 Okay, thank you very much. Over a hundred years ago, in the physics community, the tools had never been sharper. The mathematical frameworks that had been developed to describe and predict the behavior of nature had never been more powerful. And yet the more that physicists peered into the cosmos, deep into the heart of the atom, the atom itself, and then deep inside of it, and then far out into space, probing more carefully the things in the heavens and the things on earth, the more it became clear that sharp tools were revealing things that the mathematical frameworks were inadequate to describe. And into this fray was born a young man, Albert Einstein, who became a brilliant mathematician and physicist. And tonight I'm going to explore the impact that he has had in part on physics through one of his most famous things, the general theory of relativity. And so the lecture tonight will be arranged into four pieces. The first one will be a precursor to the life of Einstein, what was the world like before he was born, and into what kind of world was he born. I'll then talk a little bit about Einstein, his life, and his achievements, and put into context in his life the development of the theory of relativity, both the special one first and the general one later, which we're now celebrating a century of. Finally I'll move on to the consequences and the modern era of this amazing description of nature. And finally I will close the lecture with a preview of the things that we now face as a society and that the physics community faces as part of the society in understanding the cosmos. Now I am not going to be shy about showing mathematical equations tonight. I know many physicists when they give popular lectures, they dump that. But I think we shouldn't be so afraid of math. Being afraid of math is like being afraid of French or Chinese or Italian or English. It's a language and every human is capable of learning it. I may not be as good as some of my friends are at math, but I believe every human being is capable of learning mathematics. And why do I think it's important? It's one thing to understand the beauty of music. You can listen to music, you can appreciate how you feel, what it does to you. But to truly understand why it moves you and how you might understand how to make music that moves other people. It's important not only to pick up an instrument and play, but to be able to represent that music in a way where you can unlock the deep meaning of the notes and the chords and the sequences in the song. And so for me mathematics is like musical notation, but for the cosmos. And so as I said, I won't shy away from showing it. And I'll discuss what I show you, but I'm not going to be afraid to put some equations up here. So let's begin with the first movement of this lecture entitled, A Lever to Move the World, in which we'll explore the precursors, the things that led up to the life of Albert Einstein. It's a long story and it's not entirely clear where that story begins in the history of our species, who was the first person to really begin to wonder about the heavens and the earth and whether or not there was a connection between them. So I have to cherry pick my way through history in order to give you a thread to hold on to. And so I'm going to start with this allegedly famous quote said by the scientist, engineer, inventor, and mathematician, Archimedes, reported by Pappus of Alexandria in 340 AD, give me a place to stand and I will move the earth. And what he was referring to is that he had illuminated the working of the lever. The long bar, you wedge it underneath the edge of an object that you yourself cannot lift, you place a fulcrum, some kind of support along the bar, you push on one end and the object you couldn't lift with your bare hands will move. And once he came to understand the workings of this at an engineering and mathematical level, he made this statement, imagining a lever so large that a human could stand on one end of it and pull and the whole earth would move in response on the other side. Now I don't think that he could have appreciated this, but you and I see that lever in action every day and in fact when he looked at the night sky, when he dropped things on earth, when he tripped, he was experiencing a lever that moves worlds and that lever is gravity, the tendency on earth of things to fall toward the surface of the earth. And so when you look out at the night sky at the moon, when you look at the planet Venus as it orbits the sun that we orbit, you are watching the great lever of the cosmos moving worlds with an unseen hand. And that unseen hand bothered a lot of people who wanted to come to a deeper understanding of just exactly why it is that this all works in such a regular, rhythmic and predictable way. And so skipping ahead quite a bit, almost 1300 years from Archimedes, I want to cherry pick another figure that's quite important in the history of the story of gravity and that's this gentleman here depicted in this painting from a famous moment in his life in 1633, Galileo Galilei, one of the first modern scientists who combined experimentation, inquiry of the natural world through rigorous testing with a keen mathematical mind and refused to accept wild speculation unless a test had been done to prove a claim. He didn't make a lot of friends that way. And when he was very young, early in his career, he didn't invent the telescope, but he helped to perfect its lens systems. And he sold his designs to the Italian Navy, made a tidy sum of money off of that, secured himself a rich patron who would take care of him so that he could do what he actually cared about, science. He didn't care about military applications of technology. He cared about learning about the natural world. And so he took this military instrument and he turned it to the heavens. And what he saw there amazed him. He recorded craters on the moon. He observed the moons of Jupiter not orbiting the Earth, as everybody believed everything did in the cosmos at the time, but orbiting Jupiter itself. He recorded sunspots, blemishes on the surface of what was supposed to be the perfect sun. And unfortunately, his publication, one of his most famous publications, his long life's work in astronomy, fell afoul of the then interpretation of biblical scripture. And of course, at the time, the Roman Catholic Church was extremely powerful in Italy. And he fell into the grips of the Roman Inquisition. And so this painting depicts that moment in his life when he's brought before a trial in front of the Inquisition suspected deeply of heresy. And in fact, in 1633, they found him guilty of heresy. And because of this, they required a few things of Galileo. He was lucky not to have been killed. Others were. But his book was banned. No one was allowed to use it. No one was allowed to take it seriously. And he was placed under arrest at the pleasure of the Inquisition. Now an important thing that we teach students at SMU is that it's OK to fail as long as you know what to do next. You don't wallow in it. You don't waste your time. And he was sad. I mean, this nearly killed him, this affair. He only lived about another nine years after he was condemned by the Inquisition. This is an extremely stressful time in his life. But he managed to get condemned to house arrest. And he used the remaining years of his life, because he could not study astronomy any longer, to turn his mind back to motion. Something that he had studied when he was much younger, but which he had dropped to work on the much more interesting topic of what's going on out there. And so he revisited things that in his youth he had speculated about, but never actually done any actual experiments on. And what resulted from this was he had another great work of science, which the short title of which is Two New Sciences. Galileo spends his house arrest doing detailed experiments on the motion of objects falling in the gravitational influence of the Earth. And we can sort of recreate something of his discovery here today. What I have is a very important modern book, Gravitation. It is quite literally the Bible of gravity these days. And if you want to understand it, go ahead and try to read this. I've been trying my whole life to understand the notation in this book. And I have here a very innocent, harmless little turkey feather. Now what Galileo discovered is that in reality, the acceleration that you feel when you fall to the ground or when an object experiences when it falls to the ground doesn't depend on the mass of the object involved. I can clearly feel. Go ahead. This book is a beast. Is that feather made of lead? No. It is an innocent little