…as you know, for the motions of walls, planets, satellites, galaxies, and so forth. And that's the law of gravitation. Einstein has a different interpretation of the law of gravitation. If the sophomores feel that this is extremely low class, remember…

…concentrate on the idea of curved space. What is meant by curved space? More specifically, what is meant in this application of Einstein by curved space? Now, even that turns out to be somewhat difficult in three dimensions. So I even reduce the problem…

…But that's all technical machine business about the meaning of words. You can use words different ways. But this is the way that Einstein meant to use it when he said that the space is curved. Done with two dimensions, done with the definition of curves,…

…haven't found any deviations as far as they can measure directly. On the other hand, By arguments about gravitation and so forth, Einstein discovered, yes, that the space is curved. And I'd like to tell you how curved and what Einstein's law is. Einstein…

…and so forth, Einstein discovered, yes, that the space is curved. And I'd like to tell you how curved and what Einstein's law is. Einstein said, found out, and I'll tell you a little bit of how he found out, that the space is curved, where in the…

…you have a definition of the analog of a straight line for space-time. Now I would like to discuss the laws of gravitation. Einstein, in trying to make up trying to get the laws of gravitation to fit with his relativity theory, had to discuss many items…

…The time is the same, the distance is the same, all the time. I know, but if you insist on the principle that Einstein insisted on, that you shouldn't be able to tell whether you're accelerating or you're in a gravity field, you've got to get the…

…time varies, the rate of time or clocks or things varies from place to place. It's a difficult idea, but it's the idea that Einstein used, and it's one which turns out to be correct, believe it or not. In this thing, we can figure out that the…

…measurements over there. People have found this phenomenon paradoxical. In fact, that was the one thing of quantum mechanics that Einstein could never swallow. And the fact that you can predict anything you want over here by making the suitable measurements…

…your head against it and comparing it all the time, you can't understand it. I mean, that's what is the trouble with Einstein. He tries to compare that polarizing thing with a beam of polarized light of classical level. And he says, well, look, dammit,…

…it will, of course, absorb proportional to the intensity of the light that's already there. We also remember from this discussion of Einstein that not only an atom will radiate by itself, but if light is shining on it, it also radiates because the light…

…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 variation of…

…c. And so again, the momentum per unit volume is the energy flow over c squared. Finally, I give an argument due to Einstein, which demonstrates the same thing once more. Well, it's too bad. Too bad. Sorry, I'm sorry. Suppose that we have a railroad car…

…Now, this car has lost some mass over here and gained some mass over there, and therefore the center of gravity has moved. Einstein doesn't like it that the center of gravity of an object can be moved from fooling around on the inside. And he assumed…

…then the use of writing it this way? The use of writing it this way is because it has been discovered, particularly by Einstein, that all of the laws of physics are invariant under the theory of principle of relativity, that all of the laws of physics…

…have to change the laws in order to make them relativistically invariant, and of course that change is the discovery of Einstein that the mass must change with velocity. But in this particular system of notation, the simplicity has a meaning, the simplicity…

…slow development, ending up in the quantum mechanics of 1927, quantum electrodynamics. But in between, there was an attempt by Einstein to make an argument. You see, Einstein converted Planck's viewpoints about the oscillators of matter being quantized to the…

…mechanics of 1927, quantum electrodynamics. But in between, there was an attempt by Einstein to make an argument. You see, Einstein converted Planck's viewpoints about the oscillators of matter being quantized to the idea that they were really photons and…

…two of them anywhere. It doesn't have to be the bottom one. But suppose somewhere this is number n, this is number m. Now Einstein proposes that when such an atom has light shining on it, it could absorb that light and make a transition from state n…

…excite. Now we have the other problem. What is the formula going to be for the rate of emission from m to n? And Einstein proposed that this have two features in it. First, that even if there were no light present, there would be some chance that an…

…other way, to go down from M to N, which is independent of whether light is shining on it or not. But then Einstein went further by comparison to classical theories and from other arguments, concluded that there was also an influence of the light, that…

…more complicated, but by an average drifting. And we'll have to study the drifting problem afterwards. This problem was first solved by Einstein at the beginning of the 20th century. So we have to talk about that. Incidentally, and I say that the mean…

…Query. After a length of time, how far away is it from where it began? This is a problem that was solved by Einstein and Smolikowski. Don't ask me how to spell Smolikowski. No. First of all, I'd like to point out something that we already know.…

…thinking of, eh? Is this a... In this lecture, I want to continue to discuss the consequences of the principle of relativity of Einstein and Poincare to the ideas of physics and the ideas in other branches of the world. Just to remind you, I'm going to…

…but rather than embarrass them, I just call them cocktail party philosophers, who say that all is relative is a consequence of Einstein and it has profound influences on our ideas. Of course, if we look into the history of this thing, we discover there's…

…is relative instead of just uniform velocity in a straight line. Now, the main difference, of course, between the relativity of Einstein and the relativity of Newton is that the law of transformation connecting the coordinates since times in one system and…

