The Origins Podcast with Lawrence Krauss - Physics for Everyone, Lecture 4. The Beating Heart of Modern Physics: The Dog Who Didn't Bark in the Night.

Episode Date: August 18, 2026

This lecture, recorded before lecture 5, which was released a month ago, actually more naturally follows it, which is why releasing it after lecture 5, while unintended, actually makes sense. In the last lecture I described the most important unification in all of physics, the unification of electricity and magnetism, a unification into electromagnetism by James Clerk Maxwell in the 19th century. Because of its elegance, and its overpowering utility, the theory of electromagnetism has provided the prototype for all modern physical theories that have followed it. As I show in this lecture, the form of electromagnetism is governed by a new mathematical symmetry in nature, called gauge symmetry. It turns out the existence of this symmetry is profoundly important, and it not only governs the exact form of the theory, it turns out to govern the form of all the known forces of nature. Before we get to gauge symmetry, I want to explore more generally what is meant by symmetry in physics, and then I want to redo elementary physics by thinking about symmetry. In my mind, the fact that basic physics is introduced without reference to the symmetries of nature is perhaps the greatest failing in the teaching of modern physics. Concepts like energy and momentum have relevance because of fundamental symmetries of space and time. The facts that energy is ‘conserved’, and momentum is ‘conserved’ in systems, which rigorously fix determine the form of Newton’s laws of motion, are often introduced as if they are dictates on high, like the ten commandments. However, once one understands that these arise from symmetries of nature, the fact that these quantities exist and are conserved, becomes immediate, as the remarkable mathematician Emmy Noether showed at the beginning of the 20th century. Finally, as important as mathematical symmetries are in governing physical laws, it is equally striking that even if these fundamental symmetries exist in nature, they may not be manifest in particular situations. For example, gravity and electromagnetism don’t distinguish between left and right, but if I look around my room, the left side of my room looks very different than the right side. This is an example of what is called ‘broken symmetry’, one of the most subtle and impactful notions at the basis of what is now called The Standard Model of Particle Physics. In this lecture I review all of these ideas, which are essential if we are to go beyond the physics of the 19th century to understand the physics of the 20th and 21st centuries. Enjoy. As always, an ad-free video version of this podcast is also available to paid Critical Mass subscribers. Your subscriptions support the non-profit Origins Project Foundation, which produces the podcast. The audio version is available free on the Critical Mass site and on all podcast sites, and the video version will also be available on the Origins Project YouTube. Get full access to Critical Mass at lawrencekrauss.substack.com/subscribe

Welcome back to Lecture 4. I'm particularly excited about this lecture because I want to talk about one of the subtlest but most important concepts in physics that's probably least well understood among the public, but basically determines all of modern fundamental physics as the concept of symmetry. Symmetry has a very different meaning in physics than it does in popular parlance, at least in general as I'll try and show you. And perhaps to understand how significant it is in physics, in a different way than it's understood in the public. I want to give a quote from the stories about Sherlock Holmes. One of my favorite quotes there is a dialogue that occurs in Sherlock Holmes story

where it says, someone says, is there any other point to which you would wish to draw my attention? And Holmes says, to the curious incident of the dog in the nighttime. And his interlocutor says, the dog did nothing in the nighttime. That was the curious incident, remarked Sherlock Holmes. Sometimes nothing is very important. Obviously nothing has been very important to me. I've written books about it.

But in this case, nothing happening is the central feature of symmetry. And let me try and describe that. Here's one, of course, one of my favorite artists, M.C. Escher has lots of beautiful, beautiful examples of art with symmetry. Here are these great little reptiles. And you notice that every different color is exactly the same reptile, but they're flipped in different directions. Here's fish and I guess butterflies and or something like butterflies. And you notice that it's beautiful symmetry, intricate symmetry, or perhaps nature's, one of

nature's favorite intricate symmetry in my mind is something like a snowflake. Beautifully intricate patterns and every snowflake is different. But what's relevant in physics is a feature of the symmetry that may not be fully appreciated in art or maybe it is. Not Notice that what is characteristic of the symmetry here is that if I move every fish over by a certain distance in this drawing, the drawing remains the same. Or if I move the butterflies over by this fixed interval, then it can continue forever. It's a pattern that repeats with the periodicity, and the periodist in this case is this fixed interval between the fishes. Similarly, here, I could, I could, there's a variety of symmetries.

I could change the colors. I could turn all white into whatever color this is. I'm colorblind. Let me take white and black, at least I can distinguish them. I can turn all blacks into whites and whites of blacks there. And you get the, you get a very similar pattern. So, so there's that kind of reflection symmetry or color symmetry. But also, once again, I could move, if you look, the pattern repeats, I could move this over here, that over there, and, and, and, and, and, and, and, and, and, and, and, Again, there's a repetition. And if you remove the whole pattern by a certain distance, nothing changes. Just like this, if you move these fish over, nothing changes.

Things remain the same under a translation in space, in this case, a fixed translation in space. In the case of a snowflake like this, there's a regular periodicity of 60 degrees. If I rotate the snowflake by 60 degrees, then the pattern repeats. It has to do with the polar nature of water, as it turns out of H2O. And as intricate as it is, from a physics point of view, what's really important here is that rotating it by a fixed angle

produces exactly the same object. And that symmetry restricts the kind of things that can happen. And the fact that symmetry restricts, restricts things in physics is central to our modern understanding of nature as we'll get to. But there's another feature of symmetry that's important. That symmetry restricts how you can describe the object. Whatever physical description of this snowflake, as complicated as it is, if it's a mathematical description, it will be restricted so that that mathematical formula looks the same when you, as a function of angle, when you rotate the angle by six.

Now in that sense, the fact that symmetry restricts what's possible. The most beautifully symmetric object in physics is not the intricate slow flake or something like that of MC Escher, but rather, once again, coming back to my cow as a sphere, a sphere. There's nothing more beautiful than a sphere because there's nothing more symmetric than a sphere. In this case, let's consider the sun as a sphere. Well, it looks like a sphere from far away.

But I'm I use the board a little bit in this lecture, but not as much as the last lecture. But if I draw a sphere, to show somehow that it's it's not just a circle. The point is that a sphere looks the same no matter how you rotate it. So if you think of angles along the equator, say theta, or angles along the the the longitude, call it phi, theta phi, Greek letters we use for angles.

Clearly, it doesn't matter where you are on the surface of the sphere. It's exactly the same. So whatever physical descriptor you're going to use, whatever physical property associated with that sphere is, it'll only depend on one thing, the radius of the sphere, nothing else. And if it's a solid sphere, not just a circle,

then all physical properties will depend upon the distance from the center, but they won't depend upon where on which direction you head out from the center. So every physical quantity, whatever that quantity is, I'll call it Q, is only going to be a property of, sorry, not a big R, of little R. Every physical quantity can only be dependent upon one variable, the radius. And every quantity that describes that the physical, of what's going on can only depend on radius and not depending upon angle or anything else.

