Interview with Herman Bondi

0:00 Thank you. my recollections. Yes, that would be a good way to begin. Of course, I learned relativity essentially from Eddington's mathematical theory, where there is a distinct doubt about the reality of gravitational waves. Are they... Is it just changes in the coordinate system? Yes. And Eddington, in one place, because there's no sense asking after their speed because we can mentally imagine making coordinate transformations as fast as we like so they travel with the speed of thought and then of course I was also somewhat negatively affected by Landau and Lifshitz. I felt their treatment of gravitation in general and gravitation waves in particular was a little glim. They stressed which is their good right, the analogy with electromagnetic waves but didn't in the least stress the great differences, the fundamental differences that there are. Again, there were some people, notably Leopold Infeld, who denied the existence of real gravitational waves. There was the suggestion that, as it were, the gravitational field was just an aura that moved with the body without any actual wave phenomenon. There were several debates on this. I'm putting this in a very personal way, but there were several discussions of this at a conference I immensely enjoyed in 1955 in Bern in Switzerland to celebrate 50 years of special relativity.

2:30 so happened it came just after the death of Einstein himself and somebody who had met before two or three times and liked very much was a theoretical physicist from Zürich Marcus Fields you may have heard the name I think so and at the end of those discussions he took me aside and said I have come to two conclusions, one it's high time solved, and B, you should solve it. Well, that was quite a spur. I had only the previous autumn moved to King's College London, was joined there by Felix, and within the next two or three years we got quite a few people there to visit us, Peter Bergman in particular, but also other, Jim Anderson and various, quite a collection of people. And around 1958, we established a link with Warsaw, with Leopold Infield School, and we got their people to visit us, the first one of them was under child care. And I suspect he was with us in 58 or 59. I couldn't suspect it was that winter, 58, 59. And of course he's a great stimulator. And we had many discussions and arguments. And the other person we saw at the time was Ivor Robinson. And the first thing that came out of it all was this paper of plane waves, which was good as far as it went, but of course a plane wave tells you nothing about the origin of waves, and it tells you next to nothing about the energy of the waves. Right. Because I thought this was, you know, sometimes one says things that one regards as totally elementary, that other people then pick up and say it's important. Sometimes one says something that's important that other people don't.

5:00 Well, one comment I made at the time which has been quoted by various people to prove that such waves actually carry energy is that if you imagine two massive bodies on a rough stick, then when they are given a relative acceleration they will slide along a little and the friction will produce heat and that's undoubtedly energy. And that was taken up by some people as the first clear evidence that there was energy in it. The other thing, I have always had the feeling that many of the problems that we don't understand in general relativity arise because we don't understand the Newtonian situation either. and out of that came a paper you may or may not have seen it and the proceedings that came with Bill McCray on energy transfer by gravitation in Newtonian theory I'll just talk about it for a minute because we really got quite an amusing example you see I was thinking that energy transfer by gravitation wasn't at all well understood even in Newtonian energy now of course in spite of all I said about Landon Glischitz we know that in electromagnetic theory there are two different kinds of energy transfer inductive as in a transformer and the radiative And we couldn't obviously expect a radiative transfer in Newton in theory, but we wanted to demonstrate that there was inductive transfer. So we made this model, as we're saying, I must have reprinted somewhere, but I won't be able to find it easily. That the model is quite simple. take two spherical bodies moving under their neutral gravitation in the shape of highly eccentric ellipses.

