 OK, so let's go ahead and get started. I've got a lot of ground to cover today because of the topics that we need to span. And I will use this lecture. This is a real lecture, so I'm going to do a lot of talking. And because there's a lot of ground to cover, I'm going to have some ground rules for this process. So normally, I would allow you to interrupt with questions and comments. But in this case, I want you to focus on the lecture. I want you to take notes. And if something's not clear, write down your question and ask it at the end. I'm going to try to leave at least 10 minutes at the end for questions. The title of today's lecture is Light and the Dark Cosmos. So the lecture today will be in four parts. They're not all equally sized. So don't freak out if it takes some time to get through part one. Part one will be about a traveler of both time and space. After all, space and time and energy and matter, those are their domain of physics. And we're going to look at one of those travelers today. In fact, one of the most important travelers of time and space. In the second act, we'll take a look at a particular individual who's had a significant impact in the last century on our understanding of all of these things. Light, space, time, energy, matter. And that's entitled the Gadankan Men. Act three, we'll take a look at a hand that shapes entire universes, especially our own. It's the only one we know about. And then finally, I'll close out with the dance of light and gravity. So let's begin. In act one, we're going to take a look at a traveler of both time and space. I have a little quote here from Led Zeppelin. This title is No Accident. It comes from the song Kashmir. And later on, you can download the slides and take a look. It's a good song. It's off their album, Physical Graffiti. Let me ask you a question. So this is a participatory part of the lecture. Here's a picture of the night sky. So what do you see? Somebody from this section. What do you see? Yeah. You see stars. OK, so what are stars? How would you define a star? Give me something simple. Think about this like a way a three or a four-year-old would define it. What's a star? A light in the sky. OK, great. Somebody from this. What do you see? Yeah. OK, galaxies far, far away where possibly loose skywalkers having some crazy awesome adventures. Anderson? In fact, this does come from the Hubble Space Telescope. Yes. And this is after they put the corrective optics in, which made it work as designed. Right. So you see many things here. You see an engineering achievement after an engineering failure. You see collections of stars at great distances, possibly with many great adventures going on there as well. And you see stars, points of light in the sky. Excellent. We'll come back to this picture throughout the lecture. Let's talk about light, because the key theme of all three of the things you just said is that you assumed the existence of a phenomenon, which we call light. So light, again, looking at this from the level of a four or a five-year-old, if you ask them to describe something like light, maybe this is what they would come up with. And there is absolutely nothing wrong with describing things in as simple a term as possible. You don't have to impress anybody. You just have to be thoughtful about your response. What is light? Well, most simply, and to be fair, this is really, I think, what your average human would have thought of as light over a long period of human history, is it's merely a phenomenon that travels from one place to another. So this is the Dallas skyline with the Margaret Hunhill Bridge in the foreground. And one of the things we notice is that everywhere there's stuff, there's some light associated with that stuff. Now, physicists have a fancier term for stuff, matter. So there's a lot of matter that makes up the city and the bridge and the grass and the trees. Even the air molecules we can't see, but there nonetheless, we can feel them when we move our hand through them, that stuff. We know if we heat up air hot enough, it will too emit light. And so one of the things that we've learned is a species over a long period of time, hundreds if not thousands of years, is that light and matter appear inextricably linked to one another. And that's actually a profound insight, it turns out. It seems so simple, but it has profound implications, as we'll see later. Now, one question you might ask about a phenomenon that travels from one place to another is how fast does it travel? This is a question that vexed people for a very long time about light. It turned out answering this question about the phenomenon called sound, which also travels from one place to another, from my vocal cords to your ears in this case. This is a very basic question. How fast does the light go? Very simple question, very difficult to answer. Why? Because it either travels seemingly instantaneously, that is with infinite speed, or at least very, very, very fast. All right, so one basic question that we as humans wrestled with for a long time, not all of us, but some of us, and eventually with enough struggle it was answered, is does light travel between places in the universe, between places even on the surface of the earth, at a limited and finite speed or at an infinite speed, instantaneously? Now, let's take a look at that question. That's a question that with some basic intuition about space and time and how to make measurements in space and time, you might imagine trying to answer. So the first person that we know of who made a real crack at this from a modern engineering and science perspective was somebody we visited several times before in the class, no accident. He did a lot of things that we still rely on today as basic observations codified in mathematics about the universe. This is Galileo Galilei. He lived from 1564 to 1642. He died the same year that Isaac Newton was born. Isaac Newton was born on Christmas Day in 1642. Galileo died earlier that year after about a decade of house arrest. So he spent about the last 10 years of his life under house arrest. It's a fascinating story of history, culture, society, science, all colliding, religion, all colliding at the same time in sort of a really epic struggle, really quite interesting. He's no angel, but he did many things that we still consider to be angelic. Again, you don't have to do something incredibly complicated to make a mark on the world. You just have to do it first, whatever it is. Galileo did a lot of things first and the first first that he accomplished was that he improved on the design of the telescope which had already existed by the time he got his hands on one. He didn't invent the telescope but he improved the optics immensely by learning to and then improving on the design of grinding lenses. Very basic skill. Not many people could do it well at the time. Galileo became the best and he sold his designs to the Italian Navy. They turned it into a weapon of war. Anyone who can spot their enemies at a greater distance than the enemy can spot them has a strategic military advantage. This made him a lot of money. It made him very famous and he secured a patronage with a family in Italy that basically allowed him to do his scientific research for as long as he wanted after that with really no concerns about money. So using his new invention, the telescope as a scientific instrument, he turned it to the sky which oddly enough, nobody seems to have done up until Galileo or at least nobody recorded their observations, wrote them down and published them, okay? So he discovered, one of his first discoveries was that Jupiter has moons and this was a remarkable discovery for its time because at the time, the popular opinion was that everything in the universe revolved around the Earth and to see four little bright lights that throughout the year only go around Jupiter was a remarkable observation and in fact is the beginning of how he got himself in trouble with the church authorities at the time, at least in Italy. He discovered the four large ones, the Galilean moons as they're historically called Io, Europa, Ganymede and Callisto. We'll come back to Io in a bit. It's a player in the next part of the story. He did other things too. He discovered and sketched, he was an artist, he was an engineer, he was a physicist, he was a mathematician, he was what we would call a polymath, all right? And being good at many things makes you a better scientist. So being a little good at drawing, a little good at writing, a little good at computer code, a little good at engineering, mechanical, electrical, makes you a better scientist. It means you might get there first because you have the ability and hopefully the fire in your belly to do it. He mapped out the moon's surface structure and he was the first person to ever observe sunspots, an observation that would also get him in trouble with the church later. He discovered the phases of Venus, another observation that would get him in trouble with the church later. You can see a theme here. You can see how he got into house arrest, okay? He was also very opinionated. He really believed everything he said and he insulted the pope of his day and at that point the Jesuits abandoned him and he was hauled before the Inquisition, found guilty of heresy, his book was banned and he was placed under house arrest for about the last decade of his life. He developed extremely precise water clocks. He was able to measure time more precisely than anyone else had before him and especially when he was under house arrest, he established the basic understanding of motion and especially falling in a gravitational field with very careful experiments, okay? And he established what we now call Galilean relativity. How do you relate the observations of two different frames of reference in relative states of motion? He was the first person to really codify that. So how is it that Galileo attempted to measure light? It's actually a very basic experiment. He stands on a hill and assistant stands on another hill. There's a long but well-established distance between the two hilltops. Galileo has a lamp and a water clock. He uncovers his lantern and light can now travel to his assistant and when his assistant sees the light from Galileo's lantern, he uncovers his lantern and sends light back at Galileo. You take the time that this observation occurs from open my light to see my assistant's light and you just use twice the distance that light had to travel to go forth and back. It turned out that he was not in possession of the kinds of clocks that would be required in order to make this measurement accurately. And so he was unable to say anything about the actual speed of light. In fact, he couldn't even establish whether or not it was infinite or finite in speed. This was a real challenge, okay? It just turned out that light was a challenge that was just not within the grasp of even a brilliant engineer like Galileo Galilei. Now it would be left to the sort of next generation of scientists, specifically this gentleman, Ol Romer, who actually made his observations before Newton's Prencipio was published. This is remarkable that he's able to do this before Newton had established the basic laws of motion. He codified them and published them and shared them with the world for criticism. So this is Ol Romer. He was an astronomer and Romer decided to, I mean, astronomers make measurements. That's what they do. Astronomer is essentially measuring the stars, all right? And so he was just trying to measure things. And one of the things he was interested in measuring was the period of the orbit, a simple harmonic motion