Twistor theory for the understanding of quantum gravity (contd.)

0:00 Well, Einstein certainly did, and he says explicitly, and on the basis of that, he anticipated, and I quote, the same theoretical modification that leads to the elementary quantum, which he means the charge, will also lead to the quantum structure of radiation as a consequence. That was his anticipation, that those two would come out of one theory. Well, Meg, perhaps you can see why he failed. We still fail today. So, that's his... Well, I wrote this paper last time on the quantum math, some of this. He tried to investigate, essentially, whether he could get relativistic invariant nonlinear generalizations of Maxwell's equations, which would have some sort of stable structures in them, either singularities or, you know, stable non-dissipated concentration energies, and he couldn't succeed, but he wrote very, still very encouraged in 1909, I have not succeeded in finding a system of equations which I could see was well, was suited to the element of electricity, the electron, that is, and the light quantum, both, of course, come out of the same theory. The manifolds of possibilities do not seem to be so large, however, that one need draw back in fright from the task. He didn't succeed, of course, and if you read his correspondence from the following years, he oscillates back and forth between hope and despair. And there's a famous story about Ehrenfest visiting him in Prague at his institute, which looked out in the back, apparently, over the exercise yard of an insane asylum. And Einstein said to Ehrenfest, that's where the lunatics were not working on the Ponder Files. Well, you might make a similar remark about this guy. At any rate, within a few years, his attention was directed more and more towards general, what became general relativity, and he turned away from this problem until 1917.

2:30 To answer the question, if we develop a general theory of relativity, Einstein came to doubt whether synthetic constructive efforts starting from concepts closely linked to empirical evidence could ever lead to such a unified theory as he had it. He shifted to the search for a formal scheme. Which, starting from a small number of highly abstract concepts, would lead, after long chain of deductions, to an explanation of the quantum effects. And I quote you now from a letter of... Well, my point is, I think that the line became washed out between the two. But, to anticipate what he was going to say, he still never gave up the idea that you have to construct, somehow, an explanation for the quantum, and not build it in by hand. No, he had explained gravity. We'll get to that later. I mean, the afferent connection is the expression of gravity. Inertia and gravity are the same thing. I'm firmly convinced that every attempt to arrive at a rational theory by synthetic construction will have an unsatisfactory result. Only a new basis for all of physics, from which all possible processes can be deduced with logical necessity, as, for example, in the case of thermodynamics, can bring a convincing solution. And then, in another letter, he wrote to David, to, oh, to Kornlauer. Now you'll understand why I lapsed into my apparent Don Quixotic attempts to generalize the gravitational equations. If one cannot trust Maxwell's equations and its representation by means of field and differential, excuse me, if one cannot trust Maxwell's equations, comma, and their representation by means of field and differential equations is indicated on account of the principle of general relativity, and one has come to despair of arriving at a deeper basis of the theory by intuitive, constructive means, Then no other sort of effort seems open. And then he wrote to David Bohm, the first sentence from Gladden's Marie Delmont's heart,

5:00 I do not believe in micro and macro laws, but only in structural laws of general rigorous validity. And I believe that these laws are logically simple, and that reliance on this logic of simplicity is our best guide. I'm not so sure if that was true. Thus, it would not be necessary to start with more than a relatively small number of empirical facts. If nature is not arranged in correspondence with this belief, then we have altogether a very little possible understanding of it more deeply. This is not an attempt to convince you in any way, he adds, writing to David Bohm. I just wanted to show you how I came to my attitude. I was especially strongly impressed with the realization that, by using a semi-empirical method, one would never have arrived at the gravitational equations of entry. As I've said, this indicates that the line he had earlier drawn between a theory of principle and a constructive theory has become blurred. But the goal of deducing quantum phenomena from some unified theory, rather than assuming their existence in the outset, remains. Very often it's presented as if the thing that troubled Einstein most about Honda theory was inherently in the radical probabilistic and as I said he indicated that he could more easily conceive a completely chaotic universe than one discovered by probabilistic laws and he wrote to Chris Reichert, I still do not believe that the Lord God plays dice. If he had wanted to do this then he would have done it quite thoroughly and not stopped with a plan for his gambling. In for a penny, in for a pound. In German, wenn schon, wenn schon. If you're going to have everything random, why not have everything random? Why have laws of randomness? Then we wouldn't have to search for laws at all. And I think that's the base of this remark someplace that's published. I maintain that this issue was not the deepest source of his dissatisfaction

