Round Table Discussion I

0:00 There are so many different teaching schedules to juggle for all different countries. Already I can tell you that we can't possibly do it in September. This is the third year since the teaching year started. July and August, I understand you can go in the sense of anybody's teaching schedule, but I don't think anyone else can do it. And so the proposal that I want to put to you is that we take a working game to be something like the first week of June, three years from now. And I'd like to know if anyone has anything to say, or if there was something to proceed on that assumption. Another announcement? One more point, in fact, it's a second one. We would be glad to communicate with us by electronic media, and some of you, but we are three or four up to now, we have electronic media business, and everyone who has a bitnet, please, you send it to Josh. Oh no, it's not John My bitnet number is on the conference program and if you have no bitnet please have a bitnet and it's easier to write to you not only because it's electronic but because when you write bitnet you don't write the same way you just telex and it's easier and please do that Even John has a bit now, from time to time. I'll tell you, just one more point, it's possible to open that. Ah, it will be a problem. Ah, no, she said no.

2:30 Can I call the meeting to order, please? Well, this transit is supposed to be Around People. And the title of Around People is not made. It has been decided by... Most of the people present will remember my name from the time I was Secretary of the GRG International Organization, if not from some of my work in the field of theoretical physics. However, for years now, I have shifted my main interest from physics to metaphysics, just with people like Whitehead, who have been already mentioned, and others did. This is illustrated by the title I gave to my last lecture in my chair, namely Physical and Metaphysical Time, actually held in general. Indeed, one main interest during my career has been the problem of time, and numerous publications refer to it. For instance, This is a book written in Spanish, there are two copies here, you can take one or the other. Another item has been what might be called the philosophy of GRG. GRG is a shorthand for both the French gravitation et relativité générale and the English general relativity and gravitation. I invented it when Professor Tanula and Lishnerovitz discussed with me the possibility to create an international committee, which precisely was to become the GRG committee at Royaumeau, and was later on completed by the GRG society, perhaps you all remember, I don't know, both of which I became secretary during year. The reason was that I had planned the Golden Jubilee Conference, now called GR1, to be held in Bern in 1955,

5:00 where Einstein had written his first paper, or papers, while Marie-Antoinette Tonla and André Lichnerowitz planned a similar conference in France, but agreed to postponate in order to let Bale have the privilege of holding the said GR1 conference. Wolfgang Pauli was asked to preside owing to his great scientific prestige and in order to have Jurek also share in the event since Einstein had taught there both at the university and at the Federal Institute of Technology. I have written the history of the GR conferences in the book, Albert Einstein, His Influence on Physics, Philosophy and Politics, published by Eichenberg and Sexwell, under the title Birth and Role of the GRG organization and so on. There, I have written that it was never decided which was GR1, the Golden Jubilee Conference at Bairn, or the conference held in 1959 at Chapel Hill. Personally, I would be in favor of Bairn because Chapel Hill had not had the international character which was that of all the other GRN. conferences. American colleagues may disagree. There have been several phases or stages in the development of GRG theories. Of course, the succession of the special and the general theories of relativity is known to everybody. To my mind, we should add another main and third stage, which refers to what I would call super-general relativity, beginning with five-dimensional, arriving in our days at ten-dimensional geometrical conceptualization. One of my contentions is that Minkowski's space-time does not generalize space, but rather it generalizes time. Herman Bondi, among others, agrees with me on that.

7:30 I had a long discussion with him about this whole problem. In our effect, I developed my theory of super-time. It leads to very important metaphysical consequences, especially it can be shown that each new physical theory amounts to a new conceptualization of time. I have here copies of various publications on this matter, and also on some other matter in case some of you would be interested. The phase on general relativity coincides with the attempts dear to Einstein to unify the various interactions known. Now, to me, it is questionable whether gravitation is an interaction comparable with the other ordinary interactions, electromagnetic strong and weak, because the very fact implied in the idea of gravitation is both universal, that is applicable to all systems of the world, and identifiable with the world as a whole, whereas the other interactions are not. Therefore, even though gravitons are formally definable according to Powering Fiat and to Tundra, I am still hesitating about the possible final success of a grand unification. GRG poses several alternatives. The first one is that of the physical problem versus the mathematical problem. Indeed, the physical problem is that of the question whether the world is made of elements which interact. The mathematical problem is that of the question whether God is a mere geometer when considered a demiurge creating the world. Therefore, GRG has been from the beginning object of the reflection and in the hands of both physicists and mathematicians. And for years before Second World War,

10:00 practically only in the hands of mathematicians Until, I may rely here upon the opinion uttered by von Lauer in his concluding speech, until GR1 at Bairn broke the spell. Another alternative arose, which can be sensed to be that of the macro cosmos versus the micro cosmos. In a very simplified view, the macrocosmos is concerned by GRG, the microcosmos is concerned by Qt, for quantum theory. Grossly speaking, the former leads to astrophysics, the latter to the physics of so-called elementary particles. The first of these physics is connected with considerable observational difficulty. The second one is connected with considerable experimental difficulty. In my opinion, the difference between observation and experiment has not been discussed adequately by epistemologists up to now. By the way, both the observations and the experiments involved are connected with huge costs, both financial and of personnel of high quality. A question arises, who supports the research? One answer is the big laboratories. I was very much involved in the creation of CERN in Geneva, which is perhaps the biggest laboratory of the world. The connection between the astrophysical problematics and the problematics of elementary particles seems to lead inevitably to the problem of Cosmo Garnier. In that respect, let me remind that this problem goes back to Canon LeMay, who, with his Hypothèse de l'atome primitif, was the first to lay down the foundation of a theory called today the Big Bang, even though he did not give it that length. Between scientists in the field of the macrocosmos and such in the field of the microcosmos,

