Interview with Jim Anderson

0:00 Testing, testing, testing. Okay, here we go. Okay. So we were saying you were going to say you were going to look at it. From the point of view of the history of the subject, the most fascinating part about the EIH papers is that there's only one book that I know that describes what they did. That's Bergman's old book on relativity. it. And if you look at any book, including, I'm afraid, my own, at best they'd give it as a reference. Misner, Thorne, and Wheeler, it's a reference. Weinberg, it's a reference. I just saw a new book that came out by Ruffini and someone else. They didn't even reference it. It is almost unknown in the relativity trade. And I now think it's one of the most significant, one of the most significant papers that Einstein wrote. And it's just not referenced at all, or only in passing. And I don't know why. It's interesting that when I was with Bergman today, he discussed the first thing. It's true that I haven't seen, as you say, an empty W. It's not. It's in one of the books. Take any book that, uh, Wohl's recent book, it's not there. Just go down the line. There's no book, except for Bergman's book. There's no book that discusses it. And I don't understand completely why. I think part of the problem may have been that when they did their early work, the calculations got to be rather horrendous. And I know that they said at one point that the actual details of the calculation would not be presented, but were on the file at Princeton, the Institute, or somewhere.

2:30 If you wanted, you could see them. And that may have put, that may have put people off some of it. Also, part of the problem I think was that it came at a time, well first of all, it certainly came at a time when almost no one was paying any attention to relativity, you know, 37, And even when I got my Ph.D., Peter was about the only person in the country you could work with in relativity, although Wheeler's group sprang up shortly after. So there just weren't any people that were interested in relativity, really. And it's only in the last, oh, 30 years, let's say, that it's become of interest again. So that's a very interesting, it seems to me a very interesting aspect of the history of the subject. What I consider the most fundamental paper on the whole subject is almost not at all The only paper, the original papers didn't do the radiation, they didn't get to the radiation. The only paper that I know of that did some radiation was Hintel and Wallace. They calculated the radiation damage for electromagnetic charges. But there are some very strange—let's see, when was Hintel and Wallace? I'll tell you in a second. Infeld and Wallace was 1940, okay, and the EIH papers, and then Einstein and Infeld, they were 38, 40, and then the last one was 49.

5:00 But the only radiation paper that I know of that used the surface integral method was the Infeld and Wallace paper in 1940. And that is never referred to, as far as I know, I've never seen a reference to that in any discussion of radiation damping in electromagnetic systems. And yet it's the first attempt that avoided the infinite renormalization that virtually every other derivation required. I guess, and I was thinking it's true that some of the early papers do mention the NIH, age, but they don't actually use it, like Ninghu kind of paper in 1948 or so, and Infeld and Scheidegger did work. Scheidegger is the guy. Yeah. Scheidegger is the guy that wrote this long paper in which he claimed that he could show that you could always transform away the gravitational radiation. And I think Infeld will leave it also, because in this paper, Infeld and Wallace, he was the first one to extend the approximation far enough to see time-odd terms in the expansion. And he simply assumed, uh, he looked at two expansions, made two assumptions, one of which corresponded in effect to taking half-advanced, half-retarded solutions, in which case there was no damping, and the other taking, uh, retarded solutions. And in the paper, he said something like, to the effect, there was really no, nothing to choose between the two, but he felt that the half-advanced, half-retarned was much more symmetric, or he preferred that, and so if you did, you didn't get any damping. So it's that whole period when there was a question about, and this was electromagnetic, not just gravitational. That whole period of people were questioning whether existence

7:30 is interesting. But not as interesting, I think, as the fact that almost nobody refers to the IH, or uses it. And in my opinion, it's the only way that you can deal with it. Yeah, I guess I've seen some that refer to it, but they do say that they're not really I just looked up in Weinberg, and he refers to it, he says, but we're not going to do things this way. He does something else, and then uses some other method, but it's, as far as I'm concerned, It's the only method, the only procedure, that does not have some objectionable feature to it, such as infinite renormalization, arbitrary assumptions about the nature of the inertial and then the existence of runaway solutions. That's interesting, so you think that none of the attempts at treating the equation and I guess the problem of, that you managed to touch on there with the half advance minus half return potentials in choosing the sort of conditions, on that was another big problem. So do you think that that was the main reason, for instance, why I think that was not the internal shattering of that too? I think in part it was, because in the paper they say something to the effect that there's no way of deciding between the two, and then for some reason, I forget what it was, they like to have advanced that retarded or symmetric or something, and they didn't get regulation down there. But it can all be done quite consistently, and without any of the problems of the other

