It is an for me to introduce professor today. Sanshiro has recently become a common professor of natural philosophy at, Johns Hopkins university, and hes also a faculty at the santa fe institute. Hes a theoretical physics. And as such, he written many interesting research. Hes also a Popular Science writer and has been a New York Times bestselling. Im i always find him very insightful and thought provoking. I read his book in general relativity when i was an undergrad in argentina. And ever since then i became fascinated with the topic. Hes very committed to making complex physics ideas accessible to everyone, and he does it in a very unique and wise. So today he will be telling us about the first book in his new trilogy the biggest ideas in the universe time and motion, where he explains not only the physical concepts, but also the mathematical framework behind them in a very beautiful way. So please join me in professor sean carroll. Thank you. Thank you. Harvard bookstore. One of my favorite bookstores in the whole world. Thank you. University, one of my favorite universities in the whole world where i got my ph. D. Here a certain number of years ago that i will no longer admit to in public. And thank you all very much. I realize its a little chilly out there. I am very happy that were able to braved the elements to get here and as mentioned we have i wonder if this is a laser pointer. What do you think . Is there something i can push on it . Im a little. Afraid . Oh, yeah. Look, that ive written a book the biggest ideas in the universe volume. Volume two will be about Quantum Mechanics, field theory. Volume three about complexity, emergence. But there are too many big ideas in the book to talk about all them, so i figured i would pick a big idea and i would talk about that to give you a flavor of what you would get. Were you to buy the book. And so the thing i want to talk about was einsteins equation. And, you know, as soon as i say that, youre thinking, well, okay, ive seen that before. Good, this is familiar territory equals empty energy, mass speed of light squared. Good. You know. Ive learned something. Maybe, but its not going to be completely unfamiliar. But this is not einsteins. This is not what a physicist mean. If they said, oh, yes, i was thinking about equation earlier today. Here is einsteins equation as a physicist thinks about it. Where you to say it out loud . It would be arm you knew minus one half hour game you knew equals eight pi g team you knew this is the field equation for the curvature of space itself. In general relativity and we never tell you about this. We might give you the words we might say spacetime is curved and that curvature is gravity things that but we dont give you the equation unless youre a physics major shout out to those physics majors in here. Maybe youll get it. But even then, most undergrad graduates never see this equation. If they get a physics degree. Its considered be too hard. Theres all these greek letters in there. Theres subscripts we dont know whats going on. An hour from now, you will all whats going on . Im going to teach you this equation. So how do we get there . Well, we start with mechanics. The whole theme of book is classical mechanics, as opposed Quantum Mechanics and classical mechanics. The central there is newtons law, f equals ma, my physics teacher, when i was a freshman said that, you know, the only equations need to remember for the test is that equals m. You can derive Everything Else. Thats an but that tells you the central importance of this equation. Force is mass times acceleration. Why is this equation so interesting and important in part because its precise. In other words, its just a suggestion. This is the difference between equations and words. Its not just saying the more you push, the more the object will accelerate. But its a very precise, quantitative that you can use fly a rocket to the moon. Thats the kind of precision that you need. The other thing that we dont always appreciate, that its universal. What mean by that is its not just saying this one time i pushed a car with a certain force and it accelerated a certain amount. Its saying time everywhere, the universe that a force is exerted on an object with mass. You can use this equation to figure out how it will move much. It will accelerate. Now were this a philosophy lecture rather than a physics lecture. We would ask why there relations in the universe that are that precise and that universal happily were lower brow than that today. Were physicists. We notice that there are celebrate that and we move on so we want to learn how to use equation right f equals m if you exert a force on something, it will accelerate proportional to its mass. But you need to know the force is so. Newton himself talked about a famous force. The force gravity newtons famous inverse square law. So if you have little object with mass m, this is the one that is being forced and will start accelerating. So this might the earth and a bigger object with mass capital m might be the sun okay and you could ask how much force is exerted by the force of gravity and says that you have capital m for big object little m for the little one i remember i can also use my computer for this. Look, theres little m you draw a little vector, okay . Little thing with magnitude and direction and. If you see a vector labeled e, it will often be whats called a unit vector, a vector with a fixed length that change its length in the different circumstances. And what were asking is f what is that vector . What is the force that is acting on this object with mass little . So really equation because of the little arrows on top of the f in the e this an equation not just between two numbers but between two columns of numbers. F the vector has a certain amount of force in the x direction, a certain amount the wider a certain amount, the z direction. Thats what it means to be a vector. It has both a size and a direction. Its pointing in and the direction its pointing in, in this case is that the forces along that unit vector pointing from the little mass to the big one and the size of it is big m times, little m times capital g, which is newtons constant of gravitation and divided by the distance. Thats why is the inverse square law when youre very close objects to each other. The gravitational