7:30 with prevailing interpretation of Marx. And he expressed himself, because he had a letter to correspond to May 54, Why is less in the renunciation of causality than in the renunciation of the representation of reality thought of as independent of observation? It's important to emphasize that he did not see this as a defect of quantum mechanics as such, but as a defect of the very interpretation of quantum mechanics as the most complete possible description of an individual system. He accepted, I won't read the whole quote, but he accepted the ensemble point of view. It is not my opinion that there is a logical inconsistency in the quantum theory itself, and the paradoxon in quotes does not try to show it. The intent is to show that statistical quantum theory is not compatible with certain principles, the convincing power of which is independent of the present quantum theory. There is the question, does it make sense to say that two parts A and B of a system do exist independently of each other if they are, in ordinary language, located in different parts of space at a certain time, if there are no considerable interactions between these parts, especially in terms of potential energy, in quotes, at the considered time? I mean by independent of each other that an action at A has no immediate influence on the part B. In this sense, I express a principle, little a. Little a, independent existence of the spatially separated. This has to be considered with the other thesis, little b. The psi function is the complete description of an individual physical situation. My thesis is that little a and little b cannot be true together, for if they would hold together, the special kind of measurement of turning a could not influence the resulting psi function of b, the a and b of the first field, at the measurement of a. The majority of quantum theorists discard little a tacitly to be able to conserve little b. I, however, have strong confidence in little a, so I feel compelled to link with little b, namely, that's a side function.

10:00 I think this is very nice, what Einstein drew from EPR. And he was not always well understood, in particular by Born, who deadly misunderstood Einstein so badly that in their correspondence they reached an impasse, and Pauli intervened. I think it's a beautiful example of objective critical evaluation. Although Pauli disagreed with Einstein and agreed more with Born's point of view, he understood that Born was not on the wavelength that Einstein was speaking on, and he undertook to explain to Born what Einstein was talking about. He wrote to Pauli in these words, I was unable to recognize Einstein whenever you talked about him in either your letter or your manuscript. It seems to me as if you had erected some dummy Einstein for yourself, which you then knocked down with great pomp, and I would maintain that this occupation or this hobby still has many practitioners, to be said. It's very important to know what Einstein meant before you refute him. In particular, Einstein does not consider the... This is Pauli's words, so I think... To be taken, if not by someone who agrees with Einstein, and therefore has the Odom-Owe weight. In particular, Einstein does not consider the concept of determinism to be fundamental, to be as fundamental as it is strictly held to be. As he told me emphatically many times, he disputes that he uses it as a criterion for the admissibility of a theory to question, is it rigorously deterministic? He was not at all annoyed with you, but only said, you are a person who will not listen. And I think there are still many people in the world But one can't get a north. Or at least one should not get a north. Well, I won't go on for a bit. John Bell, who quotes these, you see, then quotes from Bourne's summary of the discussion many years later when he edits the letters, and he says, I won't bother to read it, except just Bell's comment is delightful, misunderstanding could hardly be more complete. So even all these years later, in after Talley's intervention, Bourne still had not gotten it because he didn't want to see it. Oh yes, and that's his commentary, in which he summarized it, evoked this comment from Bell, which I think is a key point.

12:30 This was, for him, the really, the real stumbling point was this, what has been called, non-metallic. And he held that if you adopted the ensemble of physical interpretations, I say, there was no problem. No, he didn't think it was, if part of the mechanical description is not the complete description of the individual system, then the problem remains finally, right? That there's no problem. I could read other quotes, maybe I've got some later on, but he says, you know, within the set of concepts in which it operates, quantum mechanics is probably the best theory you can ever have and probably will never do better, but he challenged the foundation in those concepts. That was the problem. Well, in fact, I'm going to get to that point. I don't think so. Not if you mean, well, let me not get to it. Let me just say I'm going to get to it. It is to be expected that behind quantum mechanics there lies a lawfulness and description, and the description which refers to the individual system. That it is not attainable within the bounds of concepts taken from classical mechanics is clear. The latter, however, is in any case outmoded as the foundation of physics. So that was, you see, his feeling was quantum mechanics right out of the set of concepts, which were basically outmoded, and therefore if you couldn't advance on that basis, that was not really so surprising, as you see in another quote I'll quote later, you would be surprised that it was the other way around. You'd get so far with the set of concepts that you knew were not adequate. Elsewhere, he elaborated on this inadequacy of the classical concepts, the classical mechanical starting point of quantum mechanics. That's the quote I was thinking about. I do not at all doubt that the contemporary quantum theory, more exactly quantum mechanics, of course, is the most complete theory compatible with experience, as long as one bases the description on the concepts of material point and potential energy as fundamental concepts. You see, this is interesting, and Arthur, this is from 60, let me see, it's late, 60 seconds. Yeah, well, he's writing to the end. Arthur Fine is actually, while he was in the hospital, he called for his writing pad while he was lying on his deathbed.

