into the ground. Okay, and the thing an interesting thing about Newton is this speed can get as big as you want, right, so this can get big, and then the deserve or this gets even faster, right? This if this rock is now aaceship that is moving much faster, and it shoots a rocket than the rocket is moving even faster, relatively observer at rest. Okay, and there's actually no limit in Newtonian physics how fast this can happen, right, how fast these speeds can be. You can also chain them, right? So you can have an airplane moving at some speed, it shoots a rocket and speed V, so now relative to to the observer, it's V plus V. and then that rocket shoots another rocket V. so now you have 3V, right you could just chain those and you can get arbitrarily high velocities. Okay, and this is again, a feature of the physics that came before, there's no limit to how fast we can make something new. Okay, um right, and and so so that turns out to be a problem if you want to do this this game of predicting things, right? So I said, if you know where everything is, it's a certain time you can predict everything in the future, but because things can move arbitrarily fast, you actually have to know where everything is on some infinite dimensional surface, right? You have to know where things are that are infinitely far away, because if they're moving infinitely fast, they can affect you in the next time in like in the next second. right? And one of the ways to think about what Einstein did is he wasn't happy with this, okay? He thought that if you were just if you just cared about what's gonna happen in the next second or micrcond or nanosecond or, you know, some small amount of time, you shouldn't have to worry about something that's infinitely far away. okay? And so, again, one of the ways you could think about the whole point of relativity is to stop that this happening. Okay, in in in Newtonian physics, you can get infinite speeds. There's no limit against that, but if you have an infinite speeds, you need to predict you need to know something everything is happening infinitely far away. in speed, you being just up to speed, like, not, this could be infinite. infinite beyond the speed, yes.. Okay, so one of the big things you again, there's many different ways to think about relativity, but but the big way is or or I think the simplest way is he he was deeply unhappy with this. He thought if you wanted to know what's gonna happen, locally in time, show some small time region, you shouldn' you shouldn't happen to know infitely far away, just some finite, but potentially large, but some finite space spatial. Okay, it's kind of a fancy way to say this is physics should be local, right? If you wanna know what's happening here, it should only depend on some local region here. it shouldn't depend on what's happening on the o in the next galaxy. Okay, so Einstein is trying to to fix this. He's trying to make physics local, or he's trying to put a speed limit in. that theorizes that it's the same in every galaxy it forces and causes you you have to be uniform throughout exactly.. We're assuming it is the biggest assumption. Yeah. Yeah. large. Okay, so so Einstein's big idea. Okay, the first revolution is to limit this range, okay? So he's gonna say, there's a maximum speed limit. Okay, because if there's a maximum speed limit, then if you want to predict what's gonna happen here, it only depends, you know, on this this finite region. Okay, so that's all relativity is. rel we're relativity is you take neuttonian physics, things moving in space and time. According to Newton, the forceces can be arbitrarily large. Vaucities can be arbitrary and large. Ein is gonna say there is a maximum speed level. Okay, there's for people that are interested in history, there's other reasons, not just this one, to to want a maximum speed limit, but I'm gonna just focus on this one. for for now. Okay, now. put a maximum speed limit, it looks like it's easy. You just say, there's a maximum speed limit. right? But there's a loophole, okay, and this is why Ein's a genius, okay? There' much so, first thing is, there must be a maximum speed, right? That's bobvious, everybody knows that. But there's a second thing, okay, and the second thing is where all the crazy physics about relativity comes in. The second thing is closing a loophole, okay? The loophole is, if you have a rocket that's moving at the speed limit and it shoots another rocket at the speed limit, relative to an observer, it looks like it's going twice the speed limit. Right? And so the math gets or you know, basically the relativity is changes Newtonian physics to get around this loophole, okay? And so the idea is there is a maximum speed limit, but this maximum speed limit must be the same to all observers, no matter how fast you're moving. okay? And this is really to close the loop of the plane shooting a rocket, right? It would be bad if the plane is moving almost the speed of the maximum speed, and it shoots a rocket, it's almost the maximum speed. It looks like a two observer that is going faster than maximum speed. Okay, so all the complicated math in relativity comes from the second loophole, right? Um, because again, otherwise, if you didn't have you didn't fix this one, you're back where you started, because this maximum speed, the speed of the rocket coming off of the plane is just this maximum speed plus some big number. Okay, um, and so the maximum speed we now know light travels at the maximum speed, so you say the speed of light. I think it's confusing to s to think about as a speed of light. It's really the maximum speed, okay? You just say there's a maximum speed. later, we