Twistor theory for the understanding of quantum gravity

0:00 The standard approaches to canonical quantization. As I point out, the twistor theory was originally designed for the question of quantum gravity in its own right, but there are various obstacles which have prevented the twistor theory from addressing the question directly so far. So the basic obstacle is the fact that there hasn't been a fully adequate twistor construction before the Delaware system. Twister constructions that so far exist work best for self-dual fields, but there are two less satisfactory constructions which exist for general statistics. The first one is the Ambi Twister space construction, and this is a correspondence between a complex spacetime together with a conformal structure, and it's basically complex now that we did it. So I might explain that a bit more later. The second one, which I'll concentrate on first, is the hypersurface twistor construction, so this is a correspondence between initial data sets and complex 3-manifolds, which are called hypersurface twistor states. The second construction is really one that is relevant to canonical conservation, because it is in it elegant, but it's unsatisfactory precisely because there is a force of a hypersurface. And so in the case of canonical quantization, one has something that one has learned to live with already. And what I want to do is, one of the problems with the typical constructions is that they're non-local constructions. They're making correspondence between space-time and a space which consists of sub-manifolds of space-time. And as a result, this technically can be quite difficult to work with.

2:30 I can't actually offer you any dramatic results. I want to at least show you some of the reasons why I'm going to provide a possibility of giving you a new conceptual insight. First of all, I can say that the actual nature of the new insight is going to be of the same form as what we turned earlier on today, in that the twistor construction can provide new coordinates in a gravitational phase space. And as we see from Abbe's talk, and also from Kasai's talk, such new variables can provide dramatically new insights. So I'll start off with just a brief description of the hypersurface system. So hypersurface, if you take an ordinary dimension spacetime, we'll assume it to be analytic for the moment, but if you take a hypersurface-like spacetime, we can construct a hypersurface twistor space, which I'm drawing over here. So this is a three-dimensional complex manifold, so that means it's six real dimensions. And it has referred five real-dimensional sub-manifolds in PN. And the way in which it's defined... One of the points I want to make requires the understanding of this structure, rather than seeing a space with five real-dimensional sub-manifolds. I'll just quickly explain how that comes about. So, what the basic idea is, is that you take the real three-dimensional space-like hypersurface... You analytically extend it, and twistor space is constructed of the space of torsion-null derivatives in that three-complex-dimensional manifold. So this space turns out to be three-complex dimensions. The reason why there are torsion-null derivatives in this complex manifold,

5:00 well, in the complexified hypersurface, is that the torsion encodes the extrinsic curvature. And this is completely natural. So this means that we encode the entire initial data set. This is a complexification of the free matrix. When the full manifold is self-cure, it means the intersection of a free manifold, of a free surface, with the totally null free planes, the crystal planes that you have in self-cure space-time. So that's the motivation for this torsion. So that's the analogy it is in, with respect to the torsion connection, as opposed to a... And so there's a real five-dimensional subspace that's obtained from those complex knowledge reducers that intersect the real flight. And this divides the crystal space into two halves. But as you go further away from this real part here, you come against the limit of analytic extension of the space-like hyper-surface. The thing gets cut off by singularity both on top and underneath. So that's the basic, that's the way in which the hyper surface crystal space gets divided. And just to mention some important preliminary results concerning the hyper surface crystal space. First of all, the hyper surface crystal space is a complex manifold together with the location of the real hyper surface that determines the conformal initial data set. There are certain holomorphic two-forms, that is, it's not V bar closed, but it's holomorphic, I mean, a nought two-form, I think, and the constraint equations can be written very simply on this two-form, just a closed condition, but that's, the simplicity of this form of constraints is quite deceptive in such a linear equation, but there are some interoperability conditions. So the first point I want to make...

7:30 The first reason why this may provide insight into canonical quantization is because Abbe, earlier on, mentioned that one needed a polarization on the phase space. So polarization is like complex fractions or whatever. And this is what we'll define in the wave function. This is what we use to distinguish general functions on the phase space. This is what we use to distinguish the wave function out of all the functions of the wave on the space base. So in regular quantum field theory you take the Fourier transform and you find that you get a function the field equations imply that the Fourier transform is the force from the light momentum light tone you just have a switch of the wave equation and then The field is positive frequency if the wave function was caused by a top-like current and negative frequency if it was caused by a bottom-like current. Wave functions are distinguished by the fact that they depend only on the positive frequency part of the wave function. This is rather essential physically. It means that the wave function does depend on the unphysical negative energy state. It's a physically motivated criterion. Now, there's a similar description of positive and negative efficiency on crystal space, and so you can take the solution of the wave equation and you can transform it to, it turns out to be a cohomology class, but it's just, say, an object on crystal space. Now, in the fact case, this real hypersurface that I showed you before cuts the crystal space into two parts, and it's... So this Pn here is the boundary of the top part of the twistor state.

