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Let me walk you through what they actually say in plain English, no symbols, just the ideas. There are four of them. Number one is about electric charge. Take any charge and it fills the space around it with an electric field pointing outward if it is positive, inward if it is negative. Char- >> Okay, number one. Mat- You're about to be an expert on Maxwell's equations, and so am I. Get ready. They're letting us power up again. I got to roll up my sleeves. Number one, if you have a little electric boy here, right? Imagine a little Pikachu. Got a little Pikachu here. The way Pikachu works is he zaps out in all directions, three-dimensionally, and he can either zap outwards, or he can do his reverse What [ __ ] was it? Reverse curse jutsu. He can use his reverse curse jutsu and turn his electric ability around. He can change the polarization of it to be positive, outward, or negative, inward. Deep chat. >> which is are the sources. They are where the field lines are born. That is the whole first equation. >> So, Pikachu is the source, and Pikachu has reverse curse jutsu capabilities, chat. Equation number one. >> Number two is the same idea for magnetism, except it says something strange and very specific. There are no sources. Magnetic field lines never start and never stop. They always curl back around into loops, which is Maxwell's mathematical way of saying you can never have a lone north pole all by itself. Snap a magnet in half to try, and each little piece instantly grows a brand new south pole. You always get a complete magnet, north and south, no matter how many times you chop. Nobody in all of history has ever found a single isolated magnetic pole. The second equation is that stubborn fact frozen into math. Number >> That's really interesting. Now, you say Okay. All magnets have to have a north and south pole. Even if I cut this magnet in half, then it becomes two magnets. Like when you're fighting the ghost guy and the ghost guy like breaks apart and now he's multiple ghost people you just screwed yourself over. Now you got to kill like 10 of them. That's how magnets work, too. But why? Why do magnets work that way? That must mean something about these invisible lines of force. There must be some deeper layer to it. Some deeper connection to it, some source that we're not quite understanding. I'm not going to spoil it yet. Here we go. Let's keep going. >> Number three is Faraday's discovery, the one we just talked about. A changing magnetic field creates an electric field. Move the magnet, make electricity. And number four is the one everybody already knew going all the way back to Ørsted's twitching compass. An electric current creates a magnetic field. Push current down a wire and magnetism wraps itself around the wire. Four equations, two about electricity >> Okay, a little too fast on that, boss. A little too fast. This is the most important part and you rushed through it like 10 seconds. Okay, let's go back like 20 seconds here. Okay, so law number three, a fixed coil waits for a changing magnetic flux. So basically, number three is what we learned at the beginning of the video. Is that electricity is only produced when you have a moving electric magnetic field. Can't be stationary. So we should probably combine these all these ideas together and we have to figure out what this all means. >> A changing magnetic field creates an electric field. Move the magnet, make electricity. And number four, >> Yeah, that seems like that's probably the biggest one. Why is it that movement matters? If magnetism creates electricity, why can't it just be stationary? Right away, I'll just tell you the thing that keeps sticking out of my mind is, well, what if like it's not. What if what's happening is there's a medium? What if there's a medium and what's really happening is the medium's being disturbed? And we're seeing the effects of the medium being disturbed as fee- magnetic magnetism, as elec- electricity. >> Or is the one everybody already knew, going all the way back to Ørsted's twitching compass. An electric current creates a magnetic field. Push current down a wire and magnetism wraps itself around the wire. Four equations. >> So, the last one is electricity creates magnetism. Electricity itself creates magnetism. That's what we learned from the compass getting moved when it got too close to the electric wire. That means magnetism somehow must be getting created from this. The movement one's the most important because you look at that and you say the reason why movement is essential is because it's not actually moving. It's a disturbance, a ripple in the medium. Someone referenced Dr. Yu and I always think about him because of the way he describes it. The speed of light is the speed of light, but it's the speed of light in the medium. It's the medium speed of light. We keep trying to externalize it and imagine these things as being disconnected entities all of their own, but they're not. Everything is connected and we're in a medium. That's what we're going to learn. That's what's going to [ __ ] the old scientists. And do you want to know the sickest irony of it? Keep watching. >> Two about electricity, two about magnetism, and this one beautiful little bridge running between them. And Maxwell is sitting there staring at his own equations, and he notices something is wrong. Here is the part that stopped me cold when I first understood it. That fourth equation, the one about currents making magnetism, had a hole in it. And to see the hole, you only need one simple gadget, a capacitor. A capacitor is just