…experts on this matter. I was making believe I were giving more lectures, and I was doing the theory of relativity, too, the Lorentz transformations, as well as rotations. And when I was fiddling with that, I got involved with what light does. And then I…

…for someone who uses different axes in space and time, this is a sloppy description because you have to use funny eye. Lorentz transformations isn't exactly the same as a rotation. But for someone who uses axes relative to which I'm moving, there'll be a…

…which I'm moving, there'll be a different frequency in time. And there'll also be waves in a space direction. that if I make a Lorentz transformation of this thing to new axes, I'll get a formula that looks like this, a new e, which I'll call e sub p…

…minus p dot x vector, where I made a translation in the direction p of a certain amount, a certain speed, a certain Lorentz transformation. And this is the formula for the amplitude that that would turn into if the object is moving in my system. Because…

…as Newton stated it, but contains, of course, all those square roots of 1 minus v squared over c squared, which were discovered by Lorentz and Einstein and so on, that this is the force law that I've written at the top in which I allow for the mass…

…calculate it for higher velocity, then comes a certain amount of confusion. But it's not hard if you are as smart as Lorentz and realize that this is contracted and that the fields are changed in accordance with formulas that we derived before. even you…

…impossible to say there is no such a thing and to throw it all away. And it was one of the triumphs, in fact, of Lorentz to find out where it came from, that it was the action of the electron on itself. We therefore must believe in the idea of…

…since these masses are all of the order of the mass of an electron, we turn back again to the original idea of Lorentz. Maybe all of the mass of an electron is purely electromagnetic. Maybe the whole value of 0.511 is all due to electrodynamics. Is…

…infinite difficulties if you try to arrange that in the in the relativity theory. As a matter of fact, the Lorentz relativity theory, the requirement of Lorentz relativistic invariance has seemed to have made the possible laws of nature quite restricted.…

…to arrange that in the in the relativity theory. As a matter of fact, the Lorentz relativity theory, the requirement of Lorentz relativistic invariance has seemed to have made the possible laws of nature quite restricted. It turns out that in the quantum…

Lecture S26, January 24, 1963, Lorentz Transformation of the Fields. Lecture S26, January 24, 1963, Lorentz Transformation of the Fields. Last time we began our discussion of the relativistic properties of the Maxwell field theory. We found out that the…

Lecture S26, January 24, 1963, Lorentz Transformation of the Fields. Lecture S26, January 24, 1963, Lorentz Transformation of the Fields. Last time we began our discussion of the relativistic properties of the Maxwell field theory. We found out that the…

…it can be written in a simple notation this way by a notation that's designed for the four-dimensional geometry of Lorentz transformations, in other words that as a vector equation in the four space, means that it's invariant under certain transformations.…

…those transformations and therefore they can be written in a beautiful form. But before they were written in a beautiful form, Lorentz found out that they were invariant under the transformation from the original form, of course, because it says no more.…

…of physics are invariant under the theory of principle of relativity, that all of the laws of physics are invariant under the Lorentz transformation. Therefore, if we invent a notation by which when we write a law down we can immediately tell whether it's…

…other way around, t prime equals t and z prime equals z minus vt. But it's a more complicated relationship known as the Lorentz transformation. And finally, therefore, that the laws of physics must be so written that they are the same, that if we make a…

…object in motion in the z direction is given here, and the transformations mix up of space and time is given here by the Lorentz transformation. By the way, the first thing that we have to do right away, before we get ourselves balled up, is to take…

…a moving system in the same way as time and space. Incidentally, I forgot to say that not only is it for Lorentz transformations, but also for rotations in space, that these three together must, the last three components together, must form an ordinary…

…we have that this combination is also, of course, true because the x prime equal the x. But this is general for any Lorentz transformation. Better. It's general also for any rotation. because the x, y, z's go into the x prime, y prime, z prime, and…

…t goes into t prime if you just rotate. So these two quantities are equal for what sometimes is called the complete Lorentz group. That means the whole set of operations of a Lorentz transformation corresponding to a velocity in the z direction, the x…

…other. But the origin of relativity is the theory of electricity and magnetism. The discovery of the formulas of the Lorentz transformation were discoveries that were made by Lorentz in studying the equations of electricity and magnetism. So for historical…

