Interview with Bala Iyer

0:00 Let's see. Oh, that seems okay. So, it's the 8th of August at 2 in the afternoon, and I'm speaking with Bala Iyer. So, I suppose I should start by asking then how you first became interested in gravitational ways and raised your reaction and related problems. Okay. My original interest when I was in India was really I started working in quantum field theory in covered space. That was my thesis. And then for a few years when I got a job I started getting more interested in problems which have probably some observational consequences. So in the Raman Institute I started sort of working on things like neutron stars and ultra-compact objects and so on, effects of equations of state on the existence of these ultra-compact objects, effects of precession around rotating black holes and so on. But it was very far from radiation, but after about 10 or 15 years, you want to make a change. In about 1989, I decided to take a sabbatical in Europe. At that stage, there were two or three different things which I found interesting. and then I decided that I would depending on where I would go, I would sort of pick up those areas those three things which were hot then were one was as thick as variable for what the gravity was getting to be interesting some work on cosmology which was seemed to be interesting but not it's not really hot enough the other thing was gravitation radiation since I got a chance to work with Thibaut in Paris, decided to look more seriously into that and once I got in there of course then I just kept going because there were too many things to do. So that really, I mean, my initiation really started with getting started because I started working with Thibaut. Before that, I heard a set of lectures by Thibaut in Dikajay's school in 1987, I think, where he gave one of the, that's where, in my subconscious, it sort of looked as if of some interesting problems or when I came in, when I was in 89, I really got a chance,

2:30 there's no question that, but whatever I did, I mean, really had a lot of influence, really came from the work of Luc Blanche and Kibodawan, so I spent my time getting, reading them and then joining them. And when you say that gravitational waves were hot at that time, was that primarily of the binary pulsar results? Yeah, yeah, essentially, I mean, basically, yeah, I mean, I think when I really started working, I was really not even so sure about the implications of the, the observational implications that really the detectors would sort of come on and so on, but there seemed to be a fair amount of progress which was made, you know, as a consequence of the binary repulsar work, which seemed to have been pushed forward by the French schools, so I really was frankly interested in it from the theoretical point of view, it seemed to be a rigorous way of doing things and I was mainly interested in that. But after I joined, suddenly sort of realized that whatever I was doing was not only a theoretical interest, but it would probably be very useful for the experimental work also, and that really made me persist in staying on but honestly when I joined I didn't have it would really be so crucial to the detector effort it was more of the theoretical techniques that were being developed that were attracted that has been my interest mainly the formal aspects of GR, publication theory approximation methods and so on so those are the general things which I found interesting. So my first initiation into that was basically looking at it as a nice mathematical problem to work on. I guess I'm curious as to what were the attractive features of it. Had you followed the kind of quadruple formula debate that had preceded this work? Not really. Actually I was aware of that debate but since I was not working on it as I said I was not really I don't think I critically appreciated the various issues I started really working the first critical exposure to this debate really was in this Kajesh school when I heard expound about the various issues involved in this particular

5:00 debate but earlier I was not really aware of these details and it's only when I started working and therefore at that time I started reading the historical, the paper the main papers during the after the discovery of the bind repulsar that I really started appreciating what were the controversies and what were the ways people went about solving it. But it was probably not when it happened. And the attractiveness of working on the radiation reaction problem with these techniques, was that because the techniques were relatively familiar based on what you'd been working on previously or because they were different? No, yeah. In fact, in a sense it was different because my whole thing was is tired of doing the same thing over the game. So I wanted to move to a different set of techniques and try to apply them to a different set of problems. So somehow I feel that once you work in an area for about 10 years, I found Chandra's style very inspiring. I really read a lot by Chandra and I liked his way of working, working intensely on a particular subject, trying to push it as much as possible and then just abandoning it. So in a sense, I found that whatever set of problems until, say, 1989. I mean, I had enough of them, and I didn't want to pursue anything more about them, but I wanted to work on a different set of things. So that is primarily a reason why I'm very good on this, because it was different, because I had not done anything like that before. And you mentioned that once you began working on the problem, you became more aware of the usefulness from the experimental point of view. Was that because you came more into contact with the experimentalists? I think it happened sort of both ways. As I said, in 1989, when I started working with Thibaut, Luc Blanchet had already finished his thesis, and his thesis basically was the starting point of my work. So when I joined Thibaut, the first thing which we did was something which was probably very formal, and that was something which you would think was sort of well-known, basically studying the multipole decomposition of the tensor field, the spin 2 field, the gravitational field, within the linearized gravity, but by using symmetric trace-free tensors, something which looks sort of very...

7:30 But it's a very interesting thing that the results which were then available by, for example, Campbell-Mechek and Morgan, this was one of the good work where they worked with hertz potentials to make the decomposition of the electromagnetic and gravitational fields. So, we basically did it by using the STF tensors and for the first time we got an expression for the linearized gravity case which spotted some, you know, algebraic errors in the previous calculation. So, I think for the first time we had an expression for the expansion of linearized gravity correctly, which means it took into account the tensor character of the gravitational field correctly and the coefficients were right. And it was this which really let us go ahead in when you went beyond linearized gravity and applied to 1p and 2p and so on. Yes. So this was the first thing which happened. So I was sort of excited that you know there was an area that you know where even, I mean it was sort of very algebraically heavy, you know, that was the thing I noticed, but I, it's something which has always been okay with me, I didn't mind heavy algebra though, so, and I liked it because when you, you know, you're playing around with a mess of things and finally at the end of it you get something which seems much more prettier than the intermediate details, so I found that fascinating. And then what happened was, you know, we went to going beyond, what had happened at that time was at the 1pn level, Blanchet and Damur had a formalism which could give you the mass moments for the system, but the spin moments were not yet worked out, spin or the current moments were not sort of worked out to 1pn accuracy within this particular formalism. So that was the next thing which I and Thibault did, which again seemed to be sort of useful for doing the recoil effect, because when you want to compute the linear momentum flux, have to know the spin quadruple, current quadruple moment to 1p and accuracy. And it just so happened at the same time, Alan Wiseman was looking at this particular problem at St. Louis, and he, I think, used, you know, he had one way of doing the calculation by using the Epstein-Wagner formalism, but then he also used the formulas which we invoked and then checked that, you know, they gave him sort of similar results. So, even when this had happened, to me, as I said, it was just one, I calculated the