two metal plates with a small gap between them. Hook it up to a battery, and charge starts piling up on the plates. While it is charging, current is flowing through the wire into the plate. >> Uh-oh, chat. We ran into a problem. We found these beautiful equations. We served some people that needed and deserved a serving. But but there's an experiment that proposes a problem. If we make a circuit, we can put a capacitor in here, which is two plates with a gap between them. But the current doesn't stop. How come it keeps going? Uh-oh, it needs to stop, chat. The current needs to stop, but it's not stopping when I put a gap between them. But you told me that this is just like imaginary particles moving through an empty void. But if that's the case, then this can't work. If that's the case, then that insulator, that gap right there, should break the circuit. The circuit should break, and this should fall apart. Ooh, look at the big brain on Night Slayer here. What is a simple solution to this? Uh, that is not actually a gap. Technically, that's a gap, you're right. But still, those plates are still connected. Those plates are still connected. We just don't see it. There's not an empty void between those plates. There's ether between those plates. There's still a connection. You've just made it a lot weaker. >> And a current makes a magnetic field around itself, equation four. No problem. But now look right at the gap between the two plates. The current flows into one plate and out of the other, but it never actually jumps across the gap. In the gap, there is just empty space and a growing electric field as the charge builds up. So, here is the contradiction. Right up next to the plate, in the wire, there is a current, so there is a magnetic field. But in the gap, there is no current. So, by equation four, the magnetic field should just stop, blink out of existence in the middle, and pop back on the far side. And that is nonsense. Magnetic fields do not have holes punched in the middle of them. The equation was literally contradicting itself. At >> Now, if you look at how did he explain that, too? Do you have any idea how similar this is to both the negative time experiment and also the magnetic teleportation, the magnetic wormhole experiment? That's basically what those those experiments show. What they're trying to do from the magnetic wormhole, and they've done plasma small-scale variants of this, is they can move the entire magnetic field, make it make the magnetic field invisible, entirely invisible. But you can still see its effects, so that ultimately the image of what they produce looks just like this. >> Maxwell was the only person who enough to lose sleep over it. And what he does next is my single favorite move in the history of physics. He has no experiment pointing him to the answer, no data. All he has is this one broken equation and a deep, almost stubborn faith that the mathematics of the universe should be consistent. So, he makes a guess. He says, "What if it is not only currents that make magnetic fields? What if a changing electric field also makes a magnetic field all on its own with no charges moving at all?" In the gap of the capacitor, the electric field is growing, changing every instant. And Maxwell says, "That changing electric field is doing the exact same job a current would. It is making the magnetic field." He called it the displacement current. And I really >> Chat, something just happened, chat. Woah. Woah, we're changing the rules on the fly here. What's going on, guys? Hold on, I thought we were good with the equations, but then we found out there's a real experiment that proves there's something wrong with the equations. Something's missing. And Maxwell, no experiment whatsoever, just divines it down, says, "Wait a minute. Electricity must be able to produce magnetism. Elec- electricity itself can just produce magnetism. That's the reason because we have an elec- we have electricity. We have an empty void, but now the electricity can produce the magnetism that's required itself. Displacement current. And what do I see? What do I see in my my equation boy over here. Uh-oh. I see electric permittivity and magnetic permeability as well. Ooh. This is going to get This is going to get spicy. >> I want you to sit with how bold this was. There was basically no evidence for it. He added a brand new term to the fundamental laws of physics purely because without it the equations were broken and ugly. He trusted the math over the total lack of proof. >> So basically if I want to understand where classic physics broke down immediately from a classical perspective, the answer is right there in something called the displacement current which Maxwell specifically had to add despite no experimental proof because the math didn't work otherwise. >> And that one guess turned out to be one of the most important sentences ever written down. Because watch what happens the moment you add it. Line up the two bridge equations back to back. Faraday's law says a changing magnetic field creates an electric field. Maxwell's new term says a changing electric field creates a magnetic field. Do you see it? They point straight at each other. Each one just by changing gives birth to the other. So let me paint you the picture that >> So now we just mathematically showed the duality of electric and magnetic charge just from the math. So Faraday said, "Here's some weird invisible fields." Maxwell shows up and says, "I'm going to put some math on this. We're going to math this [ __ ] out." Finds out oh wow, when you actually do the math it looks like there's this