12:30 There has been during years a kind of mutual ignorance. I even remember my colleague in Bayern, the late Houtermanns, exclaiming in the 50s that relativists were mathematicians, not physicists. Though he supported me, indeed, when I started organizing the Golden Jubilee Conference in 55. As I said before, GR1 was in that respect a sensation, for it opened the eyes of both quantum theorists and subatomic physicists, although Niels Bohr had told me on the telephone that he would not come personally to that conference. it. Yet this negative answer of his was given before the death of Einstein, who had approved of the conference, but had in the meantime said that owing to bad health, he would not attend. I consider it not impossible that Bohr preferred not to be present on the ground of the divergences of interpretation in understanding quantum theory. Also, these divergences have been a main problem of past years. I have contributed to its solution with a paper published in the Lundegfest Trift, explaining especially that GRG implies a determinism which is stronger than even the so-called Such divergences still constitute a problem today, especially in Italy and in France too, though to my mind they do belong already to the history of physics. This for my introduction. Our round table, consequently, did by chance or rather by decision of the organizer of this conference, Professor Eisenstedt, our roundtable will be entertained by four speakers whose scientific activities root in some of the important fields which I have sketched, though they may diverge pretty much from one another. They will cover four domains which

15:00 I have outlined in my introduction, and this, I hope, will satisfy Professor Eisenstedt's One, what will be called a post-Newtonian period, for which Peter Harvass from Temple University, Philadelphia, will be responsible. Second, the special, shall I say, technical and financial problem of how to support what has by and by become known under the name of big science, more particular from the United States, of which Joshua Goldberg from Syracuse University will be the referee. Third, the huge complex of the mathematical implications of GRG, about which the most conspicuous specialists will tell us what it means, namely Andrzej Jnirowicz from the Collège de France in Paris. And finally, the problematics of a unification of geometrodynamics, or however you want to call that with quantum physics, with Peter Bergman from New York University, whose competence in that respect is known to everybody. And now let me ask Peter Harvats to tell us what he has to say on his particular film. What I'm going to talk about is mainly the problem of motion, in particular the application of special relativistic methods in the problem little bit on special relativistic alternatives to the general theory of activity roughly from 1950 to 1662 there's a decisive break really around 1950 before the war almost all the work and the problem of motion was done in what's become known as the slow approximation method, and which culminated in the famous Einstein and Feldhoffman paper 1938. After the war, Einstein and Infeld still published one paper in 1949, which was simply a different derivation of the EIH equations. Levi-Civita, who had worked on that problem, was then Eddington,

17:30 dead. So, none of the major figures of that period continued, except Infield about Humadi had more to say. The only, all of these people, as I said, worked on the slow approximation method, the only person who was familiar with special relativistic methods was Marion Mattison, about whom you heard a lot this afternoon, but who had died in 1940, so he had no further role to play in what I'm going to say. Now, Infeld, who had continued to work on this, and who had described his own work with Einstein and Hoffman as as difficult as swimming the Atlantic Ocean, had said, had written next step would be as difficult as interplanetary travel. But, he said, it did not seem to me possible that anyone would ever want to take the third step. In fact, my student and I later proved that it will never become necessary to take it. As I understand it, what he thought, and even that isn't quite correct, is that to describe the motion of the planets in the solar system he didn't need any further refinements he also at that point did not believe in the existence of gravitational radiation and therefore he did not see any need to use methods which were more appropriate for a possible calculation of gravitational radiation methods. In this respect actually he was rather an obstacle for the development of the problem of motion. He did not want to include the problem of motion in the Warsaw Conference which was and he had written a book with his student Lebansky who was interested in different methods

20:00 but before the manuscript was completed Lebansky had left for the United States and he told me later that Infeld had removed any mention of other approximation methods in this law approximation from the manuscript without consulting with him contained any of this. However around 1950 a number of people started working using special relativistic methods. Now I tried very hard to see a common thread in this and I can't find it. Nobody who worked on this had been in Bern, people who worked on this I think mostly didn't even know each other and all of a sudden in the 50s there were several people who started working on this and these different motivations as far as i can tell one of them was brattotti in italy one of them was geisler in germany roy kerr in new zealand and josh rohlberg and i in the united States. We both started working independently. Josh, I think, correct me if I'm wrong, mainly because he decided that post-Post-Newtonian approximations were no way to ever get a handle on gravitational radiation, and later on decided to collaborate. Now, so this was one trend and each of these, in various ways, used special relativistic methods. I, in particular, knew about Matisse's work and made considerable use of it. I don't want to go into any technical details. During the same time, for reasons totally mysterious to me all of a sudden there was interest in special relativistic alternatives to general relativity Bellinfante made a major study of all possible special relativistic linear theories of gravitation which could reproduce the appropriate perihelion motion of Mercury there have been other special relativistic theories which had been developed in the 20s, one by Whitehead,