10:00 And so the original field was positive frequency extended over the entirety of the top part, and negative frequency extended over the entirety of the bottom part. So what I wanted to say in this connection was that this notion provides the definition of a positive frequency initial data set. So you can define initial data set because you have a pre-metric and an extrinsic curvature. If the corresponding hypersurface crystal space, before I said that it gets cut off due to difficulties in analytically extending a space like hypersurface, it gets cut off right about here, but if it can be extended in such a way that this thing, the top side of this, the top half is only had boundary of this real side, Px, then that would, that provides a definition of positive frequency which... The initial data set, which coincides with all the conventional definitions in linearized theory and those based on null data, characteristic data on null hyperspace. I think it probably is. Well, you might be able to, but in general, it is complex. Well, I suppose you can add the left-hand side, and, well, you can have, I think it has to be complex. A slight difficulty with this is that it's not obviously a polarisation in the conventional sense, unless this is defining a sub-manifold of the phase space, not a complex structure of the phase space, so this isn't quite satisfactory as it stands, but it nevertheless provides a route of investigation for the positive frequency, probably really required for something that's required to be understood for quantum gravity at some level if you need to be understood anyway. I also wanted to say a little bit about

12:30 But there's two other points that I wanted to raise. These are perhaps more easily illustrated with respect to the second construction that I had at the beginning. So this construction is a construction whereby you start off with your original spacetime and you can construct the space of, again you complexify, so everything here is now complex and polymorphic. I mean, obviously, you can do, but the remarkable thing is that just knowing this space of complex analogy of physics as a complex manifold is sufficient to rebuild the original spacetime together with its conformal structure. So, furthermore, the correspondence is stable under small deformations of either the complex structure of the space of complex analogy of physics or the matrix on the spacetime. So the basic idea is to reconstruct the spacetime. Well, I should say the correspondence. So we have a light ray in spacetime that goes to a point in the space of complex gravity physics by definition. A point in spacetime is represented in the space of complex gravity physics by the entire light code of light rays through that point. So this Qx is that light-tone. It's actually a quadrant, and it's dimorphic to S2 cross S2, or bicholomorphic to S2 cross S2. So you can just see this by writing down P squared and V squared equal zero in the tangent space. So in the complex, it's 50. Now, this is a compact submanifold for this large space. There are some very powerful theorems developed by Kodaro and Spencer to study how many such compact sub-manifolds you have in the space of complex largely physics and using index theorem or some other paraphernalia you can show that the space of these sub-manifolds is precisely four-dimensional. So you can reconstruct spacetime just with the space of these compact sub-manifolds.

15:00 And you then reconstruct the conformal structure, because if you have two points in spacetime whose corresponding quadrics intersect at a point, that means that they're now connected. So you can reconstruct all the molecules in it. So it's quite a remarkable construction, but you can just tell from the topology aspects of this space, really, that you need to know that there's one quadric here. If there's one project there with the right normal bundle, then you have the whole space part. So this point here gets identified as the space of nanopneumatism through that point, the light cone of that point. And on the other side, that's a compact sub-manifold. They're rigid, you can't put a dent in them. It's because the complex structure of the sphere is unique. There's only one part. It's because of polymorphic rigidity. It's like solutions of elliptic equations usually, in the same way that the equations of holomorphia are elliptic equations, and so you get this kind of rigidity. So, just as a little comment, it's only just in the last couple of months that we've managed to actually articulate the field equations in terms of structures on the space of mathematics. I won't go into it though, because it's a bit technical. I also want to say that in terms of concrete functions, the correspondence can be expressed by taking your full metric to, well, if you cover the space of complex algebraic physics by three open sets, three sets is minimal, then you can glue it together by means of patching functions and those determine the space of complex algebraic physics as a complex manifold, and then the correspondence is between four metrics.