phenomenon, the period of the orbit of Io about Jupiter. A simple question. How much time does it take for Io to go about its parent object, Jupiter? And he made a remarkable observation. It took him eight years to get all the data required to draw this conclusion. This is a real commitment, all right? This shows you even now, people can take five, 10, 15, 20 years in order to see their work come to fruit. As an example in my field, Peter Higgs, who's the namesake of the Higgs particle, which we discovered in 2012, he predicted that in 1964. That's a long time to wait, okay? So, Romer made seasonal measurements of Io's orbit about the parent planet, Jupiter. And he noticed that there was a three minute discrepancy, three minutes. That's how good things have gotten at this point with measurement. Three minute discrepancy between measurements of Io's period when the Earth was approaching Jupiter and Io's period when the Earth was receding away from Jupiter in our orbit around the sun. And so he concluded from this that this could be explained by a finite speed of light, that it takes longer for light to get to us as we're racing away from Jupiter than it does when we're racing toward it. And if you crunch the numbers, which he didn't do, you could establish a limit on the speed of light. So he concluded in a 1676 article that it's finite. But that's about as far as he went. It would be left, and this is a diagram from his paper, by the way. This is the orbit of the Earth, and he's got it marked here with different paths that he measured on. And then this is Io going about Jupiter, not to scale. This picture is not to scale with different points that he marked to establish the measurement of Io's periodicity about Jupiter. It would be left to the scientist Christian Huygens, who's very famous for his work in optics, among other things. He took Romer's data and he inferred the number for the speed of light. And he concluded that light travels at about 16 and two-thirds Earth diameters every second. That comes out to 2.1 times 10 to the eighth meters per second. And as you'll see in a moment, the speed of light is about three times 10 to the eighth meters per second. Not bad for a first measurement. In fact, historically, historians of science have looked at Romer's data and actually decided that they shouldn't have been, they shouldn't have concluded this accurate a number. But nonetheless, the conclusion that it was finite was already a remarkable achievement. That was a safe conclusion. So here's the current measured value of the speed of light. And it's exact for a reason that I'll explain in a moment. 299,792,458 meters per second. That is fast. That's about a foot every nanosecond. In fact, an excellent rule of thumb for electrical engineers is that if you put too much cabling in your electrical designs or too many traces on your circuit board, and the traces are of unequal length, you can cause delays in the propagation of electrical signals, which travel at about the speed of light by a nanosecond for every extra foot of conductor you put in. So fun fact, if you accidentally over-design your electrical paths in your circuits, you can cause delays that can mess up your circuits. For instance, if they're sensitive to timing effects. As noted in the very first lecture video in this class, the speed of light is the basis of the definition of the meter. So there's a reason why this is exact with no uncertainty. It's because we, in the modern world, define the meter as the distance that light travels in 1,299,792,458th of a second. So you have to be careful not to get yourself stuck in a closed loop on this. But with careful use of the meter and the speed of light, realizing that they're related to each other, you can avoid getting yourself into trouble. I should also note that the second itself is based on how many transitions a cesium atom makes through different energy states. I would also note that at the beginning of this course, and I have to change the damn lecture video now for next semester, the kilogram was defined based on a blob of platinum meridium metal under glass and in vacuum in an institute in Paris. You see the problem here. If any of that flakes off even a little bit, then the definition of the kilogram changes. And you have no idea how sensitive the world's economy and engineering is to the definition of the kilogram. It's recently been voted to be redefined based on a measurement one can make of a fundamental constant known as Planck's constant. So it is now true, and it happened while we were taking this class together, that the meter kilogram second system is now entirely based on the definitions of fundamental constants of nature, numbers that are known to not vary with time. Planck's constant, the speed of light, and because this is about transitions in a cesium atom, this is effectively about what is known as the fine structure constant, which is a constant of atomic behavior. It actually turns out to be fundamentally related to the electric charge and its size. So here are some things that light does. And you're probably familiar with some or all of these things from your own experiences. Some of these may seem a surprise to you that you just hadn't thought about it before. Some of these you may have seen previously in a physics class. Some of these you may just be like, well, of course it does that. It's light. One of the things that light does is when it strikes certain kinds of surfaces, it reflects. So there aren't mountains and a sky under the surface of this lake. We are merely seeing a second set of the mountains and sky because the light that's scattering off these mountains, some of it is striking the lake's surface. It's reflecting off the lake's surface and reaching our eye. And so we think that there's a mirror world down here. In fact, this is why we call them mirrors. They create images on the other side of physical boundaries. So those mountains look like they're underneath the surface of the water. Of course, they're not really underneath the surface of the water. It's an optical effect. So that's one thing light does, is it reflects? Another thing light does is it refracts. It can pass through the interface between two materials, like air and water. And it will bend when it passes through the interface. This is how you can make light go where you would like it to go. So you can reflect it, but you can also refract it. And this has all kinds of awesome mechanical and also optoelectrical uses. If you're going to use light to send signals, both of these properties are crucial in optoelectronics. And the next one is really crucial as well. Now it isn't the case that there are tiny little worlds, like the Bottle City of Kandor in DC Marvel or DC Marvel, DC Universe Comics. This isn't the Bottle City of Kandor trapped in here. This is light coming in from all angles behind the water drop, refracting through the water drop, and coming out and reaching your eye. So you're seeing stuff off to the side that's not in the camera's field of view. So it isn't that there's a miniature little world inside of that water drop. It's just that light is passing through it and reaching your eye, refraction. Now, reflection and refraction are topical that you'll get into near the end of next semester physics, second semester physics. They're described by two laws, the law of specular reflection and the law of refraction, which is also known as Snell's Law. But both of these laws are based on a singular theorem, a mathematical theorem known as Fermat's Principle, the principle of least time. If you assess the path that light takes through a system by assuming that it will always take the path of least time, not least distance, least time through a system, you exactly reproduce the observed behavior of reflection and refraction. In other words, the principle of least time underlies two natural phenomena involving light. And we'll see why later. You'll learn about all of this in one way or another in second semester physics. This is another thing that light does. This is a close-up photograph of a soap bubble surface. Soap bubbles are very thin films of soap and water. So they have a top side. They have a soapy, watery bulk. And then they have a bottom side where there's air underneath it. So you've got air, soap, air. And light passing through, scattering off the bubble surface back at your eye, suddenly makes rainbows of color. That has to do with refraction. But in some cases, you'll see black spots. And that has to do with something called interference. And you can understand interference if you know two things about light. One, light is fundamentally, at least partially, a wave phenomenon. Wave phenomena are simple harmonic motion. And so with simple harmonic motion, signs and cosines, and time dependence and amplitude, you can understand what's going on here. So here's an animation of what's happening. What's happening is that because of the way that light scatters off of the outer surface and inner surface of the soap bubble, it can take two pads through the system before it reaches your eye. It can scatter directly off the surface or it can scatter off the bottom surface before it gets into the air again inside the bubble. Interference is nothing more than two simple harmonic motion phenomena that coincide. When their peaks coincide, they add up. That's what the red is. The red is them adding up. That's known as constructive interference. When the peaks and troughs line up of the two phenomena, that is another kind of interference, destructive. And that's when the red goes flat. So when the red line goes flat, it's fully destructive. When the red line goes to its maximum amplitude, which is twice the amplitude of any of these two wave phenomena, these two simple harmonic motion phenomena, you get maximal constructive interference. And anything in between is just interference. This is a thing that all waves do. Water waves, sound waves. This is how you do noise cancellation in Bose headphones or any other headphones that are cheap knockoffs of Bose, for instance. I have strong opinions, just like Ian has strong opinions about Apple products. So noise cancellation in headphones and modern headphones is achieved using interference of sound waves and compensation for external noises by canceling them out with some kind of moving object or piezoelectric object or something like that. In light, interference creates bright spots and dark spots. The dark spots back here are the destructive interference, where the light totally cancels itself out and no actual light reaches your eye. So how do you understand this? Here's the air-soap interface. And here's the soap-air interface inside the bubble. A light ray coming in can bounce off the surface. That's one path it could take. Or a light coming in along a similar path could refract through, then reflect off the next surface and come out. And if these two light waves are shifted, if their peaks are shifted relative to each other, they interfere. And if the peaks become coincident with the troughs on the other wave, they totally negate each other. That's all interference is. It's two simple harmonic phenomena overlapping in space that can cancel each other out or add up, depending on how they're positioned. And so this is just a cartoon illustrating what I just said. If the thickness of the soap bubble is such that the two waves, A and B, can come out with their peaks coincident, then you get constructive interference. That's the green. If they come in and the soap film is of such a thickness there that they just are phase shifted by 180 degrees to each other so that the peaks and troughs line