Contributions of Lemaître to General Relativity (1922–1934)

0:00 Professor Saxel from Vienna has launched a book project, but he died, and so the main features behind the whole thing is now lost, and the fail of the whole thing is not clear, but nevertheless I should like to present the idea to this audience here. in order to get some ideas because there are some open questions and I should like to do some suggestions from you then afterwards. I should like to describe the book project. Maybe a good idea would be to take an example of just a talk given here which would lead to a clear-cut book of that type. Now, let's take, this is just an example to take from Stachel's talk here about the initial learning problem. Saxel's idea would be to take this talk and put the papers he quotes in these four papers together and publish this as a little book where all the papers, which are not so easily accessible, I mean, comb-found e-papers also, and also easy to access the old papers, put them together, make the book out. So, and this would be one more clear-cut example, there are less clear-cut examples, but nevertheless, that's the book project. Well, there's some organizational structure behind this, so we have a series, and this series has a series editor, editor, or rather three, they are a managing editor, so to say, and that was Seppsel, and now that's the trouble with it, and they are scientific, basically Jürgen Eders, from from the physics side I don't think so then there's my end And I included myself here, but of course, I mean the difference is not So that's sexual and that's the top and there's a volume editor

2:30 editor, which in our example would be on stage. So, the structure of the volume, then, volume, is there as a long comment, more than, on the papers to be included. That's the responsibility of the volume editor. Then there are the papers. And then, in order to sell these books, I don't have an additional incentive in those books. There should be also included, if possible, an essay written by an expert or somebody who is famous and somehow related to the whole thing. If you're always. For instance, in this case, it would be. So that's the structure. and this is one of the questions that's one of the big questions should it be a regional language well one should certainly restrict the domain of regional languages and for instance in problem of motion there's a paper by which is in Russian which is very long and it's in Russian so I think there's no question that it should be translated or omitted author with this signal. I thought that the original purpose of this series, which I've been associated with for a number of years, was to provide not translated papers but facsimiles of the papers, just to put these octogened papers between two covers. This is true. Nevertheless, the question... Because if you wait for translation, it will be years before they ever come out. That's true. Nevertheless, the question exists, and maybe there are some other I mean, these papers are so detailed, so specialized that whoever wants to read them will know the language. Otherwise, it's not that language. Okay, let me now just sketch the volumes which we have thought out. So the idea is that those editors think what kind of volumes there should be and what they should approximately contain. And they also select one or two candidates for a volume editor, and the volume editor then gives the detail content, because he's the specialist who, I should say, has to be contained.

5:00 And we have already volume one, say A and B, and that's about the electromagnetic world picture and relativity between 1905 and 1912. 11 it was? Yeah. So that's Ellumeck, 12. And special relativity theory, 1905, 11, let's say, and the born-mitted in this case, Miller. And then what is also quite clear, I think, and in preparation already, in manuscript form, and the problem is only this one here, is cosmology. log G, taken care of by George A's. And, well, then a third volume would be special relativity and quantum theory. Quantum theory. And it's the interaction between those two, especially the development of relativistic quantum field theory, expression relative spin statistics and so on all these things and originally i thought i would try to be the uh editor here but it turned out that silvan schweber is the expert since at least 83 where he already published his lectures in this so it would be schweber he also agreed Okay, then there's also volume 4, which is general relativity and math, mathematics. We are not as definite about all this, but we agreed to do something about this. Then there is a volume 5 about alternative theories of gravitation, and we would include not all of them of course, but only those that gave rise to developments that are interesting even nowadays.