That makes the physical description of that object much simpler. So, let's assume that the sun is a sphere, and now it looks like a sphere from the surface, but of course it's complicated, there's nuclear explosions, billions of them going on every second, and turbulence inside, and maybe there's rotation and everything else, and maybe the inside of that sun is very complicated

and things are very in homogeneous and convoluted, and why should we assume that the Sun, that treating it as a sphere is a good, is good. Well, we find out whether it's good or not by testing our ideas. So if we treat the Sun as a sphere and treat it as a gas of hydrogen, and through most of the Sun,

you're just treating as a classical gas of hydrogen, largely, and ignoring the rest of the stuff in there, for the most part, works pretty well. And if you do that, we can derive properties of the Sun. And we can just draw it. And we can describe the speed of sound as a function of the radius of how far you are from the center of the sun to the outside, or the temperature from the center of the sun to the outside, or the density, or the pressure, all sorts of quantities that only depend upon radius.

So that's great. Well, but how do you know it's reality? Well, that's an interesting question. This is our toy model of the sun as a sphere, and the question is, is it any good? Is that approximation any good? Certainly it allows us to solve the equations because the equations which are just a function of radius turning what is a three-dimensional problem essentially into a one-dimensional problem,

distance from the center, makes it much easier to solve the equations. That's wonderful, but nature doesn't exist so that the equations are easily solvable for us. The question is, are those easily solvable equations a good description of nature? And to see if they are, one way to try and understand how good this is

is to what you can try and actually measure properties the sun inside looking at vibrations and waves and seismology but one of the ways is to look what's happening near the center of the sun which determines in some sense the temperature the rest of the sun. And there we know something strange is happening because it's a star.

For the longest time these equations were solved in the 20s for the inside of the world. or even before that for the inside of a star. But the problem was, they might be a good description, but nowhere in that description was an explanation of why the star shines. The star is hot, but what keeps it from cooling down? And everything that, every mechanism

of people have thought that might power the sun, like in falling gas will release energy when it infalls, and so maybe gravity was powering the sun. And in a very vague way it is, but it wasn't sufficient. the sun should have cooled in less than 100 million years. And by the way, it was used by Lord Raleigh, I think, to argue, therefore, the earth was less than 100 million years old,

because if it was older than that, the sun would have cooled by now. But then it was discovered, of course, that the earth was much older than 100 million years old. Rocks and other things were discovered that eventually we now know the earth is 4.5 billion years old, as is the sun. 4.55 billion years old, if you want to be a little more accurate. And for the long time, there was a question of how the sun could be powered. And I think it was Sir Arthur Stanley Eddington who wrote a book about this,

but the internal constitution of the stars is, I think, the title of the book. And he didn't know what the power, what was powering his son. And I think he got, he, you know, and the real problem was that the temperature in the of the sun is a few million degrees, which may sound pretty hot. But in fact, you could reproduce those conditions on Earth and known physics, and we knew the laws of physics that looked like up to a few million degrees. And there was no new energy production mechanisms that might explain the existence of stars and why they shine for billions of years.

And in one of my favorite retorts, when someone was asked him, you know, surely, surely it must be hotter than that. There must be some... These equations must be wrong. It can't be just merely 10 million degrees. And he looked at the person and said, well, go and find a hotter place, which is like, go to hell.

But in any case, what was then discovered and understood, actually, ultimately, as a result, in part due to the war effort of at that time, both the United States and Germany, to develop an atomic bomb,

is that nuclear reactions could produce commend its amounts of energy. And it was possible for nuclear reactions to power the sun. And the person who first understood those nuclear actions and explained them was a physicist who was the head of the theory division at Los Alamos, Hans Beta, but even before in 1939, he had actually written down in a series of equations

that could show you could power the sun for not 100 million years, but 10 billion years, with nuclear reactions that would turn hydrogen into helium. And there's a whole series of nuclear reactions that power the sun. Protons, hit it protons, and go to Deuterium, the basis of heavy water, and then you can get deuterium and a proton. It can turn to helium three, and helium three and helium three can turn to helium four. One of the mechanisms to produce.

Each of these reactions releases energy. Or you could go helium three and helium four produce beryllium, which then captures a protein. It produces boron and then boron decays to beryllium, or you can actually have beryllium and produce, go into lithium. And there's a variety of other processes. These sidechanged, these numbers are showing 99% of the energy the sun is produced through this kind of, this kind of process.

Certainly all of it starts with p.p. going to deuterium and then various side chains. Now what you notice, as well as the nuclei that are being produced here, and things like positrons or photons, that's what that is. There are these weird particles called neutrinos, my favorite particles in nature. Neutrinos were not even, we'll go to the discovery of neutrinos in this very lecture. But at the time when Beta wrote down these equations, while it was well known, well assumed that these neutrinos were produced in nuclear reactions, no one had measured them.

It wasn't until almost two decades later when Fred Rhinus and others at Los Alamos went near a nuclear reactor and measured the existence of neutrinos. But because the central power production mechanism of the sun produces neutrinos, as to a bunch of other side reactions like boron, going decaying to beryllium, there's a neutrino. And beryllium capturing an electron going to lithium and producing a neutrino. there should be neutrinos being emitted by the sun. That should be a signal of the nuclear reactions going inside the sun. Now, we can't see those nuclear reactions directly with light because the light that's produced in those nuclear actions in the center of the sun, the heat,

it actually takes a million years to get to the surface of the sun during where it goes from a temperature of 10 million degrees to a temperature of merely 5 or 10,000 degrees. And so when we're looking at the sun, we're looking at energy that was produced. a million years earlier in nuclear reactions, so we can't see them directly. But if we could see the neutrinos, neutrinos are weakly interacting particles, so weakly interacting that neutrinos that come from the sun can go right through the Earth

without even knowing it was there. And in fact, because neutrinos are produced in the reactions of the sun, there are a tremendous number of neutrinos being produced by the sun. In fact, every second of every day, there are 60 billion neutrinos going to be in the sun. going through every square centimeter of your body coming from this reaction in the sun. During the day, they're coming from above. At night when you're sleeping,

they're coming right through the earth because the sun is now, you know, the point over on the other side of the earth, but they're going right through the earth and without knowing it was there and through your bed and through your body. Think of that when you're trying to sleep, as I like to say.

And 60 billion PP neutrinos, because this is a side chain, there are only something like 50 million or maybe 5 million neutrinos coming from this side chain. Now, if you could just detect the neutrinos in the sun, you'd therefore, first of all, prove there were nuclear reactions of the sun, but something else. All of these reactions depend sensitively on the temperature of the sun.

This, I think, depends on the fourth power of the sun. This one, I think, depends upon the eighth power. And this one, the border. or on neutrinos, which are the most energetic neutrinos that come from the sun, that depends as the 24th power of temperature. So we can make predictions about how many neutrinos would be emitted as a very sensitive thermometer of the sun. And we can see if our ideas about temperature,

assuming the sun is a sphere work. The first person to take this seriously at a time when neutrinos hadn't even been observed almost when he started to think about this, but certainly not much later than that, not much later than that, was a heroic chemist named Ray Davis. Ray Davis took these, talked to a theorist named John McCall took these predictions seriously and said, if I could detect neutrinos from the sun, I would prove the sun as a nuclear reactor, first of all, but maybe I could probe the nature of the sun.

