The Cauchy Problem in General Relativity — The Early Years

0:00 The following is English, and they're going to be following my order. I think it'll be about one cop to reach two people. A recent review article on the Cauchy or initial value problem in general relativity remarks on, quote, the resurgence of interest, unquote, in, quote, the initial value problem, the canonical formalism, linearization stability, and the space of gravitational degrees of freedom, end quote, and notes, quote, the intimate relationship between these topics of current interest. Neither this article nor other standard surveys are the same topic over the last quarter century, and you see several references here, give references to any literature on the subject earlier than with the British 1939 thesis, which seems to have become the standard cutoff for references in this field. And I'll come back to that point later on. But from 1939 on, there is more or less continuous tradition in the study of the culture problem, and yet the early history of the subject seems to have been lost, and this paper is at the beginning of trying to recuperate that earlier. Yet, leaving aside global problems, which is a big caveat to us, but if you leave those aside, conceptual advances, as opposed to the technical and mathematical ones in this field, had been made well before 1939. It's the purpose of this talk to outline the prehistory, so to speak, of this important topic, which includes work not only on the usual social problem on a space-like hyperservice, but I will also refer very briefly to the null initial value problem or characteristic hyperservices. As is so often the case in general relativity, not to speak of other fields of physics, we shall see that a number of investigators approach these problems to various angles without the later ones indicating any awareness of earlier work on the topic. Indeed, one may find a number of examples in this area of a meta-theorem which I once proposed. Nothing, anything worth discovering once in general relativity has been discovered independently, at least twice. Before turning to the subject of the paper,

2:30 some mathematical preliminaries starting with the classic results on the Cauchy problem for systems of partial differential equations based on the work of Cauchy and Sophia Kovaleskaya, alias Sonia Kovaleski. And I insist her name was really Sophia Kovaleskaya. Consider a system of p partial difference equations for p functions, the phi i's, ironically, 1 to p, which depend on q plus 1 independent variables, and I single out the first one for consideration. Such a system of equations is said to be in normal form when the partial derivatives of the p-dependent functions with respect to one of the independent variables, and as I said, I picked out the x1 for purposes of illustration, when these highest order partial derivatives are all equated to p-given functions f, f sub i, i again running from 1 to p, of at most the independent variables, the dependent variables, and their lower order derivatives with respect to the independent variable 1. Of course, it can have a higher derivative so it can have respect to the other variables and a positive to indicate that. So if that condition holds, the system is said to be in normal or quasi-normal form. If the system is not initially in normal form, of course, it's possible that it can be put into this form by a suitable transformation of the variables. We should suppose the system under consideration to be in normal form. For some values of the first independent variable, say xi0, let the values of all the dependent functions and their derivatives in respect to this variable, up to, but not including the highest order derivatives, be prescribed. These phi of x10 and the other x's, phi, comma, 1 of the same variables, and phi up to n minus 1 of all the other variables. But for a fixed value of x1, I can name x1, 0, let the rules be given. Let them be prescribed. These guys are collectively known as the initial values. Then, in the analytic case, in which the functions f and the initial values, these other functions, pi of

5:00 the x1, 0, and xj, are all analytic functions of all their arguments, then the Cauchy-Kovalevskai existence theorem asserts that a unique solution in some finite neighborhood of x10, a solution which assumes the given initial values when x1 is equal to x10. Of course, even if a system of partial differential equations is in Cauchy normal form, this does not mean that the Cauchy problem is the relevant problem to pose for this system of equations. To decide whether it is, we need the concept of a well-posed problem, a concept which, as far as I can see, was introduced by Jacques Anomar. Adamar's work itself is part of a long tradition of work on partial differential equations in France, which includes work on the Cauchy problem and other initial value, boundary value, and mixed problems by such other prominent mathematicians as, for just some examples, Elie Carton, Edouard Gossard, Maurice Chalet, Émile Picard, and Riquier, his first name I couldn't yet find, but there's only somebody here who will be able to help me on that. It's sufficient here to recall Adamar's of the Cauchy problem, culminating in his book on the subject of 1923 and also with some other references earlier and later. Anomar first clearly formulated the idea of a mathematically well-posed problem. In general, according to Anomar, a problem is said to be well-posed if possibly subject to certain other conditions than the individual case, but in general there are three criteria. If a solution exists to the problem, the solution is unique, and the solution depends continuously on the data needed to specify the solution. That's of course the kicker, the left condition. A unique solution to the Cauchy problem for a system of partial differential equations may exist, for example, for an elliptical equation, but the solution will generally not depend continuously on the initial data. for a linear hyperbolic normal partial differential equation such as the wave equation, the Cauchy problem on a space-locked surface is a well-closed problem, as Aramach proved by actually constructing the solution as a function of the initial values. He showed that for hyperbolic normal partial differential equations, linear or nonlinear,

7:30 there exist real hypersurfaces in the space of the independent variables, called characteristic hypersurfaces, on which the Cauchy problem cannot be well posed, since uniqueness of the solution fails no matter how many derivatives of the dependent functions are specified on such a hypersurface. As Ademar demonstrated, the value of a solution to the field equation at some point anterior to a space like hypersurface on which initial data is specified depends entirely on the values of the initial data on and within the intersection of that hypersurface with the characteristic cornoid which has that point as its vertex. So the value of the function the solution at the point P will depend only on at most the values of the initial data on the surface x-ronical constant on the boundary of and within the intersection of that characteristic conoid emanating from P and the initial hypothesis. The field equations of general relativity raise several interesting problems when considered as a system of second-order partial differential equations. First of all, as is the case for any system of equations which is invariant under a gauge group, depending on one or more arbitrary functions, they are not in Cauchy-Normal form. This gives rise to the mathematical problem of finding the, what Jeanne called the degree of indetermination, of the system. That is ascertaining what supplementary data are needed to completely determine one and only one solution to the system, given that solutions related by a gauge transformation are regarded as equivalent. This is the point that Norton was making yesterday. His quote. This mathematical problem is obviously very closely related to the physical problem of finding the degrees of freedom of the gravitational field, the number of degrees of freedom of the gravitational field, or the true come to be called. When I say C for example, I say I didn't put an example here, but some work of Bergman would be the appropriate reference to it. Then there's the question of the characteristics of the field equations. And here, of course, the signature of the metric is crucial. For Orenstein's signature, the characteristics are real and they indeed coincide with the null-hyperservices, which is not an obvious or trivial result. Because null-hyperservices I find one way and the characteristic to find another way to prove that they are the same as a result of another way. So I'll indicate who did that first, so I can tell you later on. It's necessary to demonstrate that all physical effects,

10:00 as opposed to coordinate system-dependent effects, propagate within the characteristic or null-conoid. In other words, since the equations are not a priori in Cochinola form, it's not obvious that that result holds in there. Demonstrating that example is an important problem, The early work involved in solving these problems was done by four men, Dilbert, Dumhoff, Ranchos, and Stelman. So I thought essentially the tale of these four people and what they have done. It's just a little bit of work. The first is David Hillard. He was certainly the first person to discuss the Cauchy problem for the Einstein equation. Of that, I'm pretty certain, since he'd better be going to be there with Einstein and Hilbert . He did this in the second of his memoirs on Foundations of Physics, which was dated in November 1960, although it was not published until 1917. Hilbert emphasized that the general covariance of the field equations preclude their being of Cauchy normal form. He's the first person to realize that, and he emphasized a serious physical difficulty his poses. His work on this question was presumably connected to Einstein's early rejection of general covariant field equations on the grounds that they were incompatible with what Einstein called the law of causality, which is causality, that's in 1914. Einstein had developed a general argument leading to this conclusion in 1913, the so-called pole argument, which John Norton alluded to yesterday. And then Einstein himself refuted this argument in 1950 when he returned to general covariance gravitational field equations. I have here a copy of that paper I referred to, Einstein's search of general covariance. I can leave that out so I can make copies of that. However, Einstein himself was always a bit vague about just what he meant by causality I do not quite agree with the remarks made yesterday that Einstein treated equations as if they were elliptic. I don't think that's quite fair, but he did. Let's just say he wasn't vague about what he meant by causality in his context. Hilbert gave the concept of causality a quite precise meaning, a meaning which I myself would prefer to call determinism rather than causality,