7:30 For instance, about these alternative theories, we would include a quick example of this, we call it Sir Klein, just because Sir Klein is still a thing that is being discussed nowadays. alternative theories, and also, we'll divide between the same, quantum theories of gravitation. But also we asked Professor Bergman, and he agreed to write about this. This is now a long time ago, and I don't know yet, and he will still be here. Okay, so I would rather put a question here. Then there's the problem of motion, and there's one volume about curved space ideas before general relativity, which is also interesting. Anyway, this is a sketch of the project, and I should like to have some comments on your side about this project, not now, but just during this. Which is the publisher? The publisher originally was supposed to be Fivik, just because Saxel had good connections to Fivik and had an influence on the publisher. Nasex was dead, and therefore only the publisher will have an influence on it, but maybe this state of affairs can be still there. The name of the series? Not yet. And also the series, all the volumes should have a common introduction, so to say, and therefore this, not only the name, but the common introductions should fit the whole series. And that also was a problem, and that's one of the reasons why this thing, which is already more or less ready for publication, has not been done. Thank you very much. I don't think we can have any more discussion this morning. No, no. But anyone in our audience, we have to go. I'm happy for any suggestions or feedback. Thank you very much. Well, our last speaker today, indeed, and I remind you again about the problem of the bust at 2 o'clock, our last speaker today calls himself not a historian, but a witness. He's too modest, but today he's going to be a witness to the qualities of the work of Georges Lemaitre.

10:00 that she didn't go there. Half of my paper has circulated here. There are a lot of mistakes in it. Nactilographic mistakes. Because I have been at some difficulty to have it done. Well, in 1914, the war interrupted the study of Le Maire at the University of Louvain. It was the link to become a mechanical engineer. He joined the Belgian army and fought in the 3rd Regiment of Achilles. After 53 months of war ordeals and military camps, he lost interest in a professional career and decided to become a priest. But before entering the major Malin seminary at the end of 1920 for religious studies, he shifted his enrollment of the university from engineering to mathematical science to pass in 1920 the doctorate with the latest distinction with the Lavallée-Boussaint and on l'approximation de fonctions réelles à plusieurs variables. He started then to be interested in the theory of relativity. the program of religious studies letting sufficient measure for reviewing the literature published in special and general gratuity and preparing three essays which he submitted in 1923 to the commission in charge of allocating scholarship for periods abroad. With the scholarship granted by the Belgian government he was accepted at the Observatory of Cambridge University by the director Arthur Eddington, where, as research, he pursued the study of the concept of simultaneity in general relativity. Pleased with the result, Eddington added a foreword to a manuscript submitted to the philosophical magazine

12:30 entitled The Motion of a Rigid Body According to the Volartar Relativity Principle. published in July 1924. I am not going to speak more of it because of the lack of time. The following academic year was spent at the Harvard Observatory Cambridge in Massachusetts under the tutorship of Arlo Champlain for astronomical studies. Its main interest continued to be relativistic cosmology, in particular at the meeting of the American like the April 1925, he showed how, by reformulating the Sitter's solution of the Einstein equation, it could remove its previous inhomogeneity, and how new coordinates separating space and time led to a linear relation between velocity and distance. The features of the visitor universe model 1917 were quite intriguing, and their consideration influenced Le Mans in its conception of the expanding universe. We are going to give you, very happily, the essentials of Romain's paper 1925, with some manuscript notes of copybooks of the same epoch. Einstein studied the development of arithmetic cosmology by pointing out that the field equation in their general form with the cosmological constant allowed the possibility of a homogeneous finite universe which is closed and has no boundary. Moreover, Einstein took it for granted as the majority of the scientists of that time, that the universe in the light must be unchanging with time. The work of De Sitter was a critic of Einstein's cosmological hypothesis, and to distinguish which both solution, the first form, the S2, is the form of Einstein, and the S2 is the form of Dusseter. But if you put chi, I don't need to realize what it means for the connotations.