15:00 Arthur Fine is probably that, usually Einstein is called the reactionary, and the quantum people call themselves the radicals, right? In my sense, they were just the opposite. They were clinging to the mechanical concepts and trying to find some way of still doing physics without another conceptual basis, whereas he was searching for a new conceptual basis, and she was out at the radical test. Pardon me? Well, let's go on. Let me go on. I would like to think it had an effect on his thinking, whether it would have seemed a fundamental challenge to his program. I don't know. I think it's a question. I doubt I would hate to double... The difficulties of quantum mechanics are connected with the fact that one retains the classical concepts of force, or potential energy, and only replaces the laws of motion by something entirely new. The completeness of the mathematical mechanisms of the theory and its significant success turn attention away from the difficulty of the sacrifice that has been made. To me it seems, however, that one will finally recognize that something must take the place of forces acting, or potential energy, or in the common effect, of wave fields, something which has an atomistic structure in the same sense as the electron itself. Weak fields, in quotes, or forces as active causes will then not occur at all, just as little as mixed states. In one of his last letters, he again touched on this point. This one was written March 20th, 1955, and when did he die? In the next month, I think. I believe, however, that the renunciation of the objective description of reality, in quotes, is based upon the fact that one operates with fundamental concepts which are untenable in the long run, like, for instance, classical thermodynamics. Everybody likes to feel that U of C is born in a generation which has finally received a great illumination. Pardon me? Mixed states. Mixed states. I think so. Now, did Einstein believe in some sort of hidden variable program to underpin quantum mechanics? Vespagnat, for example, believes that he did. Bell believes that he did. My dear colleague, Ed Mishimony, was positive. He believed the same thing. I don't think so. I won't bother to read the question board. There are statements by Einstein that might seem to allow such an interpretation, but

17:30 I believe that this view misses the basic thrust of Einstein's search for unified field theory. Let me read a couple of quotes, one from a letter to Besso written in 1950. In a consistent field theory, there is no real definition of the field. A priori, no bridge to the empirical is given. There is not, for example, any particle, in quotes, in the strict sense of the word, since it does not fit into the program of representing reality by everywhere continuous, indeed even analytic functions. The off-shot is that a comparison with the empirically known can only be expected to come from finding exact solutions of the system of equations in which empirically, quote, known structures and their interactions are reflected. I doubt it. I doubt it. I doubt it. Well, I'll read you what I have to say about field foundations a bit later. Since this is immensely difficult, the skeptical attitude of contemporary physicists is quite understandable. You see, for Einstein, once you had the unified theory, the bridge to the empirically observable was a great problem. Suppose you did have the theory, how would you connect it up to observation? It would not exist. Somehow you could automatically integrate over certain things you see. Yeah, it sounds familiar, doesn't it? And here's another letter he wrote to Moffat, and we were talking about it in it, in 53. Our situation is this. We stand before a closed box that we cannot open and try to discuss what is inside and what is not. The similarity of the theory to Maxwell is only external, so that we cannot transfer the concept of force from this theory to the asymmetric field theory. If this theory is at all useful, then one cannot assume any separation between particles and fields of interaction. In addition, the concepts of particles and the concepts of fields, you don't have those concepts available to you. In addition, there is no concept at all of the motion of something more or less rigid. Read it again? Yeah. If this theory is at all useful, in other words, in solving the fundamental problem, then one cannot assume any separation between particles and fields of interaction. You don't have these two concepts to work with. You've somehow got to extract from this the whole ball of wax something to connect. Yeah, it includes both, but in what way? Remember, the previous quote says you don't have particles. There is not, for example, any particle in the strict sense of the word. Particle has to be derived, maybe approximate, use the concept. It's not something that you start with because of the material. It's a goal.

20:00 Okay, I'm reporting here, right? I'm reporting here. Later on, if we have time, in a moment, I'll come to why he was interested in that. In addition, there is no concept at all of the motion, his emphasis, of something more or less rigid. The question here is exclusively, are there singularity-free solutions? Is their energy, in particular, localized in such a way as demanded by our knowledge of the atomic and quantum character of reality? The answer to this question is really not attainable with contemporary mathematical methods. Thus, I do not see how one can guess whether any sort of action at a distance or any type of object, insofar as we have attained a semi-empirical knowledge of them, can be represented by this theory. Now, if the concept of hidden variable theory, not to speak of local hidden variable theory, is given any precise meaning and not used just as a shorthand for anything which is non-quantum mechanical, then I don't think you could say what Einstein is talking about here is a hidden variable theory. Max Yammer discusses this, or summarizes this, or finishes this, well, Einstein never denied the great explanatory power of quantum mechanics, yet he did not feel that this success required accepting, I shouldn't say never, past 1930, let's say, yet he did, and he did, by the way, in another part of the paper I point out, he accepted the uncertainty relationships. Fully after 1930, and he did not see that as a problem. But he did not see that success required acceptance of its conceptual structure as the basis for further progress in theoretical physics, that was. He wrote to Schrodinger, the wonder about quantum mechanics is only that one can represent so much with it, although the most important theoretical source of knowledge, group invariance, finds its incomplete application here. It is the case. It is the case that a logically coherent theory that is connected appropriately to the real fate of affairs usually has great extrapolatory power, even if it is literally related to the deeper truth, bar heights and yet deeper. I will soon get back to this question of general covariance, already meant by that remark about the most important source of theoretical knowledge, group invariance. So let me detour now and talk about the other Einsteins. I don't know how long I should go on. We can just wrap this up at any point. Okay. The other Einsteins.