7:30 Easy to imagine. Now, suppose that each body has machinery driven by electric storage batteries that can make it change its shape from sphere to prorate spheroid to oblate spheroid, being the same symmetry in our circumstances. Now, of course, you know that the attraction is increased when you go oblate and decreased when you go prorate. So the two agree that when the leading one will go oblate, the other one will go prorate and vice versa, so that the attraction is always the same as though they were both spheres. Is that clear? Yeah. do not change at all but of course the tide raising force is very much stronger when they're close together when they're far apart so the leading one cunningly allows himself to go oblate every time they're close together and go prorate when they're far apart and of course he He gains much more energy going oblate, moving with a tithe, as it were. Then it costs him energy to go prolate when they're far apart. The other follower, the follower, has to do the opposite. So he gains, he loses energy going prolate when they're close together and gains damn little energy going oblate when they're far apart. So there's always energy transfer in each circuit from one to the other. I see. And at the end, if you assume it goes on for a few orbits and then stops, then at the end of the exercise, everything is the same as at the beginning, only if the batteries are one or more fully charged, then if the star and the other is less charged. So there's no doubt about the transfer of energy. and so at least there was a clear example because I don't think you can be much clearer than this about inductive transfer which of course had been talked about you understand the earth moon system has transferred after all it is transfer that leads to the moon always showing the same face

10:00 but one's got to understand the Newtonian theory well and clearly without the duities before then they I'm not sure whether it is first which came first, our plane waves or Marder's cylindrical waves Rosen had already derived a cylindrical wave equation systems and Marder used that and showed how it could be generated. What he was flummoxed by and what I became somewhat clearer to me only a very few years ago is this. As you know, a static cylindrical system in relativity is described by two constants rather than one and there's a debate which is the mass and they're both non-dimensional and since mass per unit length in the cylinder is non-dimensional this doesn't help at all well anyway he showed these outgoing waves and they led to one direction change in one of the constants and I think it was He was the first one to introduce this idea of a sandwich wave, a wave of finite duration. I mean, am I talking in a way that interests you? Yes, no, you are, I thought. I'd like to get your impression. But of course, all that only made me think harder about the actual three-dimensional case. and that had to be settled one way or the other. And although the paper was only published in 1962, that's the paper with Vandenberg and so on, which no doubt you'll see. I think most of the work was done in 1959. In fact, I think I understood it perfectly well. When I went to Cornell in early 1960 and gave talks there, it was all pretty clear, but

12:30 one wanted to be very sure about all these intricate forms. And I worked with it, who I think has never been heard of in history since, was a student who I asked while I was at Cornell in the spring of 1960 to look at the group of transformations that turned this metric into itself. And I was not a little proud of that paper, let me say. I think it had considerable clarity to the subject. Slightly to my surprise, because I didn't expect that it could be done by those methods, Newman and Penrose came out a few months later, which I'm always very low-brow on mathematics. It doesn't appeal to me as much, but it's neater if you like their mathematical methods. but anyway this was established and of course I mean I'm not sure how much more I did after that there is the paper that Pirani and I published a few years ago on the transformations in the plane wave of the orbits which are really light paths which are really quite extraordinary, you probably do know that? And the points that puzzled me then, and I think that are still relatively puzzling, at least they puzzled me. I mean, but some people may regard them as solved. In the very coordinate system that I used in this S.S. 62 paper, the outgoing wave condition is basically incorporated into the coordinate system by having the radiation coordinates for practical purposes. Now, in Maxwellian theory, of course, retarded potentials, advanced potentials, and any superposition of the two. Obviously, in relativity, you are invariant against changing the range of time. You can have advanced potentials just as easily as retarded, although the physical meaning, of course, is not clear.

15:00 But because it's so non-linear theory, you can't have combinations. At least nobody's got the sense of a combination. And I believe that problem still eludes, and it's not very clear. I mean, in the cylindrical case, since Rosen had brought the wave equation, the cylindrical case, as a linear equation, you can have a superposition, but then the cylindrical case has other unclarities in it. But in the full three-dimensional case, no. Ray Sachs, of course, generalized what we had done very skillfully to the full three-dimensional case because we had excellent reflection symmetry. but I don't think it revealed any fundamentally new features the part that is least clear to me is the aftermath three dimensions in the linear wave equation you have Huygens principle you understand that So that it is very easy for a system after the transmission of a wave to return to a static condition. Now the moment you don't have Huygens Principle, as we do not have in relativity, you cannot return to the static condition. I mean the space if you have a perfect sphere from T minus infinity to T naught and then it emits waves it's very difficult to write down even what it means that it stops emitting waves and it certainly doesn't return to Schwarzschild's solution the space keeps on ringing