15:00 And if you put chi equal pi over 2, the Sitter universe, we see the y-trace, the S2 equals 0, gives the equation minus rs squared vp squared plus d theta squared plus d theta squared plus d theta squared plus d theta equals 0. then you realize that chi and theta and phi are constant and they are an horizon of an observer you see at a quarter two of the universe a universe is an is then not homogeneous and there is also a difference between the conception of T between the two, Einstein or the second solution. Four, the meaning of T that Einstein developed is really the cosmic time understood as a time measure by a clock permanently associated to a framework in which the matter is at rest on the mean. But it is not the case for visitor. Because naturally it is not homogenous because the observer must be any place at all and as a consequence the solution is not homogenous. And to re-establish the homogeneity, Lebed proposed a new time. It is written on the equation 3, t equals tau, by introducing a new time depending on k, k, t equals tau minus rs over c, logarithm of k. And a new radial coordinate, R equals R s sinus chi A minus C tau hat on R s. Giving the metric of the classical form that we now consider the Derseter universe,

17:30 ds squared over c squared d2 tau squared minus a exponent c2 over rs, d r squared, r squared d2, theta squared, put r sin square, theta d phi squared. you realize now that the first idea of the sitter the time was not coming in the formulation the other saw an idea of the static universe in this case you don't find a static universe anymore by the change of variable and the geometry of the space here has become also an ingredient in this transformation. Now if you make the transformation a change of scale, R prime equal R exponent A minus C tau 0 over R S and tau prime equal tau minus 0, the field you see the ds2 remain the same. And as a consequence, we have a form that we could call a chromo-physical static, metastationary field. study of the visitor universe has been at the root of the following development of Le Maire time. Taking advantage of the Gordon-Marquet agreement Le Maire at the Harvard Observatory also registered as a graduate student in the Department of Physics of the Massachusetts Institute of Technology and finally under suggestion of Edithton doctoral dissertation, a memoir entitled The Gravitational Field in a Fluid Sphere of Uniform Invariant Density According to the Theory of General Relativity. In fact, dealing with

20:00 paradoxes encountered by the Schwab-symmetry in a deceter universe. This was the very first step toward a theory of the expanding universe. This dissertation was never published. It was accepted in the beginning of 1926. Coming back from America, he was appointed he was appointed as associate professor in the department of mathematics at the university of in 1926 at the beginning was a very light not possible He was then appointed and you see, in 1926, and he had ample opportunities for researches, mainly focused on the set of cosmology. In the way of the paper published in 1922 by Alexander Friedman, he was the first to show or to introduce a radius-Barin-Stein-Investitor metric, published in 1925. Then he deduced from the modified metric a linear relation between radial velocity and distances for galactic neighborhood. In 1927, he published three papers concerning relativistic cosmology in the Amnand de la Société Scientifique de Bruxelles, improving some of his previous work, one on the relativistic time, the other concerning the motion of a rigid body in the theory of relativity. The third one is the most important paper entitled, Are the universe homogènes, the mass constant of the rayons croissant rendant compte de la vitesse radiale des nébuleuses extragalactiques? Relating a solution of the general relativity to observational astronomy.

22:30 In fact, Le Maître was striving for a theory of the real universe. by the physical conditions, and have continually in mind the astronomical observations. Le MED likens the galaxies to the molecules of a rarified galaxy, when thus gets an homogeneous picture of the universe, allowing one to speak of an energy density rho of which the main part is due to the mass, the rest mass. There will also be a uniform pressure peak arising mainly from electromagnetic radiation and in a nearly negligible part from the motion of matter. If you take r, radius of the universe, varying with time t, and if you use natural units, which means to put c equal 1, g equal 1, and ds2 equal minus r squared d sigma 2, where r squared d sigma, r d sigma is the limit of distance in the field in Schumann. Lemaire deduces from Einstein's equation, the two equations are here, you don't need to read them, you could look up at me, it would be easier for me. Lambda is the unknown cosmological constant, the dot means time derivative. These equations are the same, The Friedman equation is elliptical geometry, except for the pressure term P, which Friedman did not take into account. They need the conservation of energy, which is written here, the third pressure term P. Now, if we take a best elliptical universe mass, then you put P equals zero. So, P, in fact, we thought always as P as negligible, except for certain problems.

