 Hi, I'm Zor, welcome to a new Zor education. So let's continue talking about theory of relativity. We did not start it, actually, but every lecture in this course of theory of relativity was before. It was about what's actually good about the old system of physical understanding of our nature is, or was. So I have not really started the new theories. So we are still in the end, at the end of 19th century. Now, nevertheless, one of the most important principle of physics at that time and still is, it's the principle of relativity. So basically it's based on the concept of inertial frame, which we have already covered, and the principle of relativity we also covered. It's basically saying that the laws of nature are supposed to be expressed in some mathematical form in exactly the same way in one inertial system as in another inertial system. So it's a very general kind of statement. Well, nevertheless, it follows from the statement that if you have something like second law of Newton, the force is equal to mass times acceleration. Well, it's supposed to look exactly the same in any other inertial system, which moves in uniform movement relative to the system where this particular equation is true. So these fundamental concepts and principles, the inertial reference frame and relativity principle, they were established at that time. We are talking about the end of 19th century. So basically physicists were relatively happy about the state of their knowledge about the nature, about whatever the physical laws rule our universe. Well, if you just think about it, we had mechanics basically obeying the Newton's law, the three Newton's laws. What else? We had gravity. We have the laws of gravity. Remember? Actually, it's G. Remember this? So that's the gravity, mass times mass of two different objects divided by square of the distance between them and some kind of proportionality, gravity constant. What else? We had electrostatics. We had the Coulomb's law. The Coulomb's law was something like this, very, very close, but these are charges, positive, negative, whatever. So we had certain number of very important laws which we basically have experimentally confirmed and theoretically kind of derived from some principles. Now, recently, relative to the end of 19th century, it was like 1880, something like this. Also, Maxwell equation actually appeared to be like a fundamental equations for electromagnetic field. We had four Maxwell equations, which basically guided our understanding of the wave character of electromagnetic field. And also, they actually allowed to make a judgment that the light is actually electromagnetic oscillations and not only light, like heat as well, which emits from, let's say, sun. So these are all manifestations of electromagnetic field oscillations, wave character. So it was accepted. So everything was great. Well, except a couple of little things. But here I would like to actually have some kind of comparison which I think I read in one of the books a long time ago. If you are traveling in open ocean, let's say, and you have some kind of a couple of clouds on the horizon, well, you don't really pay attention to these clouds. But as the time goes, they're growing and growing, and all of a sudden it's a thunderstorm. So these clouds, they're not really visible when they're far away, but they're coming in and it's a disaster. Actually that's what happened with physics and physicists in the end of 19th century. Well, it was not a disaster, but it was really a calamity, it was really like a fundamental rethinking of like everything in this nature, the theory of relativity, first special, then the general, then quantum theory. I mean, they completely revolutionized physics. But anyway, until that happened, and we're still not there, at the end of 19th century physicists were relatively happy, except a couple of little things, these couple of clouds on the horizon. All right, so before that, let me just think about why they were so happy about it. Let's just consider one inertial system moving relative to another. So let's say you have one system, and then you have another. And for simplicity, I will suggest that this particular system moves relative to this by changing only the X coordinate. So if you have, let's say, capital X, capital Y, and capital Z, and time T as one, inertial system coordinates, time and three axes, and then lower case X, Y, and Z, and T would be the another system which moves relative to the first one with the constant speed along the X axis. So at moment of time equals to zero, they coincide. So these are exactly the same as this. And then they start moving. So let me just go into two-dimension, or think it would be much easier. OK, so if this is X system, X and Y, so forget about Z. So this would be X and Y. And movement is with absolute speed V. And the vector is relative to the, it coincides with the direction of the X axis. So that's what actually happens. Now, how can we transform coordinates from one to another? Well, in classical, in classic physics, the time is absolute and universal. So the T is equal to T, rather than around. It's lower, T is equal to capital T. OK, now, how about the Y and Z are exactly the same? So it's only X which is changing. And that's capital X minus V times T, right? So during the time T, we move to the right by V times T. So if you have some kind of a point with coordinates X, Y and Z, then Y and Z remain. But the X component would be subtracted to this. In the system which moves, the lower case system moves to the right. OK, fine, so that's our change. And what happens in this case with some laws? Well, let's take the mechanics, the second law of Newton. A is acceleration. What is acceleration? Acceleration is basically the second derivative of position. Now, this is position. The first derivative by time would be minus V, right? X is a function of time. And lower case is also a function of time. So we're just converting one into another. I mean, more precisely, if you wish, I should really put it this way. X of T, X of T. But T and T are the same, so that's why it's actually the same. Now, the second derivative is derivative from the first derivative. And this is constant, so it disappears. So these are the same. Obviously, mass is the same as well. And force, again, these are absolute things. Mass and force acting on this mass are completely independent of the frame of reference of coordinates. Force is a vector which has certain direction and certain magnitude. And mass is also some kind of constant, which means that since acceleration is the same, mass is the same and force is the same. Everything is exactly the same in the new system of coordinate. Lower case, XYZ, as well as upper case. Now, what happens, let's say, with my gravitation at 1 and 2 divided by square distance? So these are constants. So it's only the distance which might actually be affected by moving from one reference frame to another. But let's think about it. What is the distance? If you have coordinates XY, Y1, and Z1, and you have X1, Y1, Z1, and the conversion is of this type. Now, what is the distance? Well, the distance is, yes, and then you have another point. 