 So today, I'm going to try to illustrate how everything we've been doing for the last four fifths of the class comes together and can give us an explanation of the nature of light. Light is a ubiquitous phenomenon. It is certainly one of the first things that we become acquainted with when we start to see color, shape, depth, facial recognition through pattern recognition in our brains. Light is invaluable to most of us to making it through the course of a normal day. But really, to begin a discussion of light, one has to start asking questions like, well, what is light exactly? So you tell me, what do you think light is? Okay. So you've been exposed to the idea that it's waves and that those waves. So what do the waves do? Travel. Travel. Yeah. It's some kind of phenomenon. It's kind of the wave nature in a bit, and how exactly that came to be understood. But now the modern understanding is that, yes, light is some kind of wave, and that most fundamentally is a phenomenon which departs some other location, arrives at our eyes, and our brain has mechanisms in it that have evolved to convert that light into information that tells us about depth, distribution, color. Our eyes, however, are very narrowly sensitive. There's so much more light out there in the cosmos than our eyes can show us. And so a lot of the last 50 to 70 years of human technology have been to open up our eyes to wavelengths that we were never sensitive to before, and in doing so reveal the universe we didn't even know existed because we couldn't see it. So yeah, most basically light is a phenomenon. We now understand it to be a wave phenomenon, although I'll come back to that a little bit at the end. But most basically it is something that travels from a source to us and we can interpret it. In the same way that sound is something that travels from my hands through a medium, which we now understand it's basically its displacement of air molecules in a wave, a pressure wave. The wave travels across the room, strikes Lashley's ear drums, which then vibrate in response to the pressure wave, and the mechanisms in her ear and the electrical connections from the ear to the brain then convert that into something your brain recognizes as sound. So sound is also a phenomenon that travels from one location to another. Does sound travel through empty space? If I take all the air out of the room so there's no way to create a displacement of air molecules, can I still make a sound? I know. All right, so if you're on the moon and you clap your hands, there's really not a whole lot of stuff for a pressure wave to travel through on the moon, so you wouldn't hear anything. I wouldn't expose my ears to the vacuum, that would be bad for other reasons, your blood would boil. But if you could do that, you wouldn't hear anything. Water waves. Water waves are another excellent example of a phenomenon that starts at a source. There's a displacement in a medium, it's a pressure wave again in the water molecules, and that transmits energy in some cases, as we saw with the Japanese tsunami, over vast distances and can carry all that energy back into the form of mechanical energy. So it can build things, it can pull people out to sea, these things are very destructive. Loud sound waves are also very destructive, you know, you can blow out your ear drums by being exposed to extremely loud sounds, either over a long period of time or so loud that they just shatter your ear drums. So waves are good and waves are bad, and like anything else you want them in the right, sweet spots and not die. Let's talk a little bit about light and some of the characters that were involved in the history of light. So I would argue that up until this person, Galileo Galilei, the understanding of light that people had was pretty much a bunch of myths and misconception and made up stuff. In fact this idea that you can do an experiment and reveal the character of the natural world really first was articulated by Galileo Galilei. So he is considered to be the very first modern scientist, somebody who articulated a version of the scientific method as a means to make statements and predictions about the natural world. So he was a brilliant mathematician and he combined his understanding of mathematics with keen observation and argued that this was the way to understand the natural world. So mathematics, prediction, observation, measurement, and combined the two to come to some narrative about the world that can be consistently arrived at by anybody else that applies the same techniques. Now his big claim to fame early in his life was that he perfected the telescope. So like any good scientist, he took something that already existed. The telescope was not his invention, but he improved on the lens making process of the telescopes and made them into a military weapon. So like any good scientist, he weaponized it and sold it to the government. And he made a ton of money and got a lot of fame off of it. Basically he gave the Italian government the ability to spot ships coming in from the Mediterranean long before the ships knew that they had been spotted. Support cities could prepare for attack or send out a force to retaliate before they even reached the shore. Being able to see your enemies at a great distance when they can't see you was a strong military advantage and enable an enable society. And so he got very famous and made a lot of money off of this and basically got to do whatever he wanted. And so he was taken on as a court scientist by a very powerful family in Italy. And they just gave him money and freedom. He had to teach and of course he had to serve the family's needs as a naturalist. But basically he got to build his own experiments at that