And he built in the homestake mine in South Dakota a huge tank of cleaning fluid, 100,000 gallons of cleaning fluid. and starting in the 60s, and you could do calculations that while most of the neutrinos that come through this detector go right through the earth without knowing it was there, about once a day, if the calculations were right, if our model of the sun was right, about once a day a neutrino would come in and hit the nucleus of an atom of chlorine in the detector, turning it into an atom of argon. So there should be one atom of argon produced in 100,000 gallons of cleaning fluid each day. That sounds ridiculous.

But this chemist Ray said, I could do that. I could detect 30 atoms of argon a month if I could build this detector, and I could measure neutrinos coming from the sun. And he built the detector, and he operated it for over 20 years. And when he did, something very strange came out. There are other detectors that were built later, a water detector, or another kind of detector, but this is the home state gold mine detector.

This is the predicted number of events you should see. This was only sensitive to the boron neutrinos from the sun, the most energetic neutrinos from the sun, the ones that are most sensitive to temperature. And the prediction was you'd see a number of some units of 7.6, and what he measured over 20 years constantly, with some variation,

but on average, was a number that was three times. smaller. Three times smaller. Now, big deal you might say. Look, this is dependent on the 24th temperature of the power of the temperature of the sun. Surely the astrophysicists get it wrong. Surely our picture of the sun is a sphere is wrong. And if you fiddle with it a little bit, surely you can explain that factor three difference. And the other experiments kept getting different numbers from the theory in the experiment. But the problem was, if you change the temperature in the center of the sun a little bit and change those properties. Other observables

of the sun wouldn't match. You wouldn't get the right temperatures at the surface. And eventually we did something called heliocysmology, which looked at the density of layers in the sun. And those wouldn't fit. Nothing would fit. Now, most particle physicists assume the astrophysicists just got it wrong because it's complicated. And surely the sun is more complicated than a sphere. But it was realized that if there was a property of neutrinos, neutrinos can have a very strange property. There are three types of neutrinos that are known in nature. One associated with electrons that are emitted in nuclear reactions called electron neutrinos.

And those are the neutrinos you're measuring with these experiments, is electron neutrinos. But there are two other types of neutrinos in nature, one associated with the next heavier version of the electron called the muon. We call that the muon neutrino. And now that we've discovered an even heavier version called the tau-on, there are three families of particles, electrons, muons, and tau-ons. There's a tau-nutrino.

And an amazing thing was discovered in physics, in particle physics. And that is that it's possible, given our understanding of nature, that if neutrinos have a mass, if they're not massless particles, It's possible that what begins in the center of the sun as an electron neutrino can, as it traverses the sun, turn into a muon or a town neutrino. If it does that, and then it'll stop turning into a muon and town neutrino when he gets out of the sun. Or maybe it'll just continue to oscillate between electron neutrinos and muon neutrinos and tantotrinos all the way from the sun to the earth, something that my colleague and I Sheldon Glashire called just-so oscillations many years ago. But if that happens, then maybe you could explain this experiment.

Because remember, this is a factor of three difference. So maybe if what starts out as electron neutrinos oscillates and turns into muon nanotrinos, town neutrinos, electron neutrinos, and electron neutrinos equally, then you don't expect only as third as many electron neutrinos to get out of the sun. Now that may seem like a crazy cutting butter with a chainsaw. Why assume some whole new property of elementary particles when simply fiddling with the properties of the sun and assuming it's not a sphere would work? Well, a wonderful experiment was developed in Sudbury, Sudbury neutrino observatory using heavy water That could measure electron neutrinos

But there were other reactions that would measure that would measure also muon-on-town neutrinos And lo and behold when it when it was looked at just electron neutrinos it got a number that was a number that was measure that would measure also muon-town neutrinos and lo and lo and behold When it was looked at just electron neutrinos, it got a number that was, again, a factor of sort of a three smaller than the predicted value. But when it looked at all neutrinos, it was bang on with the solar model. Telling us that neutrinos were oscillating, that this strange property of neutrinos was really true. And a new discovery, which meant, by the way, that neutrinos had to have mass. A very, very, very small mass. A mass we still don't understand

a mass of more than 100,000 or maybe a million times smaller than the heaviest particle in nature called the electron. Neutrinos have an unbelievably small mass. We don't even know exactly what it is, but we certainly don't understand it. But it explains the observations,

precisely. Electron neutrinos are oscillating in a muonetown neutrinos, And we now know that this experiment, and one like it, won the Nobel Prize in physics for confirming that neutrinos were oscillating from the sun. And it also means that remarkably this incredibly complicated environment of the sun as a sphere is a good approximation. It's good enough so that all the temperature, density, pressure, speed of sound calculations

work, and the predictions of the temperature are such that, even with the 24th power of temperature, we're bang on in the center of the sun, understanding the number of neutrinos coming from the sun. It's remarkable how good that approximation is, and it allows us to calculate. Nowadays we have modern computers, and we can include additional complications

from the sun maybe rotating a little bit and not being exactly uniform all over the surface of the sun. Certainly it was not possible early on to do those calculations, But it turns out ignoring those slight complications and treating the sun as a sphere is like treating a cow as a sphere to get the fundamental physics we get it right. There's another example that hits closer to home for me. Oh, by the way, here are the measurements. Here is the sun. We measure PP neutrinos, beryllium neutrinos, beryllium neutrinos. They vary in the in the flux and the earth by a factor of a million. But you can see here are the measured values, we have experiments that have now measured precisely all of these neutrinos coming from the sun have exactly the right value that you'd predict if the sun is a sphere over factors of a million in difference in flux. It's a remarkable saga that changed in my

lifetime. This was a mystery 30 or 40 years ago and now we understand its properties in neutrinos, not properties of the sun that have changed that. Here is a picture of a galaxy far, far away, long, long, no too far away, 60 million light years away, a spiral galaxy of our own. And here is what looks like a star in our galaxy that's getting in the way to the image. It's not. It's a star on the outskirts of that galaxy that's exploded, a supernova. The most brilliant cosmic fireworks in the universe, it's a star exploding. And when a star explodes, it shines briefly, over a period of a month or so, with a brightness of 10 billion stars or a billion stars.

You can see the brightness of this single star is comparable to the brightness of the whole center of that galaxy. And exploding stars are very important because it's an exploding stars that the elements that are produced inside of stars that are in our bodies, like carbon, nitrogen, oxygen, in the early universe, the only things that were produced in any amount, were hydrogen and helium essentially and a little bit of lithium. But carbon, nitrogen, oxygen, iron, all of those things are produced in stars. The only way they'd get into your bodies are if stars were kind enough to explode. And these cosmic fireworks are obviously the most powerful among the most powerful explosions known in nature, where stars heat up to temperatures of over a thousand or even a million times a temperature

of the sun during the explosion. An object, the size of the sun, of the core of the sun, collapses in one or two seconds into something as dense as an atomic nucleus, the size of Manhattan. The entire mass of essentially, almost one solar mass contained in a region the size of Manhattan,

where a teaspoonful of material weighs billions of tons, exotic matter, essentially while producing something called a neutron star. Now, this process had been predicted, and in fact it turns out the problem, we now understand it works for a variety of supernova only because of the energy release, only because it's so dense that so many neutrinos are produced, it's so dense that even though neutrinos can get through normal matter in the density associated with supernova, as those neutrinos produced by nuclear

reactions are produced, they actually deposit energy in the outer layers of the collapsing star, giving enough energy to finally explode. And all of this physics has, again, only been understood in the last 50 years or so. But what's amazing is, in our galaxy, we only, supernova of this type only occur something like once per 100 years in our galaxy.