12:30 but that's what I believe that question will start. Hilbert noted that for a physical system obeying laws involving no higher than, let's say, second, of this as most fundamental physical was, even up to this day, that holds for most fundamental physical order even up to this day, we got no more than high second, no higher than second time derivatives, but such a system of physical laws, causality in physics had hitherto taken the form of the principle that knowledge of certain physical quantities and their time derivatives, the law involved second order time derivatives, at some initial time, uniquely determines the entire future evolution of the system. The validity of this principle was assured by the circumstance that the physical laws in question could be put mathematically into kosher normal form. Hilbert showed that this form of the causality principle no longer holds in general relativity. Hilbert actually discussed the Einstein equations coupled to electromagnetic field equations because Hilbert was attempting to generalize in these special relativistic nonlinear electrodynamics, which was an early attempt at unified field theory. And he hoped, indeed, to obtain an explanation for the properties of matter, for example, the electron and its stability out of this theory that was Hilbert's motivation. The exact form of Lagrangian leading to the combined electromagnetic and gravitational field equations is left unspecified by Hilbert, but most of his first memoir, earlier. So the results are quite general, they would hold for Maxwell's theory, for example, just as well as for the non-linear kind of Mi theory that he had in Martin. But at any rate, in all such cases, the combined field, the gravitational electromagnetic field, is represented by 14 field quantities. The electromagnetic potential four-vector and the metric tensor, the 10 components of which act as the gravitational potential. Like Mies' original theory, Hilbert's generalization is not necessarily the ancient variance, although, of course, if it is unspecified, you can't have the ancient variance, too, as a structural case. However, it is generally covalent, so that there are four identities linking the 14 field equations, as Hilbert realized in the first milk. For the Einstein equations, these identities are actually the contracted Byacki identities, as was only later realized, as far as I can see, I wasn't going to realize that the identities involved in the

15:00 Einstein equation are really in fact beyond that. As a consequence, the field equations are not in culturally normal form, and cannot be put into that form without the introduction of coordinate conditions, which appropriately restrict general covariance. Indeed, and Hilder constructs an example to illustrate this point, by means of a coordinate transformation which leaves the field quantities and their time derivatives initial hypersurface, the form of the higher time derivatives of some solutions to the field equations can be changed completely on the hypersurface. So you clearly, if that is the case, you could not hope to put them into coaching. Gilbert concludes that the formulation of the principle of causality must be modified. Quote, let the physical quantities and their time derivatives be known at the present, that is the initial time. then an assertion will only have physical meaning if it is invariant with respect to all those coordinate transformations for which precisely the coordinates used for the present time remain unchanged. I maintain that assertions of this type are uniquely determined for the future, that is, that the principal causality holds in this formulation. From knowledge of the 14 physical, that is, metric and electromagnetic potentials, at the present time, which will always be the additional, all assertions about them for the future follow necessarily uniquely insofar as they have a physical meaning so he was the first one to face up to the significance of general covariance well for the initial value problem particularly for the physical causality and pointed out the need for identifying an equivalence class of mathematical solutions differing by coordinate transformation as corresponding to a physical solution And in that sense, one could reestablish the principle of causality in this generalized form. Note that Hilbert has dropped reference to the time derivatives of the potentials, but this is clearly a slip. He obviously realized the equations were second order, and I think that's clearly just a slip, and that's why he had to mention the first time derivatives. It is also not, and this is a little more significant, it's also not quite clear what he means by the coordinates used for the present time, but presumably he means the three-dimensional coordinate system on the initial space micro surface. He goes on to prove his assertion by adopting Gaussian coordinates, as he called them, also known today as geodesic normal coordinates. So as far as I know, he was the first one also to use geodesic normal coordinates to solve, to discuss the question problem,

17:30 in general. In these coordinates, of course, G4, 4 is equal to 1, or minus 1, depending on what you can use, and G4, or I, I would go to 0. And then 10 of the 14 field equations allow the determination of the remaining six components, Gij, of the metric tensor and the four electron-linked tensions. Hilbert does not explicitly say so, but he evidently realized that the six Einstein equations involving the big Gij, IJ running from one to three, can be put in Cauchy-Noval form for the little Gij, the components of the metric tensor, X4 is a time-like variable. He concludes, quote, since the Gaussian coordinate system is itself they have previously shown. All assertions about these potentials, that is the six little series and the four potentials, all assertions about these potentials in this coordinate system are of invariant character in the sense that he could explain. As far as it goes, Hilbert's discussion is fine. He realized the need to modify the statement of the principle of causality for general covariant theories, since all solutions related by any coordinate transformation must be regarded as physically equivalent. He also realized that the use of Gaussian or geodesic normal coordinates gives him a normal system of, a quotient normal system of equations for the remaining gravitational potentials. However, he neglected a complex of related problems. He did not discuss the remaining four equations in the set of 14. This neglect seems to be connected with a misunderstanding on Tilda's part of the role of the contracted Bianche identity as we used now, which he believed to allow the complete elimination of the four field equations. So it seems to have really thought the Bianchi identity guaranteed that four equations could be ignored, which of course was a mistake, but it's quite clear that it's a mistake that somehow was implemented. Consequently, he did not consider the constraints upon the specification of the remaining components of the metric and their time. Because of this conceptual error on the significance of the Bianchi identities, he overlooked the remaining four equations and therefore apparently did not realize that they played serious constraints upon your choice of the initial data for the other the field components. He also does not consider what happens if geodesic normal coordinates are not used. He raises that question. And he also neglects, and this is very surprising, he neglects the question of the significance of coordinate transformations on the initial hypersurface. He curiously restricts himself, in the definition of physical fluid quantities, to coordinate transformations which do not affect these coordinates.

