Interview with Felix Pirani

0:00 It's the 25th of October, after 2 o'clock, and I'm speaking with Professor Felix Karani. Well, I'm interested, so as it's explained, in the problem of radiation reaction, gravitational radiation, and ancillary topics in general, almost anything that might be loosely connected with the subject. And I'm interested in hearing about him discussing your own work in the field in the 50s and 60s. And maybe I should begin just by asking you how you first went Yes, yes. I used to review for math reviews. And one day I got a paper by T.C. McVitie to review, which we could probably locate if you're interested in knowing which one it was. and McVitie was trying to find wave-like solutions of the vacuum field equations. And so he would make some metric components dependent on x minus ct and try and find a solution that way. And he kept on coming up with flat space times. It was not very satisfactory. And then it must have been the year I may get some of the times mixed up. I was in Dublin for a year with John L. Singh at the Institute for Advanced Studies. And he had written these two books, The Special Theory and The General Theory. And I proofread, or I went through, as I thought, with a fine-toothed comb, although I missed some things, checking the equations and doing a serious... checking job and I discovered what I hadn't known up to then which was that you could classify electromagnetic fields algebraically into the general and null is what they would be called nowadays. I didn't know anything about that. And then I thought to myself well

2:30 about doing the same thing with the curvature tensor. The reason that I was interested in the curvature tensor is that Singh had been very much a guy who pushed the equation of geodesic deviation. It seemed to me this was a nice way to do things, to use the equation of geodesic deviation to squeeze out everything that you could from it. And so I was paying attention to the curvature tensor already in that environment. And so then I thought, well, if you can classify the Maxwell tensor and the null Maxwell tensor goes with the electromagnetic radiation, maybe this is the way to deal with the problem that he was addressing and let's look for a classification of the Riemann But the way I started looking was to look into literature, and I found the paper by Petrov where he did the original classification. So I thought, well, I don't even have to do it. It's all been done. All I have to do is to look for examples. I've left for some examples and I wrote a paper in 1956 or 7. I've been in Dublin from 54 to 55 and I wrote the paper about the gravitation and the radiation. Invariant formulation, the gravitation and radiation theory. So it was MacVillie not having done it right and Singh, knowing this thing about the Maxwell tensor and just serendipitously putting those together, which got me through, first stimulated my interest. And then I came here. After I'd been in Dublin for a year, I got a job here. Bondi had moved from Cambridge to King's College. Perhaps I, can I go back a little further back? I was an undergraduate in Canada. I finished my degree in London, Ontario, I went to Toronto with, INFIL, at that time. Einstein, INFIL, that INFIL, Einstein, INFIL, Hoffman, was head of the Applied Math Department. And Schilt, Alfred Schilt, was one of the lecturers.

5:00 And Schilt was about to move to Pittsburgh. And that the summer of 1949, there was a Canadian Math Congress out in Vancouver where Dirac came and talked about his way of doing mechanics with mechanics with constraints. When I got to know Schilt during the summer, he was there too, and we got on quite well. What I had planned was to go back to Toronto to do some more graduate work. I haven't got my master's degree. But Schilt was going to Pittsburgh to the Carnegie Tech. He said, why don't you come to Pittsburgh? He was going to a new place. He didn't have any graduate students. He wanted somebody to work with. Feldman and Feld said, whose initiative was this? And Schilt said, it was his idea. And I said, fine. So I went to Fitzwill with Schilt. Now, during World War II, Schilt, who was an Austrian, and Bondi, who was an Austrian, had been in, it's really a concentration camp together. They'd been interned together here and sent off to Canada when they would have the policy of sending shipwaves enemy, quote, enemy alien, unquote, off to Canada. Some of them made it, some of them didn't, those two didn't make it up to know each other. So when I finished my work with Schilt, when I worked with Schilt on the, using Dirac's techniques on the Einstein field equations for a PhD, I thought, well, where can I go and do some graduate work? about that time the steady state theory was very much in the air. I think Hoyle was on the cover of Time magazine. There was this big problem which was that the age of the earth was about four billion years and the age of the Hubble time was about two and a half billion years. And the steady state theory was really invented to get around that. So I was fascinated by this idea and interested in cosmology anyhow

