Interview with Jurgen Ehlers

0:00 It's the 14th of October at 11.30, and I'm speaking with Professor Jürgen Ehlers. Now, you've already touched on two or three things that I wanted to discuss with you, but maybe you could begin by telling me how it was that you first became interested in this problem, what attracted you to it, and why you felt it was important. Yes. Well, this goes back to giving lectures on general relativity. I always found it difficult to talk about the equation of motion aspects of general relativity in lectures because when one looked at standard textbooks or also at the literature, then first of all the treatment of our bodies move around was more involved as far as computations are concerned aspects of relativity I was familiar with and also less clean in the sense that one formed an opinion which terms might be small and on the basis of such an opinion but just left out these terms and then went on without having some control of whether this approximation was permitted or not so that was so to speak, the prehistory, EIH methods and such things, and Fox treatment of the matter. By the way, I feel that Fox treatment of equations of motion and relation of that to radiation is still one of the best treatments. He pointed out most of the problems. He could, of course, not solve all of them, but if one wants to see what the problems are, I still feel that I should go back to Fox's book and then connect it with the data works. Anyhow, when then the binary pulsar had been discovered, the problem of the interplay between the motions of bodies and the gravitational radiation which the system of bodies would commit became a concrete problem, no longer just an exercise in textbooks.

2:30 And therefore, since I always considered it as my duty, as for a while the only relativist in Germany who was considered seriously, I was asked every now and then to give colloquium talks at German universities. And of course people wanted to know, what is this matter with binary stars, is there a chance to observe relativistic effects. So I considered it, even if I am not working in the field, I have to know about it, because it's my duty, so to speak, and so I tried to follow it, and in this way I got to see, I feel at least, I got to see what are gaps in the treatment of various aspects. And in this way, I then tried to find out, can one say something decent, first of all, about extended bodies? Because Einstein's field equations do not allow the mathematical idealization of point particles, because point particles, if one wants to treat them rigorously, require the use of distributions instead of ordinary functions. and in linear theories like electrodynamics that is quite okay because distributions are in fact a tool for solving linear partial differential equations but for Einstein's field equations this is not so and physically it is also rather clear that you cannot have a stable body with a given positive mass which is smaller than the Schwarzschild radius and therefore the mathematical model of point masses is not directly available And you cannot even use the model of rigid bodies because rigidity is incompatible with causal propagation in relativity. So if one wants, at least from the start, to formulate the problem in terms which are rigorous according to the intrinsic structure of general relativity, then one has to start with extended deformable bodies. And so I wanted to know, can I really do this? as possible, and so I got into contact with Garn Dixon, who at the time had done, what I still feel today, had done the best work of formulating reasonable concepts to define for example, in general relativity

5:00 how one could introduce something like a center of mass world line for an extended body, and how one could introduce in a covariant manner the concept of a total four momentum of a single body and the total angular momentum and multiple moments and so on and so I got into contact with Dixon and I myself and sometimes also people here in the group contributed in fact then to the Dixon approach I had once a very good PhD student Shatner who wrote a number of papers and I still feel that these papers brought the best of these issues as far as the attitude of, say, a mathematical physicist is concerned, as opposed to a theoretical physicist in the usual style. I mean, he clarified really completely the treatment of extended bodies. So that was one issue, and one could kind of see from there in which sense it is nevertheless less permitted to use the schematic model of a point particle in a kind of renormalization process. That was later on taken up by the French people around Thibaut d'Amour and Libel and so on, and their method to use, so to speak, the picture of a point particle, not in the sense that that the point particle should be considered as a model of a planet or so, that would be ridiculous, The point particle is used just as a substitute for the center of a field which surrounds a certain time-like work tube in space-time. And in order to deal with that, particularly Bell and Damour used a clever way of treating distributions as boundary values or analytic continuations of analytic functions and complex methods and so on. That is very well described in one of these Lesouches conferences you might have seen in a book by Piran and Derriere. I think for the aspect of what it means to use point particles in general, that is still the best way of going about it. but that was later I come back now to the earlier stage