25:00 Then, in that case, you have the mass of the inverse, you have the relation, rho r cube equals mass of the inverse over pi over 2, pi squared. and the first equation then could be written on the integration form as the equation 10 is equal and could be integrated here is the universe of the system and the math integrated this equation in using the choice of Einstein for the constant lambda, you see, lambda equal r, rA exponent minus 2, and you got this integral, and the integral, as you realize, is a logarithmic integral, I got here his first model where he shows that the solution of Einstein is unstable in a very simple way. This is the solution. R T equals minus infinity. R equals Ra. And the redshift of the expansion, the maximum, will be the decitor value, 1 over Ra, 2 squared of 3. And delta lambda over lambda gives you this expression. When Lemaitre learned the existence of some important redshift of external galaxies, although was not yet clearly stated, he decided to publish in 1927 Schiesel and from the recipe available Reduce R over RA into 21.5.

27:30 This is the first number of the next. If t is the time and r is the model of Einstein, static model, and starting logarithically at t minus infinity. It is coinciding with Einstein model. Now going back in time, the rate of expansion tends to zero. Loginically, it proceeds in an accelerated rate reaching a maximum of 1 over Ra root square of 3 at an intermediate to the future as the versitor solution. The versitor solution will be asymptotic to this. He tried to draw the attention of Einstein on his result when he was attending the 5th Solveig Conference in Physics in Brussels, October 1927. Einstein was post-havoured, your calculations are correct that your physical insights are believable. Likewise, Le Maid fell with the sitter at the 3rd General Assembly of the International Astronomical Union in Leiden, 1928. But later on, at a meeting of the Royal American Society, January 1930, the sitter endorsing the careful observation made by Edwin Erbel at the Mount Wilson Observatory concurred with the majority involving the linear relation, radial velocity, and the law of nature, but he confessed so that he did not know how to assimilate it in his cosmology. This statement was published in the February issue of the observatory. Le Maire read it

30:00 and wrote at once at Eddington to remind him that he had already solved the problem and also to ask him to send a reprint of his 1927 note to the sitter. This time, Eddington paid attention to Le Maire's contribution, dispatched a copy of it at the sitter and sharply, and reworked his communication to the Royal Society to make of it a critical review of Le Maire's theory of the expanded universe. An English translation of Le Maire's paper, with slight amendment where it was published in the Mostly Notices March 1931. Then Eddington conceived the expansion as starting from a state of equilibrium given by Einstein Waddell in a conference of the British Mathematical Association published in Nature January 1931, under the title, The End of the World from the Standpoint of Mathematical Physics, we consider that the second law of thermodynamics can be extrapolated to the future, toward a state of complete disorganization, expressed by an infinite entropy. However, the extrapolation in the past all probably give a beginning with zero situation that it could not accept as such in the meantime Le Maire reconsidering the physics related the geometric model of 1927 thought the logarithmic solution quite artificial to describe the evolution In fact, it meant the slowing down of all physical processes in the past. Radioactivity and degradation of energy seem to indicate just an opposite evolution. Looking back are the two parameters coming in the equation lambda and m.

32:30 there was no special reason to give them the values chosen by Einstein. For M greater than zero, solution will exist with scaling factor reduces to zero So, punctual singularity, then, for a certain time in the past, and it could be considered as an origin. For m, smaller than pi over 4 R squared of lambda, r increases indefinitably. for n greater than pi for lambda r reaches a maximum to recolapse and for n it would pi, the pi at the point of n pi over 4 for lambda and r reaches a static solution there is a solution starting when this the origin is quite arbitrary the other branch of the logarithmic solution could reach the Einstein universe. He had the opportunity to show them I made the calculation, the integrated that between value of m and lambda, you see, it is possible to integrate it by a rare star elliptic function. I know of it because I was the little man who was working on the calculation. Then we had the opportunity to show them to Einstein during the state of Einstein on the Belgian coast.