feather. Now, you might be skeptical. Little feather book. If I drop them at the same time from the same height, they're not really going to fall at the same rate. You'd be right. But Galileo was clever. He knew that there was this thing in between the book and the ground and the feather in the ground. You can feel it. People in the front row, go ahead and do this. If you've never done this before, thank you. SMU students, everybody. You can feel resistance. When your palm swings down, you feel a cold wind against your hand, more cold than the room already is. When you raise your hand up, you feel a cold wind against the back of your hand. There is a fluid there that resists motion. And so Galileo very cleverly constructed his experiments to take that effect out. And we can do that in our experiment. If I shield the feather from the air, from the wind, they would otherwise feel as it falls, simply by placing it on top of the book. You can see it's not glued to the top of the book. Now if I drop them, the feather stays on the book all the way down. And this experiment was brought to my attention, this way of demonstrating it, by an emeritus professor in our department, Jeff Chalk. So thanks to Jeff for this nice demonstration of how a feather and a book that's that heavy are both accelerated in the same way by the gravitational field of the earth. And Galileo was aware of this from his careful experiments. So all he could really tell at the time was that whatever's going on, whatever gravity is, it acts the same on all objects, regardless of their mass. And so in our honors physics class, this was shot by a few of the students, we didn't ask them to do this, and including the juggling one on the left who's sitting right here if you wanna talk to her later about that skill, okay. They were dropping objects and you can watch the basketball, the football, the ping pong ball, they were dropped by the same person at the same time. And you can watch them, you'll see that they fall with the same acceleration, 9.8 meters per second of added velocity every second as they fall. And it's the same for everything. And it's a curious thing, Galileo did not understand it and it would take a lot longer before that was finally understood. Let's skip ahead, not that far. Galileo Galilei died in 1642. And coincidentally, Sir Isaac Newton, one of the other most famous scientists in the history of our species, was born that very same year in 1642. He died in 1726, but what a life. Isaac Newton, an incredible person, a whole lecture on him, on any one of these people you could do at an event like this. He did a lifelong exploration of motion and gravity and wrote the seminal work, still to this day, considered the seminal work in the subject, certainly foundational. The natural philosophy, the principles of mathematics, the Principia, as it's known. And that was published in 1687. What I like about Newton is he's a hardcore scientist. If you can't give me data that tells me what gravity is, I will accept no speculation on the subject. He derived the law of gravity, but he really, at the very end of his book, you can go and look at the last couple of pages. He refuses to speculate on what gravity might be. Because he really believes that a scientist shouldn't be just making claims about things without some evidence behind them. It's a little more hardcore than I think we would go these days. But, you know, he could afford to stick to his guns after he'd invented a branch of mathematics which we now call calculus, just in order to do the calculations that were needed in order to codify motion and write down the law of gravity. Now, one of the things that's built into Isaac Newton's laws of mechanics, as I'll refer to them for the rest of the lecture, is an assumption. There were actually even proposed experiments that you could do to test this assumption, but I won't talk about those. I'll just talk about the assumption. And so he imagined the great stage upon which all events play out, space and time, that these are absolute real things that exist independent of whether anything is there to move in the first place. And so he states in the Principia that there is such a thing in his way of looking at it as absolute true mathematical time, okay, an absolute true mathematical space. And while it is true that different people in different states of motion might disagree on exactly what happens in a situation, everybody agrees on things like lengths in time. We all agree on that. That was an assumption that was built into mechanics. And so I can sort of demonstrate the principle of relativity, which existed even before Einstein came into existence. Quite simply, I have here a little rubber ball that I got in graduate school and I ordered a very cheap book. They packaged this for free. And it stayed with me my whole life since graduate school because it's a super ball. And so it bounces back pretty high when she drop it. Now what I'm gonna do is I'm gonna walk. I'm gonna walk from here over there. And as I walk, I'm gonna hold the ball steady relative to me and I'm gonna drop it. Now in my frame of reference, as I'm moving, I'm going to see this. The ball is going to fall straight down and it's gonna bounce back up into my hand. But you're gonna see something different. Watch. For you, the ball moved a distance horizontally before it returned to my hand. It just, we all agree on the events. I let go of the ball. The ball hits the floor. The ball returns to my hand. I argue that you are all moving. That's why you think the ball had a velocity going this way as well. But I'm the center of the universe. So what I saw was it just dropped straight down, came back up, I didn't even have to move my hand. Just move it down a little bit to catch it on the rebound, that's it. But your argument is no, no, no, no, all that happened but what really happened was as you were walking, it made sort of a V shape. It kind of did this as it bounced. And your hand happened to keep moving with it and you caught it on the rebound. That's relativity. We disagree on exactly the nature of what happened but we all agree on the events. And if we measured times involved, we all should get the same answer. So that's basically the stuff that's built in to the laws of mechanics as Isaac Newton had them written down. Now a lot of things happened after Isaac Newton. Isaac Newton, as I said, invented something, he called it a different name. His rival, later became his rival, got freed Leibniz, also invented what he called calculus. That's the word that's stuck today. Some of you are snickering right now with this stick figure cartoon. For those of you that don't get the joke, I'm not gonna explain it to you. Somebody in this room gets it. Take this as an entree into mathematics. Go and figure out why this is hilarious from the perspective of Leibniz and Newton. Many historians think that their feuds set mathematics back by quite a couple of decades in England if they had just kind of moved on from their disagreement about who did what and who stole what from whom. Things could have moved along a lot faster while they were still alive, but such is the life of human beings. Now another interesting thing that happened in the 1800s was ushered in by this gentleman, Bernhard Riemann. Not perhaps outside of the world of physics and mathematics, a very well-known figure, but what he did was extremely important, although one of the key protagonists of my tale tonight failed to recognize that in his youth and paid for it later. Bernhard Riemann was wrestling with an interesting problem when he was a young man. When we take high school geometry, we learn that in a triangle, the angles inside of that three-sided object all add up to 180, 180 degrees. Now there's actually an assumption built into that that nobody tells you in high school and that is that everything you're talking about is happening in perfectly flat space. And it's true, if you take a flat surface and you draw a perfect triangle with precision rulers and pencils and whatnot and you measure carefully all of those little angles, indeed you'll get 180 degrees. Riemann's thesis, however, dealt with general geometries, geometries that are not in a flat space, like the surface of the earth. If you walk between the three points on the surface of the earth, walking as straight a line as you can make on a curved, spherical surface, and as you go, you kind of drag a chalk line behind you and you finish making this great journey, some of which takes you through deep waters so you're going to want to be careful. And then at the end, you carefully measure the angles between your chalk lines. You'll be sad to find out. It