7:30 aspect of why I became interested in this gravitational radiation reaction problem was that we had for a while here a man who had been studying with Peter Havas at Temple University Pennsylvania with the name Arnold Rosenblum, a Jewish person, and he, under the influence of Peter Havash, had become very skeptical about the validity of the quadrupole formula. And, well, it was known, of course, it had been known all the time, later since the work of Arthur Ellington, that the quadrupole had been derived in an inconsistent manner by Einstein originally because Einstein started with the linear approximation and treated and used the linear approximation even when bodies are moving around to emit gravitational radiation, whereas it is clear that the linear approximation in itself is not capable of reproducing even the Newtonian motion, because because if you stick to the linear approximation, then the stress-energy tensor has to satisfy the conservation law of special relativity as a consequence of the linearized equations. And so one had to do something about it, and the approximation methods which had been worked out contain mutual contradictions. Different people obtain different results. In fact, you described this in your paper. and one of the skeptics at the time was this Rosenblum who established a kind of contact between the group here and Peter Habasch, and so we took up this issue and tried to understand what the difficulties were, and that then led to some rather extensive computation. Under my supervision then, David Kurlik wrote a series of three long papers where he worked very systematic post-Newtonian method to the third post-Newtonian order and with the hydrodynamic model of the matter, the equations of motion are to that order. And at the time, I think that was the

10:00 most rigorous way of going about it, but that showed also, as the previous work had shown, that if you use post-Newtonian approximations, then you will, at a certain stage, get divergent integrals and therefore one loses again control of the mathematical validity of the whole method. And that is still the situation today, even very late attempts from the last year, in fact, by Alan Randall how to set up the post-Newtonian methods they still show that the standard expansion methods you always get divergences at a certain stage now then it was pointed out in fact by by Kip Thorne and the work that one should not use post-Newtonian methods globally in the overall space-time region but rather one should be aware of the fact that the post-Newtonian method by its very nature is suitable only for the near zone and not for the radiation zone and therefore it might seem to be much better to follow the example of the hydrodynamists and use matched asymptotic expansions, namely use different approximation schemes for the radiation zone where the wave equation governs the scene and for the near zone where Poisson's equation governs the scene and then in some kind of more or less well-defined intermediate zone one has to match the two types of expansions. And so therefore we also tried to understand, learn something about these expansion techniques and that was one of the reasons why at this Varana meeting which I organized, I had there, Bill Burke took me a long series of talks about asymptotic expansions and that brought Jim Anderson also into the scene. Jim Anderson from Hoboken, he was an old colleague and a new friend of mine and he then concerned himself mainly with the question

12:30 can one incorporate into the treatment of the propagation of gravitational radiation away from the sources to infinity, can one incorporate into that the fact that the radiation does not propagate in a flat background metric, as had been done by the earlier methods, but rather can one incorporate by an iteration method that the radiation propagates already through a curved space and that's of course rather complicated and he made some progress in that direction. Somehow I feel that these methods got stuck. One made some partial progress. For example, one learned how to treat the bodies decently. One learned how to treat the propagation far away from the sources recently. Even more recently, people did even exact work to justify the Bondi expansions using the conformal compactification problems. Helmut Friedrich here at this institute managed even to prove that the Bondi expansions are mathematically rigorous. So one has certain aspects which one knows how to treat correctly, but one still does not know how to combine the far-field approximations with the near-field approximations. It seems to me this matching together of the two things, that is still one of the major problems. I feel that for practical purposes, perhaps, what one has done so far is good enough. but if one looks at things so to speak from the point of view of a mathematical physicist who would like to see things formulated in terms of theorems and proofs, from that point of view that still cannot quite be done and I find it so interesting for somebody who's interested in the mathematics of the matter to look into this matching problem so to speak from the point of view of rigorous mathematics some progress there I feel has been and his collaborators recently in a series of papers in FISREF-D about post-Newtonian methods where he also uses a different treatment for the region where the bodies are

15:00 and an overall metric which describes the region between the bodies and matched to the bodies in certain intermediate zones. Anyhow, to continue with the history, under the influence of Arnold Rosenblum at the time, we were made aware of the weak points. I should say that was perhaps the merit of Arnold Rosenblum. He himself was not able of really carrying through anything, one must admit that. For us here, he had the method of pushing us again and saying, Chopra not do something about it, Chopra not be critical about this and that, and so on. Yeah, and one of the highlights, I mentioned that already before, was at one of these GR conferences that various people having different opinions together and Mr. Cooperstock in particular presented what he considered as a counter-example. He thought that the model of these two fluid balls falling towards each other would provide a case in which the amount of gravitational radiation during the free-fall stage could be much larger than what would be predicted by the quadrupole formula. And I don't think that the matter has been completely settled but nevertheless I feel that on the level of reasonable physical plausibility the matter has been clarified by work of Clifford Will and partly also by Martin Walker and that's reported in this review there the meeting there. Well, later on the interest here turned away again because different people came to the group here. Martin Walker left, he was one of the persons who were interested in this, and we turned more again to the vigorous