pull is relatively strong. When theyre far away, its relatively weak and this is how it goes. And so what a physicist would do is to start with some setup here are two objects here. Theyre masses, their distance. Heres how theyre moving. What happens next . How do move next . And theres a very nice simplification that occurs away that the mass of the being pulled cancels out. Okay, so f equals may but f also equals gmr over r squared times e. So by math you can by little m on sides of that equation and. What you get is an equation for how much the little object is being accelerated by the force of gravity. And what you notice is nowhere in the equation are any actual individual character sticks of that object. It doesnt matter what its of. It doesnt matter how massive is or how fast its spinning or what day of the week it is every the same distance from some other object will accelerate the same way. So you can do this experimental li. You can go up to the moon. So here on earth if you drop a hammer, a feather, they wont fall at the same rate. But thats because of air resistance, not because of the laws of physics at some deep level, if you go up to the moon where theres no air resistance, you can ask. If i drop a hammer and a feather will, they fall at the same rate. And this was done. The apollo 15 astronauts, hopefully they had some faith in newtons laws of physics, because otherwise they would not have to the moon to do the experiment. But happily, it turned out right can they made very grainy videos. So this is an artists reconstruction of the event but two objects even with very different fall in the same under the force of gravity. Now, that is not just a cute coincidence is going to turn into the single most important fact about gravity. Gravity is universal. It doesnt matter who you are, what youre made of, we all accelerate under gravity in the same way thats going to be crucially important. Why . Because as successful as this paradigm was, this whole set that isaac newton gave us for doing classical, it was not the final word. In 1905, we had input from this guy Albert Einstein. You know, these days when see a picture of einstein, its almost always in his later years, right, was a little rumpled. The sweaters and everything and you get the impression thats what physicists are like this what einstein looked like what he was deriving equations of special relativity, general relativity. His hair was combed. Someone was dressing him nicely. I dont want to say what the causal there is, but he was a sharp, dressed, young man. Thats all im going to say. And the theory of special relativity. 1905 is contrasted with the theory general relativity in special relativity, theres no gravity. In general relativity, there is. We will get that. But what einstein did, 1905 was he didnt really invent the theory of special relativity out whole cloth. There were already various lines of reasoning that were coming into it and really put it all together once and for all. And were not going to go into details. Special relativity. But youve heard some of the jargon, some of the phrases right motion is relative. Thats the word relativity comes from. The speed of light is constant. You go faster than the speed of light. Its an upper limit. And then theres all these phenomena that youre taught about length, time dilation in the book. I dont emphasize size these things that much because in my quirky, idiosyncratic worldview, focusing on things like length, contraction is a remnant of the fact that back in the newtonian days there was something called length and everyone agreed what it was. And it turns out in the relativity picture different are not going to agree on what length. So rather than starting with length and saying but it contracts for some people and not for others. I try to start with what is actually true and correct in the theory of relativity and derive everything from that. But all need to know right now, is that einstein didnt actually even in 1905 put the fine issuing touches on the theory of relativity. That was done arguably two years later by Hermann Minkowski g, who used to be einsteins professor. So minkowski was a mathematician and not a physicist, but you know, he was proudly following his students progress. He about the theory of relativity. It was he who first said all this great. In your theory that youve done albert can be simplified and conceptually made more clear if you just say that space and time are not separate space and time are together unified in something called space time and all of these effects that youre talking about are manifestations of the geometry tree of space time. And his famous quote is space by itself and time by itself are doomed to fade away into mere shadows and only a kind of union of the two will preserve an independent reality. No way that referees would let him get away with rhetoric like this in a physics paper today. But, you know, 100 years ago, you could do it. Not everyone was impressed by this mathematic goal. Step forward, including named Albert Einstein. Who wrote in one of his papers that mikulskis formulation makes rather great demands on the reader, its mathematical aspects. So look, einstein, let me go out on a limb here was no dummy, but he famously did as much math as he absolutely to do. He was good at math, but was a physicist at heart. He didnt do math for the sake of doing math, and he constantly resisted people who tried to take these physics theories and, just turn them and do math for its own sake. And he was worried that thats what minkowski was doing. Turns out he was wrong. And what einstein maybe his single most important feature was his ability to be wrong and then change his mind. He would very change his mind and jump on bandwagon. And he came to believe that the space time way of thinking about relativity was actually the right way to think about it. So let me tell you what that way is. The question is, is it geometry that we should be thinking about . Were thinking about relativity. If you read all the popular level expositions of length, contraction, etc. , you dont really hear the word geometry that much. But the essence of it is this you want to travel a certain distance in space. There is a formula that relates the amount of distance you travel to what we call the coordinates. Okay, this doesnt work