20:00 Clearly you have a restricted gauge group on the initial hypersurface. You can do any coordinate transformations on the initial hypersurface. to do, what does that say about physical and physical qualities, he never touches that question, so he never really got to the question of what other degrees of freedom of gravitational field or the true abilities in the language. He does not attempt also, in addition, he does not attempt to give a geometrical interpretation of his results, nor to discuss the actual propagation of gravitational effects. As we shall see, later workers, all before 1939, nine did consider these questions individually, although no one of them seems to have considered them altogether, none of them have been aware of what the others have done, or what all of them have done. Some were aware of one or the other, but none of them seems to have been completely aware of what they have been done. The first reaction to this aspect of Hilbert's paper appears to be in a paper by Vessio in 1980. It's difficult to be certain about this, why I say appears to be, is because Vessio does not mention Hilbert. He does mention Einstein, but he does not cite any of Einstein's papers, or indeed any other paper on general relativity. This perhaps may be attributed to the fact, which is remarkable enough in itself, considering what Michel Biosinski told us yesterday, that Bessio's paper was presented to the Académie des Seals on the 25th of February, 1918, while World War I was still raging. And yet he clearly did know about Einstein's work, and I would make names on the content he must have known even about Hitler's work, although he did not mention it. How did he find out And that's a interesting question, and no one I've asked has been able to give me any idea. Was there some line of communication between Germany and France even during the war? Was Switzerland? Was it how on the line? I don't know. But clearly Vestio knew the score, so to speak. How did he do it? It would be very interesting to find out. Maybe Michel de Zunstri came to me and found out what he did. At any rate, his argument about 10 of the 14 equations for the gravitational and electromagnetic potentials when Gaussian normal coordinates of Vessio's argument parallels that of Hitler. That's why I think he must have read Hitler's paper, because it's quite a special argument to take a Hitler's paper. The relevant new conclusions that Vessio draws are that discontinuities in the derivatives of these potentials of higher-than-first order are excluded for space-like initial hyperservices. They can only occur on what he calls wave surfaces, which are now called null hyperservices, along with both gravitational and magnetic waves

22:30 can promulgate. So Bessio was the first one to realize that the characteristics, because one way of defining characteristics in terms of which discontinuities of higher order can exist. So what Bessio essentially proved was that the null hyperservices are the characteristic hyperservices of an equation. He was the first one to realize that. Or at least to prove it. Okay, now we turn to George Damois. Damois appears to have been the next person We first discussed this in papers in 1923, which treat the exterior and interior problems, that is, both the problem in the absence and in the presence of certain types of matter. De Mois in 1924, in a very long review paper, gives a much more detailed mathematical treatment of a number of points, and in 1927 he had a little memoir in the series, Memorial des Sciences Mathematiques, which summarizes his approach and extends it in a few respects. I'm only discussing the question problem, I discuss there are many other things most notably in 1927 he gives his first treatment of initial value problem for null hyperservices the characteristics of the Einstein field equation Galois first of all corrected Hilbert's error noting that he doesn't mention Hilbert so I'm not quite sure whether he was conscious of Hilbert's paper or not but whether or not he was effectively corrected Hilbert's error noting that the four identities among the ten field equations for empty space what he called the exterior properties do not allow elimination of the four of the field equations but do guarantee that if the four equations g for uh for theta let's say equal zero are satisfied on the initial space by hypersurface x4 equals zero then they will be satisfied everywhere in other words one only has to satisfy those four equations initially and then the propagation of the other equations automatically guarantees the attractive gagging then automatically guarantees that the propagations of the field of the equation would mean that these four equations thus satisfy what it matters, so you don't have to worry about them as initial conditions. He rewrote these equations, these four equations, in terms of the initial data for the remaining six equations and gave the geometrical interpretation of this initial data as being the first and second fundamental forms of the hyper-surface. So Dumbledore was the first one to do the geometrical interpretation of the initial data. Thus, he first wrote down a correct interpretive of what are now called the constraint equations. He also realized that, in addition to the initial data, the four metrical components, G4 beta, may be specified arbitrarily on the initial hypersurface.

25:00 Geodesic normal coordinates represent only one possible choice, one that simply simplifies the problem, and he used it, but he used the first ones to simply realize that G4 beta are arbitrarily specified. Dunbar also considered the interior problem for matter in the form of a dust and a perfect fluid, and the problem of correctly matching interior and exterior solutions on a time-like world. But I won't discuss this here. In 1927, as I said, he summarized his earlier work on the culture problem and filled in certain details and equations missing from his earlier papers. But the most important contribution to the theory of initial value problems and general relativity in that paper, as I previously noted, was the discussion of the singular case, when the initial hyperservice is null. Without going into details here, let me just say that many of the most important results of Sachs' paper in 1962 on the characteristics of the value problem are clearly presented 35 years earlier in this monograph. And it's really a very interesting question why nobody picked up on that work of Dalmat for 35 years, as far as I can tell. And indeed, I don't think Sachs was aware of Dalmat's work either. But yesterday evening, the president always told me that when he started working on the question of problems, physicists stopped at him and said, this is who were wasting their time, what is this to do with physics? So at that time, the significance of an issue by a problem for physical consideration was at least not fairly recognized. Perhaps that's what it did. Absolutely not. So maybe that's the reason why nobody picked up on Don Walsh. It's a very elegant discussion. While Don Walsh clearly formulated the constraints on the Cauchy data and their geographical interpretation as conditions on the first and second fundamental forms on a space like Hypersurcus. He did not discuss the question of which of the constraints actually limited geometry of the Hypersurcus and which really limited the coordinates that's used on the Hypersurcus. And the first one to do that, as far as I can tell, was Lanchos, Cordell or Cornelius Lanchos. He seems to want to take his investigation in total ignorance of the previous work of Hilbert and Dumont. There's no reference to it, and not the only term on that to me, but it indicates that he was aware of it but didn't mention it. At any rate, he duplicates most of their, many of their results without mentioning their papers. And in his own way, as I say, it doesn't indicate to me that he was just critical without mentioning Blanchard set out to investigate the question of whether the gravitational field equations uniquely determine the geometry of spacetime, in particular, whether there are any other

27:30 solutions to the equations Rik equals zero, besides flat space. here I'll write IK from one of them inconsistent with my previous notation. In other words, he considered the possibility maybe five places is the only solution, in which case there wouldn't be no radiated degrees of freedom, so to speak. And he showed that was not the case. He adopted Gaussian normal coordinates, starting from initial time-like hyperservice, x4 equals zero, and showed that the six field equations, now letting IK run from one to three again, the big G IK IK run from one to three, determined the second time derivatives of the six little GIKs, the metric components, on the hypersurface, given the GIK in the first time derivatives, which he calls tau IK, on that hypersurface. Well, we recognize that the tau IK form a tensor on the hypersurface. He did not seem to have realized that this tensor is essentially the second fundamental form on that hypersurface. So it was a tensor that didn't do the direct interpretation, which I had already done. And I just received the total ignorance of that. However, we did recognize that TIK, the first time the G.I.K. determines the metric of the first neighboring hypersurface to the initial one. So he did recognize that much of the theoretical interpretation method. If you do the G.I.K. together with the G.I.K., that's determined not only the metric of the G.I.K. not only the metric on the first hypersurface, but the G.I.K. together with the first of time, it is determined the metric on the first neighboring hypersurface. That was as far as the way to do each of the theoretical interpretation. Then Lassus turns to the remaining four equations, R.I.4 equals zero. Again, I write one to three. He recognized that as a consequence divergence identity for the Einstein tensor, that these equations will automatically be satisfied off the initial hypersurface, if they are satisfied on the initial hypersurface. In other words, he rediscovered the result with double R, that we've shown many years earlier. He then wrote down these four constraint equations, as we now call them, noting that they consist of one vector and one scalar relation between the gik and the tau ik, on the vector and scalar with respect to the three-dimensional hypersurface. So far, although he did not appear to know it, he was banked with duplicate in previous work. Now he made his original contribution to the problem. He noted that the vector condition tau IK semicolon K equals zero, semicolon being the covariant here on the hyperservice, does not consider the restriction of the geometrical properties of the two neighboring hyperservices. This geometry is described by GIK and tau IK. His statistical medical interpretation was GIK is the metric on the first hyperservice, GIK