17:30 asymptotics and Cauchy initial value problems and such things. Well, let me stop for long because I have to think I should mention that this aspect can one justify approximation methods rigorously. Bernd Schmitt from the group here was perhaps the person who was most successful in that respect. He wrote some paper with Dimitrius Christoglu, which showed how at least this problem that in some approximation methods one treats the radiation as if it would be propagating for a flat background and does not take into account the curvature, how one can to some extent at least justify this mathematically. And later on, much later on, in fact, in 93, he took up similar problems again together with Thibauta Muir and how to justify certain approximation methods vigorously. Well, there's one thing I wanted to ask you about. Regarding Rosenblum, it introduces the specific problem you mentioned I should have mentioned that Rosenblum's test case was the scattering of two particles. Gravitational scattering, and then during the scattering you get some emission of radiation. I still remember that he, for a very long time, sitting here evening for evening, doing very long calculations, hundreds of different integrals, at the time I doubted whether you would ever get to something because if things get more and more complicated and you lose control of what you are doing, then there is no hope of doing something. In fact, it never worked to something useful. One, in the context of the binary systems, though, one thing that had some kind of impact On this question of the waterfall formula, the radiation reaction formula in a binary system, around that time you had the binary pulsar data come along, and after a while they produced some data in which they showed evidence of the system in spiraling slowly, and I wondered what you remembered of the impact of that of what you made up.

20:00 Yes. Well, I mean, first of all, the problem clearly was of great interest because that was a case where for the first time one had an indication that gravitational radiation exists in nature and not just in the heads of physicists. What I was critical about at that time was whether the use of an energy balance, where one uses the Newtonian energy for the source, and then just says, well, we know from the quadrupole formula and from the early work of Matthews and Peters, we know what is the rate of emission of gravitational radiation, and then one just puts this into the Newtonian energy and asks if the Newtonian energy is reduced by that amount per unit of time, how does this change the orbit? There one uses an energy balance which, from the point of view of general relativity, cannot be really rigorously derived. And up to this day, there are debates about how can one at all introduce and energy for the gravitation field. And that was one of the reasons why I pushed the idea that one should try to derive the influence of the emission of gravitational radiation on the orbits of the bodies directly via the equations of motion and not by using an energy balance. And some work on that direction was, in fact, done here by Reinhard Breuer also at the time. He was one of the collaborators. And that is also connected to this work by David Koelig, which I mentioned before. I mean, he did not directly treat two bodies, but he set up the general formalism for equations of motion up to the third first Newtonian order, including the gravitational reaction

22:30 And then Breuer took those results and with additional approximations applied them to the case of bodies moving around. I mean there have been work in the same direction of course at other places in the world. The point I want to make is that the new point of view was not to use just an energy balance in order to get the influence on the motion, but to see how it directly arises in the equations of motion. So, well, there are a couple of things, but let me for the moment then just stick to the impact of the binary pulse data around Matheson. They found a loss of momentum by the system, which within I think plus or minus 20% or so agreed with the prediction of the straightforward prediction how did you what was your feeling at the time or since about how and how confirmed, whether this was a confirming prediction of the formula in fact I was happy that one had these good measurements, in fact there was even a slightly personal reason involved why I was happy about that, because I organized, later on, for the first time, a Texas meeting outside of the United States, namely a Texas meeting in Munich. And at the previous Texas meetings, people have been usually happy that some special event has happened who was considered the highlight of the meeting. was not clear when I started organizing the meeting whether we would be as lucky as people have been before. But then it turned out that just at the conference, Bob Taylor came out with the result that he had the first clear indication that there was a change of the period which could be found on the rotation radiation. So that was the highlight. I remember that there was a press conference where that was pointed out, and we also, of course, then mentioned that some theoretical work had been done here also concerning gravitational radiation.