22:30 Indicated to you earlier that by 19, well, at the beginning, he seemed to feel that a particle or finite number to be the freedom system might be, but by 1909, they shifted to the unified field theory point of view, which more or less he held to continuously would appear to the end of his life. But there is another Einstein who was, as early as 1916, felt that maybe the whole continuum approach just was going to prove a washout. Just by the fact that this other Einstein exists. And you might say, well, this is contradictory, but, you know, was it Witten who said, I contradict myself? Very well, I contradict myself. I mean, it's part of Einstein. That's what I want to bring out, and it's not a part of Einstein's lesson. He wrote in November 1916 to a former student of his at the ETH, Einstein is now in Berlin, and he's writing to this student who's looking around for thesis problems. But you have correctly grasped the drawback that the continuum brings. If the molecular view of matter is the correct, in French, appropriate one, that is, if a part of the universe is to be represented by a finite number of moving points, then the continuum of the present theory contains too great a manifold of possibilities. I also believe that this too great is responsible for the fact that our present means of description miscarry with the quantum theory. The problem seems to me how one can formulate statements about a discontinuum without calling upon a continuum as an aid. The latter should be banned from theory as a supplement to construction, not justified by the essence of the problem, which corresponds to nothing real, in quotes. 1916. But we still lack the mathematical structure, unfortunately. How much have I already plagued myself in this way? So this is clearly, we think about this a long time before 1916. Yet I see difficulties of principle here, too. Now he goes to the other side. This letter contains both, Einstein. Yet I see difficulties of principle here, too. The electrons, as points, would be the ultimate entities in such a system. Building blocks. These are the elementata grundlagen, that is. Are there indeed such building blocks? Why are they all of equal magnitude?

25:00 Is it satisfactory to say God in his wisdom made them all equally big, each like every other one, because he wanted it that way? Sounds familiar too, doesn't it? If it had pleased him, he could also have created them differently. With the continuum viewpoint, one is better off in this respect, because one doesn't have to prescribe elementary building blocks from the beginning. You have the whole of constructiveness, you know, some type of singularities or constraints of energy, and then the fact that they're all the same would be explained by the fact that these are the only stable structures you could have in the field. Further, the old question of the vacuum doesn't amplify what he means by vacuum. The old question, 1960. But these considerations, now it goes back to the other side, but these considerations, namely the arguments for the continuum field point of view, but these considerations must pale beside the overwhelming fact The continuum is more ample than the things to be described. Old origin by 1960. But he continues to discuss this possibility over the years. I'll give you a few quotes. Here's a letter he wrote in 1935 to Paul Langevin. In spite of all successes of quantum mechanics, I do not believe that this method can offer a usable foundation of quantum mechanics. I see in it something analogous to classical physical mechanics, only with the difference that here we have not found the equations corresponding to those of classical mechanics. Now, I do not think that, in itself, justifies the thing very well today, because one of those kind of remarks people would quote, because they would have been careful if they don't really justify it. Now, what's the one? In any case, one does not have the right today to maintain that the foundation must consist in a field theory, his emphasis, in the sense of Maxwell. The other possibility, however, leads, in my opinion, to a renunciation of the time-space continuum and to a purely algebraic physics. Logically, this is quite possible. The system is completely described by a number of integers. Time is only a possible standpoint from which the other observables can be considered. Some of you may have to reference Einstein in the next paper. 1935. An observable logically coordinated to all the others. Such a theory doesn't have to be based upon the probability concept. For the present, however, instinct rebels against such a theory. There's nothing more to say against it than instinct rebels against it. And of course, even worse, he has no idea how to do it.

27:30 And in his lady... Yeah, I say, around, as I say, there's evidence by around the turn of the century, around up to 1905, the first one to say that he was thinking in terms of the, the, the, uh, the freedom, the finite number of degrees of freedom probably was the way forward, but then he switched over in 1908, and Auschwitz, although predominantly a continuum of man, as I want to say, there's another line of thought, didn't... Yeah, but he wants to, I mean, the, remember, the foundations of theoretical physics are one or the other for him. Either space-time is the fundamental thing, you know, and you explain it in that, or space-time is just a construct, which is itself, you know, not anthropologically primary, but actually built up from something which is more fundamental, which is purely algebraic physics, which has no space-time in it and no continuum in it. Those, to me, are sort of prima facie dichotomies. So you say, well, I can't get the continuum model to do a good description of Brownian motion, so maybe Brownian motion could be a good description of the field. Yeah, but Brownian motion takes place in the background in space-time, so they have that continuum. No, no, but these three. No, no, you used differential equations. Well, not in those terms, but equivalent. I mean, all of you would get down to remember that Pocahontas equation. It's some sort of a continuum background, or you can't write derivatives. He was certainly, I think, influenced by, to a relational concept of space and time, but whether he thought that he could eliminate space and time would be, I don't think he was influenced by anybody else in that respect. He read Hume, for example. He credit Hume a lot with his thinking about this specialty of relativity.