up, then they begin to negate each other. And full destruction occurs when they fully line up peak to trough. So here's a question about light based on all the stuff we've learned this semester. I want you to forget about the fact that you watched Cosmos or some series on the History Channel or Discovery Channel or some YouTube video on black holes and stuff like that. I want you to pretend that all you know about physics is this class. Here's a question. This is a question that people wrestled within the 1800s, one person much later in particular. Imagine they weren't thinking about race cars back then, the car hadn't been invented yet. But imagine you have now in a modern context a race car that can go really fast. In fact, it can go so fast that its top speed is 10% of the speed of light. So 2.998 times 10 to the 7 meters per second. So imagine we set up an experiment where we have a driver and an observer. And the driver and the observer agree that when the driver crosses this dotted line, which is a measured and fixed distance from the observer, when they reach that line, they're going to turn on their headlights. You can even rig a sensor so that this is all done automatically. There's no human intervention, none of that stuff. You cross the dotted line, you turn on the headlights. And then you time how long it takes for the light to reach you from the car. So she has very sensitive instruments that tell her the time distance, the time displacement, from when the car should have turned on its lights to when the light reaches her sensors. And the distance is known. So what will she see? What speed will she observe light moving at? Anyone want to make a statement about that based on this class? Yeah. Ah, but we haven't. That's not a consequence of anything we've learned in this class. So yeah, Kyle. 1.1c, Galilean relativity. If I'm moving along and I throw this at Anderson, good job. All right. OK, you want to change my slides for me? I'll call out the numbers. Then he sees the remote coming at him at the speed I throw it plus the speed I'm walking at him, which if I run at him, and then really, yeah, I'm not going to do that. If I run at him and throw it, it's going to go even faster, even if I throw it at the same speed relative to me. So this is what people thought based on Newtonian and Galilean mechanics. The speed of light will be added to the speed of the source, and that will be the speed you measure. OK, that's a prediction. And in fact, that's the prediction that physicists made. So then the problem is, light moves really fast. How do we measure this? Well, here's how you do it using interference, reflection, and refraction. It's a beautiful experiment. It's known now as the Michelson-Morley experiment. And it's absolutely brilliant. You take a light source, you send a beam of light out, and you have an optical device that can split the beam 50-50 into two halves. One half travels perpendicular to the other. So one beam of light gets to go up here, bounce off a mirror, and then come back to the beam splitter. The other beam of light gets to travel in the same direction as the original beam of light, bounce off of a mirror, and come back to the beam splitter. These distances are the same between the splitter and the mirrors. So if we have this whole thing sitting at rest, absolutely at rest with respect to some ideal rest frame, like outer space. We call outer space the ideal rest frame of the universe. It's absolutely at rest, and everything moves through it. Fine. So in that perspective, if the Michelson-Morley device is at rest with respect to outer space, what we should measure is that the time it takes for the light beam to travel to this mirror and back is the same time it takes for the light beam to travel to this mirror and back, if this thing is at rest. But using Newtonian and Galilean mechanics, if this whole device is now moving in the direction of the blue arrow by some speed V, then the light beam traveling this way first has to catch up to the mirror that's moving away from it. And then it gets to the mirror, and it bounces off. And then it races back toward the beam splitter that's heading toward it now. Meanwhile, this light beam, because this whole thing is moving now relative to the perfect rest frame, this beam has to travel this funky triangular path to make it back to the splitter. Now the beams are recombined at the splitter. If there's been no shift in their paths, which is guaranteed in the first case for the whole things at rest, then you should see no interference of the light with itself and some imaging device, a camera, your eyeball, photographic film, whatever. But in this case, because you've created a situation where it turns out light has to travel two completely different paths, you should get interference. This was the prediction of Newtonian mechanics. Light is a wave phenomenon. This was known by the time that Michelson and Morley did their work. Wave phenomena travel through some medium according to Newtonian mechanics. Let's imagine a perfect rest frame that is outer space. It's the medium that light travels in. And we're moving through it on planet Earth. You put the Michelson-Morley interferometer on the surface of the Earth. You aim the blue line in the direction that Earth travels around the sun or that it rotates every day. And you put the red line perpendicular to that. So now you've made your thing move in one direction and not in the other. That's what Michelson and Morley did. In fact, they over-designed this system. So this is a cartoon representation of what I just said. If this thing's at rest, if you imagine a little light pulse, the pulse goes out. It splits. The red and the blue eventually come back. They've traveled the same distance. They recombine. There's no interference. They arrive at the same time. But over here, if we move this device to the right, the blue has to travel a different path. And in fact, it takes longer for it to get back to the beam splitter as a result. And it arrives later than the red pulse. So they're shifted. And that can cause interference. And in fact, they did the math. Based on how fast the Earth is moving, they expected to see a shift of 110 nanometers between light beam 1 and light beam 2. What roughly is the wavelength of visible light? Does anyone know? Yeah? 400 to 700 nanometers. That's a big shift. That is easily detected. And they knew that. They over-engineered this device. So they given how fast Earth is moving through the empty space around it, and therefore are through the medium, light must be traveling in. Because all waves travel in a medium. Sound travels in air. Water waves travel in water, et cetera. Light waves must travel in something. Earth must be moving through that something. It should drag along and slow the light down as a result as we move through it. That's what they predicted they would see. So they should have seen interference. They should have seen the brightness of the light change depending on whether we're moving or not. And they had this really elaborate experiment to check all of this. In fact, here they are, Albert Michelson, Edward Morley. This is their device. This whole thing is isolated from vibration by floating on a pool of mercury. That violates the motion standards now. That's mercury right down there. That's a big bath of mercury. That table is roughly the size of this thing, like doubled in width. And that's their optical setup. You can see they have a light source, beam splitters, and some kind of light detector. They were probably using photographic plates back then. They didn't have cameras like we do now. This is 1887. This was their definitive experiment. They saw nothing. No change in the brightness of the light, no matter how they oriented the arms of this thing, which is now called an interferometer. No matter how they oriented it in the mercury bath relative to how the earth was moving, they saw no change. This is the most famous non-observation, or no result, in the history of science, because it changed everything about our understanding of the cosmos. Think about that. They saw nothing, and they're famous for it. So it's OK to not discover something, because if it doesn't exist, that is a breakthrough, especially if everything you know up till that point says it should. And everything we knew about the cosmos, as I'll review in a moment, said that they should have seen something. So something was wrong. And that leads us into act two, the Gadonkin man. I like this quote of something that Einstein, who's the Gadonkin man, Albert Einstein, said, the value of a college education is not the learning of many facts, but the training of the mind to think. Let's see how that goes for all of us throughout our lives. Why was this such a stunning result? Let's take a look at what was going on in the 19th century, the century that ended with Michelson morally doing this over-engineered experiment that failed to observe a key prediction of Newtonian mechanics. You have Newton's mechanics. It had ranged supreme for over two centuries, and it has assumptions built into it. What's the assumption that Isaac Newton built into his mechanics, that space and time are a stage on which all the events of the cosmos play out? That's just an assumption. And more especially, while it's true that as people move through space, they may observe different things. As I walk, I see the remote go up and come straight back down. But from your perspective, it executes parabolic motion. That's OK. We can use the constancy of time for both of us to relate these observations. That was what was assumed by Galileo. That was what was codified by Newton, that time passes the same way for all observers, regardless of their state of motion. That was just an assumption. It seemed like a perfectly reasonable one. And it took forever to find out it wasn't. So Galilean relativity gives you the tools to relate measurements in different frames that are moving with respect to each other. Now, we haven't covered this in this class. This is something you might see in a chemistry class. Classes in the Lyle School about this. We have a dedicated upper level class on statistical mechanics that you could take to learn about the deep nature of heat energy. But the laws of thermodynamics were basically worked out in the 1800s. And that was largely thanks to the revolution of the steam engine. Being able to build engines that can convert heat to mechanical work and mechanical work to heat gave us laboratories in which to understand heat energy. And it's no accident, therefore, that the industrial revolution and the development of thermodynamics paralleled each other. It allowed these careful precise measurements and modeling of mechanical and heat systems. So this was all worked out basically in the 1800s as well. And also in the 1800s was sort of the newest kid on the block. Now, people had been studying electricity and magnetism for centuries. People didn't really start understanding it mathematically until the 1700s. And it was in the 1800s that the formal laws of electricity and magnetism were worked out finally in about 1865, 1866, something like that. But they were the new kids on the block. They were the newest laws. But they made a stunning prediction that turned out to be right, that light is an electromagnetic wave. It's a wave with an electric field oscillating in one direction and a magnetic field oscillating in the other direction. And what was funky about the laws of electromagnetism is they made no statement about the medium in which that wave must be propagating. It was incomplete from the perspective of Newtonian mechanics. It said nothing