figure out the light goes at the maximum speed. for reasons we'll talk about later. but we'll call this maximum speed. C, we call it the speed of light, but think of it here in terms of just in terms of the maximum speed and Okay, so I'm gonna draw the maximum speed as a 45 degree line. Okay, so I'm the yeah. Switches unit such that the maximum speed is 45 um and so the first the first change or the first fix the physics is all the paths have to that start at the origin, that start at zero, they have to be up here. right? You can't this is the maximum speed, you can't get out here. Okay? So that's that that's one thing. again, this one is simple, you just say you can't go faster than this. the upper speed limit. The other one is is the crazy one is that this line doesn't change even if something's moving. okay? This is the this is the one that causes all the chaos, okay? So if you're if in practice with this means, if you have a flashlight, the light beam is moving a the speed of light. If you're running in this direction and you turn on a flash the light, the light is still moving at the exact same speed. Okay? turns out there's a consistent mathematical way to do that. um it's not so important here. For our purposes, it's that's needed to close this loophole, right of the rocket coming from the airplane. Okay, again, that's all relativity is. It's this idea and then then there's math that falls, right? So if you wanna do this, so it turns out, if you wanna do this, you can do this by making space and time change a little bit, again, in details that aren't important you. Um, again, it's a relatively simple principle, simple idea, but it really has profound implications, uh that we'll talk about, talk about next. Okay, so imagine what happens if I have a if I have a light bulb in the center of a room okay? So as I said, we no light is traveling at this maximum speed. Okay, so let's say it's a laser and there's a beam that goes this way, and there's a beam that goes that way. The light is right at the center of the room. So if I describe this in terms of the space time diagrams, to an observer that's in the room that's not moving, okay, if it's a rest in the room, they see the light bulb turn on in the middle and at time t equals zero. okay, and then there's one light ray that's going to the right and it's going at the maximum speed and it hits the wall. There's another light beam that goes the opposite direction. It's traveling at the maximum speed and it hits the wall. Okay, that's how you describe this in terms of these space time diagrams. So the observer that's not moving, it looks like the left and the right hand pulses of light or photons hit the wall at the same time, right? The light reaches the walls at the same time to the observer at rest. Okay? Now, how about an observer that's moving? So let's say the observer is in the room and it is moving to the left. Okay? to them, okay, again, the light starts in the middle of the room, flash goes off, you have two two light beans that are moving at the speed of light, and remember, to close the second loophole, this is the same. right? This is this is moving the maximum speed the same as the other observer. Okay, so these arrows are these lines are 45 degrees. However, the walls are moving because the observer is running, so they have the observers are running to the left, moving to the left, the left hand wall is getting closer where it's moving you know, let's say the observer is running this way, the left hand wall is is getting closer to the light beam, and the other wall is moving away. So to this observer, it's just moving in a different direction, it looks to him like the light being that's going to the left, hits the wall first, right this time is lower than this time up here. Okay, the same thing happens if you're running the other direction, so now if you're an observer this running towards the right, now the now the right wall looks like a coming towards you, and the the other wall looks like it's going away, but the speed of light is the still as the maximum speed is still the maximum speed. so here, to this observer that's running the other way, it looks like the light hits the right hand wall first. Okay, so or is so it turns out you can have a maximum speed, but if you have a maximum speed, now this notion of when when did the light beams hit the wall is gonna be observer dependent? Okay, so some observers that aren't moving looks like the light hits the wall at the same time. Different observer, the left head before the right, so the observer the right hits before the left. Depending on how you're moving. okay, this is not true. right? Now and so we can draw this like this, so it for the just putting them all together, I'm talking and I'm not drawing the walls now, but to the deserve it that's not moving, they hit the same time. Zerver that's moving one the left hits before the right, vice vers the reserver the other way. Okay, so what we say is the order of which came first, that you know, you could ask what happened first? There's no well defined answer of what happened first. What happened first depend on depends on how you were moving. to an observer that's not moving, they happen together. So one observer, this one happened first, to the other observer, you know, same observer just moving a different different direction. the other one happened first. okay? um the only thing the obser so the observer is disagree on when they happen. They disagree on when and where they happen, but they all agree that that the light was moving at the speed of light. And that was our that was what we needed to close the loophole. Okay, so although they disagree