30:00 plus epsilon tau IK is the metric on the first neighboring And he noticed that condition, how I case semicolon tables, there was not a restriction on those geometries. It's just a condition on the ratio between the coordinate systems on the two hyper-services, which can always be satisfied by an appropriate coordinate transformation. So he realized there was no intrinsic direct content in that set of three constraint equations to be recognized for the vector vectorial equation on the hyper-services, but only a condition on coordinate systems, maximum coordinate services. The scale of the condition, on the other hand, he realized, constitutes a real theoretical restriction. As he put it, and as far as I know, he's the first one to use this phraseology in the context of general activity, quote, the number of degrees of freedom in the prescription of the geography of consecutive services is thereby diminished by one. He states that quite clearly and concisely. As I say, as far as I'm going to advance the term, this is the first of the concept of degrees of freedom to the reputation of field equations. He points out that this immediately explains why the equations R, I, K equals zero in three dimensions necessarily lead to a flat measure. There's a lovely interpretation of that when it comes to the Cauchy problem. Since a two-dimensional hypersurface, which would be the initial surface in a three-dimensional geometry, in such a space, has only one degree of freedom. Essentially, the curvature of the scale determines everything from two-dimensional hypersurface. And if you restrict that degree of freedom, then there's nothing left. on the reflex-based solution. A very nice dimensional way of understanding why R and K are zero in three dimensions are two-dimensional skills in two-dimensional classrooms. And that's clearly not hard to break down in four dimensions. He explicitly notes that in the four-dimensional case, this means, quote, there still remain two degrees of freedom at each point in, quote, of the hyper-surface. As far as I say, he was the first one to understand the for the freedom on the hyperservice, that essentially the three transverse constraints are essentially the restriction of the forwarded freedom on hyperservices, and that it's only the longitudinal constraint that's restricted by one degree of freedom. It's a three-dimensional hyperservice at three degrees of freedom, or two degrees of freedom left per point. So we see that by 1932, all the formal aspects of the Cauchy problem had been investigated.

32:30 The geometrical interpretation of the initial data had been given, and a general proof given that the gravitational field had two degrees of freedom for a space-time point. The work was formal in the sense that formal power series expansions were no construct solutions without any series investigating distant fields of construct solutions. That would work back the way. At best, these methods claim mathematical validity only in the analytic case, but for hyperbolic normal systems of partial difference equations, of course, it's precisely the non-analytic equations of solutions which are a special interest as information parameters. Indeed, one way of defining the characteristics of hyperservices for such systematic equations is the hyperservice sum with non-trivial discontinuities in the highest order of derivatives in the Gertrudeau and Stan Kerwin. In the case of Gerald-Claverian's equations, trivial discontinuities are those which can be reduced or annulled by coordinates. of course. Finally, we come to Karl Stelmacher. The first study of the Cauchy problem for the gravitational field equation to emphasize such non-trivial mathematical questions was undertaken by Karl Stelmacher in 1937, on the basis of recent progress in methods for improving existence in its hydrology equations. Stelmacher was aware of and recalled the work of Bessio, who showed that null hyperservices, I'm finding the text there, are characteristic in hyperservice in the Einstein equation, as I mentioned earlier. But Stelbacher does not mention any of the works on the Kossier problem cited above. He bases his work on adoption of the so-called the Dondon coordinate conditions, which transformed the Einstein equations into a system in Kossier normal form. He then applied the methods of previous and Levy to demonstrate what he calls the validity of the causal postulate. He uses the causal postulate in the sense which I would like to use it, namely that the field at a point P anterior to an initial hyperservice which need not be analytic, because that's part of the initial data that lies on and within the intersection of the initial hypersurface with the posterior characteristic colonel, starting with the colonel 2. Stolmacher was the first one to establish that. With Stolmacher's work, we've reached the end of what one may call the pre-historical period of question problems in general relativity. Andrei Liternowicz made it clear in his thesis, Liternowicz, 1939, that he was well aware of the work of D'Armoire, which is not too surprising to a Tombois student, and the work of Stelmacher, but the Hinovich has not mentioned Pilder Omanchus. When I was preparing this paper, I was hoping Professor Hinovich would be here. I did not realize he actually had the pleasure of having him

35:00 chair this session. I think everyone here has at least some awareness of the fact that a continuous tradition of work on the culture problem has risen from the work of Professor and his students who went on to make a number of extremely important mathematical advances in people's approaching problems. I think you may notice the date 1939, which means that we're fast approaching the 50th anniversary of Professor Thorogic's thesis. I think it might be a well-plied good occasion for someone in France. I don't want to dictate some of the people. A well-plied good occasion for a conference in which these questions could be considered. Thank you for this beautiful lecture. And now, I guess you'd like to add a very minor historical footnote. I went to the United States in 1941. At that time, there were a number of French scientists there, refugees, and Professor Solomon Rosenblum, who I had known in France, approached me and said that Jacques Adama would like to give a series of lectures on the Cauchy problem in French could I find an audience to understand that in French I don't have to tell you that that's not easy so he gave a series of lectures and actually the students who were there are interesting in that connection the part from me is Ruria Kaufman Ernest Strauss Jesus asked him. He essentially covered his book. When he gave the Yale lectures, the Yale lectures were published in English. The first version of the book. The first version of the book. And Yale, and Yale, and Yale, and Yale. Yes, but did he give lectures in the Yale? After, in fact. Did he give the lectures in English at Yale? I did, in English. Then why couldn't he give lectures in English 20 years later? It was hard to question it.

37:30 In bad English? In bad English? No, no, it was. Bad English is good mathematics. Bad trade-off. I need to move on mathematics. It's all the same thing. Yes, it was good. I want to say that I had a mountain Well, I was doing the war, I think, so it was quite understandable. Yeah. I don't know if it was a refugee in the United States. Yeah, well, after the war. What's on the other one? I wanted to ask you about the work of Hilbert that you discussed. You described how Hilbert managed to recover the terrorism, in effect, in general relativity, by, I guess, stating that only assertions about invariant quantities Now, I don't know if this question is going to have an easy answer, but I'll try to answer it anyway and see what happens. I'm curious about your sense of Hilbert's attitude to that particular statement about the whole point of the term of physical meaning. Is he taking this as some kind of physical posture? Because after all, determinism, the thing that's recovered, is that it's a physical matter. Or does he think of it perhaps as a mathematical definition or mathematically necessarily something that one could not deny if one wanted to or that's two choices and I'm sure there are more well, I thought you were going to play it but I think he would have realized that it could be mathematically distinct appearing solutions and I think he did take it as a physical search if there were obviously no problem He says essentially that the equation is created a critical situation. It doesn't perform after the fact that the entities mean that the equation cannot be put in a critical situation. If the solution was obvious, why would he say it's a critical situation? And why would he need to make that solution? Sort of arguing backwards from the fact that he makes a good point of this. They did consider a problem. Problems would give down a solution, and the solution would be kind of physical. It's not physical, not physical. very struck by it because you know there are two communications and when you read the first one

40:00 it's incredibly dense mathematically okay then you get to the second one and suddenly you know it seems to be a different hill but it's very long slow and careful and very simple to read and you wonder why it suddenly seems to change gears I mean it could be the time difference between that the two papers well what was the first one written second was 1196 Well, of course, what struck me is the fact that having recognized the importance of the invariance, it then completely reflects the invariance on the higher surface. And thus, much the chance to discover the degree of freedom is not just the same. 15 years later. First, a tiny comment about my remarks yesterday. When I was talking about sort of regarding this elliptic equation, that was almost sort of in lieu of a more precise expression, and I was referring only to when he's talking about Mark's principle obviously in other places he approaches it in a different way I had a question there to what extent was as a general result this business of once you've sold the initial constraints that they will be always propagated through, am I right in thinking that that is actually sort of the general theorem for all systems with constraints in NERTA's paper have a gauge of which involves arbitrary functions. That, so to speak, said that as a general result which would apply to GR. I mean, she was presumably well aware of that, wasn't she? Because, I mean, it was stimulated by, I mean, Hilbert got her to do the paper, didn't he, because of the general covariance of GR. I once read that paper. I can't tell you remember it well. I just wondered to what extent she, I have a feeling in my memory that she does explicitly say that, you know, if you solve some, if it solves initially, that it will. a problem and I think that's why I'm with it. She certainly talks about American friends, doesn't she, in the general kind of engaged group. Well, I think Peter Bergman and his group was the first one to discuss these problems, especially with a very wide class of I never am quite sure about this. Yeah. But it's clear that if you simply have a formal system And you follow the conditions for this?