7:30 and Schilt knew Bondi because they came together so Schilt wrote to Bondi you know the sort of international old boy network and so I went off to Cambridge to do graduate work with Bondi and the way the system works another PhD so I had a Cambridge PhD as well as a Canadian Tech PhD and I worked with Bondi on cosmology and okay I'm just talking to a guy and a machine at the same time this is my friend Okay, see you later. oh, then I went off to Dublin for a year to sing, and while I was in Dublin Bondi moved from Cambridge to London. All the sociology actually matters, so I'm putting it in. to establish another lecturing post and said, you want to come to London? So I came to London and that was my first job and it was my only job. I stayed there from 1955 until I retired in 1983. So that's how I got to London. That's how I got to be interested in gravitational waves. And Bondi was easy to... who also had worked in relativity theory and is interested in stellar structure as well. He was, whilst he is very broad in his interests. And I got him interested in gravitational waves, and then at that time it was still possible to get money from the U.S. Air Force for doing things over here, so we had a U.S. Air Force research grant. Lots of people came and went, and there was a whole group running in the late 50s and 60s. A lot of it financed by the U.S. Air Force. And we had once, we had a problem, and Troutman was invited about 1957, I think, 58. And then we read the fine print, and it said that there was a whole list of countries whose nationals could not be supported by a U.S. Air Force grant.

10:00 There was this list beginning, Albania, Bulgaria, China, you know. So we had to get traveling money from somewhere else. Poland was on this list of no-no countries. So that was the context, I think, in which this work on gravitational radiation did. Yeah, it's not started. And then Bondi did his thing, and Sachs was here for a while generalised on what Bondi had done. They were coming at it starting from the metric and I was coming at it starting from the curvature. There were lots of overlap and Sachs discovered the Peeling Theorem if I remember right. I think so. Maybe he was still in Hamburg. He was in Hamburg with Ehlers. That's right. He came here from Hamburg. Maybe Peeling was just being worked out then. I don't remember exactly. And there was a very exciting meeting, exciting for me as a young postdoc in Berne in 1955, which was the first of the GR meetings really. And it was just a few months after Einstein's death, and there were all these guys, you know, who read about them and read their books, there was Pauli and Bohr and Wigner and Bergman, all those guys, and they were sort of in the flesh. And that was very exciting and stimulating. And then, you know, practically everybody who had made any contribution to relativity a small lecture hall, maybe 60 people there. Right. Was gravitational radiation aesthetic with that confidence? I don't remember that it was. I was interested in Mach's Principle at the time. That was Bondi's doing. Bondi had stimulated me and Dennis Sharma to think about Mach's Principle. My contribution to that meeting was about Mach's Principle. all the different things it might mean. Well a couple of years later then there was a conference at Chapel Hill, which I guess was a support about the U.S. Air Force. That's right. And I think both you and Bondi were there.

12:30 And that radiation radiation was more on the topic. It was, yes. You know, you told me when you wrote to me that you were interested in radiation reaction. The radiation reaction theory was something which pretty well passed me by. I mean, I knew about Einstein's calculation of the emitted energy. Right. And I used to think and talk to people about how this would show up in a change in the motion. I don't remember doing anything that was of any use to anyone else about this. Well, perhaps I'll be using a minute by explaining very briefly why I was particularly, there are a number of other reasons too, but one reason that I was particularly interested in speaking to you was that my impression that I gained, and here in fact I'm also taking it simply from a couple of people who have written down their recollections and the progress of radiation reaction gravitation when Princess Kipp unpublished a short piece. And I guess that at this time there was a certain amount of debate about whether gravitational radiation existed at all. Was there a carried energy? Right, carried energy, that's right. And an aspect of this, not the only aspect, were attempts to develop, for instance, a theory of radiation reaction in binary systems, for instance, which had run into trouble with various contradictory results, some of which said that energy wouldn't be taken out of the system. and therefore Kip's original Kip really made the proposal that I should look into this history and his original idea was to look into this particular debate for instance about Gene Fowler who's put him and it seems that and because there were a number of issues tangled up I mean Infel for instance didn't just have one argument radiation in this case. There was not only was there the problem of the radiation reaction calculations, but there had been issues raised about whether there were energy carried in the waves because of the problem of the energy amount of pseudotensor, which could be changed