on these numbers, so there's gonna be there's gonna be one one observer is gonna measure X one and T one when when this when the let's say the left one hits. this will be different. This will be different X 1 and it'll be different X&T for observer two and a different accentT for observer three. So these numbers are different in the name is the wall. However, they all agree that X1 is equal to the speed and upper limit times the time. All right? So, while they while the X and Ts are different, they all agree that the light was moving at the speed of light. Okay? So, they all agree that that these equations all these are the only equations I think. and so instead of instead of just saying this, what we do to physics is, well, I'm gonna make it a little more suggestive, so I'm gonna square both sides and then I'm gonna subtract them. Okay, so it's just this equation. X equals CT. I'm gonna square it and subtract it. So I get x squared minus CT squared equals zero. Okay, so all observers agree on this. Okay, and what we say is this is an invariant, meaning the time was something happened and the position with something happen is different, different observers disagree, but this weird funny thing reached take them you take one thing, squared, and subtract the other, is independent how you're moving out. The observer independent. Okay, and there's a direct analogy here to something you're more familiar with, and that's length, okay? So let's say you're in an airplane flying it over to campus and you look down and you see you see the the quad, right? So you and you wanna measure how big this quad is. Right? And you're in an airplane going this direction, which I guess is south? south, yeah. So your airplane going south, okay, going to Florida or something? You look out and here's your here's your next direction, your wide direction. You say, okay, well, you wanna measure how long this is. Well, it has a pretty small extent in wide and it has a big extent in end. Okay, but let's say there's another observer that's going um E east, okay, so they're going to New York, but they look out and they see the same thing, but it's at a different angle, right? Because they're traveling this different direction, and they see the extent of the quad is really, you know, it's really big and y to their you know, to in their wide direction, and, you know, moderately big in their ext direction. So these observers are looking at the same thing. They're looking at the same physical thing, and one of them sees nonvalued X and a different value y, um, and the other one sees a one of them sees one value X and one y, the other observer sees a different value of X and a different values Y. So they disagree on how far they are in X and how big they are in y, but of course they agree on the length, okay? So they agree that if you take X squared plus y squared, that's the that's the length of this, right? If you get the length of this, like a triangle, you would take x squared plus y squared here. So while they disagree on the X's and the y's, they agree on this funny combination of X squared plus y squared, which is how triangles work. Right? And so, in fact, if you were at it it doesn't so this is this is the one observer that's going south, this is the observer that's going east, of course, you could go on any direction, and it doesn't matter what direction your plane is going. If you look down on the campus, you'll see different values of X and Y.? You'll see different values of XMY, but you'll all agree that they all line on this circle. and the circle is the length the the circle is the length of the gua. Okay, is everybody everybody happy with that? Oh, no. I'm happy with your explanation, and I'm I'm unhappy with the phenomenon.. it's kind of like you know, I want I need I want to measure some object and I could measure it with different angles, right? And so you know, there's different it'll have different Xs and y's and there's this funny thing that if I swear an add that, I'll get it's independent of the angles. So, so that's the thing that has physical meaning, not the actual exis andise, the and why is dependent on how I look at it, but the length of the thing, which is the X which is any particular X squared plus or y squared, that is the disc, and that's a physical that that's what has physical value. The actual coordinates are just labels that we use to drive that physical fit. Coordinates meaning the space and the time. Well, in this case, it's just space and space. It's like space in this direction versus space in that direction. And so different observers in this case, it's different people looking with a different angle. But they're not moving. They're not moving here. in in this example, they're not moving. They're just looking at with a different angle. and they'll measure different coordinates. But they all agree if they take their coordinates, square them and sum them, that they'll get the distance squared. Right? I'm a cabinet maker, so that kind of doesn't square with building a cabinet. You build a cabinet like that, you got problems. It just depends on how you look at it is the speed of life. yeah, so that's a complicated question. Let me let meunch on that it back. I I just want to connect this in that analogy that I'll come back to that. them to So that's the photograprap here. it is the photagger theory here. X squared one wide square equal. A post be equals squared.. but that's in triangle. Yeah, so that's a triangle that's what's happened here.. you want this distance. And so what's what's so there's a direct analogy between distances and the angle that you're looking at it, in relativity, where in in the relativity