22:30 about whom we heard this afternoon, and one by Burkhoff. Singh, in 1951, apparently became very interested in Whitehead theory, which is an action-resistant theory, and gave a series of lectures at Maryland about it, and then he and Schild continued working on it in the 50s. The Burkhoff theory was developed further in two different countries, one of them I understand, namely Mexico, because Burkhoff had been in Mexico, and so he had interested some Mexican physicists in it, in particular Baratas and Graf Fernandes, who worked in published papers on this in 1951. The other one was Kustan Hammer in Finland, who, to the best of my knowledge, was completely independent of anybody else, he never showed up at any meetings, I have not met him, and he generalized Berkhoff's theory. So these were alternatives, all of which were found to be unsatisfactory, in particular because Schild showed that there was no satisfactory derivation of the redshift I mean physically consistent derivation of the redshift in any such theories and therefore these things died out shortly thereafter especially relativistic methods using general relativity have continued and work is still going on in them, but the pioneering work on this, as I said, was done between, let's say, 1956 and 1962, actually. Thank you very much, Professor Harvath. The next speaker will be Josh Gordberg, please. At the last meeting, I spoke a little bit about the role of the Air Force in support of General Relativity and some of the history of how that came to be. I did not have many solid references at that time, administrative references, and I tried with the help of Stan Goldberg to get those references, but apparently the Air Force burns its financial data, administrative data,

25:00 Because I have not been able to find anything. So what I propose to do today is to spend most of the time talking about, not about the financial aspect and the support of big science, as was described earlier, but rather to talk specifically about the kind of support that was given and what science came out of that support in particular. The period that we're talking about is 1956 to 1972. This was the period for which there was a group, like Madison Air Force Base, a strong group of research people in general relativity. It began when I went there in 1956 and slowly built up to a sizable group. I left there in 1963 to go to Syracuse University, where I joined Peter Bergman as his colleague. The first thing that happened in 1956 was a phone call from Bryce DeWitt, Bryce and Cecilia DeWitt, who wished to organize an international conference on general relativity at Chapel Hill. The Air Force was very happy to participate in this, gave it direct financial support, and to my recollection also offered some air travel to some of the European participants through the military air transport service. You're a pretty hot airplane. Right. And this was the first conference, international conference, the new generation of relativists, both from Europe and from the United States, were able to participate. It was the first place where we could meet those people who were the names to us for the most part, like Professor Michelangelo and others who were there. Unfortunately,

27:30 I have people from Belgium, or Professor Mercier was not present at that meeting. But Bondi and Gold were there, Rosenfeld was there, Bardman was there, as well as the two Peters over there. But also one of the younger people, there was Ted Newman was present, Pierre Spirani was there, Madame Marguerite, of course Madame Fulman was also there. So it was a very broad spectrum of those people who were very active in the field at that time. I think that many of us would be unhappy if that particular conference is counted out among the international conferences. whether it is number one and a half, or one and three quarters, or whatever number you want to pivot, I think in any accounting of the internationally important events that have occurred in general relativity, that must be included. Because it was immediately, I believe, in my recollection, it was at that conference that Professor Lishnaro would agree that he would host another conference in France in 1959. The Chapel Hill Conference did not have come in 1959, but in January, toward 1957. No, no, that was a minor point. So, following the Chapel Hill Conference, other conferences that were supported financial support because these other conferences were supported by the governments of other governments and therefore the American government could not do anything in that regard. But at the Royal Mon Conference, the Warsaw Conference, and the London Conference in 1965, I believe it was. And all of those conferences, for all of those conferences, military air transport service, lance transport was given to American participants to enable them to go to international interviews.

30:00 But let me focus from now, though, more on the kind of research that was done. I'm going to say that at the beginning I was not alone, but shortly I was joined by a student of Václav Bhavati, Joe Schell. We worked on equations of motion, conservation laws, and became involved in gravitational radiation. shortly after the Royal Monk Conference in the fall of 1959, Valai Kerr joined us, and we began to study exact solutions. Shortly before that, I think it was around 1956, that Felix Pirani widely advertised the petro-classification for relativists. This was something that was quite unknown to us, I think, until Felix wrote his important paper. And so, I think Shell began to study refinements of the petro-classification through the homo-nome group. that while the hetero-classification played a very important role in the construction, and perhaps still does play a very important role in the construction of exact solutions, a role for the hallinimic group in the refined classification has not yet been done. As part of the accomplishments here, of course, Roy, while he was still a member of our group, found the vote-taking solution, which is known as the Kerr Solution. In 1963, both he and I left this group, but in the meantime, we have been joined by a student of Dick Arnowitz, Stuart Fickler, who became the head of the group, and shortly thereafter he was joined by Moshe Carnelli, Jeff Winnicore, Luton Marino, David Robinson spent two years there, at the last two years there, Richard Isaacson, who now is in charge of general relativity at the National Science Foundation, spent a year

32:30 there, and a number of other people who I don't remember, sorry to say. I have sent a copy of what I've crafted here to Jeff, to try to find out more details about what happened after I left. Jeff worked on a broad range of problems with different collaborators for all of these days. With Tambourine, we studied the propagation of the gravitational field out from an inner cylinder. Rather than looking at the propagation in from infinity, we assumed that he had an inner cylinder outside of which he could have an outcome or an out surface extending out to infinity. And it was in this context that they developed the idea of flux linkages. that is relevant to define energy, momentum, and angular momentum. With David Robinson, he tested the positive energy theorem, which was only a conjecture at that time with various examples and test assumptions. In collaboration with Isaacson, he looked for the effects on the age of the universe due to gravitational radiation and in other aspects of the gravitational radiation field. With that glass, he worked on the theory of elastic deformation and general relativistic systems. For him in particular, the Air Force audience was exceedingly cool. During his stay at ARL, Moshe Carnelli continued his work on the equations of motion, although a greater part of his research was concerned of understanding the role of group theory in general relativity. And his latter work resulted in the publication of a book, Group Theory and General Relativity, after he left the Aerospace Research Laboratory. The support program, the external support, that was a brief description of what was in the internal research program. Obviously not everything is just what I can remember myself and what I can do from my files. But at the same time, there was an external support program, which was perhaps the main reason for the program to be in the Air Force in the first place, which is the part of the support of big science that was referred to, although there were quite little at the time and still small potatoes.