30:00 And he even says that if he hadn't read Hume and Machiavelli, he might never have discovered it. And I think what he got out of them was this idea, first of all, that concepts are malleable things, and that computers and words mean what I want them to. Our concepts of space and time are relational, that somehow they depend on physical phenomena, you don't have space and time and then physical phenomena, but space and time are aspects that we can draw from the definition of sound and aid and so forth. Well, obviously this is, first of all, this approach leads to the notation of the space-time continuum and to a purely algebraic physics. Logically, this is quite possible. The system is completely described by a number of integers. Time, in quotes, is only a possible standpoint, different from most other observables, in quotes. In his later years, you get more and more pessimistic comments about the continuum point of view, and the number of comments seem to build up, and rather pessimistic comments about the continuum point of view. He says, in 1952, for example, he also heard the Congo, in present-day physics, there is manifestly a kind of battle between the particle concept and the field concept of physics, which will probably not be decided for a long time. It is even doubtful if one of the two rivals finally will be able to maintain itself as a fundamental concept. Then he wrote to Besso again in 54, I consider it as entirely possible that physics cannot be based upon the field concept, that is, on continuous structures. Then nothing will remain of my whole castle in the air, including the theory of gravitation, but also nothing of the rest of it, I pray physics. I pray more like they do. And then he wrote to Lichtenowicz in 53, who certainly had objected to the singularity of the... The objections regarding the existence of singularity-free solutions, which could represent the field together with the particles, I find most justified. I also share this doubt. If it should finally turn out to be the case, then I doubt in general the existence of a rational, physical use for field theory. Field, not rational physics, but a field, rational physical field theory. But what then? Heiner's Pascal line comes to mind, and a fool waits for the answer. The reason why he didn't publish all this is because he thought, you know, unless you have a real theory to publish...

32:30 Useless to publish, this kind of thing. Well, in any way to Bohm, I must confess that I was not able to find a way to explain that amidst the character of nature. My opinion is that if the objective description through the field as an elementary concept is not possible, then one has to find a possibility to avoid the continuum, together with space and time, or together. But I have not the slightest idea of what kind of elementary concept. And I found only one place... I must admit I haven't looked everywhere, but I could only so far find one place where you can think in somewhat more detail on what a non-continuous theory might involve. So I'll read you this quotation, even though it's rather long, because it's the fullest one I could find. A letter to someone named H.S. Joachim. He's learning to me. Einstein had this tremendous feeling of responsibility to answer people who wrote him letters. Sometimes he did, sometimes he didn't. This one, luckily. Joachim? The alternative continuum, discontinuum seems to me to be a real alternative. That is, there is here no compromise. By discontinuum theory, I understand one in which there are no differential quotients. In such a theory, space and time cannot occur, but only numbers and number fields and rules for the formation of such on the basis of algebraic rules with the exclusion of limiting forces. Which way will prove itself? Only success can teach us. Physics up to now is naturally, in its essence, a continuum of physics, in spite of the use of the material points, which look like a discontinuous conceptual argument, and has no more right of existence in field description. Its strength, namely, rules. The subject matter lies in the fact that it has its parts which exist quasi-independently beside one another. Upon this rests the fact that there are reasonable rules, that is, rules which can be formulated and tested for the individual parts.

35:00 Its weakness lies in the fact that it has not been possible up to now to see how that atomistic aspect, including quantum relations, can result in consequences. On the other hand, dimensionality, that's what dimensionality is, lies at the foundation of the theory. Algebraic theory of physics is affected with just the inverted advantages and weaknesses, aside from the fact that no one has been able to propose a possible logical schema for such a theory. It will be especially difficult to derive something like a spatio-temporal quasi-order from such a scheme. I cannot imagine how the axiomatic framework of such a theory could appear. And I don't like it when one talks about it in dark apostrophes, apostrophes of apostrophes. But I hold it entirely possible that the developments will lead there. For it seems that the state of any finite spatially limited system may be fully characterized by a finite number of numbers. This speaks against the continuum of infinitely many degrees of freedom. This objection is not decisive only because one doesn't know, in this temporary state of mathematics, in what way the demand for freedom from singularity in the continuum theory limits the manifold of solutions. We hadn't given up. But even near the end of his life, I was interested to find out, he was still on the lookout for new mathematical tools which might turn the speculations which he thought best kept private into the basis of real theory. And Abraham Frankel, the mathematician, reports an interview he had with Einstein in 1951. And you'll see immediately with his background why Einstein got so excited. In December 1951, I had the privilege of talking to Professor Einstein and describing the recent controversies between the neo-intuitionists and their formalistic and logistic antagonists, which is a controversy among mathematicians, and particularly logisticians. I pointed out that the first attitude would mean a kind of atomistic theory of functions comparable to the atomistic structure of matter and energy. Einstein showed a lively interest in the subject and pointed out that to the physicists such a theory would seem by far preferable to the classical theory of continuity. I objected by stressing the main difficulty. Namely, the fact that the procedures of mathematical analysis, for example, of differential equations, are based on the assumptions of mathematical continuity, while a modification sufficient to cover an intuitionistic discrete medium can easily be imagined. Einstein did not share this tension with you. Okay?