case, it's now oops it's now the velocity is like the angle that you're looking at it. And instead of an extirection y direction, you have space and time. Okay, so different observers disagree on the coordinates, but they all agree if you square the coordinates and subtract them in this case, so there's a funny minus sign here, right? This is like distance with a minus sign. They agree. Okay, so so it's it's it's kind of like this is kind of like Pthara oforem, except there's a minus sign, and instead of space instead of like X X squared plus y squared, you get X squared minus times squared. Okay? And different observers that are moving with different velocities will disagree on the coordinates, but they will agree on this and variance. Okay? And that's just like in if you measure the distance, it doesn't matter it doesn't matter what angle you're looking at it, you'll get the same length, but you'll have different coordinates. And you see it always constant? So, see is constant, so so back to your question, so so how you met how do you determine what the the concept velocity? Well, there was a So there's experiments you can do, right? you could do experiments that to do this to measure the speed of light, but actually you had a prediction from the theory that gave you the force of the electr magnetism, that predicted that waves were moving out of constant velocity. and that predicted that that constant velocity was independent of how you move. So this was one of the the other reasons I was talking about where Einstein was motivated by this thinking, and there you could you could actually predict it from simple calcul some simple experiments with electricity magnetism. You can indirectly infer what that speed is. So that's really how they did it. but then once they had this idea, then you could you could actually try to measure, like, and there's a different ways you could do that. Okay, um good. So, okay, so in and in in this case you have a circle, right? The different observers disagree, but they all agree it lies on on the somewhere on the circle. In this case, because you have this funny minus sign, you don't have a circle, you have a hyp hyp hypererbola. Okay? And so here, this is when the light goes off, okay, so this is again, a space, this is the space and tie diagram, and I drawn this maximum uh speed. Speed them here. Right? And so you have a light goes off and then here's where it hits the left wall. okay? So it to one observer, it it hits at one value X X and T through a different observer well, you have different coordinates, different spaces and times. They disagree on these numbers, but they all agree that if you take X squared and you subtract the speed types of times squared, it lies on this on this line. Okay, so they all again, it's crazy. Things are happening at different places in space and time, depending on how you're moving, but it's constrained to be on this hyper. They can't just be anywhere, they have to be somewhere on that hyperbola, and that's because of this funny minus sign. Okay, even even more crazy, okay, note here, everything is in the future, right? The light goes off and it hits the wall in the future. Here's something is even crazier. Now let's put the origin when the when the light hits the left wall. Okay, so now we're gonna start, you know, zero is gonna be when the left when the light is going to the left, hits the left wall. and now we ask, when does the light hit the right wall? Okay, so the observer that's not moving, these habit at the same time. right the light hits the right wall at the same time, the light is the left wall. What do we observer that's moving the observers are moving, it either hits the right wall before this happens, where after. Okay, and again, these numbers differ depending on how you're moving, but they all agree that it lies somewhere on this hyperole. Okay, again, this is this is wild now, right? Because here, something whether or not it's in the future or the past depends on how you're moving. okay? And, okay, again, this seems crazy, but we've proven this to be true, and one of the things that the undergrads do is they they actually do experiments to to show this, there are these things called muons that that we' talked about and we're detailed later, uh, they're born, let's say they're born zero, they die some finite time later, and where how long they live depends on how you how they're moving. Okay? Um, so this is when the view ones are born, this is when they disintegrate. and if they're moving very fast, it looks like they live longer. Okay? And this is an effect that you can measure. In fact, um well, the new ones are hitting us now, so so they there's protons, we actually don't understand this very well, but there's protons coming from in our galaxy or even Al galaxy that hit the earth. again, we don't really have a good understanding of where they're coming from in some cases, but we know that they're it's protons main in the Europe. These pro when the protons hit the earth, we know pretty well what what they what they do. changes, you know, is variable, but they produce mulons, and among other particles. These and we know where where how far away that happens. so that happens at the upper atmosphere. These muons are, even if they're moving the speed of light, they don't have enough time to get here, uh, based on how long they live. Okay? Unless you have this effect of time dilation, because they're moving very fast to observers that are at rest, it looks like they're moving incredibly fast. And so the fact that they're they make it to Earth is a direct result of this, we say time dilation. And the the time depends on how fast