…can figure out how much energy you are going to get if the thing can be made to split in half. For this reason, poor old Einstein was called the father of the atomic bomb in all the newspapers. Of course, all it is is that he can tell you ahead of…

…it anyway. And the moment they measured it, they didn't need the formula anymore. And so I'm not trying to belittle Einstein, but the other way, I'm trying to belittle newspapers and popular descriptions of what causes what in the history of physics.…

…for over 200 years. And the first time that an error was discovered, correctly discovered, that is, in the laws of Newton was by Einstein in 1905. The equation of Newton, which is the d dt of mv, is equal to the force. Newton added the hypothesis that…

…number of people put together, of which the final result was Einstein's final discovery. Incidentally, for your interest, there are two Einstein theories of relativity. One is called the special theory, which was made in 1905. And that's what we're going to…

…experimentally possible that this is the correct transformation and not that? So that in addition to studying the laws of mechanics, Einstein also had to analyze the ideas of space and time required to understand this transformation. We have to discuss these…

…The mass of the whole thing increases by an amount, which is the energy that I put in divided by c squared. This led Einstein to the suggestion that the whole thing can be summarized not by a complicated mass formula, but a much easier idea. That the…

…of gas, That's right. No, that's right. That's right. This one here deduces only that the change in mass is equal to that. But Einstein went on and took a good guess that it's No, this was, we just demonstrated that the change in mass is the change in…

…can throw you off. I see what the trouble was now. Has there been some new system of relativity developed since Einstein? No. Someone mentioned some new explanation of the universe. Oh, that's cosmology. That's not the same as relativity. There have been…

…float and the other one would sink. And the gravity would not be the same as yanking a box. And that Einstein hypothesis would be false. But there are indirect experimental checks beside the fact that the Einstein hypothesis agrees with other experiments.…

…yanking a box. And that Einstein hypothesis would be false. But there are indirect experimental checks beside the fact that the Einstein hypothesis agrees with other experiments. It all fits together. And it's not at all likely that the antiparticles go up.…

…I mean, I could either say this is a pseudo force, or it's not a pseudo force. But I can take the equations of Einstein, give them a different interpretation, have the same laws. That's true. But if you ask, are there any other points of view from…

…is so far so good. But the interpretations can always be altered. From what I read in the book, I got the impression that Einstein is proposing that the natural straight line of space is going to be such that what we interpret is that the force acting…

…we could tell what its speed and what its position was simultaneously. In the early days of the development of quantum mechanics, Einstein was quite worried about this problem. He used to shake his head and say, but surely God doesn't play with dice.…

…nutty concept of imagination, the black hole, which is something that comes from following the logic of the gravity theory of Einstein to its ultimate. working out the consequences in crazy circumstances. Suppose you had an amount of matter so great that…

…come in that case should be, well, I'm making it sound too complicated. I'll come back and change the way of stating it. Einstein realized, and Poincaré too, and it's hard to get the history right while you're trying to explain the idea at the same…

…possibilities of reasoning interconnecting one idea with another. I would like to show you an argument, which is fundamentally due to Einstein, which indicates that if anything is conserved, and in this case I apply it to charge, it must be conserved…

…right namely the guy who's standing still in an absolute sense but such a thing shall be impossible according to Einstein and therefore it's impossible according to the relativity principle to have none local conservation of charge. This conservation, the…

…an energy that a particle has from its mere existence, an energy that depends on its mass directly. That's a contribution of Einstein, as you undoubtedly know. E equals MC squared is what I was talking about, which is a famous equation in mystic law.…

…does not come in units. And now the question is, is it the source of a field? And the answer is yes. Einstein understood gravitation as being generated by energy. Energy and mass are equivalent, and Newton's interpretation that the mass is what produced…

…in psychologically suggesting to us to guess as to what the laws might look like in a wider situation. For instance, Einstein noticed that the law of gravity, he said that he realized that signals couldn't propagate faster than the speed of light…

…of light, it turns out that the method of describing the forces instantaneously is very poor. And in the Einstein generalization of gravitation, this method of describing physics is hopelessly inadequate and enormously complicated, whereas this one is neat…

…discovery had on the history of science, what kinds of mysteries such a law entails, something about the refinements made by Einstein, and possibly the relation to other laws of physics. The history of the thing, briefly, is this, that the ancients first…

…Newton's laws were slightly off and that they had to be modified. I will not discuss the modification in detail. It was made by Einstein. Now the question is, How far does this law extend? Does it extend outside the solar system? And so I show on the…

…tremendous number remains a mystery. I must say, to finish about the theory of gravitation, two more things. One is that Einstein had to modify the laws of gravitation in accordance with his principles of relativity. The first was, one of the principles…

…first is that it's mathematical in its expression. The others are that way, too. We'll discuss that next time. Second, it's not exact. Einstein had to modify it. We know it isn't quite right yet because they have to put the quantum theory in. That's the…