2, 2, 2, 2, 2, 2. What is the distance? The distance is this, square root, right? That's the distance between two points. But if you will subtract this from this, what happens here? X1 of t minus Vt minus X2 of t minus V times t. This cancels out, and we have only this minus this. So the distance between X1 and X2 is exactly the same as between capital X1 and capital X2. So the distance is a universal constant. The distance between two points does not depend on the reference frame. As long as the reference frame obeys this type of conversion, which means inertial frame relative to another inertial frame. So that's why people were happy. Everything is great. This transformation of co-ordinates, which is called Galilean transformation of co-ordinates, seems to be holding. And we were talking about a couple of clouds, all right? So here are the clouds. As we see, the Galilean transformations agree with the second law of Newton and gravitation and obviously coulombs as well, because it depends on the distance. However, it's called invariance. So the second law of Newton is invariant relative to Galilean transformation. Well, the problem is Maxwell equations are not. And the problem is because you see the second Newton's law depends on acceleration, which is the second derivative. Second derivative disappears as long as this is a linear relative to time. So the first derivative is constant. The second derivative is 0. The Maxwell equation contained the first derivative. Now, the previous course, course physics for teens, presented all these Maxwell equations. So if you would like to know, you really have to take that part of the course. But in any case, Maxwell equations, which describe the electromagnetic field, are not invariant relative to Galilean transformation. Well, what can we do? We don't have any other equations that describes the electromagnetic field. And we cannot really sacrifice the principle of relativity, that all the laws are supposed to be the same. It's a contradiction. People didn't know what to do with this. They just live with this. That's the problem, basically. That's what they were staging. And then there was another kind of consideration, also related to electromagnetic field. Well, if light is waves, electromagnetic oscillations are waves, waves of what? I mean, when we are talking about sound, we are talking about waves of the air pressure. So the physicists were considering something which is called ether. Sometimes it's without the letter A. Sometimes it's just ether starts with E. They were considering this to be a medium, which exists like everywhere. And that's when the light goes or heat wave goes. These are oscillations of this medium. And the problem is that there are so many different qualities which this medium is supposed to possess that, really, people became very suspicious about the whole thing. I mean, again, they did not have anything else to replace it at the time. So OK, let's think about ether as carrier of electromagnetic waves. And it's like everywhere. But we understand that there are certain qualities which might actually be very, very strange. Certain qualities which certain experiments actually were conducted, which were difficult to explain. But anyway, it all actually came to one very famous experiment of Michelson and Molly. They have decided the following. If you take a look at the sound, actually, is propagating in the air, if there is a wind, it actually carries the sound. Because it carries molecules. Molecules are vibrating. So the vibration is transferred from one molecule to another faster if there is a wind. So the whole speed of sound is slightly faster in the direction of the wind than against this direction. Because the wind is slowing down the propagation of the sound. Well, now our earth is moving in space in some direction. And if you will take two different directions, let's say perpendicular to each other, one direction will be a little bit better with the movement of the earth than another. It's kind of a wind. It's not only necessary the air to be really blowing against you. Maybe you are going against the standing still air. It's still the same thing. Relative to each other, it's still a wind, right? So the experiment was trying to find the speed of light in two different directions, perpendicular to each other. And according to the theory of ether and the existence of movement of the earth and the rotation of the earth, et cetera, I mean, we should have experienced some kind of ether wind in one direction or another. Or one direction will be more than another. Well, the experiment gave negative results, which means the speed of light is exactly the same in any direction. So in any reference frame, speed of light seemed to be having exactly the same speed, which kind of contradicts this type of a principle. Because let's say if you are, let's say, inside the moving car or a train, now you're just going with a constant speed along the movement. Well, if the car itself is moving with a certain speed and you're moving inside the car, the speeds are supposed to be added together. We already talked about the addition of speed, the velocities actually, because it's a vector, actually, the addition, when we were talking about Galilean transformation. But with light, it doesn't really happen. No matter how fast the source of light actually is going, the speed of light is exactly the