something is moving. Okay, so again, it seems crazy it's and it's a direct outcome of trying to put an upper speed in there in in physics. Souons were discovered kind of by accident, looking at looking for another particle, um, and I will come back to talk about that in a later lecture. Yeah, there were very very confusing particle. we have no good understanding of why they exist to this thing. They're kind of a mystery. Okay, so it has the big effect on events, right? so there's no notion of whether things happen at the same time. That's observer dependent. different observers will disagree on when it happens. It also has a big effect on mass. I think you were alluding to this earlier. uh, so what would you at the LHC or would you what you can do in general is you could have a particle, let's say, a proton that is going around in a ring. so it's going around in a circle, and we know how to keep it in a circle using conventional physics, magnets, and so on. And what what we do with the LAC is every time the prototon comes around, it gets a little kick in this in this region. And so we actually and this this is a electroagnetic as well, you know, we we give an electromagnetic force here, kick it around, and it can it goes around and and because you can keep in a circle, this just keeps happening over and over again. So this is how we accelerate the protons. They go on a ring and they get a little kicked and they go faster and faster and faster. Okay? And so we give a force, and that means it's changing its momentum. That's what Newton taught us. every time it comes around, it gets a change in momentum. And now what's in so you can you can ask, well, how big is this changing momentum after a long time? right? So you you use this for a long time, well, this change of momentum is equal to the force and each kick that it gets times and number of kicks. times how often it comes around, okay? And remember the momentum is nothing but the mass times of velocity. Okay, now you have a problem because this number can be arbitrarily high, right? We can give as many kicks as we want. This V cannot be arbitraly high. We have a upper speed limit, right? So that means the only way for this to work is mass can't be a constant anymore. When you get close to the speed limit, or let's say you saturate the speed limit, you're moving at the speed limit, you're still kicking it, it's still changing momentum. The only way for this equation to work is that you're changing the mass. Okay, so there's a profound impact on mass as well, that all comes from the speed. I' just gonna put in the speed and everything's gonna be fine. but it has downstream effects. One of the downstream effects is the mass has to depend on the velocity as well. Okay, um, and that's what I' saying here. So mass increases was. Okay, good. Any so that's the first revolution. Any questions? So what yeah, you know, we we probably won't get through all this. can't resolution. I'm reminded of you assum.. slow down no or whatever perfect vacuum.. We put it in perfect vacuum. Yeah. I in practice in the vacuum is not perfect, there is a lot of, but we can get very close to the speed of light. even with those effects. Okay, good. um, so that was the first revolution. So again, the first revolution conceptually, it's it's relatively simple. You just put a maxi in on and you have this loophole, you got a close and that loophole means there's this funny minus sign and that means you have time dilation, things live on hyperbolaas, not circles, and mass depends on velocity. Okay? The second revolution, quantum mechanics was much harder, okay? You can tell because there's more people in this picture. a picture is just Einstein. This picture there's a lot more people, including Einstein. He's also a picture. Uh, so, the way to think about this is relativity, it took it took concepts that we were already familiar with. Space and time, and he taught us how to think about them in the right way. right? So he so he said, basically what we were doing is correct, except there's this upper speed limit, yada, yada, yah. With quantum mechanics, the revolution is much more radical. as we'll see, what what they did in quant meanics is they basically threw everything out, they said, okay, everything that you thought you know is not correct. There's no way of thinking about. You need new things. um and it really took the whole field basically a whole generation to really understand what was happening. okay? Um, and it's again, it's a much more radical departure from what came before, and it's it's much less intuitive, right? This idea of these things moving in space and high is something that kind of we have an intuitive sets for. with quantum mechanics, it's much more abstract. It's much more formal, and it's in many ways it's much less predictive as we'll see. Okay, um so many ways to talk about this again, and this could be a whole course in in a university, um and actually we have three semesters in this for the undergraduates. um but one way to think about this is to think about what Ads look like. okay? So there's this cartoon idea that Adam, the kind of like the the planetary model, you know, which is not not totally b, but the so the idea is that you have something in the center that is positively charged, um and you have electrons in kind of orbits, you know, outside of it the negatively charged. Okay, um and the so the electrons uh, they take up like all the space, so the size of an atom is really given by the size of these electrical orbits, but electronic orbits, whereas the nucleus, uh it's very small. It's like 10,000 times smaller than the size of the atom. uh bigger than