17:30 which I find a little better disturbing. Why? I'm trying to think why Huygens Principle is the crucial fact in that case. Yes, because in Huygens Principle every disturbance travels with the speed of light. in the general hyperbolic equation it travels at most with the speed of light and the singularities travel with the speed of light but there's an after effect the non-singular after effect and that doesn't seem to die out and of course you don't have Hawking's principle even in linear theory in an even number of spatial dimensions So then, as you say, the disturbances can, does it say, die out? They die out much too slow. I mean, they are quite significant even after quite the time has elapsed. and what you call a passive system is not as clear as I would like it. Let me give you a little more of my attitude to general activity. And when it gets irrelevant to your work, you can use talking. Sure. You can say that Einstein's field equations are really almost trivial. assume any geometry you like and they tell you what the space is filled with. Constraints only arise when you do not allow the space to be filled with any garbage that comes up. In particular, for example, if you have a non-negativity theory. So, in what sense are the field equations something more than something that you read from right to left

20:00 that tells you what matter there is when you have, make an assumption about your geometry. Well, that only arises if you link the various components of the energy momentum tensor. If you do, as it were, put an equation of stating, like, shall we say, the Schwarzschild interior resolution dimension, the oldest one, that the pressure is isotropic and is not unrelated to the relations debatable to the density. put some conditions on your geometry now when you go to the ordinary elastic theory you can have no let's go back a little I don't know how much you did classical dynamics well the ground you know to you appreciate there's a great between conditions that do not contain the time explicitly and those that do contain the time explicitly. And you can call them passive and active. I mean, the most obvious active one, of course, is a time ball. But if you keep rotating something at a fixed rate, Again, you have an active, you have the time entering explicitly into your equations or constraints. We are not very good at telling what constitutes a passive system in relativity. In fact, we understand that little. And if you say that, I mean, the model of a gravitational wave transmitter with axial symmetry is a star like the sun, which for reasons best known to itself changes spherically to oblator prorate. that obviously requires an active system

22:30 inside in Feld and the like a non-gravitational system and there was a feeling which only relatively recently left me totally that if you're a system in which everything actually follows a geodesic that it doesn't transmit. But I don't think it's true. We see, for example, if we have... Now, the only system in which everything follows a GDC is a pressure-free cloud, a cloud of dust. And if we have two clouds of dust approaching each other it's pretty obviously foreign to watching that there will be a mission although everything follows a geodesic but that is the clearest example of this I owe to Volkan Rindler. Have you ever talked to him? No, I haven't. Very useful. He has many very good ideas. And you see, if we take this, if you like, artificial case of a sphere, we start with the sphere and the Schwarzschild's region, we then make it go prolate and then let it relax. In that space afterwards, we do not know how to define that we don't put any more energy in. Am I making myself at all clear? Yes, I think so. I mean, what is the violation of a purely passive situation that gives rise to gravitational waves. Right. So... You see, we normally talk of gravitational waves emitted by binary. But of course, in a star, the particles do not follow geodesics

25:00 because there are pressure forces in the star. and that's not a pressure-free system. Right, but... So your concern was that in a system in which the particles were all freely moving, you question your answer. Yes, which is what Infield believed. I don't think it's true, but it's not... We don't have a very good work example to show that it's not true. Right. That it's not true, that it would not... That it would, in fact, be. Yes, I noticed in a couple of your papers that you mentioned something. Yes, it just nagged me. I think it nags me less than it used to. But we haven't got any very good gravitational wave transmitted. Now, the binary pulsar, of course, everybody says. but when the original calculation was made, many people thought it was full of holes and the person who of course was the most votary in this was Jürgen Ehlers and he then had the energy to work through the whole thing and it's because I believe Jürgen Ehlers having started as a skeptic they think the formula actually works because he came to that conclusion yes he when I spoke to him he said of course that he still had certain doubts but very much weaker than yes he felt happy on the whole that the result was correct that there were still certain issues that had not happened so you felt that that as it were that if he was satisfied that it seemed like I think that convinced me, but I still would like to see a really good example. I mean, you spoke of gravitational radiative reaction. Now, we know it thanks to these calculations for particularly aylist and refined and made clear. But I would absolutely love it if one had a good, very clear example, a simple one.