35:00 As I've indicated, the first support from ARL was for the Chapel Hill Conference, but at that conference I had a chance to talk with Herman Bondi and Felix Garandli, and shortly thereafter developed the support program at King's College. There were unsolicited proposals received from Jordan in Hamburg, from Jane Yeo in Brussels, and from Rosen in Haifa, among others. The first contracts were left toward the end of 57 or early 58. As I said, I have not been able to get the administrative information, so I can't be presigned. These contracts were written with Syracuse University with Professor Berkman in the United States and with Jordana and with Rosenberg. I had requested that a contract be written with Jane Yeo and Costos. But even though I insisted quite strongly on that, the Air Force refused to do so for political reasons. One source of pleasure for me is that in spite of that refusal, I was able to maintain good relations with J. Young, Rebecca, and Kahane. There was no corresponding hesitation about support to Yorbao, although he had been close to the Nazi government. Personally, I have misgivings about that situation, but because that support, to some extent, helped the students with Hong Kong to new containers, In the next year, the support program grew, and contracts were elected Peter Hoffens, Ted Newman, Lavati, Richard Arnavich, and Anderson, Al Schiller, and Alfred Schill, and the support continued for the Ba'kru that keeps established in Israel, and for some of them should work out as well.

37:30 A number of important reports were written with the support of ARL. The first and most important, I think, at the beginning was a publication by the group in London, of a series of lectures by Archie Troutman, called Lectures on General Relativity, which he gave at King's College in 1958. In these lectures, Troutman introduced what had become to be called the Troutman Boundary Conditions for Space Time, the Gravitational Radiation. We also discussed the propagation of discontinuities in the gravitational field and the problem of gravitational radiation that had in the presence of Russia. These lecture notes have been stimulated a great deal of interest and considerable amount of work, and they were distributed widely both by King's College and NRL. The first report from the Yodan group included the work by Ehlers and Punt, geometry of bell rays and a similar analysis of hydrodynamic flow. And again, the analysis of exact solutions, which was written up in the book within their chapter in the book Gravitation, which was edited by Goodwin. Now, in order to save time, over the years, There's a number of publications by the Aerospace Research Laboratory at Mike Patterson consisted of compilations of reprints and preprints that were resulted from the work that was done at the various universities. For example, in 1962 we had a comprehensive report from the Bergman Group at Syracuse. And the kind of things, let me just indicate the kind of things which had or were in it

40:00 and then I will stop and just indicate what other reports there were without telling me what was in them. The Berdman Report contained a review of canonical conversation, which was primarily the work of Berdman and Comar on the construction of observables for general relativity. It contained an analysis of space-like infinity, which exhibits the super-translations to it. It had the shear-free solutions of Robinson and Troutman. It had the Newman-Penrose paper introducing the spinnacle. and a long, long-unpublished paper by Penrose, The Null Hypersurface Initial Data for Classical Fields of Arbitrary Speed. So you see that these reports contained a wide variety of work which was important in the development of general relativity, and these were distributed widely by the aerospace research workers. And just to indicate where else these came, there were reports, there was a very long report out of King's College, out of Pittsburgh, there were several such reports, such compilations, there was one or more from the SHIELD group in Austin, which contained not only the Kerr solution, but also the beginning of the research on the Kerr-Shield metrics. It also had some work by S.H.I.E.L.D. on the Whitehead theories. And also, some of the work, I should say, by Arnaud Desiree Misner was also supported through a contract with Richard Arnaud both when he was at Syracuse University and then when he moved to Northeastern University. I don't mean to suggest from this that none of this work would have been done had there not been supported by the Air Force. But I do feel that the interaction, international interaction among physicists and the dissemination of the work that was done was greatly aided by the existence of this group.

42:30 And let me just say one word about why the work terminated in 1972. There was an important congressman by the name of Michael Mansfield, who has been for many years now the ambassador to Japan, who felt that the Defense Department, the military services, should only be engaged in applied research, which ultimately had some military value. We did not have the broad view that existed earlier in the services that it was important to maintain a strong basic research atmosphere in the United States. The first support for fundamental research in the United States came from the military services, from the Navy, I think the first support that existed from Professor Bergman came from the Navy, and the services in general, from the end of World War II to roughly 1972, maintained strong basic research efforts and support efforts. So roughly 1971 came along the so-called Mass Building Amendment, which said that the military services would no longer engage in such support. And fortunately at the same time mandated that the budget of the National Science Foundation should be very largely increased so as to pick up the slack that existed because of the withdrawal of the military. from that circle. I believe that in that period, when they, that the military played a very important role in maintaining a strong research atmosphere in the United States, basic research atmosphere in the United States, with minimal demands, in fact I don't know any specific demands made in return for all that so far. Thank you very much, Professor Goldberg, and Professor Nishmi Alvis will attempt a round. Please, from the back end...