17:30 So you can think of these as new coordinates on the gravitational phase space. So, well there's, this of course has its, well, if you take into account the gauge freedom, so gauge equivalence classes of metrics on space time, one to one corresponds to the gauge equivalence class of these over here, on these. There's some further functional equations that these P's must satisfy if you're going to impose the field equations, but I didn't want to write that. Well, I suppose if the metric is singular, then algebraic physics will become badly behaved in the neighborhood of that singularity. As such, you might expect some peculiar regions. If the metric is singular at a point, the quadrants as they aim towards that point will jump in some way. They'll have some singularity. It won't be easy to read off from a patching pattern. No, because the quadrants can still jump even when the complex manifold is perfectly regular. They can still behave in a peculiar way. I just want to make two points about how this can provide sort of new perspectives and gives you a new way of looking at things.

20:00 One of them is probably one of the most familiar to people who have listened to Roger over the years, although it's not one that he's really pointed to or brought up recently, so I don't know. So the first point is that in conventional approaches to quantum gravity you send a metric into an operator on some Hilbert space and he goes to T-Hack. And this has the effect of smearing components of the metric. And so this gives us a smeared light code, whereas the points of x remain well defined. Now you might regard this as an unsatisfactory... well, I suppose Roger was just pointing out that there's an alternative to that viewpoint, which is if you're using these patching functions as the variables. Strictly speaking to this argument, I should be using the d-bar operator on the manifold as a variable, using the patching functions as the variables, then what happens is that these patching functions become smeared out, and the locations of these quadrics in the space and complex analysis is no longer a well-defined... the actual quadrics themselves will be subject to... If you're working with a deep R operator, the equation for the project, the equation would be a holomorphic submanifold would be smeared. However, the points of the space would still be well defined. So the picture you'd be left with would be one of having well defined null directions, but the space-time events themselves... Thank you very much for your time, and I look forward to hearing from you in the future.

22:30 Yes, I sort of shifted halfway through from a hypersurface-based construction to a global construction, and so therefore this would require a more global notion of quantization. I think that if you quantize using the hypersurface-based construction, you get a good approximation to this kind of idea, although it's not, as you say, it's not clear precisely what that's about. You still have a well-defined light cone in the CompEx3, you have the well-defined light rays in the CompEx3 manifold without the force of the three manifolds being well defined. So the last point I wanted to make was that in the conventional approach, the gauge group is a Diffie-Morrison group of four manifolds. This has entirely disappeared from the description now. The Diffie-Morrison group only appears when you start to label the quadrics inside the space and complexity of the business. And the point is you can specify the space and complexity of the business without mentioning the location of the quadrics inside it. The gage group is now going to be the, right to speak in particular, morphological group of the cross-spacer complex and algebraic physics, but what we have is in some sense a separation of the gage group from motions of the space-time, and so therefore we could think of this as providing in some sense a separation of gage from dynamics, although where the dynamics is going is also sphere, because we're working globally at this point. Well, there's a naturally defined vector bundle on the space of a complex. A global section of that vector bundle provides a vacuum, a conformal factor for its symmetric background.

25:00 So it's a section of a vector bundle on the space of a complex. In general, these are the two forms that I had in the earlier discussion. Yeah, that's right. It's a space-time vector. I think... I haven't really worked this out, but I expect that the translation is of the form of having a large analytic extension of the data on your theme manifold into the complex in certain directions. Thank you. Yeah, well, yeah, there's a spirit moved you. Somebody leave the key with me so I can lock up. It's like the Haydn symphony, a farewell symphony. I didn't make any slides, so I just put these five points I'll try to cover. The lost leader, the structure versus principle theory, the particular part of the mechanics, the other Einstein, and three lessons from general logic. It will be ready. If anyone wants copies of it, I made some copies of the paper I put in Thailand in the month of 50 years, 50 years of study, which covers part of what I will say, so don't feel alarmed by the size of those names.

