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 fa hes a theoretical possess, and he has written many Interesting Research papers. Hes also a Popular Science writer, and has been in the New York Times bestselling author. I always find him very insightful and thoughtprovoking. I read his book on generative a day 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, and he does it in a very unique way. So today, he will be changed telling us about the first book in his new trilogy, the biggest ideas in the universe, space, time, and motion. Where he explains not only the physical concepts, but also the mathematical framework behind them. Interviewer very beautiful way. So please join me in welcoming professor jean carroll. Thank you, laura. Thank you harvard bookstore, one of my Favorite Book stores in the whole world. Thank you harvard university, one of my favorite universities in the whole world. [laughter] when i got my own ph. D. Here, a certain number of years ago, that i will no longer admit in public. And thank you all very much, i realize its a little chilly out there, i am very happy that you were able to brave the elements to get here. And as mentioned, we have i wonder if this is a laser pointer. What do you think . Its something i can push on it. Im a little afraid. Oh yeah, look at that. I wrote a book, the biggest ideas in the universe. Its one of three. There are too many big ideas in the books to talk about all of them. I would figured i would pick a big idea and talk about that, give you a flavor of what you would get where you to buy the book. But then i want to talk about is einsteins equation. And you know, as i say that, youre thinking, well, okay, ive seen that before, good, this is familiar territory, e mc2, energy, mass. Good. Ive learned something, maybe, but its not going to be completely unfamiliar. But this is not einsteins equation. This is not what if it is this would mean if they said oh yes, i was thinking about einsteins equation earlier today. Heres einsteins equation. As a physicist thinks about it. Where you would say it out loud, it would be our muniu minus this is the field equation for the curvature of space time itself in general relativity. And we never tell you about this. We might give you the words, we might say, face time is curved, and the curvature is gravity, things like that. But we dont give you the equation unless youre a physics major, shut out two visits majors in here. But even then, most undergraduates never see this equation and they get a physics degree. Its considered to be too hard. Theres all these greek letters in there, theres subscribes, we dont know whats going on. An hour from now, you will all know whats going on. I want to teach you this equation. How do we get there . We start with classical mechanics. The whole theme of book one is classical mechanics, as opposed to Quantum Mechanics. Class someone can except, the central equation there is newtons second law. F equals and a. My physics teacher, when i was a freshman, says that the only thing you need to remember is ethical and a. You can derive anything else. Thats an exaggeration, 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. Its not just a suggestion, its the difference between equations and words, its not just saying the more you push, the more an object will accelerate. Its a very precise quantitative relationship that you can use to fly a rocket to the moon. Thats the kind of precision that you need. But the other thing that we dont always appreciate, is that its universal. And by that i mean, its not just saying this one time i pushed a car with a certain force and it accelerated by a certain amount. Its saying every time, everywhere in the universe, that a force is exerted on object with mass m, you can figure out this equation to figure out how much it will move. Now, wear this a philosophy lecture, we would ask, why are their relations in the universe that are that precise, and that universal . Happily, we are lower brought in that today. We are frances says. We notice that there are, we celebrate that, and we move on. We want to use how to use this equation. F equals m a, if you exert a force on something, it will accelerate proportional to its mass. But you need to know what the force is. So newton himself talked about a famous force, the force of gravity. Newtons famous inverse square law. So if you have a little object, with mass little am, this is one thats being forced on, and we will start accelerating. This might be the earth. And a bigger object, a capitol m, that maybe the sun. And you could add how much force is exerted by the force of gravity . And news as if you have capital m for the big object, little m for the little one, look, there is little m, you try little vector for magnitude and direction, if you see a vector labeledy, it will be a unit vector, a vector with a fixed length that doesnt change. And what we are asking is, what is that factor . What is the force that is acting on this object with mass, little m . Its equation, really, because of the little arrows on top of the f and e, this is an equation not between two numbers, but between two columns of numbers. If, the vector, has a certain amount of force in the x direction, i thought about in the y direction, the z direction. Thats what it means to be a factor. It has both a size and also a direction. Its pointing in. And the direction its pointing in, in this case, this is the force along that unit vector, posting from the little m to the big one. And the size of it is big m times little m times capital g which is new ensconced of gravitation, divided by the distance squared. Thats why its the inverse squared law, when youre very close to two objects, two 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 his to start with some set up here, two objects, here