15:00 with a quarter transformation to appear to have a zero everywhere in the wave. And so these things were all rather interconnected, and a big aspect that many people have cited as easing their doubts concerning this problem of the lack of energy in a way was arguments, for instance, in, for instance, in Bondi's letter to nature around 1957, this thought experiment where the wave will move some particles. You have a rod with some holes on it and it's rough so it heats up when the wave goes by. Exactly. And of course this directly addressed the question that was told by Rosen about this energy menstrual pseudotensor, but it also, in some sense, because of the radiatedness of the issues, addressed the problem that people were having a radiation reaction, or at least made them feel that they were more confident about what they thought the right answer was. And I'm interested, you've already, of course, mentioned this aspect of this, and how you were led to focus on the geodesic conclusion. And I'm wondering, for instance, in particular, how that influenced this thought experiment. I'm interested, for instance, in what you could tell me about the genesis of those kind of ideas that in the thought experiment, what do you feel that they were Bonti's... You already mentioned that Bonti became interested in the subject, partly through your influence. There was a paper by Peter Sekeresch. Do you know the literature very thoroughly? Peter Sekeresch wrote a paper about some device where you had masses connected by springs that you dropped in the gravitational field. Something happened to it. I don't remember exactly why. We thought about it, I certainly thought about it, it always seemed in order of magnitude too difficult for what I knew, you know, to connect, the problem was connecting the field

17:30 to the sources, and if you could connect the field to the sources without cheating, excuse We realized that the motion of the radiating, the particles in the radiating system would have to be modified if the system was radiating. And there was no way of getting at this that I could see starting from Schwarzschild. There may be a way now. We couldn't see a way to get at that starting from Schwarzschild. And we didn't know how to deal with the two-body problem. And it would have been nice to... Kip was really ahead, I think, of other people in connecting the field to the sources. As I remember, he was ahead of the field. But if you were really optimistic, you might have thought that somebody could do a rotating ellipsoid, you know, a sort of a football going around its minor axis. I don't think anybody there, we talked about it, So although you did actually consider the problem of radiation per se, you... We didn't know how to do it. You rejected me to trick me. But I can remember, you know, I've thought about it since I heard from you, and I haven't been able to remember anybody having a good idea and getting tired of it. There were various spin-offs in a way. I don't know what the present status of sheep is. Do they still use sheep for curvature calculations? We did get somebody to work on computer formulations so that the computer problem could be handled if it came to the point. I'll tell you something which may have been solved by now. which always seemed to me a great difficulty in doing approximations. One of the ways that you might have done this problem was to do it by successive approximations. And that was that if you had an approximate solution of Einstein's equations and you pretended that it was a real solution of some other problem,

20:00 then you would get the solution in which the energy... I mean, a solution to the vacuum equation, say, equations outside some finite domain, then you would get the situation where outside where you wanted the stuff to be, there was still some non-zero team you knew, because you just got an approximate solution, not the exact solution. And unless you were very clever in expanding in powers of R, you might still have an infinite amount of stuff there, or at least enough stuff, enough, this extraneous team you knew to swamp the team you knew of the stuff that you really wanted. And I saw something recently by chance that suggested to me that that problem has been solved too. That people know how to get rid of extraneous team you knew down to any point that they need to. Is that true? Yeah, that's... Yeah, I think that's not so much of the problem, although there are, there are, for instance, still outstanding problems in the radiation action problem that's interesting. I mean, here, for instance, one of the things that I was talking to Jorgen Aylers about is he's someone who's, upon that, really working, or acting in the field in that specific problem. himself as someone who's been very concerned over the years to point out where their remaining problems lie. He's always been the great systematizer and that was certainly his reputation. Well, I was interested to hear something that I have been interested to ask on himself if I see you, but since you mentioned your sort of history with him and his existence, Because in the letter to Nature in which you put forward the thought experiment with the rod and so on, he mentioned that he had himself expressed doubts concerning whether gravitational radiation carried it and energy, besides the Chapel Hill Conference, for instance. Is that your memory of it, or do you remember anything about him saying that, or indeed why he was... I don't remember. Have you seen the document of the Chapel Hill Conference? Is it mentioned there? I don't remember.