45:00 I will give my relativistic terminage, my perhaps last relativistic terminage, perhaps That is to say, I take the period before our friend Roger. J'ai travaillé en Relativité de 1937 à 1967, mais en 1937, la communauté relativiste était vraiment étrangement constituée. Travaillait en Relativité un petit groupe de physiciens spécialisés, élèves ou amis d'Einstein lui-même, parmi lesquels, j'oublierai l'état d'un nom, Pauli, Ilfer, Van der Schoen, Ernst Fock, un tout petit groupe d'astronomes spécialisés, comme le maître, et un groupe un peu plus important de mathématiciens, je voudrais donner les noms, qui travaillaient fort, les uns et les autres, Chilita, Le Dander, Georges Barnoy, Whittaker et Hilsing dont nous avons parlé mais qui ont été toujours actifs et importants. Et leur domaine d'intérêt allait de la géométrie différentielle to the mechanics that was at the time rational and to the theory of the equations at the time. The physical community of the time, in fact passionate about mechanics, considered absolutely the relativist as a margin. Sol, direct, I don't know exactly what it is.

47:30 And this situation has lasted until the 55th century, and this colloque of Bern, organized by Pauli and Mercier. The development of the different geometry, in a real program since 1922 by Edith Cartan, a lot of meditation on the general relativity. The efforts of generalization and connection at the beginning of Eddington and Herman Wey about the relativity. The efforts regarding the theory unitary of the champs cher Einstein. After having shared this problem several important articles, notez par exemple le renouveau présent dont on a parlé de la théorie dite d'Einstein-Cartan. Elie Cartan s'était alors tourné vers des problèmes globaux concernant les groupes de Lie. Puis, en 1937, avait consacré son enseignement à la théorie des Spineurs, notions introduites par lui en 1913 dans une analyse des représentations irréductibles des groupes orthogonaux. Cet enseignement devait être publié en 1938, remarquablement indigé par Mercier, et ses leçons s'acheveraient par une étude, en général mal comprise à l'époque, dont Ishné Samy nous a parlé, sur le statut des spinners en relativité générale. Études qui ont fait clarifier et rendait correct l'approche de Troc tout en critiquant le point de vue d'Infeld et Van der Verde. Il faut noter qu'à l'époque, si l'on s'intéressait aux groupes globaux, on voyait bien ce que c'était, nulle théorie globale intrinsèque des variétés n'était vraiment disponible. Et cela, c'est très important. C'est au fait environ de 1936 seulement qu'avec Harald-Whitney, une telle théorie apparaît. C'est à lui que sont dues, grosso modo, la définition globale des variétés qui est la nôtre,

50:00 in terms of what we call now the Atlas composed of cartes locales, and also the terrain of existence of plungements of such a variety in a space R-L, of dimension L suffisamment large. One or two years after, very quickly, it surgically thanks to Erasmann, Mathematician, élève d'Eric Carton, qui s'est d'ailleurs toujours intéressé à des choses de relativité, grâce à Whitney lui-même, grâce à Stiffer, élève de Heinsoff, des définitions équivalentes de la notion d'espace fibré. Ainsi se trouvait axiomatisé une intuition profonde d'Eric Carton dont il avait fait grand usage. L'apparition des espaces fibrés ne suscita d'ailleurs d'abord chez les mathématiciens, et ne parlons pas des physiciens, qu'un intérêt tout à fait limité de l'économie. Quel était le paysage que j'entend voyer ? Mon témoignage ne peut être maintenant que partial, partiel incomplet, vous me le pardonnerez, j'essaierai de ne pas déformer la perspective. En 1936-1937, ayant reçu des mains d'Hélie Cartan, une solide formation de jamais en différentiel, je m'intéressais à la relativité sur les conseils de Georges d'Armois, avec la bénédiction d'Hélie Cartan d'ailleurs. En 1936, Georges d'Armois avait donné en Belgique ce cours de quatre leçons dont a parlé notre ami Stéchel, and it was in the presence of Dönder, it was all in interaction with Dönder. And the corresponding chronograph, entitled Les Equations de la Gravitation Einsteinian, was released in 1927 in the collection of Memorial, and it became my book of chevilles. On y trouve traitées en coordonnées de Gauss, ce qui, à mes yeux, nous allons voir, présente certains inconvénients sérieux.

52:30 La première analyse rigoureuse du caractère hyperbolique du système des équations d'Einstein, c'est-à-dire le fondement de la théorie relativiste de la gravitation comme théorie de la propagation par ondes, parce que c'est ça que ça veut dire. With an intelligence lucid, there is clearly the partage of Einstein's system relative to the problem of Cauchy in a system porting on the conditions of the scale and a system of evolution in the time. There is also the first interpretation of the geometry of the conditions of the coordonnées which were called the Dunder at the time, becoming for us the conditions of harmonicity. At the time, I started to think about the different structure of the variety of space-temps, in order to be able to talk about what interested me is, the problems globally of the nativity, which is, according to my opinion, the real intelligence of the theory. In 1939, when the war arrived, I published in June 1939 a monograph called Problem Globals in Mechanics Relativist. After analyzing completely, in coordonnées locales arbitraires, the problem of Bauchy formel, I gave in particular the first demonstration of the result researches then by Einstein and Pauli, an space trans-stationer extérieur partout régulier, a comportement asymptotique euclidean, so not radiation, that could be locally flat, it is to be effectively without gravitation. I don't give a complete demonstration of this announcement that in 1945, a demonstration which value at the time the congratulations of Pauli. Entre-temps, I analyzed the system of constraints on the initial conditions, by introducing the method dite conforme, method restée classique. In 1937, Stelmacher in Germany, in two articles, one of 37 and one of 38, 38 m'intéresse