in boston. But in a sensible city like new york, where the streets are at right angles, you could figure out the total interval, the total distance between two points. You go taking the different sides of a right triad, squaring them and using pythagoras theorem right in this little triangle here d squared equals x squared y squared. So what this means, number one, you have a formula for figuring out the distance. Two points in terms of their coordinates but also this is something you could measure and you notice theres a difference between how much distance you would depending on the path you take. This is a point that is so obvious. Its almost not worth saying, but you can have two points a certain distance apart and everyone agrees with the distances. But walking a Straight Line between those two points means you personally travel less distance than if you go off on a detour and then come back right again. Perfectly obvious. The distance you travel between two points depends on your path. The reason why i emphasize this perfectly obvious point is because the whole point of relative city is that the same thing is but for time rather than space time like distance is something that will the elapsed amount of it depend on your through the universe and its minkowski that gives us a formula for figuring this out. If you travel some distance in space and is some time coordinate on the universe, right . Like theres some universal time that that everyone agrees on that you know the International Bureau of standards has set up. So there are clocks everywhere. We can read them and figure out what it is in relativity, that universal time, coordinate is not the same as the time that elapsed is on your watch. The time that elapses on your watch is, something that you personally experience and minkowski is point is that time is like space. The amount of time you experience will depend on how you travel through the universe and the same way that the amount of space that you travel through depends on the path you take. And here is the formula. Its kind of like pythagoras theorem, but its not exactly the same. Tao the greek letter tells for what we call the proper time elapsed time, the actual amount time you experience, and theres a formula for it t squared minus x squared. I have sneakily set the speed light equal to one. So you dont see the speed of light in here. Theres a certain fraction of you that are doing dimensional analysis in your head and wondering how i can subtract time space so cavalierly. The answer is were using unit s where length is measured in light and time is measured in years. Okay, so the speed of light plays a special in this theory, but the real point here is that the time that you will feel elapsing is given by this formula and for a given change the coordinate time t it will depend on your path through the universe how much time you actually experi ience with a twist, right . Because in space we all know the shortest distance between two points is a straight and you can figure that out if you rather than going on this angle here if you just gone straight up you would experience less distance. But here its not x squared plus t squared, its t squared minus s x squared. This is saying that the more you move out in space, the less time elapses on your watch. So the rule in relativity is the shortest distance is a Straight Line, but the longest time is a Straight Line. The more space you traverse and come back, the less time you will experience. So youve heard of the twin paradox where theres two twins, one zooms out near the speed of light, then comes back. Its always hard to remember which one experiences more time, the one that moves fast and then comes back always experiences less time. Because the longest time path is the one that just stays stationary. There you go. So this is geometry, right . This pythagoras theorem that weve updated for the space time outlook and theres a minus sign in there that minus sign will turn out to be important but is still kind of reminiscent of things that weve seen in our good Old High School geometry classes. Why we care about this, well, remember this guy . He wasnt done yet. In 1905, he had established special relativity. But remember the first thing that newton did when, he had established classical mechanics. Special relativity was an update of the rules of classical mechanics. But you still want to say, like, what are the forces is what is it thats pushing you around . And the very first thing newton did was gravity. Now, in case of relativity, a lot of the equations are were inspired by electromagnet autism and electromagnetism fit in with relativity very, very well. Right from the start. But gravity hadnt gone away. So what einstein to do was to update newtons of gravity, to reconcile with the new rules of relativity. This turns out to be harder than you think. Theres a certain set of obvious guesses that you make. They work, einstein was no dummy. He put his noodle to work at this. He was distracted by things like mechanics that got in the way. But eventually he really focused in on how can we reconcile and newtonian gravity remember that fact that we about gravity that its universal well that was the key to unlocking the puzzle that einstein had set himself and he called it his happiest moment of his life where he realized this following very mundane fact. If youre in a sealed room like were in right now, we the force of gravity, right for me, its pushing up on my feet for you. If youre sitting down, its pushing up, preventing you from falling to the center of the earth. We can feel that theres gravity clearly theres gravity right . But einstein says, what if the earth wasnt there . But instead the whole center is on a rocket and the rocket is accelerating at one g with a very, very rocket engine. He claims you wouldnt be able tell because of course, an accelerating rocket would also like it is pushing you up just like the earth does in the force of gravity. And, you know, you can say, well, what about other forces . Whats so special about gravity . If there was an electric field in this room, you could easily measure the electric field because you take an electron which is negatively charged it would be pushed in one direction. Proton positively charged, pushed in the opposite. But remember we just learned in a gravitationa