10:00 derivations. Have you seen my paper, and I just read it in 1988, I think it was? Yeah, I only first looked at it recently. That's the only place in which there's a derivation of a gravitational radiation reaction that I believe is fundamentally sound. Yeah, Alan Wiseman actually directed it to me and said he thought it was a nice derivation of his work. Since I didn't develop the idea I don't think, I'm not taking any real credit, but the other derivation groups, people like DeBoer and so forth, their derivations are terrible. They assume delta function sources, they have to do all kinds—I mean, he had the most ornate renormalization scheme, just absolutely off the wall, and he claimed that somehow he would see that after a certain point it wasn't a problem anymore. You see, you don't have any of that in the IHC. You don't have to make any assumptions about these local structural resources. Also, there's another aspect of the problem that's that is the question of what is an approximation. When Einstein, in the original EIH paper, they expanded things in a small parameter, without really saying what that parameter was. And then they used what amounts to, do you know what a multiple timescale formalism Well, yeah, I think I have a good idea, but I don't know. Where you use, where you consider that you have some function of t, and there are different

12:30 timescales in the problem, for instance the oscillating timescale, the damping timescale, the light travel time across the system timescale, and you expand in, you assume that the function is a function of these different timescales, so it could be t and a function of t and a t and epsilon squared t and so forth. And now you treat those as independent variables, and you determine the dependence on these by requiring that terms that give rise to secular growth are zero. And that fixes the dependence on these parameters. Now, EIH used what amounted to, although they didn't know they were doing it because I don't think had been worked out by that time, used what they thought, what turns out to be a multiple time scale formalism. In a very crude sense, they assumed that everything depended upon time through slow, this lambda times t, lambda was this expansion. And that's sometimes called the slow motion of time submission. You see, that's inherently incapable of dealing with radiation problems if you assume that it holds everywhere. So it wasn't until I did my work that I figured out how to include radiation with the slow motion. Now part of it was done by a student of Kitts, Burke, who used matched asymptotic expansions, but But he didn't use multiple timescales. So there are really two approximations. And I think that's another part of the problem, is that there is a group of people that somehow wanted to derive exact results. Somehow they wanted to run this. They wanted to be able to derive exact results. So that an enormous amount of effort was spent identifying surface integrals, trying to identify dipole moments, quadrupole moments, and the like, in terms of surface integrals. And you can't do it in general. That was part of the problem. But if you look at EIH and you look at many other papers

15:00 that were written in that period, none of them recognized that the expansion parameter was a real physical number that it represented for example it was a ratio of light travel time across the system to its characteristic period or the size of the system divided by the wavelength of the radiation or some typical B over C in the system. And I remember I, De Moor, for example, formally expands everything in powers of 1 over C. And a number of other papers used 1 over C, and I'm afraid I did too. But I had the good portion to spend a couple of summers with some hydrodynamicists use these techniques all the time and they told me about them and convinced me that you can't use dimensioned parameters to to make expansions because i can always make c really one by the right choice of units so the fact that it's one over three times ten centimeters per second is irrelevant in an expansion because that way you can't tell the validity of the expansion and what happened in the EIH also was after they did this they then sort of reabsorbed this parameter without ever saying what it was reabsorbed it back into the formalism so that it seemed to disappear and they got this set of equations well then there's no way of all to what they apply so there were all kinds of But if you don't choose a dimensionless parameter that you can identify with something in the system, then my feeling is that nothing that you do makes sense. Right. And that, I'm afraid, is what's happening now with the discussion of the library the radiation damping for inspiring double stars, or bion, bion pulsars.

17:30 Just to get the next order of, next expansion, formal expansion in EIH, it doesn't tell you very much. You have no way of knowing whether it's active in the system or not, unless you pin down the expansion parameter and see what it says. Then you can tell whether the next term is large or small. And unfortunately, I've been wanting to talk to Kim about this. That expansion parameter, in the case of the LIGO binaries, is the one with a quarter of a half. Whereas in the case of the Binary Pulsar, the Taylor-Holtz Binary Pulsar, it's I think, something like 10 to the minus 4. So there you can comfortably carry out the approximation, and you have a bound on it, and that's all fine. But I've thought and thought and thought, and I really don't see how you can carry this out using the EIH formalism. As I said, I think it's the only formalism that makes any sense. How do people apply it to a system where a small parameter is as much as a half? Right. It's certainly already clear that in the case of LIGO type systems, that certainly at some point that's of interest, each successive expansion, each successive approximation in the expansion that you make is not really converging in a particular sort of... Well, that's the other problem, that all of these expansions are asymptotic expansions, of course, after some point, you know, they begin to get worse and worse in terms of the number of terms that you keep. And that depends upon the size of the parameter that you're expanding in. The smaller the parameter, the more terms you can include in your expansion.