doesn't add up to 180 degrees. You get something much bigger than that. And that's because geometry on a non-flat surface is not the same geometry we learned in high school. And yet, it has its places. I mean, we live on a spherical planet, so this is going to come in handy. We'll come back to Riemann in a bit, but I want to kind of skip quickly through the other things that happened before Einstein was born. The 1800s were an incredibly energetic period in the development of what we now think of as modern physics. You have the invention of the steam engine and coincident with that, you have the development of the theory of heat energy, so-called thermodynamics. You have an incredible burst of activity understanding the electrical and magnetic forces which by the middle of the 1800s had been understood to be united in a single electromagnetic force. This is Michael Faraday, one of the most famous physicists in the history of the field, also one of my favorite people, a whole fascinating story in and of itself. This is a woodcut of him giving one of his famous Christmas Day lectures where he would do all these incredible demonstrations of electricity making magnetic fields and magnetic fields causing electricity and the kids adored it and hopefully he inspired another generation of scientists by doing this. These are still demonstrations here we do today in our physics classes. And one of the things that came out of this incredible detailed exploration of electricity and magnetism which had once been thought to be separate things was the realization in 1864, once you've nailed all the math down for electricity and magnetism, that this other thing that we've always wondered about the nature of light is actually a wave that travels through space and it's made from an oscillating pair of electric and magnetic fields. Those things, these electromagnetic waves should travel at the speed of light. The calculation was done and amazingly you get the same answer for the speed that light moves at. And so it was believed that light must be one form of an electromagnetic wave but it would take many more years before anybody would definitively demonstrate the reality and existence of these waves independent of something like visible light. And that was done by this gentleman, Heinrich Hertz. We'll come back to him in a second. So Heinrich Hertz in 1893 published the results of an experiment and his setup is shown here. Basically what he did was he transmitted a signal from one side of his lab to the other side of his lab wirelessly. And if this were not true and if he had not been successful none of us would be texting today on mobile phones. So you can blame him for all the distraction in our modern world today because wireless communication was invented in 1893. Now to bring a little spice from SMU into all of this, let me talk a little bit about the first president of the university, Robert S. Hyer. So Robert S. Hyer was a physicist by training and he'd been a professor and then president at Southwestern University and then was the first president for SMU when it was founded. And I was digging through some of the papers the DeGolier Library made available to me last fall about Hyer. I was curious to see if he had anything to say about relativity. But I stumbled on this little gem which I think is still relevant today. You know he lived through the era of the invention of wireless telegraphy. In fact he reproduced Hertz's experiment in Georgetown, Texas a year after Hertz published his paper. He transmitted a wireless signal from his lab to the jail house in Georgetown. And he says wireless telegraphy began with a mathematical formula at Cambridge and was put into concrete form at Bonn. He worked at Bonn. This great age of applied science must remember that before there can be an applied science there must be science to apply. And so he's clearly speaking from one perspective you have all of this incredible machinery that's invented in the 1800s parallel with all these incredible discoveries about laws of nature besides the laws of mechanics that Newton had set down. And so now he's sort of reacting to this. Don't get too far ahead with the applications. Don't forget that there's basic curiosity driven things to understand about the universe. After all that's what ushered in the great era of technology including the one we live in today which basically stems from what I'll talk about later with Einstein and his contemporaries. Now one other curious thing about light before we move on to Einstein. Light falls afoul of being governed by both the laws of mechanics if it's a wave and the laws of electricity and magnetism if it's an electromagnetic phenomenon. And so because no mechanical wave that anybody had ever met up to that point traveled in something other than a medium water waves travel in water sound waves travel in air if there's no air there's no sound there's no water there's no water waves but light according to the laws of electromagnetism didn't need a medium to travel and it seemed to move at a fixed speed 186,000 miles per second incredibly fast. So the problem here was that you needed to go and figure out what the medium was that light traveled in it was called the ether and the test was proposed to search for it. A series of tests in fact were done by one and then both of these individuals Albert Michelson and Edward Morley and the most famous test of theirs after they had greatly refined their instrumentation and their techniques came in 1887, all right? So the idea was that you take a beam of light and you split it and one beam you send off in the direction of the earth as it goes around the sun if there's a fluid that light travels through the earth as it travels around the sun will feel a wind much like we feel a wind if we run through air. You just take the other half of the beam of light and you move it in a direction that's perpendicular to the direction of the motion of the earth around the sun and when you recombine those beams of light you should see some differences as a result of one beam having to go with and against the ether wind and the other one traveling with only part with and against the ether wind. But in fact, every time they did this experiment and they refined their techniques over and over again instead of seeing the picture on the right they always saw the thing on the left and no matter how they tilted their apparatus and shot the beams of light they always found that light was not affected by the motion of the earth it was as if there was no ether wind at all. And so then people said, well the wind must be moving along with the earth but then there were tests of that and that was disproven as well. And so you have this curious mystery as you reach the end of the 1800s that light which should be duly governed by two well-established sets of laws of nature doesn't seem to work it breaks them both when they try to talk together. And it's into this incredible era of discovery and confusion that a young man is born whom I'll refer to as the g'duncan man as I'll explain in a moment. Here he is, all right? So you know a lot of people see Einstein when he's got the wild hair and probably a pretty good lack of social skills which is what I'm aiming for as I age as a physicist, all right? This is him when he was probably actually he wasn't very social as a child and he later credited that for maybe why he thought in pictures so much. He was born in 1879 to Pauline and Hermann Einstein owned a factory for manufacturing electromagnetic motors very much a product of the end of the 1800s he and many other people were competing to build better electromagnetic motors for distributing electricity in Europe. This photo's from 1882 when he's aged three. Einstein grows up and he attends school in Germany and there's a myth out there that Albert Einstein was not very good at math and people tell their kids oh don't feel bad about not being good at math Einstein wasn't good at math actually he was great at math. What he wasn't good at was authoritarian systems. The German education system is extremely strict at this time and Einstein doesn't like the way that the teachers deal with him as a student and so he's mostly frustrated although he gets really good grades. His father has to move the factory to Italy but Einstein remains in Germany but he's so fed up with this he gets a note from a doctor basically saying he's having a nervous breakdown and he travels on his own to Italy to be with his family, shows up, bums around for a little bit and then is put into a school in Switzerland where he completes his education at age 17. This photo is from 1893 when he's 14 years old you can already