27:30 You know, I mean, I'm not an optimist who thinks you can do it in closed form, but at least where you have a clear method of approximation which converges. Well, let me return to something that you mentioned earlier. You spoke about the Bern Conference in 1955. Right. And you mentioned that you enjoyed it greatly. Was there much discussion of gravitational radiation in general at the conference? There were several papers on it and a lot of discussion in the corridors. and you mentioned in one instance that you were urged to work on this I'm interested in the role of the conferences partly because when I've been reading up to now of course it's only in the conferences that occasionally you see people discussing things as opposed to in the proceeding one conference where there's more of a record of the discussions that were taking place is a couple of years later at Chapel Hill It was in early 58, I think, two and a half years later. It was also a very good meeting. And there's some record in there of the subject of the existence of gravitation and radiation. In fact, I think in your letter in 1957, you make reference. What did I say? I can't remember. You say, well, partly on to this, Scheidegger and I have both expressed the opinion that there might be no energy carrying gravitational waves at all in theory. And the footnote refers to your contributions at that meeting. So really that led me to wonder if you... Yes, this was still with us. Yes, yes. I'd quite forgotten that letter. But I think it's probably quite like a sound. Yeah. And that was then done much more fully, of course, in the paper by myself, Piranhas. Right, yes, it's probably expanded on that.

30:00 yes I'd quite forgotten that I published that so there was some discussion then at the conferences around that period I mean the conference in Chapel Hill was very good but of course was dominated by John Wheeler who just came up with the results of the Yang Li experiment on the non-conservational which was a great source of it, which was brand new of the press. But it was a good meeting. That's right, Wheeler's power of the proceedings as well. You have seen John Wheeler? Not yet, but I hope to. I really see him in his show. And, uh, the, uh, one interesting thing that I noted, um, was that, uh, the final, like, here to get involved at one point in the discussion about, um... Direction of time, I remember, in getting involved. Right. It doesn't remember very directly involved with gravitational waves. Oh, you know, it was just that in the proceedings, it seemed to develop after the discussion of his time. It wasn't a very long discussion, so... I can't remember. Well, while still on that general topic, just about the paper, you were saying that you recall people taking up your... I suppose you could call it the thought experiment about the particles on the stick. But you were saying that at the time you didn't regard it as being especially important, I knew it was important. I thought it was obvious. I knew it was. No, I had no doubt about it. You see, my whole attitude is an engineering attitude. I want things to be tangible. And as you may have noticed from my work, I work very low-brow in the mathematical methods I use. so you didn't on the whole expect people to be surprised I didn't expect them to be surprised you've expressed it very clearly that's interesting

32:30 so then of course following that letter and then you went on to develop as you say with Brownian Robinson and then later as well I have the impression that this touches on something on the sort of thing that you discussed recently just earlier. I'm interested in the role of the news function. Yes, which nobody has fully understood. That, you see, was something I thought that I said that nobody has really heard. One of the formative books I ever read were Hadamard-Sillivan lectures at Princeton in the early 20s. We discussed at great length and with enormous clarity the difference between hyperbolic and elliptic partial differential equations. And many people could usefully spend their time reading those lectures again. let me just tell you one little thing which is totally overlooked now the people claim chaos and unpredictability is due to non-linearity nobody has read Hadamard could suspect that let me give you his excellent example let us take the wave equation and Laplace's equation in two dimensions They differ only by a sign. All right? The standard Cauchy proof of the existence and uniqueness of solutions deals only in absolute terms. Let's show that certain factors in series converges absolute terms. So the sign can't matter. You with me? Yeah. Nonetheless, we prescribe the solutions totally different ways. When we want the solution of Laplace's equation, we give one function on a closed boundary. When we want to give a solution of the wave equation, we give two functions on an open boundary. Am I making myself clear? And he says, let us just look what happens if we do it the wrong way around. Put the case, you have Laplace's