37:30 Of course, Einstein never felt that, from the beginning, he never felt that general relativity was anything more than a way station on the search for the . No, gold or platinum. And the team was made out of wood, building on two pillars. We'll get to that in a moment, to give you an example of that. It should have been, but let me explain to you why it was not. Let me explain to you why it was not. I picked it up now from that point when, as I read it for Schrodinger, where he said that the most important theoretical source of knowledge, group invariance, finds such incomplete application in quantum theory. This brings up one of the most profound sources of Einstein's skepticism about the ultimate stability of quantum mechanics. He attached primary significance to the concept, to a principle of general covariance, and he wrote, for example, to someone in 1954. You consider the transition to special relativity as the most essential thought of relativity, not the transition to the general relativity. I consider the reverse to be correct. I see the most essential thing in the overcoming of the inertial system, a thing that acts upon all processes but undergoes no reaction. This concept is in principle no better than the center of the universe in our proficiency. So we looked at the a priori postulation of an earth system as on the level of the experience it was postulated in the center of the world in some place in the middle of the earth, that's why it's pulled down and so forth. We looked upon it as that primitive. Even relativistic quantum mechanics, when constructed on a non-generally covariant basis, be felt with not much help. And later hope to make it general logistic in some natural way. So we thought that this was starting off the wrong way.

40:00 And then he justifies himself against Price's criticism. I have not really studied quantum field theory. And Wiley-Bogman said that once Einstein asked him about quantum field theory, and asked him to give him a couple of seminars on it. And for a while Einstein said, well, that's enough. He didn't want to know anymore. He thought it was not the answer to what he wanted. I have not really studied quantum field theory. This is because I cannot believe that special-relativity theory suffices as the basis for a theory of matter, and that one can afterwards make a non-generally relativistic theory into a generally relativistic one. But I am well aware of the possibility that this opinion may be erroneous. Now I'll adopt the method of steepest descent. Well, there's quantum jumping, yes. I mean, I'm not here to argue the point now. I'm here to convey the point. But for example, he did see the beauty of quantum mechanics. He studied Dirac's textbook and thought it was very beautiful. He thought that would be nice. The best exposition of quantum mechanics. Dirac's textbook. Not the law of division, but not the beauty of division.

42:30 By the way, since you bring it up, there is a curious quote, if I can find it, because he was not so far from Bohr's point of view on one point, although we say he never could understand complementarity in spite of repeated attempts. Can I find that one? Well, I can't find it, but maybe I can summarize it in my words. He says that, very much like Bohr's point of view, that he doesn't really believe that the The wave aspect of the electron is as fundamental as the particle aspect, and conversely, the particle aspect of the light quantum is as fundamental as the wave quantum. It's very much like, you know, Bohr does not really believe in full duality between the waves and the particles. He believes that the electron, the classical limit defines what is the more important thing, and therefore the particle aspect of the electron is the more fundamental thing. The wave aspect with more mathematical constructs will help, and vice versa for the photon, the wave theory. Einstein had a very similar quote. It's surprising. Well, that's one way of looking at it. It's got to probably do with the fact that, of course, one is Bose-Einstein, and the other is Klinger-Assegir. That's why you can't build up waves, I mean, you can't build up a wave, you can't build up a coherent wave state for the electron. Well, but that's not, the cost of limit is much more important. The reason for the cost of limit we might discuss is the fact that it's something that Einstein accepted as well, that there's something less real about the wave aspect of the electron. As I said, I think this is very much in the spirit of Einstein, and this I've discussed in a couple of other papers that I can give you a reference to if you're interested, but if you look at how Einstein developed the general theory of relativity, you see that

45:00 You can learn a certain number of lessons from what he, or he certainly learned a number of lessons from the way he did it, and we can learn, I think, from these lessons for ourselves and apply them, learn the lessons ourselves and apply them today, and sometimes when people don't tell you the history of the subject, they're not that aware of the lessons, and that's why they can't make the choice to apply them and describe them. I'm obviously not saying that because Einstein said it, we've got to accept it, but I don't think we should overlook the possibility that it might be. It isn't necessarily wrong, let's say, just because Einstein said it. It's worth considering. The first thing that I found was the equivalence principle, of course, which he very early expressed as the idea that inertia and gravitation are vasence-like, alike in their essence, essentially the same thing. And, of course, once the mathematical language for that was developed, what that essentially means is that gravitation is part of gravitation. The reason why the connection is expressed is the equivalence of inertia and gravitation, the fact that you can't distinguish the two except by the... Einstein placed great stress on the connection as the mathematical representation of the gravitational field. He's writing to Lauer, who espoused the not unknown today point of view that the real intensive is everything. He just came out of a discussion of the rotating disk problem in Lauer's book. And Lauer said he couldn't understand what Einstein had done, why he was reading geometry, because he said there was a real intensive, you know, in five spaces, zero. So there's no problem.