of the material substance, the properties of the material substance, through which that wave must be propagating. So because they made this description, and it was a description that was, by the way, confirmed in the 1880s, I should note that in roughly 1887, Heinrich Hertz confirms that electromagnetic waves exist independent of light, but that light is an electromagnetic wave. And all electromagnetic waves move at the same speed, 2.998 times 10 to the 8th meters per second. That was a direct prediction of the laws of electricity and magnetism. It's amazing. You can see why people got excited about this, because suddenly light was an electric and magnetic wave. It's not just a phenomenon that travels at some speed from point A to point B. It's a wave phenomenon that travels from point A to point B. It can be controlled. It can be transmitted. It can be absorbed. It can be done invisibly. You don't have to send light that only humans can see. Radio is an example that you all use every day for your mobile phones. I do too. We all rely on radio. Microwave is a variant of radio. We're all using it. We don't see it, but it is ubiquitous. We rely on it for everything now. Maybe too many things. In the late 1880s, the first president of SMU, he wasn't the president. Then he became the president later. Robert Stewart Hire, he was the first American to transmit a message by electromagnetic radiation. So that's his distinction in the US. You can find that on the American Physical Society website. So that was his big thing. OK, so light's a wave. That's what electromagnetism says. Waves are mechanical distortions of an underlying medium. That's what Newton's mechanics says. Waves are simple harmonic motion. Something has to distort. Could be a spring. Could be air. Could be water. Something deforms. Could be a solid. You can send waves through solids. Think of earthquakes. Earthquakes are waves that propagate through the crust and through the core of the Earth. S and P waves. I think those are what they're called for earthquakes. Geophysics people can tell me if I'm right or wrong on that one. In fact, the Mars Insight Lander that just landed is its primary job is to study Mars' quakes. So its job is to wait for earthquakes to happen on Mars and then measure the waves as they ring Mars like a bell. That's what happens on Earth. An earthquake is when Earth rings like a bell. It has terrible mechanical destructive properties on the surface. But effectively, the whole planet is ringing. You can measure earthquakes across the globe, even if they originate in one place. So the conclusion from these twin ideas, electromagnetism and Newton's mechanics, is that light has to travel in a medium. That medium was given a name, the ether. People tried to work out its mechanical properties from Newton's mechanics. They made all kinds of predictions about it. The Michelson-Morley experiment was to be the culmination of that, the observation of the existence of the ether. It failed. It did not observe evidence for the existence of a medium through which light travels. So that's the problem. Very successful, very wrong. That's an opportunity. Every time something fails is an opportunity. Other experiments were done under the hypothesis that, oh, no problem. The Michelson-Morley experiment can be explained if, as the earth is moving, it drags the ether along with it, like air current just above the surface of the earth. The reason that you don't have really strong winds near the surface of the earth is that the air is getting dragged along near the surface. But you go up where the air is further away from the ground, and those winds pick up real fast, just like that. That the ether is some medium, and it's being dragged around by the earth. And so it's carrying the ether with it. And that's why Michelson and Morley didn't see it. But if we look at stars, their light will be distorted by the dragging of the ether. That, too, was looked for. That, too, yield a null result. There is no dragging of starlight by the ether. So the ether doesn't exist, and that was a real problem for Newton's mechanics. So it's either not possible to detect it if it exists or it doesn't exist in science. If you can't prove that something exists, then you don't need to assume that it does. That's the nice thing about science. No evidence. You don't need to require that it be there. OK, it probably isn't helping, and it probably isn't hurting. So the question, of course, at the end of the 19th century is, well, who's getting it wrong? Is it Newton's mechanics, these battle-tested, mechanical laws of nature? Or is it electromagnetism, the new kid on the block, who'd only been there for about 30 or 40 years by the time all this, well, not even 20 years by the time all this work was done, then these conclusions were drawn. And it's into this that enters the sort of primary character of this part of the story. This is him. This is him when he was about three years old. So this is Albert Einstein, not very recognizable. So adorable, though. I mean, look at that outfit. Look at that little bow. So adorable. I mean, German kids must have just been either horrified later in life when this style went out or whatever. But we all have embarrassing photos like this from childhood. So he was born in 1879. This is before the Michelson-Morley experiment is done. This photograph is from when he was three years old. Now, here you can see him as a teenager. And the features of the person who would become Einstein are now emerging in the face much more clearly. There's a myth about Albert Einstein that he was bad at math, science, things like that. He actually wasn't. It's a misreading of the way that grades are handed out in the German system versus the Swiss system, which he was later educated in. So there's just a misreading of grades, basically, mistaking one letter to mean something that it doesn't. In reality, he was outstanding at math and science. He loved math and science. You know what he sucked at? Respecting authority. Sound familiar to anyone in here? No? No? You don't have to respect authority to be a scientist. In fact, it's considered a hallmark of distrusting until you verify somebody else's claims. That makes you a good scientist. You can trust. But you don't have to trust completely. And you should always verify if it's the ability to do so. This photo is from 1893. So he is, I'm terrible at math, 10, 14 years old at this point? He's 14 years old on this photo. Now, interestingly, he recalls that later on. So who knows how true this story actually is. But he recalls when he was age 16, he was taking math and physics and so forth. And he asked himself a question. If you could race fast enough to catch up to a light beam that had already been emitted some long time ago, what would you see? What is the light that's standing still as you catch up to it look like? The math didn't say anything about this. What does a light beam look like when it's frozen? And he recalls that his palms got very sweaty and his heart started pounding as he contemplated the question. I don't know. I mean, that might happen to teenagers, but I don't think it's because of this reason. I could be wrong. I don't think it's because of physics. So I think he's romanticizing his youth a little bit there. But what do I know? I'm just a physicist. So here is a more common photo of Albert Einstein. This is from 1904. This is the year before what was considered his miracle year. His miracle year was when he published four papers, all of which changed the course of physics at the time, one of which won him the Nobel Prize. And that paper doesn't feature at all in this lecture. That's the amazing thing of this. He won the Nobel Prize for probably an important, a very important piece of work. Otherwise he wouldn't have won the Nobel Prize, but not the stuff for which he's primarily remembered today. I think that's kind of funny. Now, what's interesting is he completes a four-year teaching diploma at age 21. So he's effectively gone through graduate school at this point, or what we would think of as at least a master's program at this point. Now, after this, it was typical in the system that he was in. This was in Switzerland, I believe. It was typical then to secure a teaching post for yourself after you get your teaching diploma. But he had so pissed off his professors that he could not get letters of recommendation. The professor said hintingly, no giggles, all awkward silence on that one, nothing? All right, fine. There, now we have some awkward giggles. Nobody would write him a letter for two years saying, he's a good student, give him a job. Professors wouldn't say that because he had been so arrogant, so rude in class to his professors, challenged everything they said, cut class, all that good stuff, had his friends take notes for him in class and he would go to coffee shops. Does any of this sounds familiar? You guys are all such good students. OK, none of this sounds familiar. But eventually he gets a teaching job thanks to his friends who secure him a position in the patent office in 1902. So what is he reviewing? He's reviewing patents for electromagnetic devices. This was a big period for the revolution of electromagnetism and industry. This was also a big period for the revolution of the synchronization of clocks because of the newly invented time zone system in Europe. So rather than everybody having their own random times, city to village to city to town to village to city, and that's the way it was back then, it was agreed upon that there would be time zones and that each zone would have the same time regardless of where you were in the zone. Believe it or not, that's a new idea, all right? And it was because clocks were accurate enough at that point that you could get away with it, but you needed to synchronize to a master clock. And so it's no surprise that as Albert Einstein is completing his PhD work, which he does, he completes his doctoral thesis in 1905 while he's holding this position, it's no accident that he's thinking about space and time and clocks and what it means to observe time pass. So let's talk about time. Time is a funny beast. It's very difficult to define time. Everyone knows what time is, but nobody can explain it. Think about that for a second. We all know what time is. It's passing right now. You're sitting here wasting away time in this class. You could be doing something else. You could be hanging out at a coffee shop with friends. We know it exists, or at least we can define something that passes, but then you start trying to put words to it and you're like, ah, what is time? This is a question that also really bothered Einstein, bothered a lot of physicists when basically after Galileo and Newton and this stuff really became codified mathematically, what is time? What is time? How do we measure time? What does it mean to measure time? So Isaac Newton, as I said, had made these assumptions about what space and time are, and he'd made the assumption that time moves at the same rate for all observers, regardless of the state of motion. But a very simple thought experiment, and this is where the word gedankin comes from. Gedankin is German for mind or thoughtfulness. Gedankin experiments are the things that Einstein is famous for. He would construct a scenario that was totally physically plausible in his mind. You couldn't really do this experiment in real life. You can't really do what he was about, what I'll show you, he was sort of thinking about. But you can imagine it, and then as long as everything is consistent with what you know about the laws of nature, it probably isn't wrong, and you could use