The last supernova seen in our galaxy was actually seen, I told you, Tyco Brahe, Tico Brahe saw a supernova. Turns out his assistant, Kepler, saw another supernova in our galaxy. our galaxy. And that was the last one that's been seen in our galaxy over, well over, I think, 300 years ago for now. But on average, they occur once every 100 years in our galaxy. Why don't we see them more often? Most of our galaxies obscure by dust. So even if there are stars exploding,

we can't see it. But in this case, in a satellite galaxy, a small satellite galaxy of our own, the large Magellanic clouds, which you can see in the Southern Hemisphere, in 1987, a star, this is about 100,000 light years from where we are, at satellite galaxy of our own, a star was seen to explode. In fact, it was observed. There was a camera, a Canadian photographer, took a picture one night and the next night,

and there was now a star that hadn't been seen before. This is an image of it 20 years later, and you can already see, this is the remnants of the star exploding. If you look at that very carefully, you can see it's shooting out material. But it was recognized that at 100,000 light years away, if that star exploded, then the very neutrinos that had powered that explosion would be traveling into space.

And I told you, I remember that the star collapses in the period of a second or a few seconds. It should produce a burst of neutrinos that's a few seconds long. And there were deep underground experiments looking for solar neutrinos and other things that were hanging around and the next day after this was discovered they looked back at their data

to look for neutrino events and amazingly 20 neutrino events were observed. That sounds and sound like a lot but in a single day that's immense. And in fact this was an area I worked in and what shocked me this was the data

from four different experiments of the burst of neutrinos, you see it lasts a few seconds, exactly as it predicted of order 10 seconds or less. And the amazing thing is when we did lots of groups, and I was just one of them, calculated based on the physics we understood, assuming more or less the supernova collapsed as a sphere using the simplest approximation you could make so that you could do the calculations,

you would get roughly 20 neutrino events seen. That was the number of the scene. I remember when we produce these predictions, or post-dictions, if you wish, after the fact, nothing shocked me more than the fact that our simplest approximations of nature, assuming a spherical collapse, and assuming the laws of physics were what we thought they were,

in a regime we'd never observed before in nature, produced exactly what we were seeing. It was one of the, it was exhilarating for me in 1987, to see that physics worked so well, and a simple approximation works so well. So symmetry, in this case, assuming a sphere, is very important in nature because it restricts the variables

that you use to describe physical quantities. The more symmetric, the quantity, the fewer variables needed. The fewer variables needed, the simpler it is to make predictions. But that is not the most important aspect of symmetry. The most important aspect of symmetry is how it's driving our understanding

of the fundamental properties of nature. And Richard Feynman once talked about the purpose of a physicist as basically, he said nature is like a grand chess game being played by the gods that were privileged to watch. And the job of the physicists is to merely understand the rules of the chess game. That's it, that's all.

Understand fundamental physics. It's all we can do. Not why they're playing chess, but what are the rules? If we can understand the rules of the chess game, that's our job. It's basically pretty pedestrian. And that's a fascinating way of thinking about nature, but there's something else where symmetry comes in. And I wrote about this many years ago, 30 years ago in my book,

fair of physics, where we can say, well, how can we understand the rules? Well, the rules of chess, in many ways, are governed by the symmetries of the chess board. A chess board, as I wrote, a chess board is a rather symmetric object. The pattern of the board repeats itself after one space in any direction. It's made of two colors, and if we interchange them, the pattern remains identical. The board has eight by eight squares, allowing a natural separation at two halves, which can also be interchanged without altering the appearance of the board. so you can have the black and the white chess pieces.

This alone isn't sufficient to determine the game of chess because the game of checkers can also be played on board. But when I add to this the fact that there are 16 pieces on each of the two sides of a chess game, eight of which are identical, and the others of which there are three sets of two identical pieces plus two loners, things become much more restricted. For example, it's natural to use the reflection symmetry of the board

to lay out the three pieces with identical patterns, the rook, the knight, and the bishop in mirror image patterns. And the two colors of the different opponents then replicate the duality of the board. And I go on and basically, if you think about this, the nature of the game of chess is almost completely determined by these symmetries of the board and the pieces that play chess. And I say I make no claim here that there's any rigorous proof that the game of chess is completely fixed by the symmetries of the board and the pieces. But it's worth noting that there's only one variation in the game that survived today,

suggesting to me that, in fact, those rules are pretty well restricted by the board. I use that as an example because we now understand that perhaps the laws of nature are restricted by the symmetries of nature. And the symmetries of nature tell us when things don't change. As Jorlau Kholm said in that one story. And this became codified by one of the most important mathematical developments in physics by a woman called Emi Nerther, and it's called Nertha's theorem. Emmy Nerther was a mathematician in Goodengin, one of the great mathematical institutes in Germany

before the war when those institutes became decimated by the removal of Jews and others. Emmy Nother was a brilliant mathematician and her Nuthu's theorem is perhaps one of the most important theorems that applies to the physical world today but because she was a woman that she couldn't get a job. The famous mathematician, the greatest of his generation, David Hilbert, who was there,

argued that to get her a job and they wouldn't give her a job, a paid job because she was a woman. And he said, what is this? Is this a university or a bathhouse? but in any case she couldn't get a job. Eventually, she moved to the United States where she did get a job eventually, eventually as a paying professor

after a long time. But not when she did her famous equation. And what Nerther's theorem says is something of fundamental... It almost sounds trivial, but it's not. If the equations describing nature

do not change when you make some transformation, some mathematical transformation, like in the case of the snowflake rotating at 60 degrees or in the case of Escher's pictures, in that case, a translation by a certain amount. If you can make some transformation in which the laws of nature don't change, then there must exist a quantity, a physical quantity, which is conserved, which doesn't change with time.

And basically, it is those, quantities that do not change with time, which are conserved, which ultimately in some ways restrict the laws of nature. So, let me describe this in ways which are usually not taught in introarchy physics, and it sort of frustrates me. What are the symmetries of space and time? Well, the first symmetry that you can think of is that the laws of physics don't change with time.

The laws of physics yesterday are the same as they were today and as they were to be. tomorrow, which is useful because it means you don't have to keep retaking physics classes every year. And we can actually measure this by looking at physical processes in the early universe, looking at the energy levels of atoms and stars and seeing the frequency of light coming out and seeing the laws of physics going back billions of years are the same as they are today with high accuracy. But what Nerther's theorem tells us is that for every, for, if I'm going to go to have a little bit of sip of tea here, so my voice continues. I'll try and put it here and not destroy my computer.

If the laws of physics did not change with time, there must be a quantity, which we can call energy, which is conserved. Now, so the conservation of this quantity called energy is not a commandment, like the Ten Commandments in the Bible. And it's often taught in introductory physics as if there's a energy is conserved and you just write that down by row. Okay, energy is concerned. But it's never explained why. Energy is only conserved. There is a quantity called energy which is conserved, which doesn't change with time in a closed system.