are their masses, heres the distance, heres how theyre moving. What happens next . How do they move next . Its a very nice, simplification that occurs right away, the mass of the object being polled cancels out. So f equals m a, but f also equals so biomass, you can divide, by little m on both 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 characteristics of that object. It doesnt matter what its made of, it doesnt matter how massive it is, or how fast its spinning, or what day of the week it is. Every object being a distance from some other object will accelerate in the same way. So you can do this experimentally, you can go up to the moon. Here on earth, you dropped a hammer and a feather, they wont fall at the same rate. But thats because of our resistance, not because of the laws of physics. And he got to the moon, where there is no air resistance, you can ask, if i drop a hammer at a feather, will they just the same rate . This is done by the apollo 15 astronauts. Hopefully, they already had some faith in newtons laws of physics, because otherwise they would not have gotten to the moon, to do the experiment, but happily, it turns out right. They made very grainy videos, this is an artist reconstruction of the event, but two objects, very different masses, fall in the same way under the force of gravity. That is not just acute coincidence. This is going to turn into the single most important fact about gravity. Gravity is universal. It doesnt matter who you are or what youre made of, we all accelerate under gravity in the same way. Thats going to be crucially important. Why . Because at successful as this paradigm was, this whole set up that isaac newton did, it was not the final word. In 1905, we had input from this guy, albert einstein, these days, when you see a picture of einstein, its almost always in his later years, right . He has sweaters, and everything. Hes a little rumpled. You get the impression thats what this is our like. This is what einstein looked like when he was driving the equation of special relativity and general timothy. His hair was calm, someone was rising in nicely. [laughter] i dont to see what the causal relationship 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 a theory of general relativity. In special relativity, theres no gravity. We will get to that. What einstein did in 1905 is he didnt really invent the theory of special relativity, there were already various lines of reasoning that were coming into it, and he really put it all together once and for all. And we arent going to go into details about special relativity, but youve heard some of the jargon, some of the phrases. Motion is relative, thats where the word relativity comes from, the speed of light is constant, you cant go faster than the speed of light, its an upper limit. And then theres all these phenomena that you are taught about, life contraction, time violation. In the book, i dont emphasize these things that much. Because in my quirky, idiosyncratic worldview. Focusing on things like length contraction is a remnant of the fact that back and then you tony and days, there was something called a. Length and everyone agreed on what it was. And it turns out in the relativity picture, different people dont agree on what length is. So rather than starting with length and the saying, but it contracts for some people and not for others, i tried to start with what is actually true and correct in the theory of relativity and derive everything from that. But all we need to know, right now, is that einstein didnt actually, even in 1905, but the finishing touches on the theory relativity. That was done, arguably, two years later by herman murkowski, who used to be einsteins professor. So murkowski was a mathematician, not a physicist, but he was proudly following students progress, he knew about the theory of relativity. And it was he who first said all this great work in your theory, 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 these effects you are talking about our manifestations of the geometry 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 union of the two will preserve an independent reality. No way the referees would let him get away with that today, but 100 years ago you could do it. Not everyone was impressed by this mathematical step forward, including someone named albert einstein. Who wrote in one of his papers, this calculation makes rather great demands on the radar in its mathematical aspects. So look, einstein, let me go out on a limb here, was no dummy. But he famously only did as much matt as he absolutely had to do. He was good at math, but he was a physicist at heart. He didnt do math for the sake of doing math, he constantly resisted people who tried to take these physics theories and turned them into math for its own sake. And he was worried that that was exactly what murkowski was doing. Turns out he was wrong. And one of his single most important features was his ability to be wrong and then change his mind. He would very quickly change its mind and dump on the bandwagon. He came to believe that these face time way of thinking about relativity was actually the right way to think about it. Let me tell you what that way is. The question is, why is it geometry that we should be thinking about when were thinking about relativity . If you read all the popular expositions, length contraction et cetera, you dont really hear the word geometry that much. But the essence of it is this. When you want to travel, a certain distance in space, theres a formula that relates to the amount of distance you travel to what we call the coordinates. This doesnt work in boston, but in a sensible city like new york, where the streets are at right angles [laughter] you could figure out the total interval, total distance between two points, by taking the different