Healthy democracy doesnt look just like this, it looks like this. Where americans can see democracy at work. Citizens are truly influenced a, republic thrives. Get informed straight from the source and cspan. Unfiltered, unbiased, word for word, from the Nations Capital to wherever you are. This opinion that matters the most zero. This is what democracy looks like. Cspan power by you. It is an honor for me to introduce professor sean cairo today. He has recently become a full professor of natural philosophy has the radical thesis and is red many we Interesting Research papers. Its also a Popular Science writer and has been an thats all i offer author. I always find him very thoughtprovoking. I read his book when i was an undergrad in argentina and ever since then i became fascinated with the topic hes very committed to making complex physical ideas accessible to everyone and we are very unique and wise way. So today he will be telling us about his first book in his new trilogy, the biggest ideas in the universe, space, time and motion. Where he explains not only the difficult concepts but the mathematical framework behind it. In a very beautiful way. So please join me in welcoming professor sean carroll. [applause] thank you cory. Thank you harvard bookstore, one of my favorite bookstores in the whole world. Thank you harvard university. One of my favorite universities in the whole world, i got my own ph. D. Here through number years go, what i will no longer emit and public. I q over. Much of realize its a little chilly out there. I am very happy youre able to brave the elements out there to get here. When if this is a laser pointer. What do you think . Theres something i can push on . Im a little afraid. I have a book the biggest ideas in universe flying one, 19 will be about quantum physics and and going through will be about emergence. But the two minute is in the book to talk about all the muscle take a big idea hail talk about that to give you a flavor of what you would get worried to buy the book. So today i want to talk about einstein equation. And you know im thinking about ive seen up before, good familiar territory e mc2, energy, mass. Good its not gonna be completely unfamiliar. But this is not einsteins equation. Its not what a physicist would mean heavy settle yes, im thinking about einsteins equation earlier today. Heres einsteins equation as a physicist thanks to that. Were you to say it aloud could be armenia minus one half a minute makes a five t team in you. This is the field equation for the curvature of space time itself in general relativity. We never tell you about this. We might give you the words. Space time is curve and the curvature is gravity things like that. But we dont give the a question less your physics major. Shadowed to those physics major out there maybe again it. But even in most undergraduates never see this equation if they get a physics degree. Its considered to be two armed. Theres all these greek letters in their, theyre sub script, we dont know whats going on. An hour from now we will all know whats going on. I want to teach you this equation. How do we get . There we caught with classical mechanics. The whole theme a book ones classical mechanics as opposed to Quantum Mechanics. And classical mechanics, the central equation is newtons second law, and because i may. My physics teacher when i was a freshman said the only equation need to remember is axe equals m a. Thats an exaggeration but it tells you the essential important of this equation forces. Mass times acceleration. Why is this equation so interesting and important . In part because its precise. In other words, its not just a suggestion. The difference between equations and words. Its not just saying the more you push, the more the objects will accelerate. Its a very precise quantitative relationship you can use to fire rockets to the moon. Thats the kind of precision that you need. But the other thing we dont always appreciate that its always universal. What i mean by that is that its not just saying this one time i pushed a car with a certain force and accelerated by a certain amount. Its saying every time, every where in the universe that our forces exerted on an object with max and, you can use this equation to figure out how it will move, how much it will accelerate. Now where this is philosophy lecture, rather than a physics lecture, we would add, why are their relations in the universe that without precise in that universal . Happily we are lower brown today. Where physicists, we know that they, are we celebrate and we move on. We want to learn how to move this equation. If you exert a force on something, you like celery, proportional to its mass, we need to know what the forces, so newton himself talked about of famous gravity, is famous inverse square law. Have a little object with little m masses little am, so well start accelerating might be the earth and a bigger object with matt capital and might be the sun. He can ask how much force is exerted by the force of gravity. Newton says if you have capital and with a big object little am for the little one, you draw a little vector, a little thing with magnitude and direction and you see a vector labeledy itll be called a unit vector, back to where the think length doesnt change what we are asking is what is that sector, what is the force that is acting on this object with this little am . Really this equation because of the little arrows on the afghani e, this is an equation up between two numbers but between two columns of numbers. Have the vector, has a certain amount of force in the acts direction, sort amount in the wider action, certain amount in the z direction, thats what it means to be a vector. As a both aside and a direction. And the direction its pointing it in this case is for so long in a sector pointing from the little mast to the big one. The size of it because began times little and times capital g which is newtons constant of gravitation divided by the distance squared. Thats why its the inverse squared law when youre very close to objects together, gravitational pull is relatively strong, when theyre far away its relatively weak. This is how it goes. So what a physicist would do is to start with some set up. Your two objects, you two masses, distance, what happens next . How do they move next . And its a very nice simplification that occurs right away at the mass of the being pulled cancels out. So f equals m a but f also equaled gm over r squared over t. So matthew can devote by little land 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 characteristics of that object. It doesnt matter what its made of, it doesnt matter how massive it is, or what day of the week it is is. Every object, the same distance from some other objects will accelerate in the same way. He can do this experimentally, he can go to the moon. So here on earth, if you drop a hammer and a feather they wont stop the same rate, its because of our resistance, not because of the laws of physics in some deep level. When you go up to the moon with no air resistance, you can ask of a drop of hammer and a feather late fall at the same rate. This was done by the apollo 15 astronauts. Hopefully they already had some faith in newtons laws of physics otherwise they wouldve not gotten to the moon to do the experiment. But happily turned out right. It made very grainy videos and earnest reconstruction of the event but two objects with very different masses fall in the same way under the force of gravity. Now 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 you are made of all accelerate under gravity in the same way. That will be crucially important. Why . Because as successful as this paradigm was, this whole set up that isaac newton gave us freedom classical mechanics, it wasnt a final word. In 1905 we had input from this guy, Albert Einstein. These days when you see a picture of albert as time its almost easily in his later years. Crumpled, the sweaters and everything, and you get the