55:00 encore plus, had analyzed in 1938 finement la progression des singularities du champ de gravitation along the geodesic isotope. D'autre part, si mes conditions de raccordement du champ étaient présentes dans la monographie de 39, elles n'étaient pas encore fort bien énoncées. Je trouvais une certaine forme définitive dans mon livre de 54. La structure différenciable de l'espace-temps, je vais m'insister, doit être C2, du point de vue différenciable, pi soit S, C4, la métrique étant C1, C3 par morceau, pi soit S. And, of course, we can say mathematically a such structure in the rendant, it's the infinity. But all the additional precision of the differentiability must be considered as a physical sense. physique. In particular, for the coherence of the ensemble, the analyticity must be étrangère to this framework, which has always left a little rêveur in terms of the prolonging analytics of Kruskal, which should be reinterpreted. In 1951, my first teacher, Ms. Schock-Ebrouard, a given, in the different field, the first demonstration of existence and unicity related to the problem of Bauchy's local for the Einstein equation. It was using the coordinates of harmonics and the formulas of Kirchhoff generalised. It was at the time a kind of force of an analysis function. Elle a donné, très vite après, une démonstration plus simple et plus savante, basée sur la technique des espaces de Sorboreff. Et ceci a servi de source au grand théorème de Leray, on connaît Jean Leray, vers 55-56, relatif au système hyperbolique.

57:30 strictement hyperbolique dans le vocabulaire, à coefficients variables. Ces démonstrations ont été la source de beaucoup de travaux de physiciens mathématiciens qu'ont approché. A la même époque, Singe et son élève O'Brien donnaient une approche plus compliquée mais peut-être plus intuitive de mes conditions de raccordement. These are all these results, in particular, that have been brought, brought, broadcast, and broadcast to the international colloque of Bern, this colloque which marks the real renaissance of the interests of all physicists, mathematicians, astronomers, for the relativity general. It is where I personally got the knowledge of the English school at the time, the young members of the English school. One note that I believe is important. A few reprises, especially at Berne, I had made a kind of proclamation that I was going Les coordonnées locales de la variété espace-temps ne servent qu'avec cartographie qu'au repérage des événements. L'espace fondamental est un espace fibré. C'est l'espace fibré des directions temporelles tangentes à l'espace-temps auquel est attaché le trois plans orthogonaux d'espace. It is given a system of observators, that is to say a local channel of direction temporal. The decomposition in the square corresponding to the DS2 provides, by integration along an arc of the universe, a standard time and a standard length relative à ce système d'observateurs temps et longueur qui sont eux directement comparables aux grandeurs homologues classiques et cette clé d'interprétation suffit en fait

1:00:00 à tous les besoins Carlon Capaneo a des fois pris vraiment au sérieux cette suggestion et il a développé de 58 à 61 differentials correspondant to these champs of three-plans, and these formulas which allow a direct comparison and systémical comparison between the mechanically classically and the mechanically relativistic rapportées to the planet Earth. It seems to me that astronomers have often interested in using these formulas, given in a course France, but in an Italian volume. It is then on the shock in general relativity that I was interested in. A partir of a new technique of a tenseur distribution on the space-temps, developed in 1959, I analyzed the rapport between the shock electromagnetic in which there is a flash corresponding to the electromagnetic channel, and an ones of shock gravitation, in which there is a discontinuity of the connection, which means an écriture of Einstein's equations in terms of tensor distribution, if you want, of Einstein's equations where we look for weak solutions. On voit ainsi que toute onde de choc électromagnétique, ce qui n'est pas du tout évident, discontinuité du champ électromagnétique, crée une onde de choc gravitationnelle, discontinuité de la connexion, et on dispose d'un bilan énergétique. You have also studied with these techniques the ionic shock magneto-hydrodynamic in general, which are necessarily present, for example, as large as the pulsars, due to their rotation. The approach of the quantification of a physical field on a space-time curve, global hyperbolic, cause, we know, of difficult problems but extremely interesting. I was interested in the 60's and 63's. I continue.

1:02:30 For a field sensoriel or spinoriel, we can build, from the solutions of the field, the equations of the field. It is not a field of gravitation, It is a physical champ of all species, non gravitationnel for the moment. A partir of the element of the equations of the champ, a propagator that we can call anti-symmetric, solution of the equation homogène, and the definition of the operators of creation and annihilation for this champ comes to find a symmetric propagator for a solution to an equation integral quadratically and submissive to a positive condition. The existence of a propagator, which is far from the case in general, has been proven by Carlos Moreno for the spin 0 and 1,5. But it is remarkable that in the case stationary, the existence is proven, but also proves that there is no unicity. Otherwise, there is no way to attach, without stationary, to the operators of creation and alienation in a way intrinsically. The problem of giving a mathematical sense to the creation of particles, for example in the Parker, for expansion of the universe, is, I believe, completely open for at least 15 years. I will stop there. I would say that it appears here, in any way, in what I have said and in what I have said, that the relativity general remains also a privilege field, certainly difficult, of the mathematical physics. Thank you very much, dear Ami. And now I ask Professor Bergman to give you a report. Excuse me, j'ai un papier que je vais mettre là qui contient un survey, en particulier des tenseurs de distribution, etc. Il est difficilement accessible, il est paru dans un livre de 1980 consacré à Einstein, qui coûte fort cher, qui se trouve dans quelques bibliothèques, alors je le mets à disposition si vous le regardez. Pardonnez-moi.