42:30 No, I think the whole concept of... In the 60s or the 50s? But I think Iraq was the one of the first really labelled constraints either being first class or second class. But if the constraints arise from the gauge group, then there was the first place. And that could have been known earlier. Not in that language, but that constraint arising from the gauge group must propagate. And who first said that in a general context? I don't know. You think it may have been Nurse, right? Well, I mean, I looked at Nurse's paper quite closely about 20 years ago, 25 years ago. I've forgotten really the precise detail. I know she certainly was very well aware of the initial value constraints. I mean, in the case of the general gauge group, it was stimulated by Hilbert's work. I mean, Hilbert actually asked her to evaluate it, and she says that in the case of differential systems that can be got from a variational principle, you get certain very strong and very general results. I have a feeling that she did know that if you solved them initially, they would propagate, but I can't swear to that. I think it would be interesting. I will look it up. I will do so, too. I'm not quite sure, but I think that in his lecture notes in Doti Vila, he is the treatment of also of the Kushi problem. But I don't think he has added too much, but I think it is just a historical... What year would that have been? I think it is something like 1921 or 1924. I wish that you know the date of 1924. Something like that. I must admit it. There is a conversation between Durandre and Dharma at this time. I don't know exactly. I must look at that. Because the Homoire gave lectures in Bolsao, before the 26th lecture. Do you like to go to the Homoire of the Homoire? And many descriptions between the Homoire of the Homoire. So it's difficult at this time to be separated. I should look at that. All the papers of the Homoire of 23 years. 23 is the first one in the Cold War.

45:00 I'll say one thing. When I've written my thesis, my ambition is absolutely not to give more in the Cauchy problem, but to adapt many reasons of Dhamma and other people in a way adapted to treated global problems. Lord, I have this ambition on that, and I give no offense to Hilbert, because we suspect to this, Dharma, no, no, Hilbert, very well, but unfortunately, I don't know absolutely the paper, I know the paper of Stenmark, but absolutely know the paper of Langeaux, I I took a couple of nine shows after a while. John, concerning lunches, you don't give the record. I don't? That's why I have the record. Yes, sir. Oh, you're right, you're right, I'm sorry. I will add that. Also questions? Thank you. Excuse me, but I'm a professor under the envelope of Professor Eisenstedt. I know of the doctors.

47:30 The half decade after 1915 was an inflamed period for the general theory of relativities. Einstein published the first major synthesis, although made often successful attempts to reconcile their ideas with Einstein's theory, or even to contribute to it. And most of them, for example, Lore and the Citroën as Blind Drive, carried on a more or less long but always lively correspondence with Einstein. Gustave Mee, at the time a professor of Halle University, was a physicist obsessed with the idea of a unified field theory for an e-thermonism, with other peculiar ideas of an intermediate position between classical and relativistic physics. In 1912 and 13, he published his Theory of Matter. He set himself the task of deriving the laws of electromagnetism and gravitation from a single wave function by means of the calculus of variation. However, he succeeded only in deriving Maxwell's equations and in making some coarser steps toward the derivation of the existence of the reaction. In order to obtain the laws of gravitation, he had to complete the electromagnetic collection of fundamental quantities with those of gravitation. Thus, a unified electromagnetic theory was not achieved. Mee's theory draft was held in high extreme by, for example, Hilbert and White. Mi's underlying worldview was that there exists nothing but the ether. Matter is a peculiar statement. All the elementary particles of matter are nothing else but places of accumulation of enormous quantities of energy in very small regions of the ether. And thus he defined matter in 2017. Mi's ether is, however, not a fluid or a peculiar solid body, not a special kind of dialectic.

50:00 Quote, one calls the empty space, conceived as a physical object, ether, or also world ether. He wrote in his lecture, Elexi Today. First, let's have a look at the documentary sources. The original letters are to be found in the Albert Einstein Archive of the Catholic University of Jerusalem. It was from me to Hilbert in the library of Göttingen University. It's appropriate here to express my thanks to the Jewish National University Library for having permitted me to record Einstein's unpopular letter. It's a pity that I've been unable to get permission to quote Mee's letter. I made a foreonly replayed detail very helpful. Professor Helm Speer of Freiburg University kindly informed me of the regrettable fact that Gustav Mee's estate is out of reach of historians. It consists of at least 1,000 items, among them I suspect letters of Hubert and Kretschmer. A 60-page manuscript on the Einstein Mii correspondence had already been prepared by Professor Hermes, but it had to be left unpublished because Mii's hairs withheld their permission to quote or publish anything. The documents are now kept by private solicitors in West Germany. Perhaps the committee set up yesterday could stimulate, in some way or other, the private university to start the drive for a choir in the essay. another preliminary remark I use present tense when speaking of the contents of the letters and past tense when other documents are reviewed me read a series of lectures on the 5th to 8th of June 1917. The lectures are called Wolfsker Lectures because the grant for them was given by the Wolfsker Stiftung on Hilbert's recommendation. Einstein was

52:30 hindered by illness in attending the lectures, to which he had been invited by Hilbert, and very probably by me, and his letter of excuse to me was the overture of their correspondence. this was on the 2nd of June he excused himself not only for being unable to take part in the occasion but also for a debate with me two or four years earlier in the summer of 1913 at the Vienna Natur where Einstein gave a survey of his and Grossman's novel theory of gravitation together with a sketch of similar attempts by Nordstrom published version, and also those of Abraham. In the discussion following the lecture, Mee reproached Einstein for not having mentioned his theory. Einstein apologized by saying that he left Mee's theory out of consideration because the strict adherent proportionality of inertial and gravitational masses does not hone it, and he had taken into account only theories which satisfy the principle of equivalence. This was the first account. In his first letter, Einstein comments on Mee's views, which have been expounded in the non-accident in writing letter, where Mee adhered to a covariance under linear transformations. Meanwhile, Einstein says it's sufficient to require covariance under similarity transformation. Meen's conclusion that the general transformability of coordinates, this means general covariance in these problems, is incompatible with the requirements for a closed theory. It had been shared by Einstein three years before, but not long. I think this is an allusion for the whole argument. And at the end, he joins me in his opinion that an a posterior specialization of the coordinate system would make the theory far more beautiful, but the attempts in this direction hadn't yet satisfied him. His reply is unknown, but he attached to it his Wolf-scale lectures because Einstein thanks him for it. writes, the main difference between their opinions is that he does not believe that