25:00 But this is one side of the matter, but I myself, I should say, I had, according to my interest and upbringing, I am perhaps more inclined to think a little like a mathematician than most physicists, and therefore, even when this result had come, I said to people, I tried to convince physicists that the fact that the result of a certain approximation method agrees with observations does in itself not prove that the method which one calls an approximation method is in fact mathematically an approximation method and therefore there still remains a challenge to prove that irrespective of whether it agrees with measurements or not and I would take this position also today because otherwise we are deceiving ourselves after all we would like to use these measurements in order to test the theories but to test the theory means you first have to have reliable results deduced correctly in the theory otherwise you don't have a confirmation that's true and many people i think tend to forget this aspect because it's so nice if you have agreement between theory and observation and it is kind of disturbing if one cannot prove How much progress do you think then was made between around 1980, so on the present day, that you regard as valuable for putting the quadruple formula on a more firm foundation? I think what convinced me that probably the quadruple formula is correct was mainly the work on this type of point particle approximation which also went far enough to include gravitational radiation reaction in the equation of motion-ambient work by the French School, and what I find the best formulation there is the way in which Tiwara Muir has put it. I like very much his review in the book 300 Years of Gravity, which very clearly explains the difficulties and the extent to which they have been overcome. And that is the second aspect, if one

27:30 wants to treat extended objects like the the planets in the solar system or so, for that aspect I think the most reliable method of treating that so far is this work by Dan Moore and this Chinese fellow, Xu and Zoffel, and so on, in recent years. What I still feel is perhaps the biggest gap in both of these approaches, namely this earlier point particle way of dealing with it and the later work, is that in order to be able to do computations, one still introduces the condition for absence of incoming radiation in terms of the flat background metric on which one builds the approximations although it is quite clear that it has to play a role that the radiation propagates in the past as well as in the future propagates through an already curved space-time. And I think that should still be improved. I'm not quite happy about that. Yeah. Well, to go to something that you made mention of a little bit earlier, the question of defining energy in the gravitational field and so on. Kuperstaff has written a recent paper in which he, returning to an argument really that I think was made by Rosen in the 50s concerning the energy momentum pseudotensor in the gravitational wave, in which he says that the wave energy cannot be correctly defined in vacuum, and therefore cast doubt on the existence of gravitational waves in the cells. This had much more of an airing, I think, in the period of the 50s, when not only did you have certain doubts about the question of defining the energy in the wave or in the gravitational field, but you also had various contradictory results from the radiation reaction problem. And some people, Infel, for instance, worried whether there were gravitational waves or whether there was radiation reaction from the binary system. Yeah.

30:00 Were issues like this, say, the existence of gravitational radiation as a gem, was that ever an issue for you, or was it an issue in any of the periods that you were... No, no. I never had doubts about the existence of gravitational radiation, particularly since I have been involved with the business of exact solutions and have worked myself with my colleague Kunt on properties of exact solutions which describe gravitational radiation. And although those exact solutions are, of course, unrealistic, I nevertheless felt that they clearly showed that there are propagating gravitational waves said it's by Rigolski-Ansen's equation, so I never have thoughts about that. Also, I found Bondi's remarks very helpful, just precisely in connection with the question whether there is energy transported. He had these nice engineering types of examples, how you could extract energy from the gravitational wave, even if one admits that one cannot introduce a local energy momentum tensor, that's more a formal issue. The physical issue is that you can produce relative motions and you can change the relative motion and in this way clearly you can extract material energy from the gravitational wave. I found this convincing from the very beginning. So it was merely a question of developing the formulas to describe the wave. and that's still the question today are these proposals about semi-global concepts of quasi-local concepts of energy regarding well another side of the experimental issue then is the efforts to detect gravitation waves which have been ongoing for many years and which have their own history a certain amount of controversy regarding the current efforts to detect them. Do you feel that the theoretical issues that are still outstanding are important for the... I mean, there are clearly there are many things already that are just not sufficiently well known for Michael and Virgo. And are there things that you think you mentioned, for instance, the need for a conference?