same in any direction. So that was another cloud. Ether doesn't seem to exist, because we cannot really detect it in any experiment. Light is propagating with the same speed. And well, people didn't know what to do with this. And that's kind of a crisis which is related to this Galilean non-invariance. And non-invariance is primarily about electromagnetic field. OK. Now, let's talk about electromagnetic field. And we will come up with another kind of strange contradiction. We will make some kind of a thought experiment. Now, here is the thought experiment, which is, again, it's classic right now. Let's talk about piece of wire. This is piece of wire. It has positive and negative. Let's say it's just copper or something. Doesn't matter. Now, it's not charged at all. So it has the same number of positive and negative things. All right. Now, let's put some kind of a battery to it. What happens? Well, this is a plus, this is a minus. So obviously, it's piece of wire, which means that some current will start circulating. The electrons will start moving towards the positive pole of the battery. And then will come out from the negative and go. So that will circulate. The amount of electrons which are consumed by positive pole and the one which goes emitted by the negative will be the same. So it will be circulation. But the number of electrons here will be exactly the same as number of protons. Again, nothing is changed. So from electrostatic standpoint, there is actually no charge. So this thing is not electrostatically charged. But the current goes. Now, what happens when the current goes in the wire? Well, as we know, it has magnetic fields. And these are lines of magnetic field around this wire. Again, that was part of the electromagnetism, part of the previous course which is on this website called Physics for Teens. All right, so that's the known fact. What else is known? Well, we know that the intensity of magnetic field depends actually on some kind of a constant, which is permeability. It depends on the current. And it depends on 2 pi r, where r is the distance from the wire. So we will consider this wire to be infinite. So the magnetic field will be uniform. And the intensity will depend only on the distance from the wire. Now, all these magnetic lines are around the wire. Now, let's examine what happens with, now electrons are moving this direction. So what happens if I will have an electron moving in the same direction with the same speed as these electrons? OK. Well, now this is a charged particle in a magnetic field which is crossing magnetic field lines. According to the Lorentz principle Lorentz law, there is a Lorentz force which acts perpendicularly to movement of the particle and the vector of intensity. Now, it's actually proportional to the charge of this. I'm talking about Lorentz force here. And that would be f. So trajectory would be perpendicular to both. So in this particular point, my vector of magnetic field intensity is perpendicular to my board, so which means I have to perpendicular to both the velocity and this. It would be up or down depending on whether it will be plus or minus. In any case, it will be deviating from the straight line parallel to the wire. It would be deviating this way, I mean this way or closer to the wire, depending again on the direction of the electric current. OK. That's the behavior in case we are standing still and just washing this electron going parallel to the wire. It will deviate because the result is the constant force Lorentz force. OK. Let's do another thought experiment. Let's consider we are sitting with this particular particle, let's say it's electron. Now, it's supposed to, again, going with constant velocity parallel to the wire. What happens in this case? We are moving with the same speed as electrons here. So what does it mean? It means that electrons are not moving relative to us. But what is moving? The protons seem to be moving from standpoint of inertial reference frame related to moving electrons. Electrons are standing still, but protons going to the right. In any case, it's exactly the same current, protons to the right, electrons to the left. It's still exactly the same circulation of exactly the same electric current. And it will create exactly the same magnetic field. There is no difference in magnetic field. So we have exactly the same magnetic field lines around this. The same vector of intensity on each magnetic lines, whatever its direction is in a circle. But what about our electron? Our electron is not moving. In this reference frame, electron is standing still, which means d is equal to 0, which means there is no Lorentz force, which means we are moving in a straight line as before parallel to the wire. So distance between the wire and the electron is changing. I mean, that's definitely a difference of behavior between two inertial frames. One inertial frame associated with just standing outside of this thing and watching electron going and where the electron goes up. And another inertial frame is associated with electron. We're moving with the same speed as electron. And we don't really see any kind of deviation of the distance from the wire. This thought experiment was one of the first, actually, I believe, which could not be explained using this type of change of coordinates. Something is definitely which we do not understand. That's what physicists actually came up with at that time. And again, my purpose of this lecture was to bring you to the point when something needed to be kind of done, invented, changed in Galilean transformation. Some other principles should be brought into the picture of the world, which would not bring any kind of contradiction like this. And that's where I would like to end this particular lecture, because starting from the next one, I will start explaining what exactly the theories came up were developed at the time, primarily what Einstein did in 1905 to overcome these contradictions. OK, I do suggest you to read the notes for this lecture. It's a little bit, there is a nicer picture, and maybe there are more precise words which I was using. It's all presented on unisor.com. The course is called Relativity for All. And this lecture is part of the Galilean view onto the world. So thank you very much, and good luck.