27:30 Many people in the generation that developed quantum mechanics looked upon Einstein as somehow an apostate from his own cause, because they felt he had introduced them. The idea of probability into quantum theory, and then somehow he deserted, or turned reactionary in his old age and refused to follow up the consequences of what he himself had done. And Einstein was very much aware of this, and when he was, when they did that Einstein Plastic Scientist volume that Paul Schilf edited, he drafted a number of replies to the critics, some of which he didn't print, and there are manuscripts of those unprinted replies. And in the draft reply to Born's essay on Einstein's physical theories, in which Born essentially makes this charge against him, Einstein has the following comments. This article, namely Born's article, is a moving hymn to a beloved friend who in his old age, shall we say, meaning a polite way of saying his dotage, he was quite well aware of how he was regarded in much of the Princeton city, who in his old age, shall we say, unfortunately has succumbed to occultism, In one point, however, Born does me an injustice. Namely, when he thinks that I have been untrue to myself in this respect, since earlier I availed myself of statistical methods. In truth, I never believed that the foundations of physics could consist of laws of a statistical nature. And this is quite true. And I think one of the reasons why people, I mean, you can agree or disagree with Einstein, but one of the reasons why they misunderstood Einstein and felt that he was somehow betraying his own... The first point I just want to say very briefly is what probability meant to Einstein. For Einstein, probability always was defined in the primary sense by time averages or time ensembles, if you like. In other words, you took some region of phase space and you looked at the fraction of the time that the system, let's say, looked at in time t. You look for time big T, let's say. And the system, let's say, spent a fraction of that time in the primary definition of the probability.

30:00 Now, this least-modular limit, you can see an observable quantity for Einstein. And even more important, it was quite independent of any dynamical theory of the system. You could, in principle, even if you couldn't observe it, you could in principle observe it. Without knowing anything about dynamics of the system, you just had to watch, find some method of ascertaining how long the system spent in that region. And therefore, its independence of dynamics is very important for him, and I think that's the reason why it was the primary definition for him. Now, in fact, he had polemics with Planck about this, because he objected to Planck's definition of the probabilities in the original derivation, Planck's derivation of the black-body radiation formula. And Planck takes the number of complexions as proportional to the probability. And Einstein said, well, how do you know the connections are equally probable? If you don't know that, the number of connections may not even do the probability. That's just an assumption. And Einstein felt, until you could somehow connect it up with this definition or something equivalent, that there was no justification at all for what Planck was doing, and they argued back and forth about that. Now, of course, he did indeed assume what we would now call an ergodic hypothesis, but of course this is almost a decade before the Ehrenfest's article in the ergodic terminology became commonplace. In his early fiscal papers, rediscovering the foundations of fiscal mechanics. And so he did essentially, again, he used hardly anachronistic language, assumed that time averages are equal to ensemble averages. And then he did many things very much in the Gibbs style. But all in all, he was remarkably consistent in all of his later, whenever he discusses the foundations of fiscal physics, in his lecture notes, in the asides, in letters and so forth, this is always the primary definition. He was always based on something like the system or the At the time, evolution of the system was governed by some laws, and you just see how those laws determine this average. So there was nothing in the next... Pardon me? You had to have determinism behind all of this. You had to have determinism behind that, right. Yes, I'm saying that that was... It was a classic law. Exactly. So whatever you think of the final outcome, Einstein was in no sense a traitor to his own fundamental views. People just hadn't understood what his fundamental views were. Okay, so much for the first point. Discussing Einstein's particular quantum mechanics, or what you might call his Unbehagen, his...

32:30 Unhappiness or uneasiness with quantum mechanics. You have to first look into what quantum phenomena meant to Einstein. You have to look into, again, the prehistory of what. And let me start out by saying that Einstein's first attempt at a unified field theory took place long before general relativity was formulated. It took place in 1909. He was looking for a unified field theory of the electron and the light quantum at that time. I'll come back to that in a moment. But you've got to understand that background, that unified field theory and Explanations of the quantum phenomena were for Einstein connected from the very beginning, even before general relativity got into the story. Let me start by giving you a definition of two types of theories which Einstein gave in 1919. He distinguished between principal theories and constructive theories. He says we can distinguish various kinds of theories in physics. Most of them are constructive. They attempt to build up a picture of the more complex phenomena out of the materials of a relatively simple formal scheme from which they start out, and the primary example is the kinetic theory of gases, which seeks to reduce mechanical, thermal, and diffusional processes to movements of molecules, that is, to build them up out of the hypothesis of molecular motions. And I want to emphasize this sentence. When we say that we have succeeded in understanding Understanding is his emphasis, not mine. When we say that we have succeeded in understanding a group of natural processes, we invariably mean that a constructive theory has been found which covers the processes in question. So understanding, Feinstein meant, at least at this time, constructive theory. Along with this most important class of theories, there exists a second, which I will call principle theories, or theories of principles. These employ the analytic, not the synthetic method. The elements which form their basis and starting point are not hypothetically constructed but empirically discovered ones, general characteristics of natural processes, principles that give rise to mathematically formulated criteria which the separate processes or the theoretical representation of them have to satisfy. And of course the primary example of this is thermodynamics. The science of thermodynamics seeks by analytical means to deduce necessary conditions which separate events have to satisfy from the universally experienced fact that perpetual motion is impossible. Another way, you look at the world, and by observing the phenomena of the world, you can, if you're clever enough, draw certain principles, and these principles themselves do not constitute explanations in Einstein's sense, they're not constructive explanations, they're like traffic rules.