size of a right triangle, squaring them, and using by the aggressors theorem. In this little triangle here, so what this means is, number one, you have a formula for figuring out the distance between 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 he would travel, depending on the path you take. This is a point that is so obvious, its almost not worth saying. But you could have two points a certain distance apart, and everyone agrees with the distances, but walking a Straight Line between those two points means that you, personally, travel less distance then if you go off on a detour and then come back, right . Again, perfectly obvious. The distance traveled between two points depends on your path. The reason im emphasizing this is perfectly obvious, the whole point of relativity is that the same thing is true, but for time, rather than face. Time, like distance, is something that will be elapsed amount of it depends on your path through the universe. And its been its murkowski that gives us this formula to figure this out. If you travel some distance in space, and theres some time coordinates on the universe, right . Like some universal time that everyone agrees on, that the International Bureau standards is set up, there are things 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 elapses on your watch. The time that elapses under what is something that you, personally experience. Murkowskis point is that time is like space. The amount of time you experience will depend on how you travel through the universe. And in exactly 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 pat eggerss theorem, but its not exactly the same. Tao, the greek letter tao, stands for the proper time, the elapsed time, the actual amount of time you experience, okay . And theres a formula for it, t squared minus x squared. I sneakily set the speed of light equal to one. But you dont see the seat of light in here, theres a certain fraction of you theyre doing dimensional now has in your head, and wondering how it can subtract time from space, so cavalierly. The answer is we are using units where length is measured in late years, and time is measured in years. Okay . So the speed of light plays a special role in this. But the real point here is that the time that you will feel elapsing is given by this formula, and for a given change in the coordinate times t, it will depend on your path through the universe, how much time you actually experience. With a twist. Because in space, we all know, the shortest distance between two points is a Straight Line. And you can figure that out, rather than go on this angle here, if you just gone straight up, you wouldve experience less distance. But here its not x squared plus the square, its t squared minus x squared. Its saying that the more you move out into space, the less time elapses on your watch. So the rule in relativity is not 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 sumy out near the speed of light and 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 past is the one that just stays stationary. There you go. This is geometry, right . This is by taggers theorem, weve updated it for the space time outlook. There is a minus sign in there, that minus sign will turnout be important, but its still kind of reminiscent of things that weve seen in our good Old High School geometry class. Why do we care . About this . Well, remember this guy, einstein . He wasnt done yet. In 1905, he established special relativity. But remember, the first thing that newton did when he established classical mechanics, special relativity was an update of the rules of classical mechanics. But you still want to say what are the forces . What is thats pushing you around . And the very first thing you did was gravity. Now, in the case of relativity, a lot of the equations relativity were inspired by electromagnetism, and electromagnetism fit in with relativity very very well, right from the start. But gravity hadnt gone away. So what einstein wanted to do was to update newtons law of gravity to reconcile it with the new rules of relativity. This turns out to be harder than you think. Its a certain set of obvious guesses that you make, they dont work. Einstein was so dummy, he put noodle to work at this. He was distracted by things like Quantum Mechanics, that got in the way. But eventually, he really focused in on how can we reconcile relativity and daytonian gravity . Remember that fact that we learned about gravity. Its universal. That was the key to unlocking the puzzle that einstein had set himself. He called his happiest moment of his life, where he realized that following very mundane facts. If youre in a sealed room like we are in right now, we feel the force of gravity, right . For me, its pushing up on my feet. For you, if youre sitting down, is pushing you up, preventing it from falling to the center of the earth. We can feel that there is gravity, clearly those gravity, right . But einstein said, what if the earth wasnt there . But instead, the whole Science Center is on the rocket. And the rocket is accelerating at one g with a very, very quiet rocket engine. He claims you wouldnt be able to tell. Because of course, an accelerating rocket would also feel 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 a special gravity . If there was an electric field in this room, you could easily measure the electric field. Take an electron, which is negatively charged, push it in one direction, proton, positively charged, pushed in the opposite direction. But remember, we just learned in a gravitational field, everything falls the same way. Einstein realized thats exactly the same thing that would be true on the rocket. Everything would fall the same way. So if youre in a small not able to look at the outside world, you cant tell whether youre in a gravitat