32:30 do you regard the ways that people are attempting to go about developing the theoretical techniques needed for LIGO and Virgo as being reasonable or do you think there are things missing? I find there are quite reasons I think this is very good physics as you know there has been and still is also a group of experimentalists here on gravitational radiation. First it was the group of Professor Billing, who developed Weber Bar, and the group here was one of the groups who, so to speak, demolished the Weber designs by being unable to reproduce them. And so my connection with that group was rather loose. I just sometimes help them to understand theoretical issues. For example, when it first came up that one should not use bars, but should use interferometers, then questions came up, how can one understand, how can an experimentalist who is not familiar with the formalism of general relativity, how can one nevertheless explain to him how the interferometer functions, what happens to electromagnetic waves, and so on. I was a little involved. And for the statistics aspects of these experiments, Peter Kafka at this institute was mainly very helpful and responsible. And nowadays there is a group led by Professor Carsten Dantzmann. He is in close contact, I think, also with Kip and all these people there. He now will be able to put up an intermediate-sized interferometer, real armlink in the area of Hannover. The money for that seems to be secured, but money for the big instrument was not planted. That is one of the reasons why they now plan to use an intermediate-sized instrument. No, I think for understanding the functioning of the various types of detectors, the theory Since we clearly are in the linearized zone, I mean the gravitational waves are so tremendously weak that there's no real question.

35:00 From the point of theory, what I still feel is a question which is probably not sufficiently understood, but that's also, I think, clear to everybody else, is the late stages of spiraling in of compact objects. Therefore, the post-Methods aren't fully natural. It's probably necessary to do this numerically. There's this big challenge going on. Did the efforts, the number of different efforts here and elsewhere in the 70s, I guess, to detect gravitational waves, was that a stimulus to theoretical work at the time, or were they really... Yes. No, it was. It really was. But was it more in an indirect sense? You mentioned that there was no... More in this indirect sense, yeah. But this is due to the fact that the group here always was more interested in clarifying, so to speak, the precise mathematics, rather than being directly concerned with the phenomena. Like in particle physics, You have this distinction between what people call phenomenological particle theorists and pure particle theorists. In that sense, here in the group, we were always more on the side of pure relativists and not so much applied theorists. So, yeah, that's... Well, one thing I wanted to touch on briefly was that you mentioned the conference that you set up at Dillenbrough and also a number of other important conferences like Les Uges it seems that the conferences played a particularly important role especially perhaps in view of the way that there was considerable discussion over the means, the correct means by which one could work towards the solutions that one wanted how do you feel about that? Was that something that I think in fact that this was the other day The whole role of this Warenakin conference and also discussions at GR meetings about the topic was that people who had been concentrating on particular aspects became more aware of the other aspects.

37:30 If somebody was mainly interested in propagation of waves and did not pay so much attention to the sources, he was made aware that there is a problem with the sources and the other way around. And I still feel that today one should have topical conferences which do not select just one small subgroup, but rather that one has people with different primary interests, some more mathematically inclined, some more observationally inclined. and one has to try to make both groups aware of the point of view of the other group. Because there's always a danger if one is working within a group where all people are primarily mathematically interested or where all people are primarily interested in the observations that they tend to forget the other side of the coin. That's something that I was interested in as well alluded to, this, a different, a certain difference of you, perhaps, between mathematical physicists and theoretical physicists. You found the conference is important for allowing these two sides to... To interact, at least becoming aware of each other. Right. How, obviously this is something that seems to have played a role in this particular issue, and it's Perhaps the one way, the most way in which this issue, this episode, the small episode has something to say about physics, my physics perhaps more in general, this issue of a certain difference in viewpoint. Do you see anything particularly epistemological about this difference in viewpoint between these two groups? way of approaching it, or how different are they? Yeah, well, my main wish in this respect is that people of the different, with different interests, that they should take, so to speak, seriously also the others. in my experience there is a certain tendency in fact in both camps to not take quite seriously