20:00 But there'd be parameters a half. I don't know how many turns we could be before the thing goes bluey. And I've read what a lot of people have done, but I have the feeling that it's not getting to the heart of the problem. And, of course, there's another problem that has not so much to do with the radiation, but that is, in the Taylor-Holst binary, the tides are typically in the order of about about 2 centimeters, about 10 kilometers in diameter. By the time they're essentially touching, which is, they want to know what's happening almost up to that point, and then, what is it, 1,000 hertz, the tidal force seems to is going to be enormous. And I don't know how the hell you're going to take care of that. Yeah, it's... There has been some work by, I guess, Lai and Shapiro on looking at tidal effects when they're going to get close and it's clear that it will be very significant. Yeah, so it's not clear that all of the work on the next approximation or the next one after that, enormously difficult and tedious. When I wrote my 88 paper, I had something like 88 terms. Just a miracle that they were all, they all managed to cancel out. But if someone held a gun to my head and said, are you absolutely certain you do leave out something else? I I don't think I could absolutely say that. That may be another problem on the IH, it's not been used. Some of the other techniques give answers with less work, and I don't consider them

22:30 at all reliable. So you think that you've looked at the spirit a little bit? People have been scared of, in part, as I said, it came at a time when no one was interested in relativity. And then there was an enormous number of papers done after the war on the so-called quadruple formula and a lot of stuff that just didn't make much sense, basically. They found anti-damping, for example, and they didn't seem to be as concerned as they might have, because they did what they called a fast approximation. They just threw in a parameter, a small parameter, and expanded in terms of the small parameter without ever saying, even remotely saying what it was. And then in the end said it equal to one. And so if they had bothered to calculate, for example, perihelion and mercury, they they would have found that they only got seven-eighths of the answer if they'd accepted answer. So they were throwing away terms of the same organ magnitude as things that they kept. That shows how important it is to identify the expansion parameter and make sure you know what you're doing with it. And they didn't do that, and so they came to this totally erroneous idea that a gravitation radiating system could anti-gap, and that instead of spiraling in the orbits would spiral Yeah. That's right. It's interesting that some people got the result because this chat that I mentioned, Ning Fu, he also got anti-gap. Yeah, in fact, the first time he did it, he got the right answer, and then he went back and recalculated and got this other answer, some other anti-damping answer. That's right. I was surprised at that, too, because I went to the big paper to see why he went back and he discovered a sign change.

25:00 Yes, right. That was interesting. I think he was using a slow motion approximation of some kind. Even, I mean, the slow motion approximation, unless you know what you're doing, is not going to be, I don't think he used the surface integral formulation. I guess not. I'd have to check that. He mentions EIH right at the outset, but I think he says that he's going to, he's improving on it, or taking it somewhat different. Yes, a lot of people said essentially the same thing, that they were going to improve and make it easier. So they introduce delta function sources and all kinds of things. Yeah. Um, the, um, we're just, uh, off on a slight tangent since we were discussing this question of people from the point of view of the difficulties in the radiation reaction problem, being unconvinced of whether gravitation radiation existed, one of the reasons that I was paying some attention to the Einstein-Rosen paper was that, well, first of all, as I said, at one point they had thought that the work on that paper specifically was But then also later, Rosen, in the early 50s, or mid-50s, published a paper in which he said, well, because you can coordinate, transform a wave, the energy momentum pseudotensor to be zero in the wave, then it seems like there's no energy in the wave. And only locally. Only locally, yeah. people did not understand these things very well. I remember in some of the early GR meetings, there were long sessions reported to how do you define energy density and general relativity. And in general, there is no way to define that. And there were all kinds of papers, and I remember Mueller wrote along, had a long method of discussion on how you did it, And they just thought, well, it's like any other field, people simply didn't understand things, and that's only after a lot of work went into it, that people began to understand

27:30 what was going on. Right. And in general, you can't define energy density from general relativity. But you don't have to. Nothing is gained by doing it. So, in fact, a lot is lost by doing that. You know, the first—let me go back even a little further. The first derivation of the effects of gravitational radiation was given by Einstein in around 1917 or something like that. And he looked at the radiation coming off of the spinning rod, if I remember correctly. He calculated using the pseudo-tensor, it was the solar tensor, he calculated the energy radiated. And aside from the factor II, he got the quadrupole formula. Then he said, that's equal to the energy radiated, and therefore that's minus the change in the energy of the rod with time. That was the energy radiant. So he then went back and put in the Newtonian expression for the energy of the rod to see how that was changing, how the period changed. So that was bad on a number of counts that he'd used the pseudotensor to define, which doesn't define an energy, called it an energy, and then equated that back to the time rate of change of the Newtonian energy of the system. In the end, it turns out that that's what you're supposed to do, but you have to show it. And he didn't. Now, but he did recognize then that there should be radiation. And that's funny that then later Rosen where the question arose. But do you know about, you know Eddington's book on the mathematical theory of relativity? Yeah. Do you know about his discussion of radiation damping in there? Yeah. He looked at the near field and calculated and got the right answer and in fact did the right thing. And that was in very early on also. But then he made