If and only if the laws of physics in that system don't change with time. So we now understand energy as a consequence of symmetry rather than something else. And of course, energy, the existence of energy, simplifies everything. I mean, I talked about this the other day, that we could talk about the total energy of an object, its motion and its gravitational bits,

and if we throw a coin up, we can determine if it'll come down just by counting, by just asking if the positive bits of energy are bigger than the negative bits. bits of energy. It changes, if we wanted to use Newton's laws to derive how far the coin should go, you could do it, but it'd be much more complicated. With energy, you could determine the future of the coin, and as I described, the future of the universe itself, just by discussing energy. But energy simplifies many other things. Something that really comes home to me is an example

from my late uncle, who invested in a perpetual motion machine. It was a complicated machine with pulleys and wheels. And this person had showed him that, you know, he could use gravity. And if you could just turn the pulley a certain way, and then move the levers and this object falling would cause that this wheel to turn and go all the way around and turn the other wheel and it would go faster and faster and faster.

And you'd get limitless amounts of energy and you wouldn't need oil or anything like that. And it looked, and he just had to tweak it a little bit. Things were getting really close and he just needed a little bit more money to make it up. And it was a very complicated device. And he came to me to talk, I was a graduate student at the time,

and I told him it won't work. And of course, he didn't believe me. But the argument is quite simple. Forget all the, it's losing the forest for the trees. Forget all the wheels and pinwheels and what's happening inside. It doesn't really matter. Well, there are a thousand wheels and pinwheels

and other doodads in there. After one, if at the start, of the cycle, the machine looks this way, and at the end of that one cycle looks exactly the same, then the energy at the end of the cycle has to be this, can't be any greater than the energy at the beginning. In fact, it has to be less. It, because as it turns around, energy's released as heat. But the bottom line is, it looks exactly the same, and gravity isn't going to give you any energy. That's, you can't, you can't get energy out of a system if it'll end, from gravity, if it ends up looking just like it was at the beginning.

If I bounce a ball down, if I let it go at rest here, and it's a ball that loses very little energy due to friction, it'll come back up here. But it won't ever go higher than it will where I let it go, because that would mean if somehow it's getting energy from something. And so the simple arguments of energy allow you to understand that you can't get energy out of this system just from gravity. You can't produce work, and you can't change civilization. And if you try and look at all the engineering bits, you'd get lost. energy solves a problem. So often thinking of systems in terms of energy changes things incredibly. Energy is perhaps the most important and perhaps the most abstract aspect of physics. And maybe we'll talk about that in a future lecture. But there's another symmetry of nature.

The laws of physics don't change with time, but they also don't change with space. The laws of physics are the same in this room as they are if I did this back home, this lecture back home. thousands of miles away. And that's another obvious feature of the universe. Once again, maybe we have to test it, and once again we can do it, and even in spite of periodic, spurious times

and people have made claims otherwise, the stars in that direction shine the same way that stars in that direction, in that direction, with the same energy levels, the same frequency of light. The laws of physics don't change with place to place.

And that means that something connected with direction must be conserved. And that's something we call momentum. Momentum is associated with direction. It turns out we define it in classical physics, quite simply, the momentum of an object, and why we call it P, probably because M is used for mass,

is in simple classical physics, the product of the mass of an object, and now I'm going to put the vector signals on here, times its velocity. Momentum has direction. An object, the heavy mass moving very fast has a lot of momentum. You don't get in the, if you want to check it out, just try and stand in the way of a Mack truck. A piece of popcorn shown at you, throwing out with the same velocity, doesn't have as much momentum, and you're not going to notice it.

But the truck, if it's going from this direction, will knock you that way. And if it's going from this direction, will knock you that way. Momentum is associated with direction. And a system that's closed, a closed system, the momentum of that system is conserved. That's incredibly important. And it allows us to analyze things that we couldn't analyze otherwise. And in fact, in this case, it allowed us to discover something new about the laws of nature. It allowed us to discover neutrinos.

In a little after 1930, a new particle in nature was discovered, the neutron. a fundamental aspect of atomic nuclei. In fact, the most abundant particle in atomic nuclear is a neutron. But neutrons left on the wrong are unstable. Neutrons will decay in about 10 minutes. And it was observed by looking at the tracks and things called bubble chambers and things like that

that when a neutron decayed, a neutron was neutral so you didn't see anything. But suddenly, when a neutron decayed, you'd see a proton fly off in one direction and an electron fly off in one direction. and an electron fly off in another direction. Now, what is wrong with this picture? What's wrong with this picture?

Well, there are two things that are wrong, but just from drawing it here, there's clearly one thing wrong, and it has to do with conservation and momentum. If I have an explosion, I never see all the particles go off in the same direction. Why? Because before the explosion, the total momentum of that system is zero.

Nothing's moving via zero. Afterwards, therefore, the total momentum of that system must be zero. And since momentum, it depends on mass from time's velocity, if some particles are going in that direction, other particles have to be going in this direction so that when you add the vectors, they cancel. And you expect as many particles to fly off in that direction as that direction, is that direction, is that direction, is that direction, for the total momentum to be zero. The conservation momentum tells us that.

But here we have a neutron at rest. And we have two particles going off in the same direction. That violates the conservation of momentum. It turns out there's another feature of this. And by the way, I should have said, when you take the conservation of momentum and the conservation of energy, those two things combined completely reproduce

all the results of Newton's laws. Namely, that's equivalent, you can calculate everything that you can ever calculate with Newton's laws by assuming the conservation of energy and the conservation of momentum. The two fix the properties and materials. And the conservation of energy and momentum,

together, when this goes off, tells you if a neutron decays and just a proton and electron, those two particles must have a fixed energy. You know, they never can vary. The mass of the neutron is a little bit heavier than the mass of the proton electron, and they'll carry off that energy, and it'll always have exactly the same amount of energy.

Okay? and their momentum must be canceled, cancel equal opposite, but they're not. So this violates both the conservation of energy and momentum, but the picture clearly violates the conservation momentum. How can we solve this? Well, what is interesting to me at least is that some physicists at the time were willing to say maybe on the scale of nuclei, things like conservation of momentum or energy go out the window.

And I find this fascinating because it means that Nerseth serum and Nerther was the turn of the century, had not yet fully been immersed or by osmosis by physicists, so that now it would be ridiculous to say that, because if you said that energy and momentum were not conserved on that scale, on atomic or subtotropic scales,

that's equivalent to saying the laws of physics change with time and place on subatomic scales, and there's no evidence of that. But the other solution that was first proposed by the irascible Swiss physicist Wolfgang Powley, was that maybe there was another particle being emitted

in the other direction that was invisible. Why would it be invisible? Well, if it's neutral, it wouldn't be... It wouldn't be seen to produce tracks in bubble chambers. Now, the mass of the neutron is just a little bit heavier than the mass of a proton and electron. So it had to be very light.