see the features of Einstein emerging in this boy's face. Now he recalls much later in life that when he was 16 he asked himself a question shortly after learning that light is an electric and magnetic wave. He asked what would he would see if he could run faster and faster and catch up to a beam of light. What would he see? What would it be like if light stood still relative to him? Okay so that's equivalent to me walking and dropping the ball and you running to catch up. When you catch up with me you'll just see the ball fall straight and come back up. Everyone else who's sitting still will see it make that V shape and he wondered what you would see if you could catch up to a beam of light and he recalls his palm sweating and his heart pounding as he contemplated this question. As one commentator on this story said that young man's palms might be sweating and his heart might be pounding at 16 but it's not because he's thinking about catching up to a beam of light. And so this is the first example of what I call the Gadankan men. This is a young person thinking about nature deeply whether he realizes it or not. In his mind picturing an experiment doing a thought experiment. Gadankan is German for mind or thoughtful. And so he's thinking in his mind about okay here are the laws of physics so what if I do this experiment that I can't do in real life what might I see? What might I learn about the implications of the laws of physics if I did this? So Einstein goes to university and he completes a four year teaching diploma at age 21. This is in 1900. But he fails to secure a teaching post for two years. Why? Because he really miffed his professors. He really couldn't get a letter of recommendation. This is largely because he believed that some classes he was required to take were nonsense especially these abstract mathematical courses in Riemannian geometry which seemed to have nothing to do with reality. And so he actually sent his good friend who later would become a well-known mathematician Marcel Grossman to go and take notes in those lectures so he could go to a coffee shop and hang out with some of his friends. Does this sound familiar to anybody? I think this sounds familiar. So he kicks around for two years. He gets some little teaching positions. Lots of people are advocating for him for a real permanent position but his friends eventually secure him a position as a civil servant in the Swiss patent office reviewing patents for electrical and magnetic devices. So he's very much now exposed to the technological revolutions that are going on including the synchronizing of clocks in distant locations which was important for navigation and at the time for the newly created time zones. Einstein during this period completes his doctoral thesis. He does so in 1905 and he does it because he gets his work done fast. He does his work well and his boss doesn't mind him spending some time on this physics stuff as long as he gets his task done. Not about boss. And in 1905 he gets his doctoral thesis he completes his doctoral thesis and that is the same year that is known as his miracle year, his Anas Mirabilis in which he publishes four extremely famous papers one of which would later earn him the Nobel Prize. And that one, funny enough it doesn't show up in this lecture at all tonight. Okay, go figure. Now what was Einstein wrestling with in those years prior to completing his doctoral thesis and having this breakthrough year in 1905? Well he's thinking a lot about light and he's thinking about it in the context of Newton's laws of mechanics with its famous equation that any force acting on something with mass M will give it an acceleration, a change in its state of motion F equals MA. But in this view of the world space and time are fixed frameworks upon which all events play out. We all agree on the changes in time what the durations are in time but we don't always agree on exactly why things happen the way that they do but we can all figure it out by making these assumptions. We all measure the same displacements in time. There's no effect that motion has per se on those kinds of things. This is James Clerk Maxwell. I kind of hinted at him earlier. He's the one that finally codified in mathematical laws the unification of electricity and magnetism into a single set of equations. These four equations right here which still we use today in all of their glory. These are the laws of electromagnetism and from this emerges the idea that light is a vibrating electric and magnetic wave that travels at a fixed speed and it does so even in empty space which no mechanical wave is supposed to be able to do. So Einstein is wrestling with this question how do you resolve two extremely successful time tested frameworks that have led to technological revolutions each on their own. They can't both be right and they can't both be wrong because too much depends on them. So what's going on? He's really thinking deeply about this. There are many things that happen during this period. He has good friends that he can talk to about these problems that he can get advice and bounce ideas off of. Science is believed to be a lonely pursuit but it's not, it's a social pursuit. You're constantly interacting with people and while you may have a breakthrough that breakthrough is often driven by the ability to just talk to people and get their input and see things in a way you've never seen it before. And one of the things Einstein credits with his one of his big breakthroughs in that year in 1905 was looking at this clock tower which was just a couple of blocks down from his apartment in Bern, Switzerland. And he imagined what it meant to actually measure time. How is it that we know that time is passing? And he thought very carefully about this and he did one of his Gadankan experiments. How is it that you know what time it is? Well, you may have a watch on your wrist. There may be a clock on the wall. Imagine the clock on the wall. You look at it and it's ticking the seconds away. Tick, tick, tick, tick. So whatever the mechanics is inside that, it makes these regular events and you're measuring time by measuring the distance between events in some dimension that's not space. Tick, tick, tick. How do you know that time is passing? Light bounces off the hands of the clock and strikes your eye. But Einstein knew based on things like the Michelson-Morley experiment that no matter what speed you went at, light always appeared to move at a fixed speed, 186,000 miles per second. It never got faster. It never got slower based on the motion of the source of the light. So in order to see time passing, to know that time is passing and to measure it, you have to be able to measure the intervals between regular events like the ticking of a clock. And to do that, you have to wait for light to travel from the hands of the clock to your eye. Tick, tick, tick. Imagine you could get on the street car and you've synchronized your watch to the clock on the tower and the street car starts racing along and it approaches the speed of light slowly over a period of time. Look back at the clock. In the frame of rest next to the clock, those intervals are one second apart. But as you speed up closer and closer to the speed that light itself travels at, light has to go further with each tick to catch up to you. Tick, tick, tick. You on the street car would think that that clock is starting to run slow and that time is passing differently for the people on the street than for you on the car because you're looking at your watch which is at rest with respect to you and one second is one second on this clock. But on the burn clock tower, one second becomes two, then five, then 10, then 100, then a thousand, then a million seconds of your clock as you speed up. Light has to catch up to you each time and it was with this thought experiment which really is based on an optical illusion that he suddenly had the breakthrough. He could abandon the idea that time differences must be experienced by all people the same way regardless of their motion. That was an assumption from the old Newtonian mechanics and he could just abandon it because it's not true. A person on that street car will argue later on with the people on the street about how slow their clock was running. They'll look at it and go, no, we measured five seconds and you'll say, no, I only saw two tick on your watch in the time that it took my clock to measure five seconds. You'll disagree. You'll agree that there were ticks of the clock but you'll disagree on how long the time was between them and it was this that freed him. He accepted the constancy of the speed of light. He rejected the constancy of things