30:00 remark. He said, he did it for again for a spinning rod. He said, if you have a gravitationally bound system, none of this is going to apply because the gravitational binding energy is comparable to the other energies in the system, the kinetic energy of the system. Whereas in the rod case, the stuff that's holding it together is many orders of magnitude larger than the gravitational field, and there the linear approximation really does work. But he cautioned that the linear approximation would not work when you have gravitational development systems, and that he even forgot that. So there was a lot of work done, trying to use the quadrupole formula, just blithely setting it equal to the energy, the Newtonian energy of the system at the time rate, negative time rate of change in the energy. And that's not a derivation. So the subject had a lot of false starts and ups and downs and things like that. Right. Well, in this energy balance argument, what do you feel has to be done to justify setting, so, you know, suppose you do in a proper way, draw the energy being carried away. You can, well, you can do it with the EIH. Right. And there you don't have to make any assumptions about the form of the E that corresponds to the system, which is the crucial effect, the crucial point. You don't know what that E is to start with. you can guess it that's not a derivation it's the same as the classical derivations of the electromagnetic radiation reaction you derive that in two-thirds e squared x triple dot then you set that equal to an inertial term well how do you know what that inertial term is how do you know it doesn't isn't modified uh the inertial term isn't modified when you get out to uh when you're at that high an order of approximation, that there aren't additional contributions to it. Well, you don't know that. So you just do it by hand.

32:30 Well, it turns out that it works, but that's not a justification for anything. So making that kind of an assumption is equivalent in the energy balance method to assuming that E is equal to 1 half mv squared plus m1 m2 over r squared, the gravitational binding energy. Turns out it's right, but you have no right to do this on the super. Because the quadrupole formula is derived using either the Einstein pseudotensor or the Landau-Lifschied pseudotensor. And just because you decide to call it energy, that it's energy. Any more than I could decide to call you the Pope doesn't mean that you're the Pope. So, you see, there's a lot of things that people made identifications. Well, this is the energy radiating away, and then, of course, it's obvious that should be equal to the change in the two and the energy of the system. And, you know, it turns out when you go higher, there is a two to higher approximations. It's much more complicated. So, the field has been littered with a lot of papers that, in that respect, were not very good in mind. Well, it's interesting that, given that there were the papers under the interaction go back to before the war, that there were still, obviously, the need for quite a number of papers that were produced in the 80s, for instance, Do you think that, presumably, I guess, the binary pulsar data maybe seems to have stimulated people to work on a thing? Well, I think the binary pulsar calculation, though, I do not dare to believe it. There are still issues that I'm not even sure how to deal with, never mind the tidal problems, and never mind the fact that the expansion of grammar is a half. But as you go along in the approximation, you have to deal with those coordinate conditions.

35:00 It's not clear what those mean, what they mean, and there's nothing really unique about them. I suppose I set up another set of cooling conditions. For example, there's just the kind of thing of, if you calculate the radiation reaction force using the EIH . You get an answer that doesn't agree with the answer in EIH. I mean, using there on Wheeler, there's a standard x-fifth derivative term. And when you do it, just using the Donder conditions to turn the crank, you get a long, long expression. Well, it turns out that you can find a coordinate transformation that reduces that to what's sort of accepted as the standard form, but only for systems that are gravitationally bound and in lowest order where the binding is cool. You have to use that then to get from one form to the other. So, what happens in higher approximations, I shudder to think, oh, someone decides he likes that coordinate condition, someone else decides he likes that one, and you cannot use the de Danda conditions all the way along, because ultimately you get secular terms, that is, you begin to get terms like R log R. So even if r is small, ultimately then, if r gets small enough, r log r is going to dominate over r. And so the second order terms are bigger than the first order terms. And the way you get rid of those terms is to modify your coordinate conditions. You have to add a piece to the Donder, which is equivalent to another technique that people have used, coordinates. Or if you have a singular perturbation theory, if you have a secular term, then you