35:00 They tell you that if you're going to make a constructive explanation, you better obey these traffic rules, but they do not themselves constitute explanations, and the constructive theories are like driving your car through the streets along a certain path, obeying those traffic rules. And again, taking the example of thermodynamics and statistical mechanics, as far as I told you, I have a great theory of statistical mechanics that explains that all the properties of this material, just one little problem with it, doesn't obey conservation of energy. Well, you know what you're going to tell me. What can I do with that theory? If you violate the principles, you're lost. But on the contrary, the role of the principles is to guide you in the search for the constructive theory. And then he summarizes, the advantages of constructive theory are completeness, adaptability, and clearness. Those are the principle theory, our logical perfection, and security of the foundations. You see, if you really observe correctly and you've got your principles, these are the things you can be most certain of. And Einstein says someplace or other, I think in the order of Bargatlo notes, for the benefit of skeptics, let me point out that I believe that the laws of thermodynamics, within their limits of applicability, will never be surpassed. So he wasn't a skeptic of everything, yes. He's quite consistent in that. And let me read the lessons before I do, because then we'll see the application in a moment. The theory of relativity belongs to the latter class, namely the theory of principle, of course. And so, for example, if you look at the beginning of the 1905 paper, what does he say about the principle of relativity? He says, the failure of all attempts to detect the motion of the earth through the ether or the hypothetical ether. Some phrase like that. In other words, it's the failure of a number of experiments. It's the negative principle, just like the failure of perpetual motion attempts of the first and second kind of regions of the first and second law of thermodynamics. The failure of attempts to detect the motion of the earth through the hypothetical light medium. That's the way he would justify it under physics, but that's not the way he actually... What do you mean by, assuming that you're privy to his heart, what do you mean? We're talking about special relativity. Well, that's what I'm denying. It was not obvious in a priori to me. Absolutely. This is quite different from saying the Maxwell-Mohler experiment was crucial, as some people say.

37:30 Because I think by the time he knew about the Maxwell-Mohler experiment, he knew about so many others, that it was one among the list. We now have evidence, for example, that as early as 1899 he read a paper by Wilhelm Wien. Which lists 13 experiments bearing on the question of failure attempts to detect motion through the ether, and the Maximoli experiment is the 13th. So that shows two things. First of all, that he did know about the Maximoli experiment as early as 1899, and secondly, that he knew about it a lot more. And the fact that he didn't single it out in the 1905 paper is not surprising, because there was such a wealth of evidence. But it was that wealth of evidence that constituted the warrant for the relativity principle. And I'll give you a couple of quotes to hammer this in. But again, for example, why do we accept Maxwell's theory when we adopt the relativity theory and we reject or we modify Newton's mechanics? Because when we take the criteria of the relativity theory, we see Maxwell's theory obeys that criteria. When we see Newtonian mechanics, we see it doesn't, at least when you combine it with the life principles, right? If you accept both principles, the life principle and the relativity principle, you cannot accept Newtonian. You have to modify it and bring it to the course. So he didn't do it in the standard way, Planck did it in the standard way, and Einstein pretty soon adopted Planck's way. Well, phenomenological is not in the sense of the ephemerality of phenomenological theories today. It's something which if you see no exceptions to in the world. I mean, there's always, you know, there's always some generalization involved. You can never obviously see every experiment. And if tomorrow, if somebody had been clever enough to devise an experiment which detected motion through the ether, Einstein would have given up. In fact, he says at one point, I think speaking about himself, he uses the personal one. But he says that, you know, the Lorentz's theory of the electron was so impressive and successful, that if it weren't for its failure to explain the maximology of the electron except by an ad hoc hypothesis, because he considered the contraction hypothesis within the framework of Lorentz's theory ad hoc, that one would have given up the relativity principle, you know, however much, however painful it was. Einstein was not a, at least an unalloyed rationalist. In fact, he said something much later in life, of course, that