like time and space for all observers and as he put it later a storm broke loose in his mind and he very quickly wrapped up the mathematics that he'd been sitting on. Now this doesn't lead directly to the math but later on when you go back and apply the mathematics to the situation I just described with the street car you get the same result. It's not really that it's an optical illusion. It really is that from my perspective because the clock tower is moving time is passing more slowly for it and from the perspective of the people on the street car they're looking at my clock and going you're crazy. Your clock is running more slowly. Relativity not just of motion and space but also of time. This was the big breakthrough. So he accepts it light is a constant and immutable thing. All observers will measure it moving at a fixed speed. Space and time however must be abandoned to be absolute. They must be experienced differently by different observers in different states of motion. And this leads to perhaps one of the most famous equations in the history of science, E equals MC squared by accepting the constancy of the speed of light and the relativity of space and time. He's able to very quickly work out the consequences of this on things like energy conservation, another law of nature and he finds that mass that inertial stuff, the stuff we're made of that just sits there and takes up space like me. That stuff is related to another form of energy and in fact this equation very famously led to the conversion of mass energy to other forms of energy like kinetic energy and heat. This equation has had all kinds of applications. Most famously atomic and nuclear weapons, nuclear power. You may not like either of those things but there are things that people can agree they like that came from E equals MC squared. The PET scan, the PET scan which is used to detect the presence of tumors in difficult to cut into places that you would never want to cut into a human being defined like in the brain or in delicate tissues in the body. The PET scan can help reveal the existence of a tumor long before you actually have to take any surgical procedures to cut the person open and do anything about it. E equals MC squared allows that non-invasive imaging medical technology to be possible. I take advantage of this along with my thousands of colleagues at the Large Hadron Collider to recreate the early universe in a lab. Now I will say that while this equation is simple, it's a bit deceptive. There's another piece that gets tacked onto this. This is about something that's not moving at all but obviously there's lots of stuff that moves in the world. So there's a little piece that gets added onto this. I actually think the full equation is far more beautiful than the simple one that we can all put on coffee mugs and t-shirts but it's very catchy and easy to remember. It's only three letters, one equal sign and a number. So you can't complain about that, right? Now, after this period, Einstein starts to think a bit more broadly about what he has discovered mathematically. And starting in 1907, he begins to generalize his ideas. These original ideas, they don't work everywhere for all things at all times. So he starts to think about a way to very much generalize his ideas about space and time and motion and his work during the period from 1907 through 1916 really is what a lot of people remember him for these days. These very famous claims about the nature of what gravity actually is and the effect that gravity has on a beam of light which I'll come back to in a bit. Now, this wouldn't be a lecture on the process of doing science or science literacy if I didn't mention that he stumbles a lot during this period. No scientist is perfect, you make mistakes. What matters is that you learn from them, you fix them and you move on. In fact, he had a theory of general relativity as it came to me known in 1911, but he made a very famous calculation about the deflection of light around the sun which turned out to be completely wrong. And had anybody been able to actually test his claim at the time, they would have thought he was a lunatic and he probably would have had a hard time being taken seriously after that because he would have gone and fixed his mistake but it probably would have looked like he was just making it suit the experiment that had been done and that's never good for a scientist who's trying to be taken seriously. He's quite lucky that measuring some of the things that come out of his ideas took about a decade to actually do after he started coming up with these things. So one of the things that he's thinking about at this point is gravity and let's do an experiment in our minds, a Gdankan experiment like he did. Now this isn't quite the experiment that he famously reported thinking about but it's a variation on it that gets the point across. Imagine that you are put into a soundproof windowless box. This sounds like the beginning of like one of the Saw movies, okay? But I promise that, thank you, somebody has actually seen these horrible films, all right? No, so this is kind of scary, right? But you know what's going on. You willingly agree to be put in this box, okay? So it's soundproof, it's windowless and there's a little red ball on the ground and so you pick it up and you hold it out and you drop it and you have a watch and so you kind of time the drops and you go, yeah, I'm on earth. This is accelerating at 9.8 meters per second squared. That's the gravitational attraction of things to the earth. I'm on earth. Just like I saw when I was outside this box. But imagine a more horrifying scenario in which you have been drugged and you wake up in a soundproof windowless box. Now this is sounding more like a Wes Craven movie at this point, okay? And all you have next to you is a little red ball and so you get up off the floor and things feel kind of gravitational and so you pick up the red ball and you drop it and you time it and you drop it and you time it and you satisfy yourself that, okay, I'm in a windowless soundproof box but I think I'm on earth because this thing is falling at an acceleration of 9.8 meters per second squared. But the jokes on you, your friends thought they'd have fun with you and they drug you, put you in a soundproof rocket with a booster attached to the bottom of it. You can't hear the rocket because the room is soundproof and they launched you into space and at this point you are far from earth. You are far from planets. You're nowhere near our solar system anymore. There are no gravitational fields anymore because there are no planets near you, no suns, nothing. Yet when you hold the ball out and you drop it, it falls to the ground just like it did on earth and that's because as you drop it, the rocket is continuing to accelerate. That booster keeps pumping out gas out of the back and accelerating you constantly at 9.8 meters per second squared and so you'll go along through this whole process thinking I'm on earth but you're not and you can't tell the difference. In fact, there's no test in the scenario that you can do that tells you for sure whether you're in a box on earth or in a box in a rocket in space far from any planets but that's accelerating at 9.8 meters per second squared and so it dawned on Einstein by thinking about falling this way and gravity that there is no difference between gravity and an acceleration like this. They must be the same thing and so he began to suspect that what Newton couldn't possibly have understood because he didn't have the tools to do it was that maybe gravity had something to do with that flexibility of space and time that he had been so happy to accept was a real thing in favor of accepting the constancy of the speed of light and so sure enough, taking these kinds of things into account that maybe there's something to this bending of space time, he gets back to the mathematics of it and he quickly realizes that he's ill-equipped to understand the warping and bending of space and time because he skipped out on all those abstract non-flat geometry courses that he should have been taking when he was a graduate student. So the good news is that Marcel Grossman, his friend who used to take notes for him in math class is a lifelong friend of Einstein's and helps him to become acquainted with the mathematicians and their work that he had not paid any attention to when he was supposed to be getting graded on it including Bernard Riemann and other people that graduate students learn about like Christofl and Ricci Corbastro and Levi Cevita whose names are all associated with mathematical symbols of one sort or another. It's because they came up with