55:00 the ground state of the universe is flat. So this indicates to me that Einstein did not take part in any conferences having eliminated. He was happy to be here and had he the stupid idea to have a swim in that small fjord. On the way to and fro, stundering among those damned slopes, he must have been, joined me in his preference to a flat space. So he doesn't believe in the ground state of the universe is flat, that space is filled with matter only in finite regions. He can't accept that the metric test is determined by voluntary conditions at infinity and only in part by matter. Einstein told the letter with a remark. I agree with your view on matter. I'm of the opinion that he agrees with the view that matter is energy, but not with me's statement that these energies are going to be evil. As it's well known in 1910, for example, Einstein said, quote, mass and energy are equivalent quantities, like, for example, heat and mechanical work, and it's only a step to consider mass as an enormous concentration of energy. Attached to the latter, Einstein sent me the read prints of his novel papers, among the cosmological drafts of 1916, in which he introduced the cosmological term. The others are not mentioned by title in Mees' reply. Well, Mees' first known letter to Einstein based on the 5th of February, 1918. It initiates the discussions of the distribution of matter in the universe, the cosmological term, and the preferred system of governments. Now, in order to avert this form of reproaches, I underline that I shall use terms like system of reference, co-orbit system, space-time scheme, or even Yinkovsky gravitational potential and the like in as indifferent sense as they were used by me and Einstein. It will be a

57:30 find their up-to-date equivalents. I'm sure John Norton's dictionary will have lots. So you will hear a lot of positivistic accounts of letters with uncautious comments. Well, the first point is the global curvature of space and the masses. In his cosmological retirement, Einstein derived an expression for the dependence of the radius of curvature of the spherical universe and the average density of matter in it. Me assess that any preset value of the radius admits arbitrary densities, because let's consider a particular density for the definite radius. And in this case the corresponding gravitational potential prevailing in the vacuum between celestial bodies is mean costume. Had we another constant value of density, we could change the units of mass, length, and time in such a way as to restore the Jankovskian character. Einstein emphasized that Mi's argument leaves the fact untouched that the relation between the radius and the density is independent of the choice of coordinates. he admits that Einstein is right so that it was already a misunderstanding however new doubts arouse in him about the interpretation of the theory equation with the cosmological term if they are to be valid in each element of space then he has to suppose that they are pervaded by a very rare, continuous matter of density role where the real accumulation of matter, that means bodies, is absent. The reason is that far from celestial bodies, the geometry must be uniform of constant curvature and zero-notically extrude. Here, Meese seems to discover that Einstein's equations allow an interpretation coinciding with his concept of a very rare space-fitting ether of extreme density. A further problem for me is that the theory seems to use no means to determine the amount of discrete material particles necessary for shaping the universe.

1:00:00 Einstein points for the circumstance that though with the assumption of a homogeneous distribution of matter the local gravitational field may not precisely be followed, the geometry at large can adequately be outplanned. Me only answers that these arguments have the shape in this conviction that the constant density of mass must be assumed in regions, void of stars. And the second subject of the institute was the importance of the cosmological term. Me welcomes this new term in Einstein's theory equations for two reasons. The first is that it proves to him that the Euclid axiom of parallels and general covariance are independent of each other. The following argumentation might lay behind the statement. may take of any value zero included, which means Euclidean metric without altering the general covariance of the field equations in rigid figures. Einstein noted for introducing the cosmological term that's the way more relative to boundary conditions at infinity is not respected by me as he writes, considerations on conditions at infinity may give rise to interesting ideas how the events in finite regions are to be described. He holds Euclid's axiom for a principle of physics, like a principle of relativity or Hamilton's principle. It belongs, for him, to the mathematical foundations of the universe. In his second reason why he hails the cosmological term is that it's the missing link, for him, between Euclid's axiom and physics. If lambda is zero, the universe is Euclidean. If not, it is not Euclidean. In Einstein's reply, there is no reference to this interpretation of the lambda. Only that one argument for his having a version to the quasi-Euclidean solution that lambda zero and G.U. is constant can be found in a notice attached to the latter. The notice must be his paper, the print of the paper, and five will principally surround the main relativity theory which reached the editor of Annal and the Physique on the 6th of March. In it, he insisted that the general solution to the two equations in the absence of matter is

1:02:30 which contradicts a new principle called the Mach principle. The third and most significant subject of their correspondence was the existence of the preferred co-ordinated system interwoven with the problem of the relationship between general covariance and general relativity. On the peak of February, Mee introduces the discussion by an analysis of how the real world is met under a space-time scheme. He calls Einstein's cosmological attachment in which Einstein approximated the real space-time continuum by a space-time of constant three-dimensional curvature. Einstein compared his procedure with that of geodetic surveyors who approximated the complicated surface of the Earth by an ellipsoid of revolution. Me uses this analogy to prove the necessity of an absolute frame. Just as surveyors can't do without a single geometric form when they want to label peaks and sea bottoms with numbers indicating their height, So physicists can't do without an absolute spacetime scheme in which the world to arrange. Maybe the approximation is not unique, he admits. Conventions play a certain role in selecting the approximating structure, but not through the extent of mathematicians used to think. Me mentions a convention which, in his eye, lies at the foundation of geometry, namely that the space-time scheme must be uniform in order to be able to receive the world in itself, for what happens if one drops this convention? Me reads this Poincaré's model of a universe, in which the velocity of life becomes a function of space, and at the same time, the laws of nature, the size of atoms and elementary particles and the like, change in a way that compensate exactly for the change in the velocity of life. The new description of the world, relying on measurements carried out in distorted rocks and blocks, will be the same as the old one, except that it will establish a non-nuclear

1:05:00 than geometry. However, from the standpoint of logic, this means methodology for me, the assumption that differences in the velocity of light and in other physical quantities considered real may be elicited by mere mathematical stipulations counter this physical causality. Now this is precisely the case with Einstein's fictitious field. Mi doesn't mention an important feature of Poincare's universe, its finite size, before introducing the fourth field. Supposing that geometricians in this universe have started geometry with half of rigid blocks and allegedly uniformly running blocks, they will arrive at the non-Euclidean space without field and infinite in its dimensions. In reality, the universe is finite and egregious with a field of force prevailing in it. Finkari concluded that none of geometries may have a real existence, they are mere conversions, while Mi adheres to the variant with a field of force. Mi's favorite paradox which he deploys in his struggle for an absolute system of reference Let's suppose he writes both in his lectures and in his letters, that we hold a straight rod motionless. Its straightness is checked by running our eyes along it. That's by comparing it with a large ray supposed to be straight in a Euclidean space without gravitation. Now let's assume the gravitation of field along the rod, changing both in space and time. As a consequence, the velocity of light will also change and the rod will prove the wriggle. If the adaptation of it is equivalent to a frame of relativity, and if every frame is too equivalent to each other, the rod will be straight and motionless, and or curved and wriggling, depending only on our arbitrary choice of frames. To solve the paradox, me suggests dropping the general equivalence of frames. Other paradoxes were difficult to solve, as Einstein notes, the gusps of absolute space harms it. The rest, and the riddling, take place in different pairs.