40:00 It's very important for a scientist to utilize philosophy from a philosophical point of view, but he must be unprincipled about it. Yes, the Erasmus in some respects compares to none of the others. You know, you feel your way through. You don't stick to a philosophy dogmatically. You use each element of a philosophy to guide you in this. I don't think so any more than, let's say, that the velocity of sound on the earth, you know, picks out a privileged frame of reference, violates the Newtonian relative principle. Obviously, that medium picks out a particular inertial frame, namely the inertial frame in which that medium is at rest. The raw theory of physics then merely says, if you go to another frame, you have to take the medium with you, if you want to consider all three of these things. No, I understand. Yeah, of course. Yeah, I think that would have been, again, trying to read Einstein's mind, I think that would have been his answer. I mean, there's another answer, too, of course, if you want to go to a deeper level, if you want to go to a level of general relativity and look upon... You know, class-based solutions to that. You could say that the equations of the theory have to be generally covered in a particular solution. Obviously, one doesn't have to have an additional symmetry. He was appealing to empirical phenomena, in a sense, prior to the constructive attempt. Obviously, in practice, you know, you go back and forth. And he says he was led to this point because he despaired of constructive attempts. And we have a lot of evidence that he was primed for constructive theories for a long time before he adopted this principle. Now, you might think these quotes from 1919, you know, are later rationalizations, but recently we have found letters to Sommerfeld that have just been uncovered in the last few years which indicate that he had almost identical views a decade earlier, so very close to the time in which his relativity was first formulated in 1912. We have his words, and I'm willing to believe that, you know, in those two or three years he didn't change his viewpoint that much. He was probably just expressing clearly and openly. To a fellow physicist and, you know, in 1905 he wasn't even in correspondence with people like Sommerfeld, so there wasn't really no way to correspond with him, not even Malay, but they were married by that time, so he wasn't writing letters to her. Well, let me read you a couple of quotes from what he said in 1907, 1908. Here's what he wrote in 1907 in trying to describe his own theory. This is from a published paper, not from a private letter.

42:30 Talking about the theory of the relativity theory. The word by that time, the word was just about coming into use at the time. Planck called it the relative theory. Einstein always preferred the relativity principle. His first review article was called on the relativity principle and the consequences that can be drawn from it. But Ehrenfest seems to be the first one to use the term, no, was it Ehrenfest? No, Bucherer used it. And then Ehrenfest picked it up and then Einstein picked it up from Ehrenfest. But it wasn't by no means standard terminology, but let's just use it anachronistically. In speaking about the relativity theory, Einstein says, one is in no way dealing here with a system, in quotes, in which the individual laws would implicitly be contained and could be found merely by deduction therefrom, but only with a principle that, in a way similar to the second law of feminine animus, permits the reduction of certain laws to others. So I think that's very close to the principle of constructive distinction, even though not expressed in those words. A physical theory can only be satisfactory if its structures are composed of elementary foundations. The theory of relativity is just as little ultimately satisfactory as, for example, classical thermodynamics was before Boltzmann had interpreted the entropy as probability. The early Einsteinism somehow regarded the theory of relativity as a great advance in the sense that it gave you ultimate explanations of things. You can see from this that he says it didn't. It's ultimately unsatisfactory because you haven't got the thing that underlies it in the way, let's say, that the Boltzmann principle underlies the second law of thermodynamics. So he was always looking for the constructive theory. And there's a lot of, I could put it this way, and say that theories of principle are More secure, because of the wealth of empirical evidence that goes into the principles, if you've done your job right, but they're less satisfying. And to show you what he meant by satisfying, let me again read some things he wrote, which I think show me that, as I once put it, Einstein really put the center of his emotional life in his work, and therefore there's a lot of emotion attached to the way he talks about construction of theories.

45:00 And I'll give you that play of it. Man tries, this is what he wrote in the Tribute to Planck in 1918, but clearly applies just as well to himself. Man tries to make for himself, in the fashion that suits him best, a simplified and an intelligent picture of the world. He then tries to some extent to substitute this cosmos of his for the world of experience and thus to overcome it, the world of experience. That is what the painter, the poet, the speculative philosopher, and the natural scientists do, each in his own fashion. Each makes this cosmos and its construction the pivot of his emotional life in order to find in this way the peace and security which you cannot find in the narrow whirlpool of personal experience. We call those highly emotionally charged words, and not many of us can do that. We try, but usually our families and friends succeed in diverting us, to some extent, from the path. And then in 1932 he wrote a similar line, Already completed is the most objective and personal thing that we humans know. Science has something coming into being as a goal, however, is just as subjectively psychologically conditioned as all other human endeavors. This is so much the case that the question of the goal and meaning of science will receive quite different answers at different times and from different personalities. To be sure, all are agreed that science must establish a connection between facts of experience, such that, on the basis of experienced facts, we are enabled to predict other such facts. According to the view of many positivists, the most complete possible solution of this task is the only goal of science. I do not believe, however, that so primitive an ideal would really permit the kindling to a high degree of that researcher's passion from which really great accomplishments arise. A stronger but also more obscure drive lies behind the tireless exertions tied to such achievements.