it as a mathematical argument to refute other claims. All right, so it's a way of arguing. It's a way of arguing it doesn't necessarily have to be physically correct. Many of Einstein's gedankin experiments did turn out to be wrong. He wasn't right all the time no one is. But he had enough ideas that even if he was right 10% of the time, he became famous. There's a lesson. Just have ideas. Who cares if you fail? Try again. One of them is bound to be right. Keep going. That's a lesson from this. Trust me, he was wrong a lot. How do we know that time is passing? We have a device, right? We invent something with periodic motion. Tick, tick, tick, tick. We know this is counting down because we can watch the light, shape of the light reflected off the screen, reaching our eyes from zero, and then the nine, and then the eight, and the seven, and the six, and the five. We know that time is changing because events are occurring, and they're occurring at regular intervals. And we use the interval between two events to mark the passage of time. So Einstein's simple thought experiment was this. Imagine that you and I are going to measure time. And we agree that we're gonna use a common clock. So maybe we put this up high, and we make it big, and we can watch these numbers changing. And you're gonna stand at the bottom at rest with respect to the clock. And you're gonna count nine, eight, seven, six, one second between changes of numbers. One second, one second. I, on the other hand, I'm gonna get on a vehicle that can accelerate very rapidly, up to very close to the speed of light. Yeah, 10% the speed of light. And I'm gonna watch this clock from a distance, and I'm gonna measure time intervals using this clock. The problem was, is that light travels at a finite speed. So every time a number changes, the light reflected off the screen that transmits the information about the change to your eye has to travel from the screen to your eye. And if I'm zipping away at 10% the speed of light, every time a number changes, light has to go further to reach my eye for me to detect a change in time. So while you may see seven, six, five, four, three, one second intervals, if I'm racing away, I might see instead something like nine, eight, seven, six. Okay, then I stop, okay? And we transmit at that moment how much time had passed. And you say 10 seconds, and I say no, no, four. Four seconds have passed. I only saw four changes of the clock. What are you talking about? This was the thought experiment that Einstein finally had his breakthrough moment in. He realized that with this simple observation of the world as it is, Newton's claim that two observers in different states of motion will observe the same passage of time was utterly flawed. Now, he used this as an excuse to do what came next, but it was a comfortable way for him to say, you know what, Newton doesn't have to be right all the time. Let's try something a little different. He actually did this thought experiment while pondering the clock on this famous clock tower in Bernd, Switzerland. He was riding on a street car, there are the tracks for the street car there. And as he was riding away from the clock, he thought about what it would be like if the street car could suddenly go very, very fast and the light from the ticks on the hand of the clock would take longer and longer and longer and longer to catch up to him. And he would think that time is passing more slowly as a result of that, but somebody on the ground in that same amount of time would disagree with him. And so basically he said, okay, look, Newton's assumption that time is the same for everybody, just it's demonstrably false because of how one measures time. You need to be able to see the difference between two events in order to measure time. That's what it means to measure time. Two events occur, the duration between them is what we call time. So here's what he did. This was his radical approach. Everyone says, oh, it was a revolution and it was, but it was a revolution where basically he just kind of pivoted in one direction and started walking this way. Revolutions don't have to burn everything to the ground, they just have to change the way you look at the universe. So Einstein's radical approach was basically just to accept that the Michelson-Morley experiment was telling us something deeply fundamental about the universe, that no matter what your state of motion, light travels at the same speed for all observers. That was his postulate, based on the observations of the Michelson-Morley experiment and the absence of evidence for the ether, this frame in which light has to propagate like a mechanical substance of some kind. But this has consequences. If light is the thing that all observers agree on, not time, this then alters the reality of space and time and how it's perceived by people in different states of motion. So postulate one, this is a postulate. It's an assumption made on a reasonable guess, in this case observational evidence, but it's still postulate. You have to revisit it and you have to check and make sure it's always correct. So we're always testing this. We've been testing this for over 100 years now. That the speed of light is measured to be the same by all observers, regardless of their relative states of motion. It's light speed that we can all agree on. That gives us a meter stick to measure time and space. Light is the meter stick, not time. The consequences of this, however, is that space and time displacements are now no longer consistent between observers in different frames of reference, different states of motion. We all agree light travels at 2.998 times 10 to the eighth meters per second in empty space, but we disagree on the distance it had to travel or the time it took to get there. That's what maintains its constancy. Postulate two is actually maybe not so radical that the laws of physics are the same in all frames of reference regardless of their relative states of motion. Okay, again, that's a postulate. You can test that. You can do physics experiments in different frames of reference and see if you see a violation of the physical laws of nature. We haven't seen this yet, but it doesn't mean it doesn't happen, okay? We just haven't observed it. So if we don't observe it, we don't have to worry about it, at least for now. Now, as I said, these are only postulates. And while we've seen no violations, they are constantly up for grabs in terms of doing a new experiment to test the assumptions. And people still do. People use astronomy. People use particle accelerators to test these assumptions. It's really quite exciting. So here's some consequences of Einstein's relativity. Speed of light becomes a universal constant for all observers. Time will slow down in frames moving relative to others. Prove it, right? Fast-moving subatomic particles that can decay that have a finite lifetime, for instance, the cousin of the electron, the muon, it only lives 2.6 microseconds before it decays into an electron and other things. But if you accelerate the muon so that it's created moving relative to the observer, it appears to live a lot longer. That's a measurement that's been made. In fact, there's an experiment in the basement in the hallway. It's got a little tube in it, and it measures muons getting stuck in the tube and then decaying, and it measures their lifetime. Muons should not be making it from the top of the atmosphere where they're created to the basement of fondren science if relativity isn't true, if Einstein's relativity isn't true. If the speed of light were not a universal constant, then time would be the same for all observers. And that would mean no muon would ever make it from the top of the atmosphere where they're created to the surface of the earth, but they do it all the time. In fact, they penetrate through the earth and they go down into caves below the earth and then they decay. That's because for the muon, or for us, we think the muon's internal clock is running slow because it's moving fast. The muon, from its perspective, would say, no, no, no, no, no, no. Your problem is that your clock is running slow and the distance between me and the earth is shorter than it appears to you. You think I have to travel all these kilometers to get to the surface of the earth. I don't. Distances appear contracted to moving objects along the line of flight. And if you wanna know more about this, you can get into this in third semester physics. It's the first subject you encounter in third semester physics. So Galilean relativity, where time is constant, is replaced by Einstein's relativity where the speed of light is constant. That's the bottom line. It's hard to notice this unless you're moving very fast or unless you're trying to make very precise time measurements, which is what the GPS satellites do, and that's why every day you have to apply corrections based on these and other consequences of Einstein's relativity, or every day the GPS system would drift by 11 kilometers. Those corrections are because the satellites are moving very fast. They have precise atomic clocks that have to be precise to better than a nanosecond, synchronized to each other, to better than a nanosecond, and gravity also influences the passage at which time goes and the clock on earth has to be synced to the clock in orbit and there are different places in the earth's gravitational field. That affects time. Deeper in a gravitational field, time passes more slowly. Farther out in a gravitational field, time passes more quickly. This was put on display in the movie Interstellar in a dramatic way. So after Einstein, light is still an electromagnetic wave. This is the thing he won the Nobel Prize for for figuring out that when you shine light on a metal, it only emits electrons from the metal if the light has a certain frequency. It has nothing to do with how bright the light is. It only has to do with the frequency of the light you shine on it. So you can blast 4,000 watt light bulbs at silver all day long and you'll get no electrons that are ejected from silver. But if you take a dinky little sanitizing wand for a toilet that's got like a four watt UV bulb in it and you shine at the silver, it spits electrons off like there's no tomorrow. That's the photoelectric effect. It's based on the frequency of the light which is related to its energy and that's what Einstein figured out and that's what got in the Nobel Prize. Incidentally, the photoelectric effect is the basis of almost all modern electronics. So you can see why that's kind of important. Ultimately, light would become to understood as having both wave and particle-like behaviors because they are twin aspects of an underlying electromagnetic potential or electromagnetic field. Second semester and third semester physics and quantum mechanics is what you'll need to dig into that. Coming back to light itself, what we've learned is that light travels on the shortest paths, not just in time but in a four-dimensional space, space-time, three-space and one-time dimension, okay? That is a singular framework that was united into one framework in Einstein's relativity. Galilean relativity keeps them distinct from each other but Einstein's relativity mixes time with space and space with time and that's what causes observers to disagree on space and time measurements. And in general, if you imagine an n, 20-dimensional space with like a time dimension as well, the paths in those spaces are generically called the shortest paths are called geodesics. So why is the speed of light the limit in the universe? The best explanation we have now is that in a three-plus one-dimensional universe, if you