point. So what he did was he took his invention, which essentially now had been weaponized and he said, nah, not interesting. And he turned it to the sky. Now there were a lot of ideas about the sky and its perfection and about the nature of the earth and its role in the cosmos. It was a very popular belief that the earth was the center of the universe and all things went around the earth. Now, prior to Galileo, the notion that the sun is probably really more likely the center of the universe was posited. But it was Galileo that really cemented observationally that the idea that everything goes around the earth was a false idea. Because he turned his telescope to Jupiter and he realized that there were tiny little, he called them wandering stars that seemed to orbit only Jupiter. They didn't go around the earth, they went around Jupiter. And that broke immediately the idea that everything in the heavens goes around only the earth. So he published his book on these wandering stars and he became very famous as a result of these observations. He was the first to observe that the sun has spots. The sun was believed to be unblemished and perfect. This seeing spots on the surface flew in the face of biblical interpretation at the time. He got into a little trouble, but other people confirmed his observation. Galileo had quite a mouth. He wouldn't shut up and he really believed that he was right and he got himself into a lot of trouble because he collected all of his observations into a great work. And that work he published in the form of basically a conversation amongst three friends. One who mediated the discussion of the other two, one that mouthed his observations and the other named Simplicio, that mouthed the positions of the Roman Catholic Church. The pope, who was a friend of Galileo's, wasn't too keen on the idea of the mouthpiece of the church being named Simplicio and the simpleton, which is what that means. And so he was dragged before the inquisition, the inquisition. He was condemned as a heretic and asked to repent or face death. So he got on his knees and he repented and he was put under house arrest for the rest of his life and he died in his home. But when he was under house arrest while he was ill, he had a lot more free time again. And he started exploring motion and space and time in ways that when he was younger, he just hadn't bothered to spend the time exploring. And he came up with some interesting ideas about what space was and what time was as a result of that. He died a year before Isaac Newton. Perhaps one of the greatest scientific minds in human history was born, which I think is just very interesting, okay? Now Galileo was very interested in light and he wanted to know if light was an instantaneous phenomenon, that is that from the time it's emitted to the time it's received is zero time. He wanted to know if light travels at a finite speed. So he proposed an experiment and that experiment is something that the physics of musical instruments class here at SMU does, but they do it with sound. He proposed that he sit on a hill with a lantern that is covered and he has an assistant, probably the equivalent of a graduate student these days. Go to a very distant hill that's still visible with another lantern that's also covered. Galileo had built very sensitive water clocks that he could precisely do timing with and he proposed that he uncover his lantern. Now the light is free to travel to the other hill. When the assistant sees the light from his hill, he uncovers his lantern and when Galileo sees the light from the other lantern make the return trip, he times it. So he starts his clock when he uncovers his lantern, he stops his timing when he sees the light from the other lantern. That distance is far too short on the surface of the earth to make a measurement of the speed of light to even say whether or not it is finite. The furthest you can see because of the curvature of the earth is roughly 60 miles depending on whether it's a clear day and whether you're up high and things like that. Sound on the other hand travels about 300 meters a second as opposed to light which travels extraordinarily much faster. So you can actually go to the steps of Dallas Hall and Professor Fred Oleis has marked out the distance to the flagpole and to a point further down the boulevard here. And he knows that this is almost exactly 100 meters and then you go and go another 100 meters down this way. So you have a team of students here with an air horn, a team of students here at the flag with another air horn and somebody in the first team with a stopwatch. So the first team fires their air horn and the stopwatch starts at the same time. When the team at the flag hears the first air horn they fire theirs in return and then the first team when they hear the return horn they stop timing. And you can do that measurement and then do it 200 meters away to take out human reaction time as an uncertainty for about 0.2 seconds. And you can get a very precise, maybe 5% or so uncertainty measurement of the speed of sound over just 100 meter and 200 meter distance. I want to do this in Fort Stadium someday. I think that would be a lot of fun. Don't get shut down by the cops. One of our very enthusiastic new graduate students last year was in charge of this lab and he had them firing the air horns a little bit too much and he was standing here with a little pink card which he would hold up to signal the first team should fire their air horns. And I was standing here taking pictures of some students that had won some honors so we could put them shamelessly up on our webpage and three police vehicles pulled up around that graduate student in a circle. And they told them that you