duality to it. After after he corrects it finds out there's this duality. We now know there really is this duality. There is this duality to it. But now we're going to learn something and we're learning this from hopefully this is the right terminology, first principles. We're going back from the starter. We're going back. Faraday saw magnetic fields. Maxwell put them on the paper. Mapped it out for us. We saw this duality to it. Can we understand anything important about our universe? Because if we can predict things about our universe from this, then it's very powerful physical theory. That's how physics works. Put math on paper. Check it to reality. Does it look like reality? Yeah, there we go. Ooh. Here we go. >> Makes this entire video click. Imagine you reach out and grab an electric charge, an electron, and you give it one little shake. That shake is a changing electric field. And a changing electric field, thanks to Maxwell, creates a magnetic field right next to it. But that magnetic field had to grow up from nothing. So it is changing, too. And a changing magnetic field, thanks to Faraday, creates a fresh electric field a little further out, which is also changing. So it makes another magnetic field further still. Do you feel what is happening here? Each field, as it rises and falls, hands the baton to the next one. Electric, magnetic, electric, magnetic, leapfrogging over each other, sprinting away from that first little wiggle, and racing out into space. And >> When you look at this, when you have it explained to you like that, where it's like a baton and they're handing it off, moving off to the next, because the electromagnetism impact or the electricity electric field impacts the magnetic field. Magnetic field impacts the electric field. Back and forth, back and forth. This is an electromagnetic wave. Why do why are why is electromagnetism in the form of waves? We know because of Maxwell's equations. Maxwell's equations define the geometry of their relationship. They must be orthogonal. They must be at 90° to one another. They must be interacting with one another all the time. Sort of like yin and yang, yes. So, we didn't we didn't pull an image of electromagnet magnetism wave up here. What we did was we derived from the math just now, this is what it should look like. This is why it does look like this. >> Here is the kicker. It does not need anything to travel through. The two fields just keep regenerating each other out of raw empty space forever. That right there is a wave. >> They keep regenerating each other out of raw empty space forever. They don't need a medium to go through. You know what? This was a great video. It was a great video chat. I'm going to have to mark it a one. I'm going to have to mark it a one, unfortunately. It was good video, but you just lost me. It only took you 5 seconds to lose me. You built me up for 20 minutes and then you lost me in the last 20 seconds. You do need a medium. You do need a medium. This right here is exactly where classical physicists are wrong. And when they do the debate, this is what they're going to say. They're going to say electromagnetism regenerates itself from nothing. The [ __ ] you talking about regenerates itself from nothing? These are the people arguing that free energy is not possible. These are the people telling us that we're silly for understanding zero-point energy is tappable. What do you mean it's regenerating itself from nothing? How is this not proof that we're in a medium? >> And this is the one idea I need you to carry for the rest of the video. Shake a charge and electricity and magnetism take turns building each other outward as a self-sustaining wave. Everything else we are about to see is just a consequence of that one thing. So, Maxwell being Maxwell does not just sit back and admire his wave. He asks it a question. How fast do you go? And his equations hand him an exact answer. The speed of the wave equals 1 divided by the square root of two particular numbers. >> Holy [ __ ] Chad. You thought we had just divined all the information we are going to divine? Uh-uh. All he did was he took his own equations that he just made and he said, "Well, how fast are these electromagnetic waves moving?" Anyone Anyone have any guesses? I mean, for us, I know what that equation is right there. I knew instantly. Obviously, I've been studying enough physics if the moment I saw that equation appear on the screen, I knew what the calculation was. This is so profound how big this is that we are about to derive from first principles the speed of an electromagnetic wave. >> And this is where I got genuine goosebumps. Because those two numbers were already sitting in the textbooks. They had nothing to do with light or waves or any of this. The first number you measure by rubbing charges together and studying the electric force between them. The second you measure with wires and magnets studying the magnetic force. Two >> The permittivity and the permeability, Chad. The permittivity and the permeability. This is how you determine the speed of an electromagnetic wave. What's the permeability and the permittivity? >> Two ordinary constants, measured on a workbench with batteries and coils that any physicist of the day could just look up. Maxwell takes those two numbers, drops them into his little formula, works out the square root, and out falls a speed about 300,000 km per second. And Maxwell freezes because he knows that number. Everybody knows that number. It is the speed of light. >> Boom, son. Electromagnetic waves must be light. What? Uh-uh. Are we Are we calculating magic up in here?