47:30 I find the idea that there should not be laws for being, but only laws for probabilities, simply monstrous, a nauseatingly indirect description. But again, you see what I mean? This is a very emotional thing. For Einstein to grasp, to comprehend the world is not just an intellectual experience, it's an emotional experience, which he regards as necessary, the drive for that is necessary for really great accomplishments. And we'll reacquire it with Einstein, in this respect anyway. So you see, for Einstein, in a sense, the theory of relativity was a last resort. It was the failure of the constructive attempts that led him to the special theory of relativity. Robert will come to that. He says... All my attempts, however, to adopt the theoretical foundations of physics to this new type of knowledge failed completely. It was as if the ground had been pulled out from under one, with no firm foundation to be seen anywhere upon which one could have built. Again, I put your attention to the emotional charge attached to it. And then he goes on. Reflections of this type made it clear to me as long ago as shortly after 1900, that is shortly after Planck's trailblazing work, that neither mechanics nor electrodynamics, which you remember were the two competing theories for world views on the mechanical world picture and the electrodynamic world picture, which is one of the challenges, but Einstein knew by that time, he says, that neither mechanics nor electrodynamics could, except in limiting cases, claim exact validity. By and by, I despaired of the possibility of discovering the true laws by means of constructive efforts, and now you understand what it means by constructive efforts, based on known facts. The longer and more despairingly I tried, the more I came to the conviction that only the discovery of a universal, formal principle could lead us to assured results. But still more, that only can lead us to assured results, but not to satisfying constructive theory. It's a way to make progress and give yourself a guideline. So his approach to the quantum hypothesis, I could go on about the relativity theory, but we're not going to talk about that, we're going to talk about quantum. I maintain he approached quantum theory in a very similar spirit. He never regarded the

50:00 work he had done on what he called the quantum hypothesis in 1905 as an explanation. It was not a constructive theory. It was just a way of attempting partially to describe what was going on. And set the problem, in other words, in a framework in which you could then apply constructive efforts. And in 1911, in his report at the first Solvay Congress, for example, he says, We have all agreed that the so-called quantum theory of today is indeed a useful tool, but no theory in the ordinary meaning of the word. At any rate, not a theory which could now be developed in a coherent manner. On the other hand, it has been proved that classical mechanics As expressed in Lagrange's and Hamilton's equations, no longer can be regarded as a usable system for the theoretical representation of all physical phenomena. So the question arises on the validity of which general principles of physics we may hope to rely in the field of concern to us, that is, quantum phenomena. In the first place, we all agree that we should retain the energy principle. A second principle, to the beauty of which, in my opinion, we absolutely have to adhere, is Boltzmann's definition of entropy by means of probability. The weak, glimmer of theoretical life that we see today over equilibrium states of processes of an oscillatory nature be owed to this principle. And then he goes on to discuss this principle, but I just wanted to give you the flavor of the way he approaches it. So, what Einstein was trying to do is, first of all, formulate a quantum hypothesis and apply it to various phenomena, but this is only a way station on the search towards a constructive theory. It's like the formulation of the problem rather than the solution, and in that sense analogous to the way he looked on the relativity principle as a guide, a sign. Then, now I get to his first attempt at unified field theory, which I mentioned. In spite of the fact that he had earlier flirted with the idea of replacing fields by particles, perhaps it's better to say replacing systems with an infinite number of degrees of freedom with systems having only an infinite number of degrees of freedom, because fields and particles to him, I think, essentially meant that. In spite of the fact that there's indication in the footer with that idea earlier, in fact, his earliest utterances about electromagnetic theory in a letter from 1899 is very much sort of like the Wheeler-Feinman approach, get rid of the fields, the fields are just ways for talking about the interaction between particles, summing up the interaction between particles. And then, you know, he starts in 1805... ...quantum paper by pointing out the formal dissimilarity between the way we treat Maxwell's theory with infinite degrees of freedom and the way statistical mechanics treat systems with infinite degrees of freedom, and he opines maybe this is the reason for the problems we have in electromagnetic theory, you know, we can discover the ultraviolet divergence, of course, and he does in the paper prove that if you take statistical mechanics and Maxwell's theory seriously, you have a perfectly definite answer to the radiation distribution, the Rayleigh-Jeans law, which is obviously nonsense, excuse me.