And the Italian physicist, therefore, said it's like a neutron, but lighter, and the little baby neutron in Italian is neutrino, and it became called the neutrino. Now, it turns out that this neutrino, the properties of it would be quite remarkable. In order not to be seen and to be invisible, it couldn't interact with electric charges. It couldn't interact directly, but with another force of nature called the strong force and inside nuclear eye. It would be so weakly interacting that, as I say, it could easily go right through the earth without being detected. And so that was first proposed in the, I think, in the 1930s by Pauley. And then, as I say, Fermi, both Pauley and Fermi won Nobel Prizes for the work they did in different areas. There's Fermi actually for understanding the decay of a neutron and having a theory that tried to predict that.

Well, actually, he won the Nobel Prize for something he didn't do, which was producing new elements. But his work on understanding beta decay is an essential part. The decay of a neutron is an essential part of understanding physics, as you'll see in a few minutes. But this was predicted, and it's so weakly interacting that people actually thought it would never. be observed. But as I said, Fred Reynos, an American physicist who actually was at, for a while, was chairman of the same physics department that I was chairman of many years later, went to a nuclear reactor with a colleague of his in Los Alamos, and you could calculate that if neutrinos were produced in nuclear actions of power the sun, they're also produced in nuclear reactors. And if you get

close to them, there are enough of them. Turns out a million billion of them going, well, not quite a million building, but 10,000 billion neutrinos per square centimeter per second were coming out of a reactor. And if you put a detector close enough to the reactor, you should detect neutrinos. And in 1956, I think, he finally discovered the neutrino and wrote a sent a telegram to Pauley saying your particle was discovered. And of course, many years later, 40 years later, I think Fred Brunitz won the Nobel Prize for the discovery of the neutrino. But it was discovered because of the conservation, because it was proposed in order to be consistent

with the conservation of momentum. So these fundamental conservation laws not only are related to understanding, again, motion and simple facets of physics, fundamental aspects of physics, why nature behaves the way it is, but they lead us to discover, in this case, new elementary particles.

But you'll see that they do even more than that. Here's another symmetry of nature, going back to the chessboard. Benjamin Franklin mistakenly assigned electric charge, it turns out, to not electrons. Electrons are the things that carry electric current, but he assigned them, it turned out negative charge. You'd think the thing that would be the thing, the prominent carrier of electricity in an object, you'd call it a positive charge.

He didn't know what the fundamental carrier was, and we now understand it's electrons and in his criminology, they have a negative charge. But it doesn't matter. It's semantics, right? If we call it the charge on an electron is negative, the charge on a proton is positive, but that's just words. We could, if we wanted to, rename it. So that electrons have positive charge and protons have negative charge. All that matters is they have equal and opposite charges. It's a choice of us determine globally what we call negative and what we call positive. So that means we could change every negative charge into a positive charge and every positive charge and negative charge

and the laws of nature would be exactly the same. They wouldn't change. It's just semantics. That is a fundamental symmetry of nature. And it's like, basically, in this case, if negative charges are black and positive charges are white, what you can do with a chessboard. With a reflection, a 90-degree rotation,

you can turn the same chessboard into this where the white squares are turned into black squares, the black squares are into white squares, but you can still play chess. It's just that you, the white team, one team is up here and a different team is there versus here and here, but the game is still the same. That conservation of charge,

that symmetry of nature leads to the conservation of charge by Nerther's theorem. It basically determines the fundamental law of electricity and electric forces. that charge is conserved, that it can't be created or destroyed. It can't be created or destroyed because fundamentally, the sign of charge is arbitrary, globally. And that conservation of charge determines the nature of electric forces

and their properties. And so charge conservation is another fundamental symmetry of nature, and we'll talk about electricity and magnetism in a later lecture. Okay? Great. Now, I want to now go to what is essentially the most important symmetry of nature now, and it's the subtlest and hardest to understand. And I want to try and develop it by going to something I haven't talked about yet,

which is general relativity. But I can kind of put it in a framework this way. So I just flew here today, and recently I was, across the, I was in Hawaii a little while ago. And when one's flying on a plane, say, in this case, from Madrid to New York, planes take the shortest distance. And what they do is, of course, because the earth is curved, they go on what's called a great circle.

In fact, if anyone's ever flown, say, from Scandinavia to North America or from Iceland to Seattle, you often go over the North Pole because that's the shortest distance. And as anyone can see, because the Earth is curved. But now, let's draw a map and take that curved surface of the Earth and put it in a flat, make it flat, like the standard pictures on a globe.

If I look at that same trajectory from Madrid to, in this case, it's California, but it doesn't really matter, you see, of course, that that straight line on a curved surface becomes a curve when I project this curve surface onto a flat surface. But you also see something else

that lengths change. Because of things, if you're near the North Pole, things get stretched out. So Greenland, which is not as big as all of North America, in this picture looks like it, because if you wish rulers on Greenland are stretched or made smaller, depending on how you want to think about it,

because in order to take that region near the pole, you stretch it out here and you take rulers and stretch them. So Greenland looks bigger. Antarctica looks huge because it's near the South Pole. So the laws of physics must be the same here as here. And so this plane takes the simplest path in a curved surface, but it takes a curved path on this flat version of this when we try and project that curve surface to a flat surface.

And the way to think about it is, well, you know, this plane is going to straight line at a constant velocity, a la Galileo. But if you want to try and explain the same trajectory on this flat surface where rulers are arbitrarily changing in size as you go from place to place, if length is not constant, which it clearly is if I project this curved surface

to a flat surface, lengths are not constant. The laws of physics will apply and turn this sort of straight line into a curved line, and the only way you can understand that is basically saying, well, there's like a gravitational field that's causing that object go up and then down. So if I take that curved surface and make it look and approximate by a flat surface,

the physics is the same, only if I add to this a fictitious, if you wish, gravitational field. Now, but gravity isn't fictitious. The fact that you have to add it here says the laws of physics are the same for this system and this system, only if I have gravity here really tells you that the underlying system is curved. And this is in miniature, what Einstein said about the real universe.

universe, that there's a fundamental symmetry of nature, he called a general covariance, that allows us to, if we wish, arbitrarily define rulers of different lengths here and there. But if we do that, there must be a rule that tells you how to go from one place to another and how length changes, and that rule is equivalent to producing gravity. So gravity is really a signature, if a non-trivial gravitational field is a signature of the fact that space is curved. But this symmetry of allowing you to not just globally change lengths, I mean, we could all say our rulers, what we defined by an inch is now a foot, and everyone could throughout the whole world change their rulers. All that is is changing systems of units. That's arbitrary.

but we couldn't very well effectively operate where if in Cincinnati rulers were 12 inches long but in Cleveland rulers the same rulers were two inches long unless we had some rule that told you how to translate between them and in the universe that rule says if you're allowed to change it and the laws of physics remain exactly the same

but only if you allow for the existence of a gravitational field in certain cases if there if there is curvature in space and no gravitational field if there isn't curvature in space. I realize that sounds a little abstract, but it's going to allow me to introduce something else. Herman Vyle described this idea of being allowed

to change length, if you wish, and he called it a gauge, like gauges in railroads, arbitrarily from point to point. And if the laws of physics allow you to arbitrarily change some quantity locally from point to point without changing the physics,

as long as you add some extra field in nature, he called a gait symmetry. Now, the interesting thing is it doesn't work for just going to gravity. It turns out to be a fundamental property that defines electromagnetism. I told you about charge conservation for a static electric field. But it turns out the properties of electromagnetism are even stranger.