22:30 Well, he discusses quite a bit there, and I mean, not only in fact he and the Letter to Nature, but I've seen a recent article by Joshua Goldberg, which actually is a description of the role of the US Air Force at that time, And he also mentions, remembering, he says, Bodley and Gold at this conference expressing his thoughts. Well, my impression reading the manuscript is that, well, it's clear that there, that Bodley, for instance, is open on the subject. It didn't seem so much that he was leaning one way or the other every time. I'm surprised that there was still doubt at the Chapel Hill conference that radiation carried energy because Joe Webber was there. And he was designing receivers, detectors, and I can't see how a detector would possibly work unless it was going to absorb some energy. That is an interesting aspect of it. It's certainly true that at the conference people people were still saying, Bondi was certainly saying this and others that, well, if gravitational radiation really carries energy, so, reading the manuscript it seems to be a lot of issue. And it's interesting that Waver did, Waver and Wheeler were both at that conference, and they didn't, I guess, not so long after that, write a paper in which they were trying to say, well, here's why we can get rid of that disease, and so maybe he had to work to convince himself. But in any case, you don't particularly remember him. I'm sorry, I don't. When are you seeing Bondi? I hope to see him in about a week in a half. I had some trouble finding a time. Is he away now? Yeah, I think he's away in a moment. I'm glad to hear that because I was in Cambridge yesterday and I was in a hurry and didn't get in touch. He's going to be 75 next... Tuesday, I think, really. That's what I didn't know. Yeah. Here's another question about somebody else, but it just occurred to me since you mentioned that Info was at Toronto when you were there as a student. He, of course, was very much at the standard era, in a way, of those who were saying that

25:00 that gravitation and radiation maybe didn't carry any energy. Do you remember the topic of gravitation and radiation? Coming up in Toronto? Yeah. And I was not on everyday conversational terms with an infant, so I wouldn't have it. But on the other hand, I went to Poland in 1957. Travelers. When I first met Troutman, he was a graduate student, I talked about radiation, and I don't remember him from with whom I was in on much more conversational terms. Eight, nine years later, raising this problem. He might have, but I don't remember. I cannot remember a time when it seemed to me, I knew about the pseudo-tensor business and I tried to deal with the pseudo-tensor business by a trick, by introducing GD's normal coordinates and showing that you could force the pseudo tensor to be non-zero around a place where it was zero by tying down the coordinate system and that this wasn't very arbitrary. So the attitude we took to the pseudo tensor was that it wasn't the right way of tracking down the radiation. And one of the things which we did, or which some of us I know Peter Bergman had a very low opinion of my contribution to this, was to try and find ways of transcending the pseudotensor problem. One of the things I tried was to introduce a preferred congruence of observers to have a time-like flow of guys who people guys, girls doing the measuring

27:30 and to try and construct something that was like a pseudotensor for them to measure and I got some way with this I spoke about it in one of the Paris meetings and it didn't go very far I couldn't see how to take it further and it was pretty clear it always seemed clear to me I'm not sure about that as long as I can remember it was clear that that made me back to 1957 that the Cedar 10 cell was not the way to look at it and that gravitational radiation had to carry energy So, um, well, just, um, um, one brief note concerning Info-Lotrata. I, I've, I've read, seen some papers, read some papers by some of my big collaborators with Info-Lotrata, a chap called Scheidegger, um, who, oh, Scheidegger. Oh, right, Adrian Scheidegger. Yes, he was, yeah, I've forgotten the, the first name. And he, I think, did some radiation reaction that I'm more from the point of view of the radiation reaction didn't exist as such. Was he someone that you knew? Yeah, I used to know him. He went off to one of the other Canadian universities somewhere further west. Yeah. I know. Had he been a student? He was an Infel's graduate student, and one of the reasons he was not doing his PhD in Switzerland was at that time, if you did a PhD in Switzerland, you had to have 600 copies produced. He figured there was no way he could afford to print his thesis, so he ended up in trauma. But what his thesis was about, I don't remember. He published it, didn't he? He surely published it. He published a couple of papers. I read some of the papers in which he more or less advanced than it was that radio's reaction. Oh, yeah? Then there was that guy, who? Who, yes. He got the sign on, didn't he? Because he had a thing in the Dublin, Royal Dublin Academy or somewhere.