35:00 equation, d squared v dx dy squared equals zero, and we give both v and dv binding y on y equals naught. That will correspond to dealing with the Wake Equation, and this solution must exist, of course, by the Cauchy theorem. Now, let us assume that on y equals naught, v equals cos nx over n, and dv binding y equals zero. then the solution is obvious. It's cos nx cosh n y over n. Alright? Now let n become large. Then the initial perturbation becomes smaller and smaller the larger n is because of cos nx. But at any point other than y equals 0 because of the cosh n y as n becomes large the effect becomes larger and larger. That is to say, if we give, in this revolution of Laplace's equation, by prescribing two conditions on one line, the slightest ripple in these conditions will totally upset the picture. Any uncertainty in your given conditions is fatal, totally fatal. and that's what's called chaos and there's no non-linearity in any of this and you see most people who talk about chaos haven't understood that read some stuff that's 70 years old and it's there and he talks again very much that where is the characteristic of the equations that then are analytic functions except possibly on the boundary where you describe them. For example, if you have a circle and you have one potential in this half circle and one potential in that half circle so that's a discontinuous function. At any distance however small inside, the potential is an analytic function of the coordinates. It smoothies it out instantly with any distance from the collision.

37:30 This is totally different with hyperbolic equations. And of course, if the radio station is silent for half an hour, I could predict from an analytic function that it's silent forever. If all the coefficients of the power series vanish, then it's always permanently zero. know that's not how radio works. And that's the news function. That because something you have to put in something that is not determined by what goes on before. That's not determinable, not deducible by what's on before. That's the characteristic of the hyperbolic function. Of the hyperbolic equation. And if you cut out the news function, you cut out the essential character of hyperbolic equations. Had I understood that 70 years ago, I understand it now, not that very few other people understand it. interesting, I guess, that it's, uh, that I guess it is an idea that hasn't, that didn't develop, that didn't become part of the mainstream. You see, when you take the essential model that is most considered to a binary star that is closer and closer to each other, then of course, originally, there are certain densities and pressures in the two bodies. as they get closer and closer they are they go into new ranges of density and pressure so that you could have two bodies that originally are identically in every way and as they get closer because they react differently to the higher pressures that they arise and that would be totally unpredictable. You make myself, okay, you see, suppose you have two materials

40:00 that at up to certain pressures behave identically. Then the orbits of two bodies with these two different materials would be identically up to a certain point. But suddenly they would differ they differ. And you get news. You couldn't deduce how they behave later from how they behaved earlier. They show a new characteristic. Now, I know this sounds very concitious. Why did I get there in the 62 paper before other people did it? It's because I had a clearer and particularly this news functionally, that it was a hyperbolic system. Right. Now, if I remember correctly, in that paper, you discussed the question of the relation between the existence of the news function in a given case and the existence of the gravitational radiation. So, for instance, am I correct then in thinking that, So this is connected, then, with the question of supposing you have the two binary stars and they move around each other without, for instance... No news is news, too. The fact that they do not change is itself an item of information. So, in that case... You can have waves without anything new happening, but the fact that there's no news is news itself. So the news function still exists. Even if the system exists. There's room for a generating function, whether the room is used or not. And the structure of the equations has to allow for that. So would there be an example of a system in which there isn't a new function where there's no room for the information? I don't think so.