shouldn't be making noise on a college campus in a post 9-11 world. Go figure. Now, Ol Romer. Ol Romer in 1676. So I should say if we go back here to Galileo so he died in 1642. So just about 30 years later Ol Romer was the first person to measure that the speed of light was at least finite. Didn't quite get it right and actually if you re-look at his data now he misinterpreted his data a little bit but you can definitely no matter what from his data you can conclude that the speed of light is not infinite. It doesn't go instantaneously from source to receiver. And he did this by being here on Earth and in fact in a sort of beautiful twist of science he looked at Io which had been discovered by Galileo as a moon of Jupiter in 1610 and he measured the orbital period of Io around Jupiter at different times of year for our orbital period around the sun. And at different times of year we're at different distances from Io so light has to travel further or shorter in order to get to us so we can make the measurements. And by looking at the variation in the measurements he was able to place a bound on the speed of light. He bounded it at, he estimated it to be about 220,000 kilometers a second which actually isn't too far off the mark. That's pretty good. All right. So what is actually the speed of light? Anyone know? Three times second to eight meters per second. 3.0 times 10 to the eighth meters per second. I'm gonna go one further and say it's like 2.998 times 10 to the eighth meters per second. So I know I'm not too bad for good old Romer here. He did pretty good getting close to that. Okay. Let's go back and talk about what we've been doing for this whole semester. There are four fundamental laws of what's called, of electricity and magnetism which are collectively known as the laws of electromagnetism, okay? And that name is not an accident. It's not just for convenience. We now consider these to be a single phenomenon, okay? Faraday's law which we've just learned that a changing magnetic flux induces an electric potential difference in a conductor. Now I showed you an alternative form of this. I substituted with electric field in for the potential. And you can actually write Faraday's law in what's considered a much more fundamental form. A changing magnetic flux induces an electric field. And after all, an electric potential is just an electric field over a displacement, okay? So when you say a changing flux induces a voltage, what you're really saying is it induces an electric field. So changing magnetic flux can cause electric fields to occur. We also have Ampere's law. And Ampere's law is really just the B.O. Savart law in another piece of clothing, okay? But it's a simpler, more compact form and it's traditionally the form in which this law is written. Ampere's law tells us that electric current is the source of magnetic field. Moving electric charge, I, is the source of magnetic field, B. Now, way back in the beginning of this class, we have this thing called Coulomb's law, which was similar to Ampere's law in that it says that electric charge is the source of electric field, okay? So Q is the source of E. Now I skipped this chapter, but this law, much like the B.O. Savart law can really be couched in this thing called Ampere's law. There's a more simple and fundamental equation than Coulomb's law and it is known as Gauss's law for electric fields. And all Gauss's law says is that if I take a region of space and I enclose it in an imaginary three-dimensional surface like a sphere, that if I take the dot product of the electric field penetrating a little piece of the area of that sphere and I sum up all of those dot products across the surface of the sphere, if I find that that integral, that sum is zero, no charge is enclosed. If I find that that integral is non-zero, then there is electric charge enclosed. This is just another way of saying electric charge is the source of electric field, okay? It just says the same thing in a different mathematical form, okay? And finally, there's also a version of Gauss's law for magnetic fields. Gauss's law for magnetic fields says that as far as we know, there are no individual north and south poles, there are no individual magnetic charges. And therefore, if I take and do the same integral for a magnetic field, penetrating an enclosed three-dimensional surface, I will always find it to be zero because there are no magnetic charges enclosed. I can never enclose a bare magnetic charge. So this integral will always be zero. That's a really nice law. That's a nice, easy one, okay? We'll be on to us if we ever find out where magnetic monopoles, because that's gonna make this equation look like this, basically, but with some other constant numerator. Okay, these are the laws, as they were essentially understood before a man named James Clerk Maxwell came along and tried to understand what these four laws were actually describing. If you recall, it was Michael Faraday that initiated this concept of the field as a force per unit charge that reaches out from one charge to another charge and communicates a change in energy or an acceleration, a change in spatial position to the other charge and causes it to move. So that Faraday's concept of the field is beautifully embedded in all four of these equations, two of them for E, two of them for B, okay? Now B also appears up here. We'll come back to that in a bit. This is the, on the right-hand side, this is the one equation where one of these fields, B is buried in the magnetic flux, B dot A. Okay, that's magnetic flux, B dot A. So B is buried in that right-hand side. Now, Maxwell, among others, considered the following question. So what if I take these equations that I just written down