1:07:30 Nephi is a place in Einstein's paper, Neuringsweiter-Integration, where Einstein himself followed a similar train of thought. Indeed, Einstein devised six types of gravitational waves among which three do not carry energy. arise from the circumstance that a very derived oscillating co-ordinated system is used. Given the square root minus g in unity that's offered a particular choice of things, these wave types disappear, which supplies for this choice a deep physical justification. The correspondence having come to an end, Einstein's reflections remained unknown. The next and most serious objection to general relativity was the non-existence of the relativity of rotation. He considers Einstein's example of two good bodies uniformly rotating around the common axis with respect to each other at a distance sufficiently large enough to observe gravitational effects on each other apart from other masses of the universe. The shape determined by local measurement is a sphere and an elusive revolution respectively. Einstein asked why they differed in shape. The Newtonian answer goes as follows. The laws of mathematics are valid in the space in which the sphere is addressed, but not in a space in which the ellipse is addressed. You must observe another expression that is relative spaces which they use, but I faithfully ate Einstein just as I promised. This Galileo space is an unobservable, mere fictitious cause of the different behaviour of the body that Einstein maintained. No other spaces moving in an arbitrary way lack these defects. Consequently, the laws of physics must be immune to frames. All frames are equivalent. Mr. Marxist, as the only observable causes, must take over the role of absolute space. He insists that the frames fixed to the bodies may be considered as equivalent only if a universe filled with a sourceless, fictitious gravitational field may be taken as equivalent to a universe having a homogeneous space-type scheme and filled with a gravitational field produced by material sources.

1:10:00 to reject this possibility without argument. Obviously, the fictitious fear this could be interpreted as a field geometries away by changing the structure of the Euclidean-oform in Kostian manifold, and means aversion to the equivalence of frames is an aversion to the geometrization of the so-called impressed forces. Moreover, as I know, Einstein never stated explicitly is a gravitational effect, though it is suggested by his comparing static gravitational effects to those of electrostatics and inertia to electromagnetic induction. Einstein's replies early that the two bodies behave differently because their motions are different in respect to the distant masses. In his other case is the rotation of the Earth. The statement that the Earth rotates, he writes, expresses shorthand a number of phenomena, a Poucault experiment with Passat winds and life. If we imagine the Earth at rest, we must attribute to the scheme of space-time setting, particular properties that means a long event. This metric will not depend on the presence of real bodies. No doubt, the phenomena will be described adequately before the procedure is mathematically impeccable, but it will include arbitrary moments, me uses Schliek's expression, thereby violating the kind of principle of possible. Einstein object that according to his theory of 1915, there is no ground to consider the earth rewarming action, because one can't distinguish between gravitational and inertial field. It's their sum, the total field, which governs the motion of two-course pendulum, and which satisfies the differential equations in the frame of trust with respect to the earth. Wee's last example of the absurdity of the relativity of rotation is the place of the rotating electron. The principle of special relativity, he begins arguing, is a true principle of relativity

1:12:30 because by its means the field of a uniformly moving electron can be reduced from that of an effluent address. However, the principle of general covariance has so far proved unable to produce the field of an electron rotating around the central body from that of the motionless electron, which eloquently proves that the principle of general covariance is not identical with the principle of general relativity of motion. I remind you that Professor Babu regretted yesterday that Einstein hardly ever even spoke of relativity of motion. So this was also emphasized, almost a bit emphasized by Me. Me is mentioning Kretschmann, oh excuse me, yeah, it's identical to the principle of relativity of motion. Should such a principle exist, when Me continues, it should have the form Kretschmann gave it. Mies' mansion in Kretschmann is not a mere reference to a paper. There was a closer contact between them. There are features in Kretschmann's paper, the 1917 paper, that suggest that he shared Mies' view in some respects. He also used the term ether and denied the general principle of the PBT in Iceland's sense. Kretschmer remarked in a footnote to the paper that Meek had given him advices in a letter of February 1916. Well, Einstein agrees with Meek in that the transformation of the electron into rest, though Meek called the English problem, may formally simplify this solution in a number of cases, but not in the measure the Lawrence transformation did a fascinating electron. He adds that the peculiar feature of special relativity lies in the fact that its empirical character is guaranteed by the Lorentz transformations. We turn to the problem of the rotating electron in 1920, as is at Nauheim or a poor force of Rosano. He set form in detail how to calculate the electromagnetic field of a charged particle

1:15:00 He called attention to the fact that to derive the field from that of electron address is possible only if the electron moves in a gravitational field. The Einstein's theory fails when acceleration is due to non-gravitational effects. As a consequence, the principle of general relativity does not merit its name. It's only a principle of relativity of gravitational effects. The problem for this is, however, wealthy of consideration, he adds, because according to that principle, a rotating electrode must not radiate energy. He was fully aware of quantum theoretical connotations. But how does Mead conceive the preferred frame to construct? By approximation. The process starts with terrestrial observations, for example made on the earth covered by thick clouds. Phenomenal thus observed speak of the earth's revolution around its axis and and of its center of mass being a test. A frame fixed to it suffices for the description of observations. If the precision of our instruments goes higher, a precession of the Earth may be revealed, with the consequence that an additional motion must be attributed to it, a curvilinear motion around the Sun. Switching over to a frame with its origin at the center of mass of the planetary system, the Newtonian theory could be reconstructed. As precision continues to grow, more and more bodies are to be taken into account in order to understand phenomena, and a series of frames could be anchored to the centers of mass. In this way, a frame is approximated, which may be called prefab or absolute in inverted commas. Because approximation depends solely on the precision of instruments available, In principle, there is no obstacle to reaching this frame. The only obstacles are practical. Einstein's answer is that the covariant equations are always satisfied, no matter how fast space is stretched and how frames are chosen. For me, the absolute frame of mean does not contradict Einstein's assertion that it's only the relation to the masses of the universe that math was,

1:17:30 because relation somehow means a position with respect to the frame determined by it. Einstein's motive to reject Mink's frame might be that in his eye this frame was a chart, while his own frame was a physical manifold, co-ordinatizable at will, and not only in a way to be preferred. The necessity of a preferred or natural system of reference is argued also by Mee's claim that Einstein and Schwarzschild, with their apparently pure mathematical stipulations, also selected a frame, though implicitly. Schwarzschild arrived at the solution of Einstein's equations in the case of a sphere, in fact of the last one, with two constants of integration and an alpha and a rho, and with the stipulation that is minus the square of the unity. Alpha was determined by the mass of the central body, rho was left arbitrary. As me suspects, Schwarzschild raised the discontinuity of the solution in the origin of the train out of Newton's potential M over R. Me, however, sees no reason of why it can't be put at another place within the body. According to his calculations, the field of a gravitating sphere in the natural system of reference proposed by him in the Waldskill lectures, turns out to be that of Schwarzschild with rho as zero. Outside the sphere, the square root minus g unity, that's untrushed in creation, in fact leads to postulating his natural coordinate system, at least in the case of a spherical symmetric field. Well, as a matter of fact, it would have been difficult for Schwarzschild to put the singularity not at the center of the body, because as I mentioned, he considered that the sphere as me asserts, but the mass point. towards the end of his last letter Me raises the question of what's the physical sense in the whole wonderful theory of Einstein if in the end general covariance is concerned by the introduction of a preferred system of coordinates he emphasized that just this problem was the subject of the