1:05:00 And Professor Mercier's suggestion that I should confine myself for one hour to half, and I hope it will be less than 15 minutes. So it's hardly a report, this sketch. Let me first, since we are talking about the time of the middle 50s, let me first contribute one little item perhaps of historical interest, and that is my perception of Pauli's preparation of the Berm Conference. He was in Princeton in 1974, a full year before the conference, and asked me to make a report and quantization, giving me to understand that I expected the report sufficiently worked out that I needed a year to prepare. I presume we did the same with others. And so for all of us, the Bernd Conference was a fantastic experience. Perhaps less for the older people, but for me, for instance, it was the first international conference of any sort that I intended, to indicate how naive I was, I figured the conference was in the German-speaking part of Switzerland, therefore I prepared a manuscript in German, which is the language in which it was eventually distributed. But just before I went on, a day or so before, Madame Tonla and one or two other French people came to me and said, would you perhaps talk in English? Because you will not understand if you talk in German. So our presentation was in English and of course almost all of the talks were given either in English or in French at the conference.

1:07:30 I think this never happened at any of the GR conferences. Again, most people do. Most conferences were predominantly English. Open English, accented English, but English. Even in Poland, Fock, I think, translates himself. He would speak one paragraph in Russian and then repeat the same sentence in English. Fock was not very good at hearing, he was almost deaf, but he was an excellent linguist But, anyway, let me come from the episodal part to the historical research. As we were told, the physics seem, or the foundations of physics, seem to be dominated by two huge areas in the middle 50's, or even before. One was micro-physics, in which quantum theory was dominating, and the other macro-physics in which then relativity was no doubt the most sophisticated and philosophically interesting structure of the 20th century. We all felt uncomfortable about these two huge areas of conceptualization that didn't seem to have any fundamental contact with each other. And so the idea that gravitation should be quantized, at least in principle, seemed a challenge that ought to be followed up, either to be successful or to teach us something about the lack of measure.

1:10:00 The earliest serious attempts I think are due to Leon Rosenfeld, who published two papers, one in German, one in France, in 1930 and 1932. This was one year before he wrote or published This famous Boer Rosenfeld paper on quantum electrodynamics. If you have ever studied the paper, you know that it is not a paper that is concerned with the formal aspects, you might say the mathematical aspects of quantum field theory, but with the physical foundations. It is an attempt to analyze what can and what cannot be observed. Now, I mentioned the close timely coincidence, the temporal coincidence of his paper on quantization of computation and quantum electrodynamics, only to point out one important difference. In the Bohr-Rosenfeld paper, there are all kinds of machineries that are electrically neutral and can be used mechanically to move test bodies around, because if any tool that's electrically neutral, this only can be used in such a way as not to affect the electromagnetic field. In gravitation theory, if you take the principle of the kernel seriously, you cannot do that. When you introduce a tool to move the test particle, the mass of the tool profoundly affects the gravitation theory. So, I mention this because I think it's very important for people who may want to work in the field of quantum gravitation to see that the difficulties are not just formed, but are profound and conceptual.

1:12:30 Well, just five years before the Brown Conference, I'm sorry, I'm getting ahead of myself, there are historically two ways of attacking the problem of quantization. One is to say, well, limitation is a weak deviation from the Minkowski. If we linearize the field, it will be quantized by standard procedures. The other is to say, no, that means that we disregard the most fundamental aspects of general relativity. you want to work out a formalism that does full justice to the invariance group of general relativism and general relativity. And then, together with the idea that you want to study the non-commuting operators giving rise both to the dynamics and to the change in coordinates leads you to canonical kind of canonical practices well the first success in this endeavor came in 1950, when Pirani and Schild published two weeks before our group Hamiltonian Formulation of General Relativity. If you look at these ancient papers, you will see that they use the same notation, that Pirani and Schild on the one hand and the Syracuse group on the That was not an accident. We heard of each other just before publication and decided for the benefit of the readers to adjust the two papers to use the same notation. The Bernd Conference contributed to the canonical formulation primarily by forcing us to rethink to make our constructions to make it comprehensible to people who may not work on it.

1:15:00 But the next great progress was achieved by Dirac and published in 1958 and 1959, two papers, one in the Proceedings, the other in the Physical Review, in which he put the canonical formulation, still on a classical basis, but the canonical formulation of general activity in a very elegant form. He discovered the best classical closed form variables at that time, namely the components of the three-dimensional metric on a Cauchy surface on the one hand, and the canonically conjugate momentum densities that were closely related to the extrinsic curvature of the Cauchy surface. He overcame the problem that had bothered everybody up to that point, namely how to formulate the algebra of infinitesimal transformations without violating the requirement of a canonical presentation in which the quotient data include only 0th order and first order derivatives of configuration values. This worked out very fine with the variables introduced by Dirac that left one of the question, which I don't want to go into boring details now, but it was mentioned several times at this conference. This re-algebra that direct formulated is an open algebra, it doesn't close. If you take the constraints that generate infinitesimal coronal transformation You find that the commutator of the lapse operators is not the...