and I consider them in a region where there are no charges and there are no currents? This is called free space. So picture the empty vacuum of space with no matter anywhere presence in the region that you're looking at. So you make a volume, like a imaginary box in space and you say, okay, any atoms, no atoms, any electrons, no electrons, this is free space. There's no matter in here whatsoever. In that case, Q is zero and I is zero. And these equations beautifully simplify. These are the four laws of electricity and magnetism in free space. These are really nice, right? You've got B dot D equals zero, E dot D equals zero integral. B dot DS is zero. Yay, Ampere's law is easy. Ah, okay, well, let's see, this is just changing flux. Flux is just magnetic field penetrating an area. That doesn't require that there be charges or currents inside my volume, so that flux may not be zero. I have to leave that there, okay? And what Maxwell kind of recognized as he looked at this was something's amiss. There's something wrong about these equations. Somebody who listens to the language of mathematics too long looks at these four equations and thinks, well, these make sense. These are nice and symmetric in empty space, E dot DA, that integral is zero, B dot DA, that integral is zero, that's nice. But here, this path integral of E dot DS is something that may be non-zero. And this path integral of B dot DS, well, it's always zero. This sort of breaks a lovely symmetry in these equations. So Maxwell, who was this brilliant scientist working in Britain, how to hypothesis. He hypothesized that actually this equation is incomplete, that there's a piece missing from the right-hand side that nobody had observed before, and that it is related to a changing electric flux. So he hypothesized that a changing electric flux induces a magnetic field in the same way that a changing magnetic flux induces an electric field. He envisioned that symmetry may be required, and he made a prediction. He predicted that a changing magnetic, changing electric flux would induce a magnetic field. So that was a prediction that he made based on looking at these equations and saying something doesn't feel quite right. Among his many accomplishments, he lived from 1831 to 1879. He, well, as you'll see in a moment, he united electricity and magnetism into a single force. He developed the theory of how large numbers of particles will behave. He was very interested in thermodynamics and the study of large systems of gas particles and things like that. He made the very first true color photograph. This is him actually holding a color wheel. And in 1864, he published what was perhaps the most important paper in the 1800s to set the stage for everything that followed. And it was entitled, A Dynamical Theory of the Electromagnetic Field. And dynamical meaning time-changing, okay? And that is what he essentially insisted had to be over here, a time-changing electric flux inducing a magnetic field. That piece is missing because we haven't observed it. Let's predict that it exists and go see if it exists, okay? And so experiments were essentially done to do that. So for instance, you could take a capacitor and you could change the strength of the electric field inside a capacitor over time. That changes the electric flux penetrating an area inside the capacitor. And you could look for the creation of a magnetic field. And in fact, this was observed. In fact, after working through the math a little bit to see how one would relate this path integral to this time-changing electric flux, okay? That these in fact were the four equations of electricity and magnetism in free space. A time-changing magnetic flux induces an electric field. A time-changing electric flux induces a magnetic field. And in free space, there is no source of these electric fields, but you can still have time-changing electric and magnetic field passing through that region of space. That's what these two equations tell you, okay? So what you notice is that here you have these lovely constants again, the permeability of free space and the permittivity of free space, mu naught and epsilon naught. These are just numbers we've been using so far. They were empirically determined by experiment, but they're just things that we've been writing down, right? So epsilon naught is 8.85 times 10 to the negative 12, and that's Coulomb squared over Newton meter squared. Okay, and mu naught is a little bit easier to remember. It's four times pi times 10 to the minus seven, and that's going to be Tesla meter squared per amp, thank you. Thank you very much. Okay, very good. All right, so those are these numbers. We've been throwing them around just as constants, but it was through this work of Maxwell that we finally understood what these were. So Maxwell said, well, okay, I have some differential equations. Maxwell recognized this and he solved these equations. What are the functions that solve these differential equations? Here's what we have. We have some magnitude, some constant, some maximum strength of the electric field, some maximum strength of the magnetic field. This is the electric field as a function of both space, x and time, t, same here. The magnetic field is a function of both space, x and time, t. What is the time relationship? Well, he found that it was sinusoidal. This is the sine function. It acts on both space, x and time. This number here, k, is called the wave number. It basically tells you the number of waves per unit meter. Okay, so the number of crests in a sine wave per unit meter. All right, so that's a counted. All right, so if I have a wave and I have a meter, I count one, two, three, four, five. Okay, there are five crests per meter. That's the