35:00 and then he learned Einstein informed him calculations of that time were already made by Friedman works in your parliament at that time this is not on the written paper but he said he didn't believe those calculations at that time Einstein was not he thought we called Le Maître did not publish those calculations, but left drawings of these solutions, 1928, published in the 109 Lecture of North, Physics of the Expanding Universe, published in 1979. They were, however, used type A in its proposal of universe model with initial similarity in 1931, as well as its scheme for the formation of galaxies, the type B. Type B, the series will collapse, the solution is like this, and the solution will collapse of type A is like that, taking lambda slightly higher, this is the second The matrix is a second type. There is here what we call a stagnation period. This may be an important idea in his conception of cosmos. The reading about the difficulty experienced by Einstein for the variation of entropy in the past,

37:30 triggered off his imagination. Convinced that the quantum theory must play a significant role in the primitive universe, he sent to nature 21 March 1931, a letter entitled The Beginning of the World from the Point of View of Quantum Theory. He introduced the revolutionary idea of a supreme initial concentration of all matter five minimal atoms, identifying matter and space-time. Atoms splitting irreversibly into smaller and smaller pieces, giving them a first version of what has been called the Big Bang. Le Met was invited to participate at a meeting of the British Association on the question of the relation of the physical universe to life and mind. Besides, he took part of the discussion of Jeans, Verceter, Eddington, Millikan, General Smith, Bishop of France, and Lodge. The communications were published in The Supplement of Nature, October of 1931. In the discussion of his hypothesis, Lemaire proposed big stars as a random of the successive splitting of the primal atom with a fine work of radiation, source of the actual cosmic phase of high energy. Receivers, in the respect to some dogs, that hypothesis it had to be worked out unscientifically with more detail. From the general scenario of the Metroposal, the universe expands rapidly from the very and it got into a stagnation period and it is during that stagnation period that it could show my variation calculus that galaxy could form. And the interest of such a model is

40:00 that you have, instead of a linear expansion, this scenario will retard the moment of singularity to allow enough time for the formation of galaxies, stars, and planets. The Met looking for a proof of the initial firework thought to find it in the cosmic rays. The studies extended during 20 years, mainly in collaboration with Professor Valakta, but we are not to speak about that. Beside the topic of this conference. During the end of 1932, in the beginning of 1933, he was in California where he met numerous astronomers, in particular Hubble, Professor Husserl, and finally he had a lively discussion with Einstein in Pasadena. this meeting was more cordial than the preceding ones although Ayseng accepting then the expansion of the universe was very skeptical about a singular beginning he thought that it was due to the isotropy of the modern study and a reflection of the religious dogma of the creation in the thinking of a priest However, the discussion was mainly centered on the cosmological constant, lambda-turn, that Lennep kept in his cosmology against the strong opposition of Einstein and after him of most of other cosmologists. But there are articles of the papers of Pasadena, because the newspaper men heard they were discussing of little lamb, and they thought, just little lamb, they heard little lamb, and they said it was very clear, but they were discussing. I have the clip with the... The conception of the cosmological constant as expressed by humanity, 1933 paper, Evolution of the Expanding Universe, was that the vacuum would exercise a repulsive

42:30 force introducing a negative pressure turn. Back in Belgium, he felt that he had to present a structured version of his theoretical researches in relativistic cosmology. In that paper, entitled Renevers en Expansion, it is fully expressed the proof of the non-singularity of the so-called Schwarzschild singularity, although already implying the phytics of the decitor in verse 1922, in the copy book, and in one of the manuscript form of the thesis thesis of 1925. In the same paper he shows his answer to Einstein about an The paper starts like this, starting in a quadratic form, you see there is no rectangular of the quadratic form and that, then we calculate explicitly the equation, the equation, express the equation of gravitation, and then we choose a case where the r is i are only functions of times t, what you put x4, or if you want, unique function of x4, x4 equal to t. Element shows that modems with initial singularity is deleted to the condition I am going to write the condition is T1 1 plus T2 2 plus T3 3 minus T4 4

45:00 smaller than 0 if you take an homogeneous universe This is rho, the density of A and D, and this term is P and T, the tension. This condition that you see here is for a particular phase, is very much the same condition of Hawking introduced 40 years after. And he showed that in that case, you must have singularity. And now, he studied in particular spherical similes. and he showed in general a particle choose x-fl constant along the universe line the line is four equal t constant are trajectories perpendicular to each one then all the rectangular term of t into 0 and then you get a relation between t and one the previous relation scalar function N, in such a way that this relation could be written in those two equations, a scalar convention, 4 pi rho r square v r dk and dm dk, 4 pi t r square v r dk minus dm dk.