42:30 I can't say that I'm as clear about this, maybe, as I was at the time, but if you take this classical case of the double star, it is, you still, from space outside, you have of this continuing orbiting in which the temporal change does not lead to anything. I mean, I can't say I'm as clear as I used to be, but the equation must allow for it. It must allow for something extraordinary happening among the stars, whether it happens or not. Well, So, connecting then with the question of the freely-moving particles, which, as you say, at that time, was still... Hello. I was thinking of... Oh, so the question of, say, the two, for instance, two clouds of gas, or the question of the freely-moving particle system. Yeah. Yes, that worried me. I'm now reasonably satisfied that they do radiate in spite of nothing happening. But for many years it gave me, I was doubtful. And you, was that connected with the news function? Was there a question in your mind of whether they were... In such an uninteresting situation, waves could arise. But I'm now reconciled to it. So the question really was, in such a system, there was little or no possibility of anything interesting happening along the way. No, quite. So you couldn't say that somebody... That it's news. But I'm reconciled to it. But still, I think there are many things we don't understand very well. I'm toying with it at the moment, but that's something I don't think of time to go deeply into it. It's a cylindrical situation where you have a cloud expanding and coming back where everything moves on geodesics.

45:00 And whether one can analyze this system with a single spatial coordinate sufficiently in particular to get not only the retarded but the combinations of the two, which is something which is singularly absent in the gravitation literature. Right, there was certainly a question of dealing with the superstition being going on. That is very elaborate. And of course if we follow Wheeler and Feynman on the observer theory of the late forties, understand both the incoming and the outgoing waves. And we totally failed to do that in the radiation theory. It's certainly one of the interesting problems in the radiation reaction problem. Right. So, I'd like to ask you just for a minute then about the work, the general work on radiation reaction that took place at that time, because up until the period that we're discussing for you, around 1960, there had been a number of attempts to work out the radiation reaction government, say a binary system, with a number of conflicting results. Great. Starting, of course, even earlier with the NSAID-infeld-coffman analysis. That's right, which was the basis for... For much of it that we've done. That's right. And, of course, I've always been very skeptical of this, of this kind of approach, because they assume point particles. Now, I regard point particles wholly alien to the theory. I mean, the theory is very much a continuum theory. And when you are, I mean, how, the idea of, if you look at Einstein and Infant Hoffman, the difficulty of the problem is they want particles without dipole and higher moments, who the dipole being with it. And in a curved space, locally to eliminate a dipole is very difficult.

47:30 You can, of course, with a dipole, you know one of my papers long ago, I looked just at a pure dipole. and you can get a solution which is strict in relativity there's nothing in the mathematics where you have a uniformly accelerated gravitational dipole because negative mass of course repels I mean you understand the idea you have to exclude this and that is so artificial in a curve I never liked any of that. Right, so you felt that that sort of approach... Or did you feel that that sort of approach, therefore, was unlikely to come up? I thought that the approach was certain not to read the convincing answers. At least not the answers that would convince me. Especially in the view of the fact that there were a number of different answers. Yes. So... and that's why I always you need you need an equation of state to get any equations in relativity as I said earlier again Ehlers I find very interesting and you have great admiration for him he's one of the few people who has understood my criticism of the way we handle things you see when you consider an isotropic liquid the Schwarzschild interior solution, you have two or maybe three conditions connecting the world, three conditions, two connected pressures in some direction, one connects value back with density. That's two conditions. When you write down for empty space R mu and U equals zero, You suddenly give 10 conditions. Isn't that a bit ridiculous? Why 10 instead of 3? And what stops empty space of growing positive and negative gravitational mass? and Ehlers proved that the positivity theorems

50:00 of Hawking and Penrose definitely exclude that option. And that really means that having that if space is initially empty it will stay empty. but the previous assumption that space is and remains empty is a highly over determined hyperbolic system it so happens it's consistent but not through the merits of those who said do I make myself at all clear? yes I understand Well, I was going to ask you then because you explained very well your doubts about the early work on radiation reaction and you also spoke of your doubts the radiation reaction work surrounding the binary cluster and so on. Well, the pulse had been still. Right. And was there particular work on the radiation reaction problem in, say, the binary system that answered some of your doubts No, I think it's the analysis of Ava's that's my balance. But I was surprised. Thank you.