the math in curved space geometries to describe all of this. So that math was all basically done in the 1800s but it was Einstein that started to apply it to physics in a very deep way. And what resulted from this was not quite this equation, this is a variation on it that I'll touch on later. But in November 25th of 1915 he published what is considered to be the foundational solid work on the general theory of relativity. He published many papers on the subject before but this one was the big summary of not only the whole mathematics of the theory but also its implications including as he would come to do in this one year period proposing three tests that would show whether his ideas were right or wrong. And that is what makes his ideas scientific. Not only do they explain things that couldn't be explained before, not only did he make a calculation and figure out what was going on with the funny behavior of the planet Mercury as it orbited the sun, but he proposed other tests that if they were wrong, proved him wrong. That takes courage and that's what makes a scientist a scientist, you don't like to be disproven but you want good ideas and if you want good ideas you have to risk being wrong. And so Einstein like a good scientist proposes tests. Now what does this equation tell us? I like the summary that's been made by this man, John Wheeler, one of the authors of this textbook on gravitation. I'll mention another one later. Wheeler is credited with paraphrasing this equation in quite a lovely and poetic way. T is energy and matter. G is the curvature of space and time. And so what Wheeler famously said and here I paraphrase it, is that space and time, they tell matter and energy how to move. But what Einstein understood through developing the relationships between space and time and energy matter, is that in turn, matter and energy will tell space and time how to curve. So it's a mutual relationship, a dance of space and time and energy and matter and the result of this, one result of this is what we call gravity. And so I'm gonna give you an analogy here and I'm going to put a star next to this and show you why you have to be careful with analogies in physics. Imagine space and time are a flat rubber sheet. Nice and smooth, nice and flat. We introduce a bowling ball into the sheet. We'll call the bowling ball earth. This is equivalent to the effect that earth has on space and time around it. Earth warps the surface of space time. Remember it's three space dimensions in one time dimension. You can't picture four dimensions in your head. So this is already flattening this out so you can even imagine what this looks like. Earth causes space and time to bend and if you imagine another little ball being rolled in here at some speed, if it falls into the little pit, the little well created by the dimpling of the earth, it comes in with just the right speed. It might get trapped in an orbit going around this little pit. That's equivalent to an asteroid or a comet coming into the gravitational influence of the earth and then maybe getting trapped in orbit or putting a satellite up in orbit around the earth which we do all the time. This is how you can visualize that equation. Energy and matter tell space and time how to bend. Space and time tell energy and matter how to move. Now, one of my favorite comic strips and I showed you one of these before is one called XKCD and this is me right now. Understanding gravity, space-time is like a rubber sheet, massive objects distort the sheet and one of you out there is thinking wait, they distort it because the sheet's pulled down by what? This is the danger of an analogy. All analogies are an approximation to what the math actually tells you. And so at this point I sigh heavily and then I turn around and say look, space-time is like this set of equations for which any analogy must be an approximation and of course at that point you get up and leave because you're bored, right? That's the risk of being an honest scientist. The math contains what's really going on. My words, the stories that we tell about math, those are approximations. It's translating math into English. It comes at a loss of meaning, okay? So you have to be careful with these. You can visualize a little bit but you don't want to take it too literally. Now one of the most famous things that Einstein said was a test of his ideas was the bending of light around heavy objects like our sun. You might think that light traveling from a distant star along a line would pass right by the sun, undeflected. After all, light, if you study it a little bit you find out it has no mass, okay? So why should it be attracted to anything that does? Well remember the book and the feather both fell at the same acceleration under the influence of gravity regardless of their mass. So even people working on Newton's mechanics had speculated in fact that light passing by a heavy object like a star probably bends just like an object with equivalent speed would fall in the gravitational field. So actually Newton's mechanics makes a prediction about this. And in 1911 when Einstein was germinating the general theory of relativity he made a prediction on his early work and he got the same number as Newton. And if anybody had gone out and tested his paper that year or in the years up to 1915 they would have proved Newton and Einstein from 1911 wrong. Because once he fully worked out the equations of general relativity he found out he'd been wrong by a factor of two. In fact in the general theory of relativity light bends about twice as much as it does in the Newtonian view of space and time. And so it was in 1919 that finally an eclipse occurred that an astronomer could look at with sensitive enough instruments that they could look for the bending of starlight around our own sun. A very difficult measurement to do. Sir Arthur Eddington pictured here is credited with this. This is a photo from his 1920 paper and he announced that his observations preferred Einstein's calculations over Newton's and certainly over being undeflected at all in the first place. And it was this moment that launches Einstein into public fame worldwide. You have these, I love these headlines. Lights all askew in the heaven. Stars not where they seemed or were calculated to be but nobody need worry. All right, I love that. I love that. It's like, you know, fire is falling from the sky but it's okay. It's got that lovely tone to it. I love it. There were lots of headlines like this. Einstein became the toast of both the public and the scientific community. He'd risked everything by saying how he could be disproven but he was right. His ideas were vindicated. That is the true test of any hypothesis. That's what turns it into a scientific theory. Theories not only explain facts, they predict new ones. They are a powerful tool for understanding the universe and that's why scientists cherish them so much. So let me talk a little bit about the implications for this idea in the modern world. One of them you probably took advantage of maybe to get here and that is the global positioning system. So how many of you use the global positioning system to navigate as opposed to those old Rand McNally road outlaces that I grew up with? All right, few people are willing to admit it. Yeah, right, you take out your phone, you go okay Google or hey Siri and then you ask how long is it gonna take me to get home and it does some calculations somewhere over in California and then it sends the numbers back. Well, how does it know? First of all, you've programmed where your home is. How does it know where you are? It talks to these satellites. There are 24 of them in orbit around the earth, the GPS satellites. If you see three of them, you can get a lock on your position. So your phone within a few seconds can get a lock on your current position. That's good to within 10 feet or so. How? It does it by coordinating radio signals and that coordination is all done by syncing up clocks that are on the satellites with clocks on the ground. But objects in motion experience the passage of time differently than objects at rest on earth. And so because these satellites are moving very fast, they're not in geosynchronous orbit, they're moving very fast around the earth, we observe their clocks to be running slow. So without Einstein's theory of relativity, we wouldn't have known that. We could have perfected rocketry in the 1800s, launched the GPS system with these fancy new wireless telegraphs on them and then tried to triangulate positions on earth and every day we would have been wrong by about 11 kilometers more than we were the day before. We'd watch our position drift. One day