that, um, maybe 100 thousand times. but it has all the mass, almost all the mass of the atom is in the nut tools. Okay, this was this picture and and this was something that was forced on us by experiment, I, you do experiments on atoms and this is the picture that looks like, and it kind of looks plausible because you have these orbits, you get we know we have orbits from inverse square law for gravity, right? That gives us planetary orbits, you have an inverse square law for that lux of mechanism too, so it looks kind of plausible. but it's problems. One is, if you apply the the physics that we know, electragnetism to this, it would predict that almost immediately these electrons would spiral into the nucleus. so they would be unstable. Okay? So question, why is why is matter stable? We don't wanna be because this is the before bond against have no idea. okay? Um this is a big deal. What, you know, also important is you can ask, what is the light that, you know, how how do you interact with this atom of light? um, and physics says, this is much less of a problem, you can't you don't pres atoms exist, but so assuming atoms exist, you would predict that the atoms while they existing for like 10 of the minus seconds, they give a continuous spectrum of light, so they interact with light of all colors. That's what they would predict. It's observed that they only interact with very specific frequencies, special colors. Okay, again, this is more of a detail when you don't, predict that atoms can system in the first place. and there was also this idea of particle wave duality, right? So some things look like behav like matter, and some things behave like light, likeaves. Okay? Again, chemists were how fine with this? physics physicists had no idea how to do this. okay? Here's an example of what, um, what I mean by these special colors. So this is if you so physic physics would predict the light given off by an atom that kind of look like this. You have all colors, right, more or less, whereas what chemists observe is if you burn the particular atoms or particular elements, like sodium, hydrogen, calciumylon, you don't see this. You only see light at a certain well defined colors, right? And this was super useful for chemists because they could burn something, finger this is like a fingerprint for the atom or for the molecule, they could fingerprint it and f figure out what stuff is made of. right? So it's super useful. um, but phys physics, you know, where are these magic numbers coming from? No idea. Adam shouldn't exist in the first place. What' causing frequ before they knew the ship, the structure you had them. So they assumed it was continuous, why would they assume anything you burn it? It just a fire gives off all frequencies, I mean, what was the then? So the detail is um the frequency so the frequency of light depends on the frequency of the app or the electron in the app. But before they knew that, I think that's, so they you know that from ENM. They already from electromagnetism, you know that they assume the the initial spectrum that it was it can use. This is a prediction from electromagnetism. that it would just be everything. okay, okay, I got. electromchnetism, which is the theory that they knew, you know, you have tele telegraph wires, you know, they' they're using it's like a tech modernate technology that they know well. It predicts this. and it way predicts an atom shippists, and then this is what it says it observes. It's even worse than this, because of the catastrophe. Well, that that yeah. yeah that is that the next step is that yeah, that's it's worse than this. It's it's not yeah, it's not only that I don't even it's like this, it's also infinite. The amount of energy is infinite in some sense. Which shows it's a basic obviously wrong.. Um, okay, and there's a long period of confusion, okay? Because you can imagine what's gonna be the how are you gonna solve this problem? Well, either this model of the of the atom is wrong. Either it's not this planetary thing, you know, maybe that's wrong, or maybe the force is wrong. right? Because that's the only thing going into it. It's you have this picture of nucleus electron, and you have the force. And so you might imagine that the you know, the well, the obvious thing is the model's wrong or the force is wrong. and so that's if you read this, if you read the history of science in this time, there's really there's a long period of confusion, because that's the obvious thing to think. It turns out, again, after several ad hoc theories that giftgiving partial answers, um, we we we have a unified and consistent theory now, um, it turns surprisingly solution is not a modification of the force or the model, right? So the model was right, basically it's like these orbits. The force is right, it is electric mechism, just like we know before. but it's a completely new framework for how electrons are allowed to move. Okay? can't you wouldn't think of this, right? You would you think that, we know, right? It's we've been doing it since Newton. We're not gonna change that, it's probably this latest thing ENM, or or maybe it's, you know, this model of electron is added was discovered a couple of years before this. Right? And so it's um the big surprise is that those things were right and it's how electrons can move in space and time that needs to be changed. Okay? That's that's the upshotant mechanics. Okay, so the so the so what again, the kids very formal and I'm gonna try to just focus on the concepts here. But the idea is that you shouldn't really talk about trajectories within the app, okay? It's it's kind of wrong to draw these lines, like what we were thinking