47:30 What characterizes the existence of a gravitational field from the empirical standpoint is the non-vanishing of the gamma, the components of the alpine connection, not the non-vanishing of the r. If one does not think in such intuitive or visual ways, one cannot grasp why something like curvature should have anything to do with gravitation at all. In any case, no reasonable man would have hit upon anything in that way. The key to the understanding of the equality of inertial and gravitational mass would have been lacking. A couple of comments on that. I recently came across something nice on Einstein's intuitive visual way of thinking. He met a student who came from Göttingen to speak with him, to learn from him, when he was in Berlin in 1917 during the war. And they had the following conversation, I'll read part of it before. Einstein said that he doesn't really trust what we in Göttingen do. He has never thought formalistically. His conceptual armory is very closely connected to reality. He says, for example, that he visualizes gravitational waves with the help of an elastic body, and he made motions of his fingers as if he were compressing a rubber ball. Einstein was the forerunner of the rubber ball. It's very characteristic of Einstein that his way of thought was in terms of visual or even kinesthetic imagery, and he says as much himself, and that's the answer to the Audemars story about how he thought about physics. Secondly, I think this distinction between, I mean, this emphasis on the inertial connection, the connection that the fundamental of space and gravitation field is probably much more palatable for physicists today than, and even relative than it was some years back because the disengaged theories now have made everybody think it's an inertial connection. And also, the discovery of the thermal ambience of the accelerated particle detectors. Again, you can't make a distinction between quantum and thermal fluctuations. You have to take the connection seriously as a representation of gravitation, so that the real intention isn't everything. Okay, but then what this says is that no division like this has any absolute significance.

50:00 So a division like this would be home free, because once you have a tensor to represent the gravitation, you can solve, on the classical level, dozens of problems, like you have an energy, locally defined energy and so forth, and quantization would become trivial and so forth and so on. The first person to seem to realize this was Rosen. He did a biometric theory, what, about 1940? Very carefully undoing what Einstein had done, the lesson of which he could express in the old biblical injunction that God has joined but no man could asunder. And Einstein gave Rosen, I think, a very good piece of advice which he didn't follow. Throw it in the wastebasket. But what I want to point out, of course, is that people who quantize general relativity by using a background metric, flat or not, are essentially violating this injunction. They're essentially using an inertial connection, whether they do it swiftly or not, and therefore they have a gravitational tensor. And as I said, if you give me a gravitational tensor, I can regain two, but the point is... So not only is there the problem of what's the conformal structure of the background, they've got to do the actual propagation, made it non-adherent to the composition, and then treated this as a part of the background and quantized that. And there's one thing they regard this as a... As long as you know what you're doing. You'll admit that some people who approach general relativity from the side of quantum field theory and look at it as just a theory with a particularly messy gauge group... Many of these mathematicians are very guilty of this kind of thing. I once was in a discussion with, well, a French physicist who remained nameless, and his idea was, it's simple to quantize general relativity, you take a conformal flat metric and you quantize a conformal factor. And I said to him, and he went on and on for an hour, I said, well, what makes you think that you have to have a conformal flat metric to deal with the quantized general relativity? Well, because if you don't have that, I don't know how to do it. This falls under Einstein's comment about He doesn't think much of a carpenter when he has to bore a hole in a piece of wood and look for the sin spot. It makes the hole there. You make the hole where you wish needed, for whatever reason. Anyway, so that's one lesson.

52:30 The next lesson is... I haven't really got time to go into this in any great detail. I did a long paper based on a book I gave eight years ago, but I finally caught up with it and wrote the paper. Explaining what he started with, what general covariance meant to Einstein, what it really means, and it's got to do with the question of what held him up for... Almost three years from the time we knew that the correct mathematical representation of the gravitational field was a metric tensor, is the time when we wrote down the general covariance field equation. And it was essentially connected with the fact that we didn't realize that the points of a manifold, although they are mathematically individuated by a coordinate system, are not physically individuated before you have a metric. And therefore the idea of putting two solutions to the field equations on the same manifold... One obtains from the other by dragging it, does not give you two physically distinct solutions, but merely that you drag the physical meaning of the points along with you when you take the second solution. So this is, you could say that the fact that the events, you don't have events, you just have points in a manifold, which are mathematically individuated, but have no physical properties at all until you have a metric. And it's fairly easy to solve this. The moral of that story really is that general relativity should be done on a fiber bundle, because if you do it on a fiber bundle, you will realize that the points of the base manifold do not represent events. Events can be represented mathematically by mappings from a cross-section into that space, and clearly if you have no cross-section, you have no mapping, and therefore you have no events. So that problem is easily solved, but I think that's the way to handle that problem. It's not a big technical problem to do it, but the moral, of course, is when you come to do the quantum theory, you have to really remember that, that you have no, you do not have events to start with, and therefore, when you have this wonderful formalism, what do you do with it? When you have your waypoints, you have to interpret it. You don't know, for example, neither one says, well, you put an apparatus here to create a particle, and then you put an apparatus there to make it, but you have no here nor there. Here nor there are part of the things you're solving for, and, well... To take what Gell-Mann said yesterday as an example, I thought perhaps he had some way out of that. If you could show, let's say, how one part of a system could be used to measure the other part, without introducing a space-time structure after you, maybe you'd have a way out of this problem, but at least you've got to deal with the problem, and he clearly hadn't, because he has an underlying space-time structure. And if you give the background in space-time, there's no problem, but you haven't solved the problem either. You've just debated that there's a problem. So again, that's a question we can learn from this.