30:00 That's right. I guess he'd been at the Dublin Institute, but... He'd been gone by the time I got there. That's right, he had the wrong staff. So these had contributed to a certain, I guess, era of skepticism. And concerning, but then I guess that towards the late fifties there was a number of war, So yours, for instance, in the GED-seq equations, and so on, and this Fodd experiment, and some of the other words that you mentioned, by Sachs, and I guess that's going to be in Grons. Something I mentioned I was interested in earlier, do you recall whether this emphasis on the genealogical equation was maybe what inspired this thought experiment idea that was put forward by Gandhi? because it seems on the whole that that was the gist of the thought that was saying, well, let's ignore the question of whether the energy is in the wave let's say that because of looking at the waves look at the regent answer, look at the geodesic equation and see that the wave is actually moving You mean, how was Bondi sure that the wave was going to move the point transversely? I think the geodesic equation yeah because I wrote that paper here and I said I talked to him a lot about that stuff and I wanted to put his name on the paper as well and he very generously refused to put his name on that paper said no no this is your piece of work and so he ended up with an acknowledgement at the end but he knew all about that him about it at length and he knew that remontence of stuff. He'll probably tell you that he doesn't read. He got where he got by talking to people and working things out for himself is what he always says. I don't know how true it is. But he certainly knew that transverse

32:30 thing and that certainly could have helped. Well, do you know what the date was of that letter to nature? I don't remember. If I recall, I had a copy, but I think it's 1950, but I guess just after the Chapel Hill conference. Well, maybe the Chapel Hill meeting stimulated to think it out again. Because there aren't especially issues like that. And you, I think, gave it a talk. I gave it a talk. Were you, I believe that the child I don't know how it worked on the actual radiation mass result per se, in his thesis, but was it more his... Was that work that you were familiar with, or was it his later work on gravitational waves in general? It was his later work, I think, which I knew better. So he came to London, about 1960, I don't know, and gave a whole series of lectures. Yes, yes, they had the book. You had that. So that's that. And that was really when we got to know well what he'd been doing. Because I was in Poland for three weeks in 1957, but I didn't see an awful lot of someone. A good deal of the conversation was about what it was like being in Poland, which wasn't as easy in 1957. Well, there'd been a little trouble in 1956 in Hungary. And... Was that when speaking to me about he alluded to... Was that, that was from Oklahoma? From Oklahoma had just come to power and told him that in fact, or it was only because the climate at the east somewhat in Poland that they were able to invite people to... That's right, yeah.

35:00 One thing that I mentioned that I've been looking at is the Chaplin Conference and other conferences. And you mentioned, for instance, the Berne Conferences, one of which made a big influence on you. Were there other conferences that were important? For instance, were you at the conference in Warsaw in, I guess, 1862? Were there other conferences where gravitational radiation... Well, there was the Rayamont conference. I was at that one. That was quite entertaining. But I don't remember if gravitational radiation was discussed then. I can't do that. I'm from China. I don't remember. You also mentioned Sachs as, okay, sort of like a way for the radiation reaction, but you mentioned Sachs' work, the PILO work, and did you, you also did some work. On PILO? I used to lecture about it. I gave some lectures at Brandeis in 1964 where that work was mentioned. I don't think there's anything in that about radiation reaction. You know, Bondi, Troutman and I all lectured at Brandeis in the summer school in 1964. Do you have that, Dr. Long? Right. Yes, in fact that, that's right, that's the book that I have. In fact, I guess the lectures you mentioned earlier, the travel made here, I suppose, I recall the travels that those weren't actually published. No, they were, they were duplicated. Yeah. And they were fairly widely, so... Can you give me a document? Yes, the book that I have. I'm then thinking of Troutman and Bondi should be in the Brandeis Lexus. Don't you ask me something else? Say that again. I was...