you'd say, how long will it take to get home? 40 minutes. And the next day, how long will it take to get home? 55 minutes and that's not traffic and Dallas, that's just like imagine perfect roads empty, you have a straight shot home, okay? Every day it would get worse and worse and worse. Why? Because the clocks are out of sync on the satellites and on the ground. It's even worse than that. It's not just the motion of the satellites. What Einstein's general theory of relativity taught us was that clocks down here in the stronger part of the gravitational field on earth should run more slowly than the clocks up on the satellite. So there's a bit of a compensating effect, but it nets out to this 10 kilometer, 11 kilometer effect per day that I mentioned. Without the general theory of relativity, we never would have made this successful. You have to understand time and space before you can make a system like this work because it's based on clocks and light. So if you wanna drop a pin on a map, you need Einstein's general theory of relativity to do it in the modern era, okay? None of us should ever get lost again on this planet, but all of us owe that to Albert Einstein and his ideas. Now let's take this to the extreme. This is something known as an Einstein ring, and it takes its name from the fact that light is strongly bent by strong gravitational sources. This yellow blob you see in the foreground is a massive cluster, probably of stars, I didn't do my homework on this, and I'm sure the astronomers in the audience will correct me afterward. But whatever it is, this yellow object, it's in the foreground of the photograph, and it's very heavy. Now the blue thing you see here is actually behind the yellow blob. So it's a bit like if I had spent the whole time talking to you by being behind the podium. You shouldn't see me, right? I'm behind the podium, it blocks your view of me. You should never be able to see me. Any light leaving my body runs into the podium and stops. But if this podium is really massive, it can actually bend light that heads out this way, which these folks would see, and bend it back for the folks over here in this section. And that's exactly what you're seeing in this photo. There is a background object, probably a galaxy or a cluster of galaxies, some blue thing, and light from it is spreading out in all directions in space, but most of those are missing Earth. But this yellow foreground object is so heavy and space-time is so warped around it that the light bends back and makes it to Earth. We can see it. And so there's an image of it there, an image of it there, an image of it there. It's kind of blurred out in between. And if this were fully complete, this would be what's known as an Einstein ring. And it's like distorting light through a glass lens, except there's no glass here, it's all space-time. This is the cosmic horseshoe, that's its name, and it's in the constellation Leo, the lion. Now this is one of my favorite characters from a recent movie, and anybody who's affiliated at all with the Morrison, McGinnis Commons knows that we had a lot of fun doing a viewing of this movie, Interstellar, and then talking about the physics of it afterward. Dr. Cooley and I did that afterward. So this beast here is perhaps one of the most important characters in the movie, Interstellar, although it says not a word the entire time. Its name is Gargantua. It is a super massive, rapidly spinning black hole. It probably has a mass of 100 million suns, and so much mass is concentrated in one place in space-time that space-time is bent so strongly that not even light that falls into this pit will ever make it out. Light is not fast enough, space-time bends too much, and it gets trapped inside the well of this thing, the black hole. And so this dark region you see here is not the surface of some alien world. It is an impenetrable zone that your eyes, nor any radio receiver or any instrument ever built, should ever be able to get any meaningful light out of, because no light is supposed to ever be able to make it out of this thing. You see here a hot disk of gas that's orbiting Gargantua? This bright ring here you might think is some ring of gas that's trapped around this black hole. It is not. This image here, and this image here, is the gas ring on the backside of Gargantua, laid plain to your eyes because light is so strongly bent around Gargantua, you can see behind it. You are seeing behind Gargantua things you should not be able to see with your eyes because space-time is so strongly warped here. This is Miller's Planet. And in the movie, the protagonists have to make a landing on Miller's Planet to see if it will serve as a habitable world for humanity as Earth is dying. The problem is that Miller's Planet is so embedded close to Gargantua that for about every hour that passes on Miller's Planet, 25 years passes back on Earth. Gravity so weakens the passage of time that even though the astronauts on Miller's Planet think it's just an hour, time is passing, everything's moving at the same speed, they don't notice it. To their friend left behind on the ship, far out of the gravity well and to their families back on Earth, 25 years go by, they miss whole life experiences with their loved ones. It's a human drama laid bare by general relativity. It is giving up your family, it is giving up your history to make a better home for your world. It's a true story of self-sacrifice. If you wanna learn more about this, I highly recommend The Science of Interstellar by Kip Thorne, one of the co-authors of this lovely book up here. Kip was the science advisor to Christopher Nolan on this picture, wrote a whole book about the experience afterward, including some very interesting back and forths and fights with Nolan about what had to be true about Gargantua and Miller's Planet to make the script work. But he did the math and he found out it's not impossible, it's just extremely improbable. It's a great story, okay? So one of the other things that general relativity has done for us is it gave us the ability to finally write down a singular equation, a singular equation that can capture the whole history of the universe. And from this, we're able to look at the stars near us, very far from us, to look at the most ancient objects in the universe, including a light leftover from near the beginning of time. And by understanding the details of all of this stuff and working with the equations of general relativity, which in every other arena have proven to work extremely well, we can come up with an equation that tells us about the expanse of the history of the cosmos and how it is influenced by the things that are in the universe. This on the left tells us about how the history of the universe changes with time, how it evolves in size and in scale and time and space. This tells us what the matter and radiation like light in the universe does to affect that history. This tells us what the curvature of space and time does to influence the history of the universe. And this over here with this little symbol lambda, which was in the earlier Einstein's general relativity equation I showed you, this is the energy density of empty space time itself, no mass, no radiation needed. It's possible that space and time itself contains some kind of energy density. And I'll come back to that in just a moment. This singular equation, which I think fits beautifully on a coffee mug or on a t-shirt, this is our shared cosmic history. We are in here somewhere. That is us. So what have we learned by looking at the universe and then trying to understand it from space and time and energy and matter? Well, we've learned that the universe began about 13.74 or 75 billion years ago. Space time expended extremely rapidly and then much more slowly after that. During this period of time, stars formed, galaxies formed, we formed. We are way down here, we're a tiny hiccup. As Neil deGrasse Tyson put it, we're just a blip at the end of the cosmic calendar, barely a footnote on the last day of December at the very end. And yet, and yet we can look back at this beast of the cosmos and we can learn something about it. I find that enthralling. Now something amazing that happened when I went to graduate school was that two competing teams of scientists led by Saul Perlmutter shown here, you'll see the others in a moment, Adam Rice and Brian Schmidt, their teams both observed by looking at regularly detonating cosmic objects going further and further and further out in space and thus further and further and further back in time that very recently, the expansion of the universe has not slowed, it has not reversed, it has rapidly accelerated its