55:00 Difficulty which held Einstein up for two and a half years. So it's not a trivial problem. And again, I think many people who study general relativity today don't understand that problem. But there's still a third problem, which I call the no metric, no nothing point of view. On the basis of, again on the quote from Einstein, on the basis of general theory of relativity, space, as opposed to what fills space, has no separate existence. If we imagine the gravitational field, that is the function's GIK, to be removed, there does not remain a space of the type of special relativity, but absolutely nothing, also not topological space, by which I mean the manifolds. For the function GIK described... That's a very serious one, that physicists, that the metric is what makes the manifolds. They wouldn't use these barbarisms such as spontaneous compactification. Well, I'm going to challenge that. Let me finish the quote first. For the metric, for the functions GIK describe not only the field, but at the same time also the topological and metrical structural properties of the manifolds, there is no such thing as an empty space, that is a space without a field. Space-time does not claim existence on its own, but only as a structural quality of the field. And in another place, and that's the place I want to read the other quote here, it required a very severe struggle to arrive at the concept of independent and absolute space, indispensable for the development of theories, referring to Newton's. It has required no less generous exertion subsequently to overcome this concept, a process which is by no means as yet completed. And I think again he means that. One hadn't adopted the point of view of no metric, no nothing. And if you look at the way we mathematically formulate the general theory of relativity, you see we have not yet reached the stage where we have overcome that. We start out by introducing a manifold, right? And then we put structures on that manifold. Is that the way you solve the field equation of general relativity? You solve in a patch, right? And then you try to maximally extend. You don't know before you solve the equation what your manifold is. So you're really doing, you know, you're pulling a swindle when you tell students that what you do is first you start with a manifold and then you solve the equations on the manifold. This even the fiber bundle doesn't get around that, because the fiber bundle assumes you have a base manifold. So I say an outstanding problem is how to formulate the theory, you know, the rigorous mathematical formulation of the theory in such a way that you make it clear in that formulation that the manifold, the maximal manifold, whatever criteria you use to define the maximality, is part of the problem of solving these equations.

57:30 You know that there's more than one method. Yes, that doesn't, no, I'm not saying one topology, one metric, but what I'm saying is no metric, no topology. You don't start out with topology and then look for the metric. You look for a local solution to the field equation on a patch, and then you see how far can I build out that patch. Why not? But you know there are all sorts of implications you can make on flat space, and you can get all sorts of complicated solutions. The metric is going to control everything. All we need to do is to ask how far we can go. Oh, I see what you're saying. If I start on Apache, I might not get a unique answer. Yeah, right. Okay. But I don't start out with the topology and then say what metric's compatible with this. That isn't the way we work, is it? Well, I don't know whether you understand the interpretation of arbitrary. It doesn't seem like an unreasonable theory to say that it's artificial. I mean, I think that's the theory we've got, right? I don't think it is, David, because you don't actually operate that way. Lee wants to say something, then Lionel. Yeah, I just think if you put that to me, because no one seems to just hear Einstein has a class that he can't resolve between philosophical legacy and his mathematical legacy. And if the mathematical, the legacy of the machine is some working out of the notion about physics. I remember saying the other day, which is how, I forget how,

1:00:00 All of this is in the same spirit as that. Einstein had the philosophical legacy of Leibniz and Mach that space could be relational, that he had a mathematical legacy of absolute space, and it almost seems to be the end of the alphabet. That's why one almost wants to calculate that his want to go to the discrete theory was a way to resolve this contradiction, although maybe he never mentioned it. I'm not talking here about going to an ultimate theory that surpasses general relativity. I'm just talking about what we actually do in general relativity now. And it seems to me like I once investigated the Curzon metric, right? I start out with a coordinate patch, and then I try to see how, you know, how can, how, what topology is compatible with that patch, that's how we stand it out now, now, now, and that's the way you actually work, and there ought to be a mathematics, you see, I've got this integral over this now, and I can look at all, plug in all different kinds of metrics and then optimizing the... If I'm interested in the spherical symmetric solution, I don't look, I don't say, I don't take manifold by manifold and say, can I put a spherical symmetric on this one, can I put a spherical symmetric on that one. I take a patch and I say, how far can I expand this out? And if I'm smart, I come to the crystal solution. And I'm saying we ought to find a way to formalize that. Maybe, I've speculated, maybe sheath cohomology will do it, but I don't know enough about that yet to say. Okay, that's another good answer to that question. The first thing to do is the intersection of the objects and the sub-manifolds, the actual points. You don't have an a priori topology, the topology results from the... There's no a priori topology.

1:02:30 I thought you had the mathematical stuff, but then it didn't get through, you started with the points of the complex. It's not the points of the complex.