37:30 You did some work with Penrose, I think. Is that connected with the classification scheme? Well, Penrose resuscitated Spinnus. Spinnus had been introduced at least once before by Schrodinger in the 30s. 1960, Penrides resuscitated spinners for PR. So by 1964, they were sufficiently in use that I remember using them in my Brandeis lectures for doing the classification. One of the nice things about the spinners was that they very clearly picked out the null case from type 2, which from the Petrov method, you really didn't get that coming out cleanly. Can I ask a couple more? Absolutely. Yeah, I'm at your disposal. Thank you. I'd quite like to go swimming at quarter past four, but that's now nearly an hour and a half. Okay, so I'm sure we've done well before then. Let me see if that can be right back. Something just occurred to me, just to come back to Singh for a minute, was he, since Hulu had been earlier at Dublin, and since you got interested in the problem with gravitational radiation, was that a problem that Singh was interested in at all, or was it merely that he indirectly... Not particularly, no, I don't think so. I can't remember I must have known at one time where, who got his idea and how he came to write that paper and I think somebody has subsequently sorted out how he got the sign wrong maybe it was Kip I remember reading something somewhere about how that sign comes to be wrong maybe it was Kip maybe it was Dumas I don't know I think Kip has some ideas but without having checked it very precisely. And I don't remember discussing it with that, seeing what you would think that I might have done, but I'm afraid I don't. About that time there must have been a

40:00 paper or two by Dirac about radiation reaction in electromagnetism. Yes, which I don't know if people first have cited to me as being as being influential in the present case because it's traveling, I guess. Yeah, and there was discussion about how that could be generalized to GR. Yeah. I don't remember any progress being made. In fact, when I read the... I ruined my amateur status in the spring of last year by giving some lectures on GR to high energy physicists in Florence where I had to do a lot of reading. And one of the things I read was the Halston Taylor paper and the Damore paper that had, I think, preceded it or maybe followed it, was linked to it. with that collection of results, you know, that somebody had actually... Excuse me. Yeah, I was so delighted that they got it all tied up. They got the system decaying just as the theory said it would. I thought that was going to be... No, it's interesting how the problems sort of came together well, off each other that at last there was some experimental data to work with and at the same time because although there have been various results and in fact the particle form and radiation reaction have been derived by a number of different mutations once getting the now accepted result yeah of course people there for instance and others have pointed out that that there was a definite lack of and some of the results, and so I think that this satisfied maybe a lot of people when you had these results of de Mors. Although I got it that some people still have doubts, not regarding the final answer, but just regarding how it's derived. Is there a derivation which is regarded as better than the others? Well I think that De Morse is the most

42:30 and in fact De Morse and Glache have gone on now to go to the next order in the radiation reaction which actually, as it were, gives you the quadruple formula which has been a certain matter of debate and then they have, as it were, got the next order so they now know actually to what level the quadruple formula is now So it's very interesting how a lot of these issues happen, which is nice for someone who's doing history on this and so on. It's not quite such a problem anymore. Does this use the language of Scry Plus or is it all done more finitely than that? Well, this actually I believe, as they were saying to me, is one of the things that he still has worries about, the behavior that Scribes tells us, and that this, he says, hasn't been, is one of the things that hasn't been properly dealt with, so in general, in And this is in the De Moore case, he is principally interested, and he was principally interested in the problem in a, you know, in the actual concrete problem of the binary closer. And so he's not strictly speaking worried about what's there, just what you're detecting. So that's, that's one of the things that I mentioned that some people are still undertaking certain more abstract issues as being targeted. but at the time we were speaking you were saying that your feeling was that really the radiation reaction problem was quite intractable it wasn't really so much an issue of what was the right answer it was certainly intractable for me but then I was not one of these people that did the long heavy calculations here it was Bondi and Sachs and Bondi had some a student called Maddenberger, worked with him on that. And, of course, Kipp was the powerhouse. Long, heavy calculations.