37:30 can get rid of that by stretching your coordinates and choosing the stretching to get rid of the… So it's an artifact of the approximation. And the equivalent thing here is to change the Donder conditions in the next order, and add a small piece that gets rid of these hour-long times. It can be done, but again, it's good. For example, if you expand another place where you are in difficulty, if you use, you know the work with Chandrasekhar did. He wrote a lot of papers on this. And I think the post-Post-Lutonia approximation, the next one beyond that gave rise to infinite intervals. Well, it turns out that those infinite intervals are a consequence of the fact that the expansion is not uniform, you have to include terms like epsilon, log epsilon terms. And if you don't, then you get infinite answers. They, again, are artifacting of the way in which you've done the approximation. So there's all these pitfalls along the way that if you're not careful, you run into terrible inconsistencies, you don't know what you've got. Uh, this reminds me just, I haven't thought of it until now, but when I was talking to Peter Bergen earlier on, he was saying, and I wasn't familiar with this at all, but that in the EIH formulas, that once you go to a certain point in the approximation, he was saying that the energy density fall off towards infinity. it begins to get so small that the total energy, the total energy average up to infinity divergence. Oh, right. But I think that that is involved in this kind of thing that I was just telling you. that you can get intimate integrals if you're not careful.

40:00 And that means that you have to do some fancy—use some fancy approximation procedures, non-standard perturbation theory. Singular perturbation theory comes in all over the place. And if you insist that I'm going to just use an ordinary expansion, then you're going to have terrible troubles. And he mentioned that to me, I'm not sure exactly what he was talking about. But, nothing that I've done or nothing that I've seen, and these things can crop up somewhere always along the line and clobber you, but there's nothing that I've seen that suggests that there's any fundamental difficulty with using these singular perturbation techniques. But relatives don't like that sort of thing, they like, they tend to like, at least some of them tend to like kind of rigorous techniques, and they don't exist for the second, they just, they're not going to get answers that way. This is one thing that Kip was very interested in, the historical aspect of it, this question of the difference in opinion is to what rigors have had some people who wanted at very high I think that you're going to get, that you're not going to get anywhere that long. Jorgen Ehlers, for example, at least for a long while they have this high standard of rigor. It's a messy, messy problem. I don't think we're going to be able to prove theorems. He always wanted to prove theorems to show that this term was less than this one. I don't think you're going to do anything like that. It's just too messy a problem. Even in the The simplest applications of, say, matched asset type expansions or multiple timescales,

42:30 I don't know of any existence there is, you know, like you can give for, uh, um, expansion and equations and things like that. You always seem to want something like that, that can exist, even, even outside of relativity. And now you're going to try and do it in relativity, lots of luck. What? Maybe some very clever person will figure out a way to do it. I don't think it's been done. Yeah. What you were saying about how people having derived the quadrupole formula in the beginning often by sort of dubious steps that then this was, you know, taken on and used by later people doing various types of derivations. Now, it's often claimed then that, specifically, that the binary pulsar data after, you know, justifies the use of the quadruple formula from an experimental point of view. fair interpretation. If you just hand me the formula, and you give me the data, then I'll say yes, it justifies the use of that formula. But there are two parts to the question. What you really, it seems to me, what you want to know is does it justify the use of general relativity. So here's general relativity, here's the quadrupole formula, and here's the binary pulsar, and those two are okay. But how do you know this justifies that? You really want to start here and go to there. That's to some extent an attitude. I mean, If you read, for example, the derivation in Landau-Lipschitz, it's all full holes. Nevertheless, a lot of physicists accept it because it's, quote, physical, and the holes

45:00 because of just nitpicking. But that's not the case at all. In fact, if you look at Landau-Lyfsch's derivation of the electromagnetic radiation reaction force, they don't give a derivation, they ultimately just write down the answer. And I guess if you believe that Landau was But you could say, well, all right, so what's wrong? It gave the right answer. So that's a question of attitude. What are you after? And if you could just take that formula. See, in a way, that's been a problem. It's been a very successful formula. It works. So people tend to say, so what's wrong? It works. agrees with observation? What are you going through all this other work for? And, well, as I said, it depends on what you're after. If you want to base it on the fundamental theory, then you have to derive it from a fundamental theory without pulling in a lot of assumptions and identifications and things like that. In fact, I guess people even have a tendency to say that, well, the quadruple formula appears to work serving in the theory even before there were observations, even before the Banyu-Palser data came along. So the people, interestingly, given that there wasn't any actual experimental evidence, felt that it was sufficiently justified on these kind of physical arguments. As long as nothing depended on it, No one was going to do the hard work to try and derive it, once the binary pulsar beta came about then. It seems to me we didn't want to try and derive it from basic theory and not just in fact assume it. Or argue it by some kind of handling the arguments. What else can I do?