Electromagnetism, the properties are such that I can define not just what's a negative charge and a positive charge globally, but the laws of electromagnetism don't change and describe the same physics. If over here I define negative, and over here I define it as positive, and over here something else, so that I can change that black and white chessboard into a chessboard that say all white, As long as I have a rule that tells me how to go from one square to another as I move along here to account for the fact that I have a changing definition of charge, as long as I have a rule that does that, and that extra rule requires a field, in this case, it's the electromagnetic field.

So the laws of electromagnetism, Maxwell's equations, which we'll describe later, are restricted in form to be consistent with a world in which we could describe charge, differently locally, but only by introducing light in a very specific way restricted by the set of equations and those equations have a mathematical symmetry, which we call gauge symmetry. I'm not gonna write that down. But it's a strange, remarkable symmetry

that's characteristic not just for, well, the two long-range forces we know of in nature, electromagnetism and gravity. This strange fact that remarkably, the entire, form of the equations has this mathematical symmetry so we can understand the existence of light, if you wish, because nature has this gauge symmetry. It allows us to define charge locally, differently, but the equations remain the same if you introduce an extra quantity that tells you

what happens when you go from one place to another, and then extra quantity is associated with the electromagnetic field. I know it sounds vague and strange, but gauge symmetry is complicated mathematically, it's even more complicated, subtle to understand physically. But it's a fundamental feature of the equations of electromagnetism and the equations of general relativity. And what I want to talk about is how that's led us to something interesting. Because it turns out, we now know that all the known forces in nature had that same mathematical symmetry. And that may mean that the search for the rules of the chessboard, which means looking for the forces in nature,

is equivalent to understanding the symmetries of nature. The kind of gauge symmetry that general relativity has is different in nature than the kind of gauge symmetry of electromagnism has. But it means that we now think that what's possible in the universe, the dynamics of what determines what forces are possible, and the way they work is determined by the fact that the symmetry exists in nature called gauge symmetry.

We have no evidence of any force that isn't governed by gauge symmetry. Now, the realization of that was a long route, and to end the story, I want to talk about the discovery of the nature of not just electromagnetism, but the other force in nature, the weak force, which governs the decay of neutrons. And in order to understand why the weak force has a gauge symmetry, but looks very different than electromagnetism, I have to describe the concept of broken symmetry. And the physicist Abdu Salam, who won the Nobel Prize for, along with Shelley Glashow and Steve Weinberg for the theory of the symmetry of the weak force and electromagnetism, described

it this way. It often used to happen to me. I'd go to fancy functions and I'd be a big dining room table or a big table. And there'd be every place setting would look exactly the same. And there'd be a glass there. And I never used to know which glass was mine if I was sitting to my right or left. It seemed arbitrary. Turns out there are rules for it.

We now know. In fact, I learned something very useful. I hold my hands out like this. I learned this at a very fancy function once. And there's a B and that's a D. So I learn my breadplate is on my left. and my drinking glasses on the right. It's very useful.

Now I've given you that information. But what he pointed out is the minute the first person picks one up, before that it's completely symmetric. Whether your glass is the right or left, nothing about the table tells you which is which. But the minute the first person picks one up, it fixes everyone else has to pick one up. If I pick it up in the right,

everyone else has to pick their glass on the right. If I am doing the wrong, thing it picked it up and left, then everyone else has to pick it up and left. Suddenly left and right are no longer the same. So the table itself has an intrinsic symmetry that left, not distinguish between left and right, but once I pick it up, the manifestation of that symmetry is broken. You can no longer see it. That's called broken symmetry. Let me give you another example. In cold places like where I used to live, there are icicles on windows.

Okay, now we don't think that the laws of nature depend upon their they don't depend upon directionality Okay, whether ice crystals form in this direction or that direction if we look at it from outside We see they form in all different directions But if I happen to be born and be a little in miniature being living on say this ice crystal here This direction would be very different than that direction So while the fundamental equations in this case of just electromagnetism that depend on that's basically what determines the laws of chemistry and how ice freezes. They don't depend on direction.

The manifestation of, if I live on this thing, that doesn't reflect the underlying symmetries of nature. It's in this room. I don't think, at least as far as electromagnetism and gravity, that looking in that direction, laws of physics should be different than laws of physics in that direction. They're not. But clearly, I can tell which is right and less.

in this room. If I look to my right, I see that screen. If I look to my left, I see this whiteboard. So the manifestation, this particular situation I live in, may not reflect the underlying symmetries of the laws that determine it. Obviously, the laws that determine that govern the nature of the physics of this screen don't depend on right and left, but the screen is to my right and the whiteboard is my left,

and therefore I know which is right and left. It's a subtle idea, but broken symmetry is important. is important. Because it turns out, here's another example I just put, I guess I threw another one in, if I happen to live in a magnet and I'm a magnetic particle, you know, I have little magnets in my, say I'm a bird that flies by detecting magnetic fields. Clearly, in this magnet, if I live in the magnet, one direction is very different than the other directions. Even though in the world, there's nothing special about, say, this north or south direction. And there's a place where that really comes in the most.

And it has to do with superconductivity. In the superconductor, it turns out something very strange happens. When I cool materials down, a very specific configuration of electrons combines into things called Cooper pairs, and it becomes a superconductor. They conduct electricity with zero resistance. And that specific configuration that occurs when you cool things down changes things inside the superconductor. Electromagnetism disappears.

What do I mean by that? This is called the Meissener effect. It means that inside the superconductor, light becomes massive. And light, which is massless and therefore has no problem traveling throughout nature, inside the superconductor, it can't permeate inside the superconductor. So the superconductor expels any outside magnetic field. There's a great experiment you can do a demonstration. You can do any classroom if you have a superconducting magnet.

And you'll find that because it expels magnetic fields, that magnetic fields can't go through it, and it levitates the object. So if we lived inside a superconductor, there would be no law of electromagnetism, or at least the law would change, because light would become massive. and basically light would disappear.

It could never permeate beyond a very small distance from the outside of the superconductor. Electromagnetism would no longer be a long-range force. If I have a charge here, it can affect a charge on Jupiter in normal nature. But inside a superconductor, if I have an electric charge here, it can't affect an electric charge somewhere else because the electric field can't permeate through the superconductor. or in this case the magnetic field can't permeate throughout the superconductor.