47:30 I know the fourth component of Einstein's equation is written that way. P when four equals zero gives this relation. If we write normal conservation theorem, you have this relation. In the external field, p and tau would be neglectic, p and tau are neglectic, c is then a function of only p, you could see from this equation, and then you could reduce c to the the speed of light is zero, by a change of variable. We get, then, from this equation, 1 over rA drdp. We have that of t, and the big creek is becoming e squared, this matrix, this and here. And it is rather not to prove that the trust in the R equal to M, the similarity R equal You see, the proof is given, where the proof is given and taking into account lambda. This is very, it's a bit complicated. I have simplified for the meeting because it's already quite late. to simplify I'm going to put the cosmological constant equals zero and use natural coordinates putting g c zero equals n space and using space which means f the key equals n and in the back room m is a constant then the equation

50:00 is becoming, can be written r vr vt squared equal to m. In my integration, you get 2-3 r exponent t r to a whole square of minus 2m, t minus k. It took as a constant function of integration, because it's a partial differential function, it took a linear relation with k. with this linear choice of the function dR dP minus dR dP equals dR dP and then you get dS2 to minus 2mR dP dP square minus r square dP square Then you see, on this combination, the singularity is simply r equals zero. No, no, you have to, the expression, the ordinary expression of Schwarz's equation, and you could do it by a transformation. Let's go again. If we take R as a coordinate, we define a coordinate And express the field in Schwarzschild form, dT, dT, minus V square of R over 2m dr, dT equals dT, dT, minus 2m r over 1 over 2m r dr.

52:30 Then the S squared, take this form, and finally, Schwarzschild form for, take the Schwarzschild form for a punctual mass, and integrate in 11, the transformation, because the differential transformation, we have P to Tau minus 2, R square of 2mR plus 2m logarithm of R minus 2m, R plus 2m. It is the transformation that gives the dimer of Schwarzschild, which is tau, and from the dimer T, and it is a transformation which is inadmissible for r smaller than 2m. then R equal to 2m spurious singularity similar to the one of the centers of horizon in the original form of the sitter unit is exactly the same you quoted from Lemaire you quoted from Lemaire yes always but I made I simplified Simply, Le Maître took lambda, then he had to introduce more complicated lambda difference from zero. I shall give you the, I have one read print of Le Maître. I think my time is over. If you really have finished, don't feel obliged to finish if you have more to say. I think we can still... No, no, no. I could speak more, but... We have to answer questions. well thank you for your lovely canonical account

55:00 and let's ask for questions that I think we can manage a few minutes still I will resist the temptation to say anything but I'm sure that other people will want to say something can we start with you we all laughed when you reported Einstein's worry that Rimetra's interest in expanding models was related to his religious commitment but I won't put the question seriously the man who's a Catholic priest is there a connection between his working no connection no connection at all himself answered to that at the is that we have no connection we are not this absolutely not I could I have been a paper published I'm not here I could give you the reference no connection at all I was wondering that Lemaitre is not the only one of prominent 20th century physicists when he first studied engineering, he arrived to see another thing, and we could know how a new mission goes. Therefore, my question is, as you work with the new Lemaitre, did you feel that his initial introduction to engineering in any way affected his work or... Yes, he was quite interested in mechanics. He has always been... He has worked on the free body problems, he has worked a lot of a lot of mechanical problems, but he was also a physicist, you see, he wanted to have a model that tried to explain, and he started a physical cosmology, frankly, because before Before that it was more, more mathematical, but he wanted to be very near.