40:00 people from the other camp and I think this is a kind of obstacle to the progress of science. If both groups would also take seriously the other point of view and would try wherever there is a bridge actually to establish the bridge that would be more helpful this is not only so in this particular case this is an example for this where this has at least happened sometimes to get a connection it's also visible in particle physics where in quantum field theory where sometimes the the hard-nosed physicists, they do not at all appreciate work like what has been done by, say, Arthur Weidman or Rudolf Haag and so on. I think those people who are mathematically inclined are usually more inclined to also regard highly the work by the phenomenologists than the other way around. And somehow, if one could change his attitude by making people understand that both issues are needed in the long run, that would be helpful. Yes, that's interesting. Certainly, it seems interesting insofar as this episode might be sort of a case study for the interaction between groups. By the way, it might be nice, if you write something about these matters, if you would send it to me, I could then perhaps check certain things. No, I absolutely intend to check anything. I'd send you drafts specifically anything that I intend to use, for instance, from this conversation. Are there other ways besides the conferences that were valuable for bringing about communication between the groups, or was it conferences? For instance, you mentioned people who, through joining your group, brought your attention to certain issues and so on. But were they mostly also tended to be more mathematical physicists? No, that was quite a mix of people. That was one of the aspects of this episode which I found enjoyable, that we had connections with quite different types of people. we had as visitors

42:30 sometimes, several times Jim Anderson for example who came from a different not the type of mathematics we were used to, he was rather more inclined to work with approximation methods never mind whether one could precisely justify them or not and we learned to appreciate the aspect and the other way around and also Dixon's visits with his The theory of bodies from England came several times. So this mixing of different people with different interests that I found particularly enjoyable in this time, which was such that everybody could learn things which he had not been aware of before. Another aspect then that you referred to was the tendency of, especially perhaps on the one side, to dismiss the views of the other side. And you also, referring to this episode involving Cooperstock's Photics from a Counter-Temple, you referred to a certain acrimony perhaps that devout what memory do you have of this sort of dispute? Yeah, but what I found strange there is that sometimes, and this example with Dr. Kuperstorp was a case in point, that sometimes when people have different conjectures about something which cannot yet be established, that in spite of the fact that they ought to be aware of seeing that they are struggling, they are talking about conjectures, Nevertheless, they cannot separate their personal feelings and their friendliness from the scientific dispute. That was very open there. In fact, people were afraid whether this session at this one GR conference, whether this would go on without peeping people starting to actually attack each other. I think it is an important part of the education of a young physicist to learn to be in good, friendly terms with somebody, even if you have different opinions. To me, it's ridiculous to mix these issues.

45:00 But that was also made particularly clear during these times that some people cannot separate differences of scientific opinion from personal difficulties. One must learn to disagree without being disagreeable. Yeah, yeah, exactly. I think this is one point, anyhow, which should be part of the education of a scientist. One of the things which I think one can perhaps learn better in a scientific education than in any other field to separate these things. Was that a particular feature of that conference? It was a particular feature of this 1GR conference where I pointed out this report that took place, yeah. But at other conferences there wasn't so much pressure? No, not so much at other conferences. I remember that another rather heated discussion took place during one of the Texas meetings when it had become clear to most people, at least, that the results by Joe Webber were not real. And Joe Webber still tried to defend himself. That was very heated also. Yes, on the experimental side of the issue. Yes, yes. well we should perhaps try maybe you can since we know each other now if something comes to your mind you can also call me or send me a fax if you want to have done quickly thank you that would be very nice so just to conclude then just what we were discussing there There was a debate over a number of years, and on the one hand, you recall that it allowed a certain very fruitful mixing between people with different views, although at the same time there was a certain unfortunate friction that developed at the time. To put it like Peter Bergman once put it, in some discussions, more heat was produced than light. So, overall, though, what do you think was the ratio of light to heat? Do you think that the debate was fruitful? Altogether, the debate was fruitful, yeah. In fact, it has produced better approximation methods.

47:30 You're happy with what developed, even though, of course, there are still issues. Yeah, yeah. No, I think that was quite useful, and somehow this was achieved. So, given your experience also, you've experienced in other, somewhat different work within Relativity, how do you, did this episode stand out to you as being rather unique to itself in the way that it developed? Or was it more characteristic of the way that you experienced it? No, I think it was rather unique, it was a special case, not so, not as things go on. At least, as far as I was concerned with matters, things go more smoothly, not so pointed like it was with this issue. Pointed mainly on the quadruplephonia. One had a slogan, really. Quadruplephonia was the thing that they pointed to. That is usually not so, I think. But that did tend to, perhaps in comparison with, say, for instance, the labor case, that did tend to attract people, you think, towards working on the issue? Yeah. Okay. Well... Thank you.

50:00 Thank you. Thank you. Thank you.