A magnet here can't affect the magnet there because magnetism doesn't go through there and it's expelled and light becomes massive. And the equations become that of what are called massive electrodynamics and they're very different. So inside a superconductor because of that broken symmetry, because of the fact that a very specific set of charges line up inside the superconductor, the laws change. And the underlying symmetry, the gauge symmetry, which ensures that light is massless, by the way, gauge symmetry ensures it's equivalent to saying that light is massless and can propagate. The fact that light is massless is mathematically equivalent to the fact that the equations of electromagnetism have that underlying symmetry. In the case of a superconductor, those equations don't have that underlying symmetry,

and that's because light is massive. So suddenly the underlying symmetry of nature is broken because of the specific formation of these things called Cooper pairs. So the next question is, well, that's inside a superconductor, but could we be living inside a cosmic superconductor? Could it be that the laws of nature we're seeing here are not fundamental, but only a property of the fact that the universe is in some specific state

and we see things differently than that might be fundamentally, and the answer is yes. The remarkable answer in producing one of the most important unifications in modern physics and something we built the Large Hadron Collider

in Geneva to test has to do with the unification of two very different forces in nature. Here is neutron decay to a proton, electron, in this case, an antineutrient, something called an antineatrinotrino. As I say,

Fermi started to describe a theory to do this. And we now, when it comes to when it comes to understanding electromagnetism quantum mechanically, we draw these weird things called Feynman diagrams. But basically, two electrons are seen to repel each other because they exchange a quantum of electromagnetism called a photon. It's called a virtual photon. But that produces the repulsion. And this is the quantum version of Maxwell's equations. And it's the best

theory in nature. This quantum version of electromagnetism allows us to calculate the properties of atoms producing an agreement between theory and experiment at the level of 14 decimal places. There's no other theory in any kind of science in nature from fundamental principles you can compare theory and experiment to that accuracy. This is the best theory in all of nature. Well, it turns out you can use the same idea to explain how a neutron, which is made of quarks, decays into a process. proton, which is made of different quarks, and produces an electron and antitrino. If another particle is exchanged, not the photon, we call it W particle.

This idea was proposed independently in different contexts by Sheldon Glashow in 1961 and well, in different contexts, and Weinberg in 67, along with independently Abjah Salaam. But the problem is electromagnism is a long-range force. But the weak force, which produces this decay here, only occurs on the scale of nuclei. It's a short-range force. That implies that this particle must be very massive, because it can't travel very far, whereas photons can travel as far as you want because they're massless, and that's why electromagnetism is long range. Okay, so far, so good.

The problem is, if you try and mimic this theory with a theory with a massive particle that looks the same, it doesn't have a gauge symmetry because the gauge symmetry implies the photon is masses so this theory doesn't have a gauge symmetry and it turns out because of that when you try and do the quantum mechanics of this you get nonsense you get infinite results

ultimately the theory doesn't work how are you going to solve that well it turns out the solution is remarkable it turns out you can write down a theory and they're not only these particles called W particles, there's a particle called Z particle,

where the weak force looks identical to electromagnetism, and it is identical if these particles have zero mass. So if you have a theory where these particles have zero mass, everything works out right, and this theory has a gauge symmetry, just like this theory does, and everything's fine. But of course, that's not what nature looks like. How can we understand How you can go from this theory where things look nice

to the world where these objects, if they exist, are super heavy, and this one's massless, the answer is broken symmetry. Maybe in nature, there's something like a superconductor. Something about empty space has a configuration. In this case, we call it a Higgs condensate, made of these particles which were first proposed by Peter Higgs in the 1960s, 1965.

would be such that they screen out the W's and Zs. Going through that condensate would be like electromagnetism going through a superconductor, and the W's and Zs would get very, very massive. So intrinsically, the theory would look just like electromagnetism, or maybe a little more complicated version of electromagnetism, with the same symmetries, but because of the particular configuration nature, as the universe cooled down, basically this superconductor-like,

phase emerged, we call it a Higgs condensate, it would screen out W's and Z's making them massive, making them look very heavy, just like a photon would look very heavy in a superconductor. And even more, the Higgs might actually interact with other particles in nature. Maybe all the masses of all particles that we see, more or less, comes from their interacting

in different ways with this background condensate. But most importantly, the fundamental gauge symmetry that makes the theory work is still there at a fundamental level. It's just not manifest in the world we see because of this Higgs condensate. This allows this theory to be sensible, and not only did the theory that was proposed by Weinberg, Glashow and Salam, for which they won the Nobel Prize, but then shown to be mathematically sensible by Herard de Tuft and Tini Weltmann, who also won the Nobel Prize for showing the mathematics works out. All of that worked. The problem is it requires this new condensate of these new particles called Higgs particles.

And for 40 years, people looked for the Higgs particles and not found them, but then on July 4, 2012, I think, in the Large Hadron Collider, the Higgs particle is discovered. And in fact, as I'm going to talk about in a podcast that I'm going to record tomorrow, it's just been shown that in fact the Higgs has exactly the properties you'd think of to give masses to other particles as well as the WZ. The theory works out. It's the most beautiful unification in nature that's occurred since the laws that combined

electricity and magnetism of Maxwell, well over 100 years ago, the unification of the weak force and the electromagnetic force into the electroweak theory. because this theory has an underlying gauge symmetry, makes sense, requires this, it's there, it all works out. And it is an amazing thing. This unified theory is wonderful, and it leads us to think maybe all the forces in nature, which may look very different on the scales that we exist on,

are different only because of accidents of our circumstances, not because of fundamental physics being non-gauge-like, And maybe there are other forces in nature. And ultimately, as I told you, gravity has a gauge-like symmetry that's very different than the symmetry of electromagnetism. Maybe we could unify gravity and electromagnetism and the other forces in nature with the kind of mathematics. We haven't yet been able to do it.

It turns out gravity can't be unified effectively unless we do something strange like string theory, which so far has no evidence of being correct. But as far as we know, all of the forces of nature, all the dynamics that determine the universe is determined by the existence of this fundamental symmetry in nature called a gauge symmetry. It's remarkable. And it means our search for the rules that Feynman was talking about is just equivalent

to the search for the symmetries of nature. So symmetry not only simplifies our understanding of how to do things like Understand the Sun, but it's more fundamental than that. Thank to Emmy Nerther, it tells us that it restricts the nature of the equations, It implies that energy and momentum and charge conservation must exist. And if we go further to the existence of a gauge symmetry, it applies to the equations of nature have a very specific form, and any new forces must have that form,

and therefore reflect a different kind of gauge symmetry, and therefore the search for the fundamental forces of nature becomes equivalent to the search for symmetry. And we are therefore, I brought you to the forefront of ignorance in this second lecture. We don't know if there are other forces. We don't know how to for sure unify gravity and electromagnetism. We don't even know yet whether we know electromagnetism and the weak force are unified.

There's another force in nature called the strong force. Does it get unified by some new symmetry of nature in a so-called grand unified theory? And then do all the four forces of nature get unified? These are open questions. But they're all questions that come from the simple, not so simple, but the subtle notion of symmetry, which is what guides modern physics in a way that's very different than it guides modern art. Where in modern art, the more complicated asymmetry looks the better. In physics, in some sense, the more simple a symmetry looks, the better,

because it restricts the nature of the equations fundamentally. So that's symmetry, and we go once again from something very basic, energy and momentum to the forefronts of our understanding, or in this case, our misunderstanding. So that's it for this lecture, and we're going to go on to understand more fascinating facets of electromagnetism in the next lecture. Thanks. Hi, it's Lawrence again. As the Origins podcast continues to reach millions of people around the world, I just wanted to say thank you. It's because of your support, whether you listen or watch, that we're able to help enrich the perspective of listeners by providing access to the people

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