impression thats what physicists are like. This is what einstein looked like when he was driving the equations of special relativity and general relativity. His hair was calm, somebody was dressing him nicely. I dont want to say with the causal relationship was, but he was a sharp dressed young man. Thats on unison. Three of special relativity 1905 contrasts with the theory of general relativity. In special relatively theres no gravity, generally the tv there is. Well get to that. Einstein did he did not really invent the theory of special relativity, there are already various lines of reasoning that were, that and we put it all together once and for all. We wont go into the details of the special relativity, but you heard some of the jargon, some of the phrases. Motion is relative, thats where the word relativity comes from, the speed of light is cognizant, it cant cope faster than the speed limit light. And theres all these phenomenon that you talked about, length contraction, time dilation. In the book, i dont emphasize these things that much because in my quirky idiosyncratic worldview focus on things that in the plutonium days or something called length and it turns out in the relativity picture different people are not gonna agree on what it is. So rather than starting the flight saying 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 drive everything from that. But all we need to know right now is that einstein didnt actually even in 1905 put the finishing touches on the theory of relativity. That was done arguably two years later by herman murkowski who used to be einsteins professor. When kasky was a mathematician not a physicist, but he was proudly following the students progress, he knew about the theory of relativity, and was he who first said all this great work in your theory the if 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 these effects the you are talking about or manifestations of the geometry of space time. And his famous quotas space by itself in time by itself are doomed to fade into mere shadows, and only the union of the two will achieve an independent reality. A way the referees would let him get away with rhetoric like this in a physics paper today, but 100 years ago you could do it. Not everyone was impressed by this mathematical step forward including simply call i blurred einstein, wrote one of his players the murkowski formation makes rather great demands on the reader in a mathematical aspect. Let me go admiral in here, ice time is no dummy. 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 and he constantly tried to take the physics theories and trying to turn into mouth for its own sake. He was married thats what exactly murkowski was doing. Turns out he was wrong and one of epsteins most senior important feature was to be wrong and change his mind. He would very quickly change his mind and jump on the bandwagon. He came to believe that the space 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 isnt it geometry we should be thinking about when we think about relativity when you think about contracts with history, dont hear the word geometry that much but the essence of it is this. When you want to travel a certain distance in space is a formerly that relates the amount of distance he travel to the coordinate but in a sense role city like new york where the streets were right angle, you could figure the total intervals the, total distance between two points ago a taking to different sides of a right triangle, squaring them using five tiger assist theorem. He, squirrel coves ex squared, equals y square. It means number, when 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. There is a difference between how much distance you could travel 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. Everybody agrees with the distances, walking a Straight Line between those two points means that he personally traveled less distance and if you go off in a detour come back. Again, perfectly obvious the distance you travel the whole point of relatively is true for time rather in space time. Its been kasky that gives us the formula for figuring this. If you travel some distance in space and there is some time coordinate on the universe. Like theres some universal time that everybody agrees on, the International Bureau standards are set up we can read them and figure out what it is. Universal time corn is not the same as the time little apps on your watch. Timelapse is on your watch is something you personally experience and men kaskys point is that time is like faith. The amount of time you experience will depend on how you travel through the universe. And exactly the same way but the amount of space that you travel through depends on the path you take. Here is the formula. Its kind of like pythagoreans is theorem but its not exact of the same. Cow the greek letter cap stands for the proper time, the elapsed time, the actual amount of time you experience okay. There is a formula for. It peace corps minus x square, i sneakily set the speed of light equal to one. Theres a certainly fraction of you that are doing dimensional analysis in your head when herrera can subtract time from space or cavalierly the answer is we are using units where lengths is measured in light years and time is measured in years. How . Case of the speed of light plays a special role in this theory. But the real point is that the time you will feel a lapsing its given by this formula and for a given change in the coordinate time t, it will depend on your path through the universe how much time you actually experience. In space we all know the shortest distance between two points is a Straight Line. You can figure that out rather than going to tangle here just go straight up, he would experience less distance. But here its not peace quirk x where. This is saying that the more we move into space, a less time elapses on your watch. So the rule of relativity is not shortest distance is a Straight Line, but the longest time is a Straight Line. The more space you traverse and come back, the last time you will experience. Youve heard of the twin paradox where theres two twins one comes at the speed line comes back its always hard to remember which one remembers more time. And one moves back in then comes back always experiences last time because the longest time past is the one that just stays stationary. There you go. So this is geometry right. This is pythagorean theorem, its updated for the space time outlook and its a minus there l 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 gravitational field everything falls the same way. Einstein realized thats exactly the same thing. That would be on the rocket. Everything would fall same way. So if youre in a small region of the universe, not able to look at the outside world, you cant tell whether youre a gravitational field at all you could mimic all of the of gravity by just accelerate in a small enough region of spacetime you or i would come up with that insight. We would pat ourselves the back, then go have some pizza or something. Einstein was not done yet because he was trying to think how to reconcile gravity with relativity and he realized that if gravity is universal russell, if it has this special feature that you cant know that its there in the room. That means that gravity in sense isnt a force like the other forces of nature like electromagnetism. Its an intrinsic feature of space itself. What feature is it . It is the geometry the curvature of space time. He knew about mikulskis work. He begrudged he began to think that maybe this was a good idea in minkowski geometry, theres a sign in pythagoras theorem, but its still flat. Geometry is still in some sense like the euclidean geometry, we learn in high school what einstein was that when we feel gravity its because you need to generalize flat geometry to curved geometry maybe he said the force of gravity is a manifestation of the curvature of the geometry of space time. The problem was einstein knew nothing abou