about. Instead, there's some new mathematical concept called the amplitude, okay? This is a made up word, or the amplitude? and the idea is, this amplitude is a is the only fundamental physical entity. So forget what you thought about things moving in space and time. it's this amplitude. okay, this describes everything there is to know about the electron. um and with quantum mechanics tells you is it tells you if you know what this amplitude is at a certain time, okay, so this amplitude is will be a function of space. If you know what it is at a certain time, it tells you how it changes in time, okay? So that's what quant mechanics is about. And these behave like waves. that's all we'll need to know here. um and then the other thing that's important is these amplitudes are not it's not like the position of the electron. They're related to probabilities, okay, so so now everything's probabilistic, and the probability of finding the electron in some, let's say some position is given by the amplitude squared. Okay, so you have this number that describes the electron, and that number, in order to convert it to something physical, you have to square it, and then that thing is just gives you the probabilities. Okay, so again, much more abstract, right? You imagine, people are not this is why tech takes so long, right? People are not happy with this. you have probabilities, um and so, right, so what do I mean by probabilities? Well, so these we were talking about these muons, okay? So muons live for a finite amount of time and then they disintegrate or they turn into other particles. and here I have two muons and they have exactly the same amplitude. Okay? So, as far as physics is concerned, these new ones are identical. There's no difference between them. Okay, one of them might might decay in 2.1 microconds. Okay, so it might there these last variond two miccond, the other one can identical amplitude, the case at 2.3. Okay? So so how an individual new one will will behave is different. There there's some randomness to it. Okay? They're all roughly 2.1 micrconds or or roughly two micrconds, but but the detail is different. and and you can only predict how a large ensemble of mons will be the case. And that's what you predict the pability distribution of of a big sample of muons, not how an individual mulin will decay. So this is a huge loss in predicted power. right? So at any given time, physics or quant quant mechanics or physics cannot predict what's gonna happen. So it can't tell you this mon is gonnaate at this time. it can just tell you the probability of this can decay within a certain amount of time.? This is totally unlike Newtonian physics. The physics of Newton you knew everything you knew everything and infinitely far away, you could predict everything in the future. I signed was a little better, if you knew everything a finite distance away because there's a speed limit, you could put everything in the future. Here, you can't predict anything with certainty, you can only predict on average. okay? Huge loss in predictivity. God doesise. Einin famously was not happy with this. He thought, there's no way the fundamental this must be we don't maybe there's some other property about the mule on that we're not measuring, and that's why this one in the case worth that one. He thought, God doesn't throw dice. um, but he was wrong, something. And he realized that he about the amplitude, how do you know the amplitude?, how do you measure the amitude? Is it is it a constant? No, it's it's a function and and it's a complex number in general. Is thatman? Is it what? Is that? Richard Fman, we'll get to findman. he gave us a way to calculate the infages. Yeah, he gave you a way to copy him. Okay, so, again, is is is amplitude does it have any relationship to our thinking of what amplitude is? like amplitude of a away? I look like waves? They like waves and that's where the term amplitude comes from.. I mean, I would think of it more wasn't made up. It just that it's Hey, Shakespeare did it all the time., so inventing we're basically inventing. You could have named it anything. amplitudes. It's often called wave function. It's different like the probability behaves that way. If you square it, but if you right, and it's it's related the probability of where it exists, a lot of physical amlication. I think that's That's what I'm asking I think that's you answer my question, thank you. Okay, yeah, so again, the there's a lot of map that you, this is very precise, okay? the probabability is very precise, but it gets complicated, differential equations, kind of um you know, undergraduable map. But if you would just focus on the concepts, it's actually we can map it onto our simple picture. So, before the simple picture was, it's about how things move in space and fine. One of the up this is this is without all of mechanics. and one of the things that you could do is you could know, I mean so I didn't trust this, but this line you could think of this as being infitely thin, right? And this angle is and being infinitely sharp, right? So you know this angle and you know um the X value. of course, on on the slide, there's some thickness, but you can imagine the limit when this is when this is up known, and the the angle is related to the momentum, remember, which is mass times the velocity, and and then the city exper. Okay, in quantum mechanics, if you want the kind of the upshot of quantum mechan says, you're not allowed to draw if it was bin lines. You have to draw wedges. okay? There's some thickness to the lines. So if you really zoom in and there's a couple different ways you can do this. So, if if you if you know if the X