1:17:30 If you assume that the lapses are numerically given two sets of the same causal surface, we find that the communicator involves components, the dynamic components. To this, that is to say, the communicators are linear combinations of the original generative constraints, but multiplied by the traces of the dynamic variables. This gap in the open V algebra can be closed, but in the best of my knowledge, the only way to close it is to consider all lapses that are functions or functionals of the dynamical values as well as arbitrarily true invariants. This means that you have it, that the components of the Neal and One are infinite in number. And maybe at this point, of course, everybody realizes that this, that the reformulation of and relativity in the canonical formulas didn't solve the problem of quantization, but merely was one small step in the right direction, or hopefully in the right direction. One of the nasty questions, if you really want to go into quantization, that the generating constraints is formulated by Iraq in 1958-1959 are not polynomial. This problem of the non-coloniality apparently has been resolved by a number of people, by Ashton Kahn and by George Goldberg.

1:20:00 So, the trick that they used is, in a way, related to Uttayana's reformulation of general relativity. By going away from the free matrix and replacing it by spinners or by triads, that is triplets of vectors, usually in particular vectors. You apparently increase the number of variables of the number of components. You increase also the number of generated constraints, but you get polynomial structures. That's a very recent accomplishment. It goes back to approximately I mean, in 86, Habe had essentially his paper together, but hadn't published it yet. Again, supposing that the polynomial problem and the problem of factor-ordering of the original constraint has been said satisfactorily, does that mean we have quantum theory or quantitative? I think there are still some open problems left. construction of a fog space, the construction of a ground state, quote unquote, remain difficult conceptual problems. There is a lot to be done before we will know whether there is a quantum theory of gravitation, or if not, why not, and what needs to be replaced. Thank you. Thank you very much, Mr. Bergman. Now the round table will go on very shortly within this, on this side. I may first perhaps tell Mr. Bergman that I've got an idea. Why not call the Bairn Conference GR0 and then again, so that's the language is solved and we would not make the same mistake as the French Revolution which invaded again the year 1 instead of beginning but with 0.

1:22:30 I may perhaps add, since I'm going to ask you to talk a little to one another, that after having completed the manuscript on the spin-offs, which I handed over to Carton, I wrote to Mr. Boer, asking whether I might be allowed to work at his department. Of course, I sent my various things, and he answered very nicely all this mathematical material was very interesting and important, but I would have to learn to be a physicist. And I don't remember in school, although he was a very good mathematician, Talking otherwise or on other matters than physics proper, and this is something which among relativists is perhaps not so usual as is the case among other physicists, let's say quite a few theoreticians. Now, the discussion is open for you gentlemen, the four of you. Do you have a question? We might begin perhaps with, do you want to say something? Yes, I want to say something. The fact on quantization of gravitation. Before there was a quantum electrodynamics, classic electrodynamics was extremely well understood. of, in particular, the question of waves and the emission of waves and the absorption of waves within the old Maxwell formalism was understood. This is not the case at all in general relativity. I mean, with all the... I did not go beyond 62 in what I mentioned about work on gravitational radiation, but But at this point, there is still nothing known on interacting particles in gravitational waves, except in the very question of approximation.

1:25:00 And I would say that within the last 15 years or so, I think people working within the classical problems of gravitational radiation and defrages of motion with radiation reaction have become a lot more skeptical than they were at the time and I somehow feel that before one really understands these problems one is not really ready to tackle the questions of principle people which people have mentioned, and not just the formal questions of quantization. There is, I mean, everybody of course really satisfied experiments are concerned, because the situation again is entirely different from what it was when quantum theory of radiation was invented, there is just nothing, either classically or quantum mechanically, on the horizon, and so there is certainly no need for that is concerned. But an understanding of interaction is very important. In the question of pure waves, pure gravitational waves, that is not sufficient in my mind to understand things. Again, unlike electrodynamics, because there was no question that when you talk about waves, when you talk about plane waves, let's say in empty space you understand very well how they can be connected to an emission or an absorption problem. In general this is just not the case yet. Professor Gromberg, do you want to intervene? I want to begin with this question. The work on a new variable is really passionate for his work, and anything that I've done is really quite trivial in comparison with his accomplishment, which was to conceive of using a self-dual connection as a basic bearing of quantum gravity.

1:27:30 Part of the stimulation for him came in two directions. One was the work of Barden in introducing complex variables in the discussion of particle mechanics upon mechanics. in the department of representation. Another form of stabilization was the work of a mother taught by Sam who first constructed the social connection but didn't use it in the formulation I'm sorry, of Hamiltonian for general relativity. In particular, the introduction of the spin and representation on the three senses was an important contribution. and the recognition that the use of the self-dual connection around the freestyles leads almost directly to the constraint equation of general relativity, which in some sense is almost a little bit of black magic. So the use of a trigat instead of a spinner is almost trivial in that sense. I will give some stimulation to this discussion, because I am, from a long time, a septic on a general project on quantum gravity, because we have two different types of fields. On the carbon background, it is very clear what it is, quantized, quantized, general physics

1:30:00 field. It's absolutely not clear what it is, quantized, gravitational field. Not clear Why? Because the habitational field is a metric imposed to all the other fields the part between space and time. It is a cone which defines what it is time-like, what it is space-like. And if you have, as Pauli says all the time, a code which is such, it is not present. So it is necessary to consider what it is this field of codes for a quantum gravity. is possible to have some status. It's possible, probably, certainly probable, certainly to quantize fluctuations of the gravitational field with a macroscopic gravitational field But I have very good, very good paper, very good things on quantum gravity from a long time ago now, very interesting, very precious also for the clear intelligence of generality. But my impression it is we are at the same distance of this project now past 20 years ago. Would you add something also of your answer? I want to add something totally non-scientific. Thank you.