45:00 Regarding the clerical part, which later became an issue in itself, I mean, is this actually correct, were, for instance, I guess the Lando and Lipschitz had produced a derivation of the particle formula in the binary case. I mean, did that sort of treatment satisfy you that probably the particle formula was correct, or were you really not interested in that question? I thought it was probably correct, but the proof needed to be fixed, scope for improving the proof, but I didn't know what to do. What were the most signaling things that you felt needed to be dealt with? Well, it was this business that if you did any kind of an approximation that didn't involve powers of one over r, that you were going to have this infinite amount of tenuous stuff. If you took your approximation as an exact solution of In other words, if you calculated the energy tensor, if you did an expansion not in powers of 1 over r, but in power series in something else, in some parameter. and if you stopped at any stage sure the parameter was small but there could still be a lot of stuff left over and it was getting over that that seemed to me the crucial thing so yes that was and then if I remember right the Landau Lush's derivation has nothing to do with 1 over R. It's an expansion, a weak field expansion, in fact. And any weak field derivation seems to me to have to face this objection of what's really on the right-hand side. I don't know, has anybody else mentioned that to you, that what's left over on the right-hand side is an objection to a weak field of expansion? Well, I think that, of course, people certainly mentioned that they were skeptical of the weak-field case in that, well, for instance, later in the binary pulsar case, where the actual detective, obviously, that was a strong-field case.

47:30 So that's the chief objection that I'm proud to believe for the case, that probably for actual systems of experimental interest, which really wasn't an issue for animal shoots anywhere, since there just weren't such systems as these things for a long time afterwards. But nevertheless, people have said, well, it's only a weak field of treatment, where what we really want is a strong field of treatment. So that's the chief objective. But it's clear that one could make a number of more changes. I guess another issue that I've heard people raise is connected to what you mentioned earlier, the giraffes or AI. electromagnetism, and so you had a similar problem of the best classical re-organization. If you were going to, say, try and do it with point mass as well. Yeah, sure. Well, actually, you've told me a number of interesting things. Since one of the things that I was sort of interested in concerns this, the business of your work, focusing on the genealogy equation, just go back to that for a minute, you, was that, you mentioned that perhaps that was something again that Satan influenced you in, was it, because he was very... If you remember it, since the Einstein-Infeld-Hoffmann work, which was in the late 30s, 36 or 38, one believed that isolated particles moved on geodesics. Then it had better be isolated spherically symmetric particles because there was the work of Papa Petra in 1951.

50:00 I think it was, or 52, on the motion of a spinning particle, which showed that the spinning particles were deviated by a... do you know that one? You've heard of that or seen that. But certainly the general, as I remember it, the general ideology was that three spherically symmetric non-spinning particles moved on geodesics. And Singh was, I can't remember if he invented the geodesic equation or re-derived it for himself, the geodesic deviation equation. I don't know what I'm talking about. Maybe Skelton, Soltan was the guy who first discovered it, I don't remember. In Seng and Schilt's tensor calculus, there's a good deal about the equation of geodesic deviation, using it to do geometry, you know, to do elementary differential geometry as well as for more sophisticated things. So it was much in the air. And it's—there's a good deal about curvature in his general relativity. Yeah. Well—oh, and I remember—yeah, we were talking about—Singh and I talked about geodesics, and about transport. He was interested in transport, too, and he had written about Fermi transport. And I wrote a paper about Fermi transport when I was in Dublin. And somehow connected with this, neither of us knew about Lee transport. We didn't know that it was at least...

52:30 Thank you. Thank you. Thank you. Thank you. Thank you.

55:00 Thank you. Thank you. Thank you. Thank you. Thank you.

57:30 Thank you. Thank you. Thank you. Thank you.

1:00:00 Thank you. Thank you. Thank you.