value is very precise, so if you know the particle is here, then there has to be a significant spread in its momentum, okay? So so so you're allowed to kind of know one or the other, right? So in this case, I know really where it is very precisely. It's like right around here, but I don't know the angle, or I don't know the momentum. So I can't draw if the line, I have to draw a triangle. okay? or you can take the other thing. you can know the angle find in this case, I know it's momentum very precisely. I know the angle. Well, I but if you're in that position, then you have to be uncertain on its position. Okay? So, you you can you can kind of be in this position or in this situation or in that situation, um, but the bottom line is you can't draw infinitely thin lines. There has to be some thickness. And you can you can either be like a triangle or it could be more like a wedge. Okay? um right, and and so that's the same thing, and so so so this is often written as so, um in this way, so this delta X is like the uncertainty on its position. times the uncertainty on its momentum. this is something that's bounded by some new number, so there's some new fundamental constant in nature that says how thick these things have to be. okay? um and yeah, I think that's all I wanna say. So so this is how we're gonna think about quantum mechanics. It said that we have probabilities, we need to talk about probabilities, and if we're thinking in terms of space and time, it's these thick lines, not different that lines. Okay, um, and sorry, you can think about this in terms of there's another way of thinking about this in terms of energy and time that might be useful later if we could I'll come back later. Okay, um and then the thing that I want to end with is this is not this is not about our uncertainty. This is not a statement that we can't know the position and the momentum at the same time, It's a statement that those concepts are different. They're fundamally different. And so that the example is here. So here's a sketch of this now this is not space and time. This is like the amplitude in space. Okay, so the amplitude is a function of space, and let's say piece here very sharply, okay? This represents the particle that has a well defined position. If I square this, I'm gonna get the probability and the probability is gonna be around here or it's gonna be zero out here, so I know the particles within here with very high probability. Okay, so this is what it means to have a small probability independent how we measure it. This is what it means to have a well defined momentum, so to have a well defined momentum will matters is that difference the distance between peaks, okay? So the distance between peaks tells you how big the momentum is. So if the distance between piece is bigger, the momentum is smaller, if the distance between peaks is smaller, the momentum is bigger. this is something that comes out of the map. but note, the only way to have momentum is to have multiple peaks, right? Because you' it's the distance between peaks. If you have multiple peaks by definition, the particle can't be localized, can't you can't have one peak. Right? And so it's it's either in this state or it's in that state, in this state, there's only there's the momentum is totally ill defined because there's only one peak. Here, if you there's the position between peaks is very well defined, but if you square this, you're gonna have probability good probability for seeing the partle over all of space. Okay? Another way to think about this is if in order to make up this thing in order to make this wave function, I have to take copies of this wave function that have a well defined position and put them at different positions. right? So in order to be in a state where you have a well defined momentum, you have to have you have to be made of many states with different well defined positions. And it's the same thing with momentum and complicated way. If I want to get a peak in position like this, I need to add up I can do it by adding up waves that have different frequencies, different dist between P. Okay? the math doesn't the math doesn't matter, but what I wanna stress is it's it's not about how we measure the particles. It has nothing to do with how we measure them, that means that they can't have a well defined position momentum. It's if you're in the state of having a well defined position, by definition, you cannot have a well defined momentum and vice versa. Okay? And then the last thing I'll show is typically we deal with part with wave functions or ampludes that look like this. They kind of have a sort of well defined position, you know, it's zero outside of this region, uh, but within this region, there's many different peaks and there's a well defined distance between these peaks. And so this is what typical wave functions would look like, where you would have a reasonably well defined position and a recently well defined momentum, but you can never have both of the same time. Okay, um and I think that's really what I wanted to get there with with on again, so next time we're gonna start and we're gonna see how this explains the stability of matter. Right? So is now this is help our stability matter. And then we're gonna get to the big drama, the big drama of the 20th century is how do you put these things together, okay? You have these two revolutions, and we'll see, it looks like they are impossible to put together, and we're gonna find that it's just barely possible, and that dictates how physics can be, including eating all these crazy part of. and so that's that Nice job, man.

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