take the shortest path in three-plus one dimensions in the shortest time, that's as fast as you can ever go. Light does that. Light travels only on geodesics in space-time. What's a geodesic? You've probably encountered them before. How many of you fly? How many of you fly cross-continental? Okay. Have you ever wondered why the hell airline trajectories cross-continent are curved and not straight? That's f'd up. Are they just trying to milk the ticket price? Throw a little more fuel in there, make you pay a little more, reap the overhead. Earth ain't flat. Exactly. Earth is a curved surface. And so airlines are not stupid. They don't want to carry extra fuel that costs extra money. They want the minimum amount of fuel to safely get you to Heathrow and maybe circle for 20 minutes when you get there because that's what Heathrow is like, okay? So they pick the shortest path in this three-dimensional space, which is a curved surface. They have to follow a curved trajectory. So when you flatten that out in the Merkiter projection, it looks stupid. But when you actually look at the earth and realize, oh right, it's a ball, that is the shortest path between those two points. If you were to go what looks like straight here, like this, you're actually following a bowed path out like this, which is much longer on the curved surface. So geodesics are instrumental in plotting efficient optimal trajectories for airlines, among other things, okay? We lived on a curved space. We live on a surface of a curved planet. That's why these things happen, okay? There's math classes at SMU if you want to study more about this. Topology is one of them, okay? I think in the interest of kind of getting to the last bits here, I want to skip that stuff. You can read the slides. That's not too much more than what I already said. So let's take a look at a hand that shapes entire universes. We have light as a phenomenon that goes from one place to another. It can reflect, it can refract, it can interfere with itself. These are all its properties. It travels at a fixed speed in empty space. It's the fastest anything can go in the universe because, as far as we know, the universe is a three plus one dimensional space and light follows the shortest paths in those space in the least time. There is nothing that can go faster as a result of that, okay? But what does this mean for the structure of the whole universe? It turns out that the work that Einstein did laid the groundwork for what we now call cosmology. The physics of the structure, the history, the origins and the fate of the cosmos. People have been doing cosmology ever since people started telling stories about the universe and its origins and so forth. But modern physics is able to tell a story that can make predictions, you can make observations, you can check the predictions and we have a remarkable picture of the cosmos, its history, its origin, its possible fates. And I think as the Nobel committee elected for the 2011 prize, they posted a line from this poem at the bottom of the prize page and I think it's very appropriate to the story that we've learned about the universe. So if we take a look at the universe, we see beautiful things. If you get even a modest telescope and look at the night sky, you can see incredible things. You can see the gas clouds left over from exploded stars. You can see galaxies. They appear as smudges in the sky but they're huge and they contain a trillion stars. The Milky Way, our home galaxy, contains about half a trillion stars or thereabouts. This is one clump of stars in the Milky Way. It's what's known as a globular cluster. These stars are all entwined to each other through a mutual gravitational interaction and they're kind of orbiting a center of mass in this giant cluster. This cluster is called M4, not a very sexy name. It's because of the categorization system, what catalog, the messier catalog is what it was entered into and it's the fourth object in the messier catalog. So it's 5,500 years away at the speed of light. I'll come back to how we know that in a minute. That's 5,500 light years. Light year is the distance light travels in one year. Now because light takes time to travel to us, this has consequences. That means when you're looking at this cluster, you're not looking at it as it exists now now. You're looking at it as it existed 5,500 years ago when the light left the cluster and it's just now reaching Earth. This thing, however, is not that far away. It's well within the Milky Way galaxy, which is our home galaxy and the Milky Way galaxy is something like 50 to 80,000 light years across. It depends on how you're counting the suburbs and so forth. We're about 26,000 light years from the Galactic Center. We're safely out in Frisco or something like that in the great suburb of the Milky Way. We're pretty far flung. It's a long walk to the center of our sort of Galactic City. Now some of the stars in this cluster, we actually know are moving toward us and some are moving away from us and we can figure that out by looking at the light that they emit and how that light changes depending on whether you're looking at stars over here or stars over here, stars up here, stars in the center and so forth. So this whole thing is revolving around a center of mass and we actually can use light to figure out its motions and whether it's going away from us or toward us. So some of these stars on average are heading toward us and some of these stars on average are heading away from us on average that all zeroes out. This is another collection of stars but it's much further away. This is our closest neighbor galaxy. This is Andromeda and Andromeda is about a trillion stars. It's more stars than the Milky Way. It's 2.5 million light years away which means that if you take the history of humans on the planet or human-like things going all the way back to our ancestral ape ancestors, two and a half million years ago who inhabited the planet? In our family, it was Homo habilis, all right? So basically what that means is that we know from archeological evidence that stone tools had already been invented. The earliest bipeds, the Homo habilis was a biped just like us, walked upright on two legs, okay? So astronomy, math, that has stuff as far as we know hadn't been invented yet but lots of other things that we rely on today like tools and so forth did. That's a long time ago. That means we're seeing the Milky, or seeing the Andromeda galaxy not as it appears now but as it appeared when these earlier ancestors of ours roamed the earth. Now another fun fact, Andromeda's heading toward us. We actually know from measuring the light in its stars that it's aimed straight at us. And in about four billion years, Andromeda and Milky Way will collide, they'll merge. So they'll become effectively one distorted galaxy. This happens very commonly in the universe. We're not immune to this. Now how do we know distances to things that are two and a half million, four million, a billion light years away? How do we know this? Well, we know this in the same way that if somebody told you, look, this is a 40 watt bulb. 40 watts tells you something about its brightness at a certain distance from the bulb, all right? So manufacturers make 40 watt bulbs according to the same standards. And somebody says, this is a 40 watt bulb. And then they run it across the campus and they plug it into a light and they say, how far away is the bulb? And you look, you use an instrument, you measure its brightness. You know how bright it's supposed to be when it's viewed like a meter away? And you see how bright it really is. And you do some math and you go, oh, it's 200 meters away. You didn't have to bust out a tape measure to figure that out. You just use the fact that the intensity of light falls off as distance squared, if I remember correctly. And you use that math and you figure out the distance to the lamppost. And then your friend comes out with like a measuring tape and goes, yeah, it is 200 meters. Yeah, yeah, good, all right, good. We have a way we can figure out distances using standard light bulbs and their brightness as perceived from, say, Dallas Hall or Fondant Science at some distance away. In principle, if you knew the brightness, the manufacturer's rated brightness of all the light bulbs that are used in downtown Dallas, you could measure the distance to downtown Dallas every day just using the perceived brightness of the lights in an office building in Dallas. It works great. We don't have light bulbs in other galaxies, so we have to wait for something to happen. And that something is called the supernova, specifically a Type 1A supernova. So this bright spot here and here, this is visible light. And I believe this is ultraviolet light, OK? Visible ultraviolet. There's a bright dot there. That dot is a star that has detonated. And for a brief time, can often outshine its host galaxy. Roughly speaking, there's one supernova per galaxy per century. We are way overdue. There hasn't, as far as we know, been a supernova in the Milky Way for something approaching 400 years. And astronomers all over the world are anxiously waiting for one to go off, because we will learn a lot about the universe if even one of these goes off again in our galaxy. The last time a supernova went off was roughly around the time the telescope was invented. And that's a big FU from nature, as far as I'm concerned, OK? That was a long time ago, like 400 years ago, like screw your nature, what are you doing? But if you look at other galaxies, it's roughly one per galaxy per century, OK? Now, this galaxy is about 76 million light years away. That's 55 million years before the earliest modern apes existed on Earth, all right? So life was much different back then. There were no telescopes at all, at least as far as we know. Now, what's kind of remarkable about this is that these are not light bulbs. These are detonating stars. And the reason that they're so regular, that wherever we look and see one of these supernovaes, they look the same everywhere. Their fingerprints are the same, is because they're due to a kind of star called the white dwarf, which is how our sun will die one day, will become a white dwarf. But it's got a partner star, a big red giant with a loosely bound atmosphere. And the white dwarf over thousands or hundreds of thousands or millions of years will gravitationally slurp gas off the red giant. And it will feed, that gas will build up around the white dwarf. And eventually, it reaches a critical mass where the pressure exerted outward by radiation in the dwarf or by the, actually the pressure between neutrons and protons inside the white dwarf is no longer capable of overcoming the gravitational implosion force that this thing wants to exert on itself. And so this white dwarf will suddenly collapse and blow itself to pieces. It will also probably destroy its partner. So it's kind of bad for both of them. But the good news is, is because these detonations go off in the same way every time, no matter where this occurs in the universe, the fingerprints of this detonation are the same. Once you know that, all you have to do effectively is measure how bright this is, and you know how far away it is. That's remarkable. Astronomers have spent over a century building up these kinds of tools. We knew that was gonna happen. Building up these kinds of tools for studying the cosmos at various distances. What are these fingerprints I'm talking about? They're the fingerprints of the atoms that make up the object, okay? So these, not this, this. This is the atomic fingerprint of our sun. And you can see, it's like reading a DNA chart. There's