wave number. Omega is the frequency. It's the rate at which crests pass you as you're standing there, okay? So if I count one, two, three, four in four seconds, then I know that the frequency with which crests of the wave pass me is about a hertz or one per second. That's the unit of frequency, the hertz. And you'll see why that is in a moment. Now, what he found was that these solutions have direction. The electric field points, for instance, in the y direction. The magnetic field points in the k direction, but the wave propagates along x. So the wave is propagating in a direction perpendicular to both e and b. So what do these equations describe? They describe waves, as I just said. So this is a generic equation for a wave. The wave number, k, is two pi over lambda. Lambda is the wavelength. Okay, so that's actually the wavelength of this wave. All right, so here it's, actually it's about, from crest to crest, about two meters, probably on the screen, to a little bit over two meters. So this is, let's see here. This is about a meter, from here to here. Okay, so a little over two, maybe two and a half meters is the crest to crest distance on this wave. F is the frequency, and again, that's in hertz. So we have, we'll start counting here. So one one thousand, two one thousand, so about two seconds, all right? So that's one wave going by every two seconds or half a hertz, okay? One over two, half, half a hertz. Okay, so this just illustrates what I was saying. These are the crests of the wave. These are the troughs of the wave. The distance between peaks and the crests is the wavelength, and the frequency that crests past you is the, is this frequency F. These are electromagnetic waves with an electric field in one direction, a magnetic field orthogonal to that and the direction of travel perpendicular to both. And you have this self-propagating, self-contained disturbance that once created can travel until it's received. So what is electricity and magnetism describing? It's really describing the motion and behavior of electromagnetic waves from one place to another. And those four equations together tell you that that's the picture that's really going on. Electric fields and magnetic fields all individually play a role in this, but it should be possible to create a self-sustaining propagating wave that can be sent out from one location and then received at another by some kind of electromagnetic device. Timerick Hertz, as in the Hertz, was the first to satisfactorily demonstrate the existence of electromagnetic waves. He basically took an inductor capacitor circuit so that what he could do was create a time-changing magnetic field by charging up the inductor and then the capacitor would cause a discharge which would drain the inductor. And then he had a coil someplace else and he could show that the time-changing magnetic field on one side of the room induced a response in the coil on the other side of the room. It was Marconi, Guiano Marconi, who lived from 1874 to 1937. He was an Italian inventor and he developed the very first radio telegraph system which he demonstrated in 1894. Wireless transmission of information which is the foundation of our entire society. Now look at what it's done to the internet. Robert Hire, he lived from 1860 to 1929. He was a physicist. How many of you knew that? Yeah, I didn't think so. Yeah, that's not something they just go around selling at SMU, right? He was a physicist and he was actually the first American to communicate using electromagnetic waves. Oh, look at that, it was in 1894, the same year that Marconi demonstrated the wireless telegraph system. Hire attended a lecture by Hertz. I believe it was Harvard. Got the idea that, oh, well, I should build a device and use it to transmit a signal. And so if I remember the story correctly, he transmitted a signal from his laboratory at Southwestern University in Georgetown, Texas to the nearby jail. So that was the first wireless transmission in the United States. This is a picture of him. Here's Hire demonstrating to other faculty at Southwestern University the use of X-rays. Okay, so he was a real practicing physicist before he became a founder and first president of Southern Methodist University. Now, like any good wave, these waves travel at a speed. What is that speed? Well, Maxwell could figure that out. He could ask his equation, well, how fast are these waves traveling? And the answer he got was that the speed of an electromagnetic wave is always the same speed, no matter what, in free space, regardless of how you were moving relative to it or not. And this was the answer. So what's the number of the speed of light? And it was at this time that people realized what light was. Light is an electromagnetic wave that travels from the source to the receiver at a fixed speed of 2.998 times 10 to the 8 meters per second. And Maxwell's equations, oddly enough, said it doesn't matter how fast you are traveling relative to the source, if you will always measure the speed of light to be 2.998 times 10 to the 8 meters per second. And that's weird. That's what initiated the following revolutions. So this is just to illustrate the wave nature of light. So this is a very simple experiment that was done by Newton originally, right? This was Newton who originally developed these optics and put it around a split light into its spectrum. So you can take white light, you can send it through this thing called a prism, which is just a carved piece of glass. And different bands of color will appear on the other side. And this is because the white light is made of a series of frequencies of light and each frequency corresponds to the color and those colors can be separated in the glass. We now