52:30 So, at that time, he seemed to feel, well, maybe the trouble is we haven't hit another degree of freedom. In other words, he was, to use modern and more highfalutin language, he was tending towards getting rid of the field and replacing everything with a particle ontology. Particles are everything, or systems are finite, and there's just a number of degrees of freedom in everything. Then you've got to explain why it appears like there are fields in the world. Oh, yes, I'm coming. No, but it came in 1909, that's what I'm saying. By 1909, there were diverse fields. And he's now trying to explain the particles as somehow structures in the field. And let me just read you a couple of words on that to give you the flavor of that. He never published a full theory, but he did give a few hints as to what he had in mind. The basic problem was that he felt that the quantum electric charge remained a stranger, a friendling to Maxwell's theory. Just to put it in my hand, how could you explain this? As you see, obviously, he didn't like the idea of simply postulating such structures. You had to explain them in his sense. And he opined in 1909 that the next phase in the development of theoretical physics will bring us a theory of light which may be regarded as a sort of fusion of the undulatory and emission theories of light. This is the first hint of what this lady came for with the wave particle. But this mentions that what he really needed was some sort of modification of the wave theory which would give him structures which could be interpreted as ...explaining the particle-like properties of both radiation and matter in the sense of... Yes. Me, not for me. Gustav Me.

55:00 Slightly later, but Me was following up the electromagnetic program. You know what I mean by electromagnetic program. All attempts to derive the electromagnetic equation from mechanical principles have failed. Let's play the game the other way around. Let's assume that somehow the electromagnetic field is fundamental, and let's try to explain mechanical principles. Electromagnetic, you know, to assume that the electromagnetic field quantities are the basic things, and then from them explain the construct electrons and so forth and so on. In a sense, this is much closer to Maxwell's original point of view, but that point of view of Maxwell's didn't have much influence in Germany, and I'm not sure that Mie was directly influenced by it. But at any rate, Mie was continuing this electromagnetic field program, which had been first formulated by Dean around 1900. But Einstein, by the way, Einstein was well aware of the Mie program and had discussed it in the teens. I'll get back to that in a minute. But he had his own ideas, which were rather different. So they were competing ideas at that time. Me published a full theory, Einstein never got to that point. He just hints at some speculations in his, a little bit more in his private correspondence, but he never did anything with it. But he did state what he thought the idea was. So you're probably incorrect then when he begins to talk about unified field theory by saying the first unified field theory was developed by me. No, he's not. As usual with Einstein. Well, I mean, you could say Maxwell was trying to do it too, as I indicated. Let's say the first one in this century, which certainly the first one which was attempting to explain the light quantum as well as the electron, and Einstein, indeed, I was about to read, he anticipated, because of the fact that he knew about the fine structure constant, which involved the E and the H in the same, you know, that you could make a dimensionless quantity out of that, he was a little bit bothered by the fact that it wasn't the order of one, but the order of a hundred, but the fact that two wasn't that bad. In fact, you could form that E squared over Hc was a dimensionless. Yeah. Oh, yeah. I think Planck even observed it first, but Einstein drew the following... Planck, of course, invented the Planck way. Yeah, yeah. Exactly. Yeah. Well, I mean, if you play around with dimensions, it doesn't require great genius to form that point. If you didn't notice that dimension, the question was what you make out of it. But Einstein... But he had units with E rather than H for it.

57:30 Well, Einstein certainly did, and he says it's supposed to be... 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 the truth that would come out of one field. We still fail today. So I wrote this paper last time on the quantum math, some of it. He tried to investigate essentially whether he could get relativistic invariant nonlinear generalization of Maxwell to say it would have some sort of stable structures in it, either singularities or, you know, stable non-dissipated conservation energies. I have not succeeded in finding a system of equations which I could see was suited to the construction of the elemental quantum of electricity, the electron that is, and the light quantum. The manifolds of possibilities do not seem to be so large, however, that one need draw back in fright from the task.