red, orange, yellow, green, blue, indigo, violet, roachy-biv, laid out in rows. But there are gaps. And those gaps tell us something about the atoms that are present inside of the star. Not all light can be emitted by every atom. And the pattern of light that can be emitted by an atom is unique to it. That becomes the fingerprint. And it turns out that roughly all middle-sized, yellow, middle-aged stars, like our sun, and there are a lot of them in the universe, basically look like this. So anywhere you see this, you're seeing a star that looks like our sun. And astronomy has gotten so precise and has such a huge data bank of information that we have the fingerprints of all kinds of stellar objects. It's a lot of labor to collect all this information. I said earlier that light that's being emitted by something that's moving relative to you, the speed of light doesn't change, but something does give. Something gives in light, depending on whether the source is moving away or moving toward you. And that is the wavelength or the frequency of the light. For a source that's emitting light and racing away from you, its waves appear stretched, so-called redshifted. The wavelengths get longer. Things that are red go infrared. Things that are orange go red. Things that are yellow go orange. If you stop the source moving, everything snaps back. If you then take the source and move it toward you, the wavelengths get shorter. It's blueshifted. So indigo, violet becomes ultraviolet. Indigo becomes violet. Blue becomes indigo and so forth. It's very simple. And it's something you would study in third semester physics. So what's cool about this is if you have a thumbprint of a sun-like star and you look at all the black gaps in it and go, yep, that's just like our star, but the gaps are all shifted one way or the other relative to, say, our sun, then if it's shifted one way, you know it's moving away. If it's shifted the other, you know it's moving toward. This is how we measure speeds. The shift in the wavelength is proportional to the velocity of the object as it recedes away from or moves toward you. This is how we measure speeds of objects in the sky. So what we've learned is that the further away we look at big objects like galaxies or clusters of galaxies, the more we note a funny feature. Whereas in our local galaxy, some stars are headed toward us and some stars are headed away from us. If we look at other galaxies, not Andromeda, because Andromeda is close by and gravitationally is being sucked toward the Milky Way. We're racing toward each other. Four billion years will collide. Go further, go bigger. Look at galaxies that are four billion light years away, two billion light years away, one billion light year away. And you find out that they're all moving away from us. Every distant object, on average, that we look at is headed away from us. That's weird. That suggests it isn't random. I mean, randomly, if the universe is just a static thing and everything can move in any random direction, then you'd expect random motion, like a gas, a hot gas. But we're not seeing that. We're seeing a gas where all the molecules are headed away from us. That's weird. That suggests something's pulling them away from us. And in fact, as a consequence of Einstein's realizations of space and time and energy and matter, that in a universe of spacetime, space and time are not passive players in the universe. They're not the stage on which the play is played out in the cosmos. Space and time are active participants in the play of the cosmos. And their motion, their curvature, has implications for matter and energy. In short, energy and matter tell space and time how to bend. But the bending of space and time tells energy and matter how to move. And what we've learned is that the universe is not static. It's not collapsing in on itself. It's actually expanding. The universe gets bigger every day. 68 kilometers per second are added to the universe for every megaparsec of distance in the universe. You know, you had those funny units in the neutron star, the pulsar problem, seconds per year, the spin down rate of the pulsar. This is another funny unit. It tells you how much universe is added to our universe per second in spacetime for every megaparsec. A parsec is about 3.3 light years. So for every megaparsec of distance, that's how much distance in the universe is added per second. Spacetime is expanding. And you can see it in graphs like this, where you look at the distance to an object and how much it's redshifted, how much it's moving away from us. And we see that distant objects are moving away from us more and more and more. This is the Virgo cluster. This is a gravitationally bound cluster of galaxies that's near us. They are all kind of orbiting a center of mass. So some of them are moving toward us and some of them are moving away. It's cool that you can see that. Here's some blue shifted, here's some red shifted. But on average, as we look back further and further and further, and this actually is not that far in the universe, we see things tend to be moving away from us. And in fact, what was discovered in 1998, 1999, and then confirmed over and over and over again as we measured more supernovas and more distances to distant objects was that the universe isn't just expanding. It's actually expanding faster now than it was 4 billion years ago, which is weird because if the universe started as an explosion of space time and it's been slowing ever since, why would it start speeding up again? What's driving this inflation of the universe now? And it was these three astrophysicists who led the teams that made the original discovery of the accelerated expansion of the universe. The universe isn't just getting bigger. It's getting bigger at a faster rate than it used to. That's kind of neat. And this is actually the evidence for that. These are measured distances using supernovas for more and more distant objects. So this is redshift. And this is sort of their effective brightness. And what we found out is that things are not as bright as we would expect them to be at a given distance. Basically, we're moving away from them faster than we should have been. And that's weird, just based on the slowing expansion of the universe. So the universe is not slowing to a static point. It's not reversing its expansion and collapsing. In fact, we now think that what may happen if this continues unabated is that in trillions of years, the universe will expand so much that the average temperature will drop so low that even atoms won't be able to find each other anymore. If they are, it'll be very lonely existence. Stars separated from planets and things like that. So this is what's known as the heat death or the ice death of the universe. The universe will end in ice, not in fire. And that goes back to that Robert Frost poem that I showed you earlier. So that's one of the main things I wanted to show you today. As always, I overplan for these things. So let me go to the last slides here and close this out. I always prepare too much information. So there'll be plenty of stuff in the slides if you want to look at dark matter. I didn't get to dark matter. That was ambitious, it turns out. I'm going to close with this. Every mystery is an opportunity for discovery. And to review here are just a few. Of the matter in the universe, and I didn't get to the dark matter stuff today, but you can go look at this on your own. Of the matter in the universe, 84.5% of it is in some form that exerts gravity, but neither emits nor absorbs light. That's what dark means, dark matter. We have no idea what it is. Matter, however, is even less interesting. Because that accelerated expansion of the universe could be explained if space itself contains an energy density, independent of matter being there. And that would exert a negative pressure that causes space time to expand, kind of like a balloon. Careful with that analogy, but you can think of exerting pressure and making a balloon expand. Sort of like that. That makes up 68% of the universe, that energy density of space time. We have no idea what causes it. We don't know where it came from. We don't know how to explain the magnitude of its size. This is an even bigger mystery about it. And so one of the things that we need are new telescopes and new surveys that are coming online in the next 10 to 20 years to keep measuring the expansion history of the universe. And what's even worse is that the mathematical framework that you're learning about in this class and in the second semester and in later physics classes, electricity and magnetism and the nuclear forces, all of that is very good at describing all the matter we know about. But that matter only makes up 4.9% of the stuff in the universe. So we have an excellent handle on the tiniest part of the entire cosmos. So what's the complete description of nature? The first way to maybe get to an answer of that is to figure out, well, what are the other things in nature? And that's an active area where you could make discoveries. So I showed you this earlier. What do you see? And what people said they saw was they saw light. But at the end of all of this, what I want you to realize is that this stuff, these islands of light, these galaxies and stars in the foreground here, while they burn bright and while they are a distraction, they are not the kings of the cosmos. They are not the rulers of the cosmos. Most of the dynamics of the cosmos are dictated by what's going on in the seemingly empty spaces in between. And so the thought I'll leave you with is that when I look at the night sky, I don't see a universe ruled by these distracting little islands of light. They're pretty. But don't get distracted by them. It's all the vast dark places in between where all the new discoveries waiting for you, some of you, I think, will make these discoveries. So the code of all of this is if you thought any of the stuff in this lecture was interesting and you'd like to go deeper, because there's no way I can do more than scratch the surface in a lecture like this. Here are some classes you can take at SMU to get more depth on this. Research is a great way to actually get engaged in these subjects. Even if you don't understand them yet, that's OK. Dr. Cooley, Dr. Keough, and Dr. Myers all have programs linked to the things I've talked about today, Dark Matter, the expansion history of the universe. I didn't get to it, but the light left over from the beginning of time. If you scan this QR code, if you like physics and you didn't like it before and you think you might even want a minor in it, which is only three courses past the introductory sequence, and we recommend you take 3305 and two other classes, you can get a physics minor. Scan this QR code or follow the link to the degrees website. Email Professor Simon Dalley, our director of undergraduate studies. And you can pre-declare your major today, even if you can't formally declare. And hey, why not share physics with friends and family? If you like reading or even treat yourself, here are some books. Maybe you don't want to buy this one because some idiot co-wrote it. But these other three are really good, and I recommend them, especially if you're interested in science history. Thanks, everybody. I'll see you around. In the final act of this last lecture for Physics 1303, I want to show you a little bit about the concept of dark matter in a section of the talk entitled The Dance of Gravity and Light. I thought it might be useful to see a quote from a physicist in the modern era that has been regarded as quite famous and quite brilliant to show that a person who is all of