understand that that's because different frequencies travel at different speeds inside the glass. So in material, the speed of light has changed. It's slower than it is in free space, but it can be calculated and that's sort of the basis of geometric optics, which is what we're going to do next. So this picture summarizes the things that you're gonna be doing next. Light comes in, it reflects, some of it refracts, passes through the surface of the glass and then hits the other surface. And when it comes out, you can have these effects where you split the bands of color. These kinds of effects are really unfortunate in camera lenses. You get things like chromatic aberrations where if your lens is not properly corrected, it will split the colors before sending them to the film and you'll get all kinds of distortions in your picture as a result. So understanding optics, it not only gives you an understanding, for instance, of a human eye, which is essentially a lens system, but also how one builds a better camera, how one builds a better laser, things like that. Now, I mentioned earlier that humans are sensitive to what we call color. We refer to color. Color is here, it's visible wavelengths. Different colors of light, different frequencies, different wavelengths correspond to different energies in the electromagnetic spectrum. We're sensitive to light that's between 700 nanometers, which we call red, to 440 nanometers, which we call purple or violet. That visible spectrum is compressed here, right here. That's what we are exposed to as organic creatures from our particular species. There are creatures that can see infrared. Infrared are subred wavelengths. We use infrared, for instance, for, well, this is actually wireless transmission, but for TV remotes, TV remotes using infrared. If you, fun fact, your most cameras, the charge-coupled devices, CCDs, that make up the camera sensor, are sensitive to the infrared. So you can take a webcam, aim your TV remote at it, push the button, and you'll see the light come on in the infrared remote. Your eyes can't see if the camera can, and the camera converts it into visible wavelengths for you. Okay. As you go to even longer wavelengths, okay, you hit the microwave. So pretty harmless. Your phones give out microwaves. You put food with microwaves at the right frequency and make water molecules vibrate. That's not the frequency your phones use. And you have, and yeah, the TSA loves this now. So they can see metal on your body. Down here, we have the broadcast and wireless spectrum. Okay, so radio. Nice radio with an antenna. Okay, that's long wavelengths, long antenna. Those are used to receive music, audio broadcast propaganda, you name it, okay? Ultraviolet, now we're getting into higher energies. We can't see ultraviolet, all right? But this is high-energy stuff. This is the stuff that the, there are bands of ultraviolet that penetrate the Earth's atmosphere, make it down here, and tan your skin. They also, interestingly, break chemical bonds and cause cancer. So these are high-energy nasties. You wanna be careful of ultraviolet. X-ray, you don't wanna mess with X-ray. Okay, yeah, it's great for seeing bones and getting through skin and stuff. There's soft X-ray and hard X-ray. Those are nice ways of saying they're both bad for you. There's just lower-energy X-rays and higher-energy X-rays. You really don't wanna get hit too much by either of those. And then up here, you have gamma rays, which are just the do not disturb of the electromagnetic radiation. That's bad stuff. But there's all kinds of stuff in the universe that makes gamma rays. And PET imaging, actually, where you use matter and anti-matter in the body, this creates a pair of gamma rays. And you can look at the pair of gamma rays and figure out where in the body it came from. So gamma rays are our friends, too. You just have to be careful of how much you get, all right? All right, so that's what we see. And this is what the universe is made of. There's a lot more going on in the universe than our eyes, and certainly our ears and sun waves can tell us. And we've learned over the last century or so to begin to listen to this stuff, listen in the sense that we are looking at the universe in electromagnetic radiation. All right, so here's a question. If water travels, if water waves travel in water, that is that they're a displacement of a medium, and sound waves travel in air, that is they're a displacement of a medium, air, then what the heck does light travel in? Because Maxwell's equations describe in free space, free space, there's no matter there, no charge, no electrons, there's nothing. So what the heck are the electromagnetic rays waves traveling through to propagate from point A to point B? This was a question that really bugged people about the laws of electromagnetism. They didn't seem to require a medium for these waves to travel, and that flew in the face of all understanding of the mechanical universe. So it was proposed that there was in fact a medium, and it just wasn't in Maxwell's equations, and Maxwell's equations were the new kids on the block and they're probably incomplete and wrong, okay? They called this medium the ether, and physicists set out to find it, and they did very sensitive experiments that absolutely was going to detect the existence of the ether causing light to slow down in some directions versus others as we moved through the ether, and they saw nothing, they saw absolutely nothing. So there was actually an experiment to see if the ether is, if the earth is moving through the ether in the universe, there was a prediction about how that would affect light waves, and they did the measurement. It's called the Michelson-Morley experiment. They