1:20:00 in which he gave a solution by formulating the so-called extended principle of relativity effect which starts like this. The physical laws preserve their form in non-Minkovskian religions too where it makes no sense to speak of transformation. The general validity of fundamental equations presupposes their general co-wagons. He closes the letter with a remark that he's playing with the idea of attacking the special problem with this principle and expressing in his way what he has in mind better than he can in words. He was true to his promise. In 1919, he published a paper on the subject, which, as Professor Eisenstadt, he showed in his paper of 1982, he is of importance for the history of Schwarzschild's solution, too. The discussion over the preferred frame entered the field of philosophy, too. In his letter of the 8th of February, Einstein promises me that a copy of Maurice Schlieck's Ramonzeit would be sent to him by Berliner, the editor of the Naturwissenschaften. Schlieck's booklet was also published in his journal, though omitting the final philosophical chapter. Upon receiving the booklet, after identifying himself with Schliek unreservedly, me quotes Schliek saying that, quote also, theories describing the same observations and proposing the same prediction are only various ways to express the same situation. among them however one must be found which is the simplest not because it is the most practical or most comfortable but because it contains the smallest number of arbitrary modes the principle of general covariance means continuous affords a transformation of the earth but it would entail the introduction of a method which would not depend on the presence of real bodies that it would represent in Schlieb's sense. What was a real body for me? He answered this question in his Orskeh lectures. I quote, when we suppose that the body exists, with it we reveal our

1:22:30 expectation that its existence will at some time be probable even if it's unknown for the time being. An material body, unobservable in itself, would be a logical uncertainty, like a four-angle triangle. The temporary impossibility of its observation does not weaken the, in principle, possible existence of a physical body, because, as we emphasized in the lectures and in the letter to Einstein, the world exists objectively independently of our perception. Because this statement had postulated lying at the foundation of scientific principles without which there is no experimental science. Einstein agrees with what Schick wrote, but not with the conclusions that me and Joe funded. I do not contest that the description of the work turns out simpler if one uses a system of reference for respect to which the Earth revolves in a certain way. that the corresponding preference of a single plane of preference should have a primary importance. Einstein's reasoning against the preferred system of preference is this. Me adheres to the flat ground state of the universe because a sufficiently small region of the constant curved manifold may always be taken as flat. In it, gravitating masses appear as sources only of local coordination. to the ancient idea of the surface of the Earth being flat. An essentially flat and infinite universe demands non-relativistic boundary conditions and, in order not to be curved by its masses, the assumption that for the most part is empty. Non-relativistic boundary conditions, however, must be dropped because, in theory, covariant under co-ordinate transformation but not covariant under boundary conditions would be inconsistent. these boundary conditions, the argument for the preference of frame and losses in thinking, loses its ultimate. The correspondence came to end not because they had suffered any of the disputed problems, rather because Einstein, as it seems, lost interest in a quarrel for

1:25:00 which he hadn't had much interest even earlier. Although they assured each other several times that they versed on full harmony. In the last letter, Mee confessed that their exchange of views was a squabble from which the only escape would be repeated talks. Einstein was at the same opinion already in his very first letter called, a talk is usually much more useful than a mere correspondence. They succeeded in meeting in Einstein's Berlin home not long after the 24th of March. The discussion incursed me to the extent that, as he confessed to Einstein, for about half an hour, his doubts about Kirk's face were partially resolved. But as time went on, the impression lost his strength. One night I observed that I used past terms instead of present, but I think it is still contingent inside the letters. We found a deeper reason why Einstein was unable to understand him fully in the difference between mathematical and physical trains of mind. The mathematician is allowed to make the most paradoxical assumptions and hypotheses, and to accept the most arbitrary conventions. However, these must be revised by physical considerations. For example, a physicist has to distinguish between a frame in which a power in the gravitational field is prevailed and a frame in which there are only real fields. We have the impression that Einstein oscillated between the two positions, although essentially he was on the side of the physicist. When Einstein emphasized the fundamental equivalence of frames, he acted as a mathematician. when he distinguished between frames or implicit details, he was a physicist. The pure mathematical procedure does not satisfy the physicist because it's far from the concept formation he needs in order to draw experimental important conclusions from his theory. In his opinion, Einstein had achieved his wonderful results, both and only as such by me, precisely because he didn't hear to the mathematical siren song of the libertarian world. May admit the psychological motive too. In a letter to Hilbert on the 22nd of December

1:27:30 he wrote that the terms like equal and infinite may connote other senses for him than for Hilbert and Einstein because he is a calculator physicist means equal up to such and such decimals, and infinite, never connoted actually infinite. Although Einstein ended his correspondence with Einstein in 1919, he returned to the most important issues in a witty dialogue in denatourism, between critical relativity and relativism. The critic poses a question, how can one accept that mere fictitious, that's called real, gravitational fields can exert an influence on the balance of flux? The relativist answers, the distinction between real and unreal does not favor us much. Instead of drawing a distinction between real and unreal, we will distinguish quantities which are due to the physical system as such, independently of the choice of the coordinate system from quantities which depend on the coordinate system. Accordingly, no quantity independent of the choice of coordinates corresponds to the components of the gravitational field at the space-time point. Nothing physically real corresponds to the components of the gravitational field at a given point. However, it does correspond to this gravitational field in conjunction with other data. For this reason, we can't claim that the gravitational field at a given point should be something real, nor that it should be something merely fictitious. The difference between the two distinctions that I see is not one of kind, but one of degree. The historically evolved vague distinction gives way to a more precise definition. The reason why scientists are not ready to accept or at least to understand the difference is, as Einstein put it, in the circumstance that according to the general theory of relativity, the connection between quantities in the equations and measurable quantities is far more indirect than in customary theories. The method of selecting the quantity is independent of the frame from all those

1:30:00 figures in the equation that seeming out of the absolute object is one of the theories cardinal points even today. But to draw conclusions requires a meticulous physical and of me's work, which I intend to do in the future. Both kinds of analysis are a way to be done. My brief remarks covered here and there only indicate some of the instructions. A question must however be asked before putting an end to my review. Did Einstein and me, through very pronounced personalities influenced each other with any respect. I think they did. A minor sign of changing Lee's position is to shift in naming his preferred frame. He started with absolute, then he continued with absolute in inverted commas, then in the natural, and in 1920, rational. He also accepted non-Euclidean geometry, medical device. It's not so easy to show instances of Einstein being influenced by me. I have the impression that he gathered an additional indivis for me, ranked behind it of the Sitter and Lauren, in his progression from a definite negation of the existence of the Iter towards its acceptance in 1920. Meanwhile, in 1916, he only felt that Chandler relativity was nearer to an interconcept than the special relativity. In 1919, in the Dialogue of Other Dimensions, he accepted that space, void of ordinary matter and the electromagnetic field, might have physical properties. This is equivalent to stating that space is a physical reality The decisive impulse to vote for the ether was given to him by the Sitter's metaphoric solution of the theory equations in 1917 and 1918. At the end of 1919, Einstein confessed to Lorentz that it would have been more correct had I limited myself in my earlier publications to insisting that it's the velocity of the ether which is not real instead of having defended at all the non-existence

1:32:30 of the ether because since then i've realized that with the word ether nothing is said but that space must be considered as the carrier of physical quality i only remind you how we defined ether in 1910 of course one calls the empty space concealed as a physical object ether When the case of Einstein and me underlies a rather skeptical thesis, there is no perfect understanding of each other. The theories change in the hands of scientists, taking part in a relay race called science with each member of the team leading the fingerprints of his commitments and beliefs on it. Fingerprints are not rationally incomprehensible for others, but this is the way science actually girls. And to quote Emmanuel Myerson, les croyants scientifiques forment parties entre grandes de lettres intellectuelles representing the law. Thank you for your attention. Applause Applause Applause Thank you very much. Thank you very much. Thank you.