those things can also be very wrong. Stephen Hawking famously gave this lecture as his inaugural address as the Lucasian Chair of Mathematics at the University of Cambridge. The title of the lecture is the End Insight for Theoretical Physics, was given in 1981. And 1981 is a remarkable time because at the time, it seemed that the tools of mathematics honed in the 1960s and 1970s and shown to work when compared to new experiments in the 1970s and very early 1980s, they seemed to have all the answers. But they only seemed to have all the answers in the context of us believing that we had discovered all that there was to actually see in the universe. Hawking made this statement about wanting to discuss the possibility that the goal of theoretical physics might be achieved in the not too distant future. And he was even thinking by the end of the 20th century, that time has come and gone. And we do not have a end of theoretical physics. We do not know everything that there is to know. And we know that fact better than we did 20 years ago. Now, as I've shown you before in this image, wherever there is matter in the universe, there appears to be light. And this picture of the night sky illustrates this beautifully. You looked at this before. You saw stars. You saw galaxies far, far away. You saw matter entwined with light. But it is also true as we've learned in this course that wherever there is matter, there is also gravitation. Newton's law of gravity tells us that two things with mass will influence one another through this force we call gravity. One piece of mass will pull on the other. And by Newton's third law, you'll have an equal and opposite force from the first. Wherever there is matter, there also appears to be gravitation. The idea of combining these two tools in order to come to a measurement understanding of the universe was beautifully exemplified by the Swiss astronomer Fritz Wickey, depicted here on the left. So far as we know, he was the first person to attempt to measure the mass of clusters of galaxies. And specifically, the coma cluster was the focus of his investigation. And he did this in 1933 using both light and gravitation as independent tools. The light from galaxies and clusters had been calibrated so that one could use the light in principle to infer the amount of matter in a distant object. But the motion of those objects in that distant place can also tell you the amount of gravitating matter, the way that gravity from one piece of matter influences another piece of matter in that distant object. And in fact, using conservation of energy beautifully expressed through something known as the virial theorem, it was possible to relate the gravitational potential energy to the kinetic energy of objects in motion about each other in a gravitational sense. And infer the amount of gravitating mass that was present. And he looked at the coma cluster and he did very careful observations and measurements. And he found that when one did the accounting of gravitating matter and one did the accounting of luminous matter, that these two things disagreed in the same object. In fact, the amount of gravitating matter seemed to outmatch the amount of luminous matter by a factor of about 400. And while refinements of that observation since Zwicky's original work have had this gap close a bit, it's never closed to a gap of zero. The difference between gravitating matter in this coma cluster and other clusters of galaxies like it and the light emitting matter is a big gap. Now at the time he postulated that there must be some unseen matter, a perfectly reasonable postulate based on everything we then knew about the universe. And he referred to it as a duncle mattery or dark matter. Now it didn't have to be anything exotic. It could have been black holes. It could have been failed stars called brown dwarves that don't emit that much visible light. There were many possible hypotheses that could have explained this and require many more decades, many more tools and much more work by a large number of astronomers to close the door on some of those more standard explanations. At the time his observations and conclusions were not taken very seriously. Many decades later in the 1970s, a different astronomer Vera Rubin would make the next crucial measurement in this light versus gravity story of matter. And in about 1978, she and instrument builder Kent Ford designed and operated a telescope that could measure the atomic spectra of stars and galaxies. Not just the spectrum of an entire galaxy, but the spectra of stars or clumps of stars at different places within a single galaxy, even one very far away. Now this allowed her as an astronomer to make measurements of stellar velocities in those individual galaxies using the red shifting and blue shifting of atomic spectra that we discussed earlier. It was possible to observe a distant galaxy, measure stars on one side and stars on the other side, stars close to the center of the galaxy and stars far from the center of the galaxy and build up a picture of the motion in that galaxy and not only that, but infer the amount of gravitating mass that must be enclosed within the orbits of those stars in that galaxy. And one could of course then compare to the mass inferred from the luminous matter that one can see in the galaxy. And an example of this is shown in the bottom left. This is a whirlpool or spiral galaxy. You can see the bright arms and the very bright center of the galaxy. And using this method of calculating the amount of luminous matter that should be present and comparing it to the speeds of stars that is comparing it to the gravitational mass enclosed by the orbits of stars, what was found was not what was expected. What was expected was that stars in the far flung suburbs of distant galaxies would be moving slower than the stars closer to the core of the galaxy. Why? Because those closer to the core can move a bit faster than those further out and still remain locked in orbits in the galaxy. That is, the galaxy can remain whole and stable even if things are moving faster closer to the center. But what was observed was not this. What was observed was that stars far, far out in the galaxy's edge are actually moving faster than those closer to the galactic center. So fast in fact that they should be exceeding the escape velocity that one would infer from the luminous matter that should be pulling on those stars. Those stars should not be locked in orbits around the center of the galaxy. They should have left that galaxy long ago. And so how can this be? How can galaxies be stable with stars moving this fast so far out in the suburbs of these vast stellar collections? And another answer seemed to be here again that there must be some unseen form of matter. It neither absorbs nor emits light but exerts gravity as a force on other forms of matter including the visible kind. These are not the only observations that imply that there is an unseen, non-luminous form of matter in the universe. For instance, if one assumes that there's some kind of dark matter out there that's complementary to the normal matter we already know about and if one puts it in sufficient proportions in the universe compared to normal luminous matter, one finds that over the history of the universe, the 13.7 billion years that the universe has existed that this dark matter would have clumped in a filamentary way creating the seeds of places where galaxies and clusters of galaxies could later form. This is beautifully illustrated by the computer simulation of the clumpiness of dark matter which would be the seeds of the formation of galaxies and clusters of galaxies in the upper left compared to a picture from the Sloan Digital Sky Survey of exactly that kind of structure in the universe. And it's very hard to tell the computer simulation on the left from the observation on the right. And there's a reason for that. If there was less dark matter in the universe or none at all, the universe would be more like smooth peanut butter. But instead, the universe is clumpy and chunky like peanut butter that still has bits of peanut left over inside of it. The bits of peanut are the places where galaxies later form in our cosmos. They are not smoothly distributed throughout the universe. They are clumped and there are places where there are no galaxies or clusters of galaxies. They're also voids. And what's even more incredible is that this clumpiness that we see in the universe maps onto the light left over from the Big Bang, the event that initiated the cosmos in the beginning of time. That light is shown in the lower right. This is a map of the variations in the temperature of that light coming at us from all directions in the sky. This is an all sky map. These are the variations in temperature around the average temperature of that light, which is 2.7 Kelvin, 2.7 degrees above absolute zero, which is the temperature of the universe on average across the whole cosmos. These fluctuations you can also see here are not uniform. There are hot spots and there are cold spots. This is telling us something. This is telling us that the universe became very clumpy early on near the beginning of time before this light was free to stream. And once this light became free to stream through the universe, it left imprinted in it the indelible thumbprints of the players and the cosmos in that moment just before the light became free. And if we look at the thumbprints that are left in that light, we find the inescapable conclusion that the kind of matter that you and I are made from, stars and the planets and all the things we can see using light in the night sky, but that matter accounts for a tiny fraction of the matter that influenced the light from the Big Bang from near the beginning of time. Rather, other forms of matter and energy have had a much more substantial influence on the history of the universe. The modern picture based on a large number of astronomical and astrophysical observations is the following synthesis, that the ordinary matter that you and I are made from composes only 4.9% of the cosmos. This pie chart, the so-called cosmic pie chart is a depiction in simple terms of what all the lines of evidence tell us about the ratio of the different players in the structure of the cosmos. Atoms, the stuff of chemistry class, the building blocks of life and whole worlds makes up only 4.9% of this energy and matter budget of the universe. A full 26.8% of the cosmos is comprised of a non-luminous form of matter that can gravitate and about which we have little to no other information. It's a modern puzzle, a challenge to modern science to identify what this form of matter is. We call it dark matter and that says two things about it. One, it seems to neither absorb nor emit light and two, we have absolutely no idea what other properties it may have besides the fact that it can exert a gravitational influence on normal matter. But most strikingly is the fact that 68.3% of the universe appears to be best described as a kind of energy of empty space, a pressure that is causing the cosmos to expand faster and faster as time evolves. This negative pressure on spacetime, this thing that could be causing the rapid expansion of the universe now makes up most of what influence the structure of the cosmos and has left indelible thumbprints on the pattern of hot and cold and the light leftover from the Big Bang and the structure of galaxies, their motions relative to one another and in the largest scale structures of the cosmos as we can observe them today. And if you thought dark matter wasn't well understood, dark energy is even less well understood. The Big Bang