did it over and over and over again, and they never saw anything. They went well beyond the sensitivity required to see this ether. And then I thought, okay, well what if the earth, as it's rotating, is dragging the ether with it? So then people used telescopes to see how light would be deviated depending on how the ether is dragging the light with it as it's on nothing, it's on none of this. So there were repeated ways of testing for the presence of the ether, and none of them ever observed it. And so if Maxwell's equations require no medium for the propagation of this electromagnetic wave, and yet all the laws of Newton and all the greats that came before Maxwell and Faraday and Ampere and all these people required a medium, who's wrong? And it was this guy, Albert Einstein, who lived from 1879 to 1955, who in 1905 published three papers, one on the theory of atoms, the atomic theory, one on the nature of light, and one reinterpreting space and time based on the theory of electromagnetism. So Einstein took the radical idea that electromagnetism has the correct description of space and time and motion, and that it's Newton's laws that are incomplete. That is not what most people were doing, okay? So he ran with that. He said, okay, well look, the laws of electromagnetism don't require a medium, and if you observe that the speed of light is the same regardless of your state of motion, well then maybe that's the way the universe really is, and all this business about if I travel, if I run at light according to Newton, I should see light speed up as it runs toward me in the same way that when you're heading toward a car at 60 miles an hour and you speed up to 75 to go at it faster, it appears to be moving at you much faster than it was before. Light doesn't do that. Light always travels relative to you and that 2.998 times 10 to the 8th meters per second regardless of your state of motion, and that is a weird truth, but it is the truth. So Newton had it wrong. Galileo and his understanding of space and time was incorrect according to Einstein. Electromagnetism has the correct description of space and time, and he ran with it. And so as a result of this, we have a completely reimagined universe which is observation we've been held up for a century. Einstein reimagined space and time. Newton and Galileo and all their colleagues and people that built on their work, they just assumed the space and time were a fixed frame of reference in which all events happen. Imagine an invisible grid that fills the universe and for all observers that grid is the same. Space and time are the same for all observers. Einstein said, well, no, Maxwell's equations tell us that all observers definitely agree on events happening in space and time, but they disagree on why they happen. Some people will think they happen because space is contracted. Some people will think that they happen because clocks are running slowly for some observers and not others. Space and time are different for different observers moving at different speeds. That is a radical idea that has also been held up experimentally over and over and over again. Einstein also recognized that there were some experiments that suggested that, yes, lights a wave, but you can't explain the outcome of some experiments by assuming it is only a wave. If you assume it's sometimes a particle, like a little blob of energy that scatters off of something, that better explain some experiments out there like the photoelectric effect. The laws of electromagnetism describe light as a wave, not a particle. Einstein proposed, however, that under certain conditions, light may have a particle behavior as well and that's culminating this experiment called the photoelectric effect. And these concepts launched twin revolutions relativity, which was a general theory of space and time and quantum physics, a general theory of matter and forces. Those were united in what we now call the standard model of particle physics, which is a stupid name for something which describes everything we've ever been able to do in the laboratory with matter and forces. But that, when you put these two together, at least special relativity, motion, space and time and quantum physics, you get the thing that we're testing at the Large Hadron Collider to see if we can make it great for a change. Okay? So if you'd like more, I encourage you to go watch the first two episodes of the fabric of the cosmos, which is hosted by physicist Brian Green from Columbia University. You see here the idea that time is relative. It can be warped and stretched like a fabric. The first episode is when is space and the second episode is the illusion of time. You can kind of see where these are going, right? All right, so if you were interested in this topic, go check these out. They're each about an hour. They're on public television. Enjoy. And then the last thing I just, yeah, pbs.org. And then the last thing I wanted to show you is this. I love this because it culminates everything that we've been doing for the whole semester. So if I turn this on to dynamo, okay, so no power, right? No sound coming out of this. All right. Probably sort of tuned to the station. That actually comes in. There we go. The little pig yellow from one hour. Heat and then burn. Perfect. So I can use mechanical work to induce a electromagnetic field that charges the EMF device, the battery that's in the back of this. And then once that battery is a little bit charged, it can now receive and amplify electromagnetic waves coming in from this antenna. So electricity, magnetism, magnetic induction, inducing electromagnetic radiation and receiving electromagnetic radiation all nicely held in this tiny little plastic box.