57:30 But he made a mistake that he thought that cosmic radiation could be the primitive background radiation. And he didn't change his mind early enough. It was a pity. He continued to believe that cosmic radiation was out there from the beginning of the universe. At the end, he changed very slowly his mind. And one thing about this idea is this, I wanted after the war, the other one, after the war, myself, I, I'm sorry if I speak of myself anyway, And myself, I made my thesis on cosmic aviation, and I worked on cosmic aviation, not on cosmology. And after the war, when I came back, I tried to explain to him that cosmic aviation was not the solution. and they also get in touch with Gamow. Where Gamow are the polyneutron hypothesis. The polyneutron where and the man he started to believe that we are the primitive star, big star. Then after he dropped the idea. But he has some difficulty, you see, practical physics, elementary physics, it's more entomology than science. It is very difficult. No, he couldn't. Then, you see Urino-Od, he was far away from everything in Belgium, and after, he studied a lot of celestial mechanics, he did quite a lot of work, and also informatics,

1:00:00 that's what he called informatics, quite a lot. He was a good expert. Oh, he was a good expert. Very, very good expert in informatics. And what happened with this, I remember because myself, I became a meteorologist, and at the end, I returned back to the university. and I went with him to the meeting of 1961 in Berkeley and then at that time it was all for the oil and so on, you see, they were on the theory of oil with this sense of creation, and it was much against it, but it was in the favor of the moment. And I remember when it got they were laughing at him telling, this is the Big Bang Man joking about it because he didn't like the theory of continuous creation that was the situation it was on the end when the discovery of the P degree coming back on the nation and we realized there was a proof of the crime. But it is a pity we made the step to get in touch with Gamow and the school. I thought myself, Gamow was right in his 1950 paper, the formation of the nucleosynthesis and some kind of a step of the big time. Naturally, we didn't discover the crossing back on radiation a lot later on. It was a bit too late. He was a mechanician, but he was also a physicist in some path. He had the last laugh.

1:02:30 someone have a hand mine is an entirely frivolous question the little lamb intrigued me did the reporter put a Christian theological interpretation no, no, no, there you have a puzzle and you see the change of mind about interpreting it's a parameter existing and we want to keep it and then the question of cosmological constant will be discussed here again I suppose tomorrow somebody and you see it is still although Einstein tried To have it disappeared, reappeared, non-disappear, no, it's a theory of change of space in the beginning of the universe, they are a period of de-inflation theory, we are a period of where you reintroduce number. Actually, the Casimir experience shows that it remains of energy when they are taken over the mother. But the value of land life is a lot smaller than you can imagine by Einstein or the man. There is a poem in English, Little Lamb Who Made Thee. I can see a footnote in the future, Einstein. I think I just had a question about your reports on conversations in the Metro and Iceland are fascinating are these based on personal reminiscences or did the Met keep a diary or letters, how do you know no, he was not a writer myself, you see, I've been when I was a young student I've been drafted as a technical assistant to make his calculations And then after, I made my degree on cosmic radiation, and I left Louvain in 1938. Then he started to have some assistance, but I was the only one who was working alone. And, oh yes, we were quite, he was a, naturally, I wouldn't say a friend because, yes.

1:05:00 He told you about the conversation. Oh yes. This conversation, with Einstein, I was there. You were there? Yes. And here in this book I have written a picture. I have written with Ella, who came and pushed me to do something. they have written a book I mean you like the circulation you see a picture of Lomé and you see Lomé and John Thank you. I think the best solution might be to leave the book out to the front here. People who wish to look at it afterwards will use it. We will put it here. Oh, okay. With the purpose to give it. And then we are ready to see. I think, with that, we really must draw the morning session to a close. We thank you once again for... And it's now a question of two o'clock for the bus.

1:07:30 that's the point because he cannot have a so we must go up to the physics laboratory just 200 meters ahead do you know where it is? it's behind, near the middle I would follow you like little males. Thank you.