expansion. For reasons that we still do not completely understand, the universe is getting bigger and bigger, faster and faster. This is remarkable. Einstein added a term to his equation, I showed it earlier, that lambda thing to try to make the universe sit static. And it was Hubble, Edwin Hubble who looked at the cosmos and said, no, the universe actually appears to be expanding, but it was believed when I went to graduate school that the universe, its expansion was slow as radiation and matter pulled back on the cosmos and then it would collapse and we'd have a big crunch and then we'd bounce back in another big bang and start the whole thing over again. But that's not what the data says. The data says that in the last few billion years, the universe has been getting bigger, faster than it had been before and this is incredible. Another prediction from Einstein's general relativity is that mass and energy should be able to make waves in space-time, so-called gravitational waves, they might look something like this and rippling through space-time. There are at least, now two operating and more planned, large instruments that are designed to look for the wobbling of space-time, interestingly enough, using an instrument very similar to what Michelson and Morley used to look for changes in the speed of a light with respect to the motion of the earth, but these are kilometers long. This one's in Washington state and its twin is in Louisiana and together these form gravitational wave observatories spanning the continental United States. No one has definitive proof of the existence of gravitational waves yet, but it's a prediction of general relativity that has yet to be verified and I hope in the next century or hopefully not longer, maybe even in my lifetime, we'll see some evidence that these ripples in space-time are there and it might usher in a whole new era of astronomy. Galileo used light to look at the universe. Recently physicists have used other particles to look at the universe, but now we might use space and time itself to look at the universe and I find that really quite interesting. So let me close here with a short last reflection on the cosmos, the tale of the lion. We have looked at the light leftover from the beginning of time, the so-called cosmic microwave background and we have learned from that and we have learned from colliding clusters of galaxies and from the spinning of galaxies and from the structure of large expanses of galactic clusters and how they all relate to one another and many other lines of evidence. They've all intersected to tell us what the cosmic budget is in energy and it is not what we thought it was 25 years ago. 25 years ago, if you'd asked a physicist what most of the universe was made of, they would have said star stuff, ordinary matter, the stuff we're made of, hydrogen, helium, carbon, oxygen, less and less of the heavy stuff but atoms. But it turns out, based on very careful observations that are all independent but they all line up at the same numbers that in fact the stuff we're used to thinking about, ordinary matter, only makes up 4.9 and that is a significant decimal place there, 4.9% of the energy budget of the universe. About 27%, 26.8 if you wanna split hairs is made of something that appears to act gravitationally on normal matter like you and me but whose constituents we have no information about. So it's called dark matter and the quest is on including here at SMU to try to figure out what dark matter is actually made from. But even more mysterious is that 68.3% of the cosmos is made of an even less well understood thing which we label dark energy. We believe that whatever it is it's the thing that's causing the expansion, the more rapid expansion of the cosmos and again there's work going on at SMU and places all over the world to try to understand better the kinds of cosmic objects that you need to study in order to measure this thing's properties better and maybe one day even figure out what the heck it is. If you combine the best mathematical tools we have for understanding the cosmos right now they utterly fail to predict this. It's amazing. But that's our budget based on observing the cosmos. Now one interesting blip that I'll put on the radar here although I'm hoping in six months I'm either proved right or wrong a lot of other people are feeling the same way is that recently at the experiment that I work on and our competitor experiment the Atlas experiment where I work CMS our friendly competitor around the large Hadron Collider we both had blips in the data that shouldn't be there according to the best mathematical understanding we have of nature right now. They both occurred at pretty much the same location in mass about 750 times the mass of the proton here and here little blip little blip not that statistically meaningful right now but interesting that both experiments see it and what I find compelling the reason I even mention it is that this blip was discovered while looking for a subatomic connection between gravity and light. Sort of a subatomic general theory of relativity implication if you will. A curious blip but we won't know whether it's real or a mass hallucination of statistics and very overworked and tired particle physicists for about six more months we don't take any new data until March so keep your eyes out in March when we cook up the accelerator again and get moving and that data will get analyzed over the summer and maybe we'll have some results by summer maybe by the end of the year for sure I don't wanna commit to anything right now because nature is fickle. So let me close with a quote here and I'm sure you can all understand this no problem at all, here comes the translation. It's one of my favorite things that Einstein said because for me personally as a scientist I think it reminds you to be humble in the face of discovery and he said nature shows us only the tail of the lion but there is no doubt in my mind that the lion belongs with it even if he cannot reveal himself to the eye all at once because of his huge dimension. We see him only the way a Laos sitting upon him would. We're a pretty smart Laos but we haven't figured out everything yet. We have probed the cosmos at every scale within our technological reach so far. We've looked at the light leftover from the beginning of time. We've looked at routinely detonating objects that send out tremendous bursts of energy. We can see billions of light years away from where they started. We've seen the expanding size of the cosmos. We've looked at colliding galaxy clusters, rotating galaxies and the vast structures of the cosmos out to the edge of the visible universe which is about 80 billion light years or so. We have probed the subatomic. We have developed incredible mathematical understanding. This combines relativity and quantum physics in a singular equation that fits delightfully on a coffee mug. See isn't it nice? Everything we know about the cosmos fits on a coffee mug. I think that's telling us something. That's telling, or tea. I mean if you wanna be biased about it you could say tea mug. We have a pretty good picture of what building blocks of nature you and me we can make in the laboratory. We recently discovered the Higgs boson, the particle in this mathematical model of nature that is believed to give mass to everything we've seen so far. But we may have a mystery on our hands. In searching for a connection between gravity and light at a subatomic particle collider we found a blip. It may go away, it may remain. But to be good scientists we have to keep digging to see what happens. And so I would say this. Over 100 years ago we had the sharpest tools. We had the most powerful mathematics that humans had ever had hands on. We studied the universe and we were confused. And it took brilliant minds including the mind of Albert Einstein to make sense of the information that we had gathered about the cosmos and resolve the paradoxes of competing systems of laws of nature. And today the tools have never been sharper. The mathematical frameworks have never been more powerful. We have made increasingly detailed observations of the universe and we are confused that several systems of well-established laws do not seem to play nice together and make sense of the things that we see. And so I would say that it's good to only be saying the tale of the lion again. Because the last time this happened it was a period of incredible discovery and opportunity for everybody that was involved. I hope that some of you will get involved one way or another in this active discovery and join us in a better understanding of the beast that is the cosmos. Thank you very much.