…of electricity and magnetism. The discovery of the formulas of the Lorentz transformation were discoveries that were made by Lorentz in studying the equations of electricity and magnetism. So for historical purposes, in order to appreciate where things have…

…to appreciate where things have come from, I would like to show that the Maxwell equation contains the information about the Lorentz transformation. That's how Lorentz got it. And therefore, I would like to calculate the potentials of a charge moving at a…

…have come from, I would like to show that the Maxwell equation contains the information about the Lorentz transformation. That's how Lorentz got it. And therefore, I would like to calculate the potentials of a charge moving at a uniform velocity once…

…time to write comes out exactly the same with a V up here. Now this, as you can see, the beginning of the Lorentz transformation coming up. This is related in what way to the potentials in which a particle is standing still. For a particle standing…

…any other coordinate system moving, say, with a velocity u in the z direction by taking it to be exactly analogous to the Lorentz transformation in which the time is given by something and the new x is given by something we've seen before. by mere…

…how to express that, and that is that the mathematical equations of the physical laws must be unchanged under a Lorentz transformation. As a matter of fact, it was the study of the relativity problem which concentrated physicists' attention most sharply…

…relationships, again, from long ago. You don't have to copy it down, and you know where to find it. Then, this is the Lorentz transformation, an inverse transformation, and I need to do the algebra. It's just the same thing with minus v for v. If you…

…see that it's the same. formula that we obtained by a much simpler physical argument without all the shenanigans with the Lorentz transformation. But it shows that the shenanigans with the Lorentz transformation are all right, or else it really shows that…

…much simpler physical argument without all the shenanigans with the Lorentz transformation. But it shows that the shenanigans with the Lorentz transformation are all right, or else it really shows that our careless argument before is all right, or something.…

…the other equation will be the exact correspondent of the first one here. Therefore, omega and k transform the same way under a Lorentz transformation as do t and x. This is what we call a four vector. When something transforms the same way as time and…

…times the z component by the definition of this dot product in four dimensions. So we know that this is invariant on the Lorentz transformations if k mu is a four vector. But this is precisely what's inside the cosine. It ought to be invariant under a…

…something. And you can see it in one step, you know? So we have our, each has its talents. How would you put that if the Lorentz What? You mean if I wanted to do it formally? I wouldn't. I wouldn't do it that way. No, but I could, but it's a…

…and t's in an accelerating coordinate system and one that is not accelerating is a matter that is not decided by the Lorentz transformation, because that has to do with uniform speed. And when it's accelerating, it's no easy matter to decide what the…

…to get some idea of this in more detail. So I'm going to consider this subject now. First, I've written here the Lorentz transformations between the positions and times as measured by an object standing still in motion, rather, and the same coordinates and…

…up to make the new depth, a new width, of the object as seen from a different angle. Can we not look at the Lorentz transformations the same way? There is a mixture between the positions and the time, a mixture between a space measurement and a time…

…with experiment. And the various discussions as to whether these square roots and so forth, which appear in these transformation of Lorentz, has meaning. The reason that we have to discuss the behavior of clocks and so forth is to demonstrate that although…

…they are when it's in the y direction. Just use y's for x's and so on, or for any other angle. You can have Lorentz transformation for any directions, but we just take the x direction. So we'll suppose the motions are all in the x direction here. and…

…didn't work. And so it gradually became apparent that the laws of electrodynamics were probably quite good. In the meantime, Lorentz noticed a very remarkable curiosity. which was that if he made the following substitutions in the Maxwell equation, x prime…

…c squared, which is different than this. If he made that substitution in the Maxwell equations, this transformation called the Lorentz transformation, then the Maxwell equation would remain the same in form. Now, what Einstein's, or actually it was Poincare's…

…the form of the equation will be the same. Any phenomena to determine that the thing is moving. This is called the Lorentz transformation. And just for the sake of discussion, this is called the Galilean transformation. I don't know how to spell it.…

…there's no effect of turning the apparatus. Therefore, there's something the matter with this analysis. And after mumbling around a while, Lorentz pointed out that it would all be straightened out if you will assume something, which is that when a rod moves…