10:00 current, so I was not really interested in what, I was not really sure, you know, what implications the whole thing would have. But then, after this, in a year, I sort of, saying, oh, you know, this is the action people are talking about, these experiments, this gravitational interferometer coming up, it sort of, it was really coming to me, you know, not directly, because somehow I was not moving it's not exposed to all the people or all the experience you're going on. So I think it really took some time for the whole implication of it to sort of sink in. And I think as far as I'm concerned, it was really the famous paper, one of all of you people, the first three minutes paper, which really sort of said, hey, whatever I'm doing is not only going to be useful to me, but it's going to be useful to somebody else. really what sort of pushed me. I mean, I think the first time at this Caltech workshop which kept organized, so that's the time I sort of really realized that it was going to be very useful to go ahead on this post-Newtonian work. So that is the reason when I went back and I started working with Luke on the 2PM project because it was clear that it had to be done. And then, therefore, Thibov and Jokai started working on the 2pn thing. And then, once that happened, it was sort of really clear why it had to be done. Then it was, it was after that stage, I think I really became aware of the implications of what I was, I started to do in 89. So, I think it's probably two or three years before the relevance of, I think probably it is definitely true that this three-minute paper has really brought to me the implications of the theoretical thing, which fascinated me. It specifically highlighted what the theoretical relevance would be. Exactly, of me if you did this. Interesting. Just as a quick aside, did you find yourself how relevant was your work for the binary pulsar people and their work in the 80s when they were trying to compare their increasingly more accurate results

12:30 with them? Yeah, in fact since all my work in this area has been in collaboration with Thibaut it is always, every time we work on this particular problem I go back to what he has said or written in the context of the binary pulsar and he also tries to keep that analogy always in mind when one is working so not only at the level of picture but also at the level of details because and that was one of the reasons we could make such rapid progress as far as the 2pn case was concerned because most of the formalism was done rigorously do the binary pulsar very well so if you wanted to work up to 2pm if you wanted to do gravitational wave facing up to 2pm everything was there, the equation of motion was there up to 2.5pm including all terms so that is the reason even within about a year or year and a half we could get the basic results in fact we discovered that from going from 2pm to 3pm it's probably taken we've been working for the last 2 or 3 years So, and the basic reason was because the binary pulsar results were not available, I mean the accuracy which was, you know, which was sufficient to do the binary pulsar problem was not sufficient. So, you had to go to the next order in the equation of motion, which has been almost one complete thesis of one of Luke's students. So, therefore, I think all the theoretical framework and all the insights, I think, which were there in the binary pulsar case, I think they have really carried over. At least in my work, it's definitely played an important role. so do you mean that even that the accuracy of the binary pulsar observations are such at this stage that even the 3pn corrections influence the comparison of the 3pn no not that if I said that I I don't think you did I just wasn't too sure the statement is that which you need to discuss the binary pulsar, that was sufficient to do the gravitational

15:00 wave facing up to some particular order, but not to go beyond. But the effects which will come from this particular work, we don't think are at a measurable level for the binary pulsar. so actually from a conceptual point of view or a technical point of view the requirements of going to the order that's maybe required by LIGO actually require new conceptual methods and the point is that up to 2pm level at least conceptually we didn't need anything in the formalism we didn't need anything new it's just a question of doing a little more and you got the result but the problem seems to be that at the 3pn level both the level of the algebraic complexity and the fact that the divergences are much more stronger really seems to require for example very effectively Thibaut had used the method of regularization to handle divergent integrals but those things are maybe you have to do a little better. So in the work with Guillaume Faye and Luc have been doing, they have been trying to go beyond that regularization to find other methods which you will handle. So I think what is happening now probably is maybe you are sort of extending the domain of validity of the theory in the sense that you are now forced to discover or invent new techniques to handle more divergent quantities and probably this some input back to maths I think mathematicians probably will start looking up at these objects I think and maybe these methods and maybe we'll come up with better ways of handling these objects in general so but I personally think that there has been some some new things which have been necessary to handle the problem at 3pn level and which is why I think probably it's taking much more than much more time interesting so in this case it might actually prove that instead of Yeah, I think there might be something going the other way also. I mean, somehow I get that particular impression because somehow they have not yet found the need to handle such divergent functions.

17:30 So probably I think that is the reason they have not really looked at it. Maybe once it's clear that maybe it's useful in some particular context, probably they will look back at it. I mean, that's my impression. So there would be renormalization? it's more yeah exactly something along those lines well you mentioned how heavy the algebra is for much of this type of work and obviously one of the things that I'm sure is a factor is the difficulty of making sure that you don't have errors and we're hiding all that thing and I was struck when you mentioned earlier about how pretty the effect is when things simplify down and indeed Chandra I guess has written quite a bit about that. So I was curious to ask what are the principal things that you look for, what do you principally use to guide you when trying to deal with heavy algebra to make sure that you Well, you know unfortunately I mean in addition to sort of the final results I mean we have had to rely on the fact that we had to do things in many different ways and different people to really check. So for example, at the 3pn work itself, at the 2pn as you are aware, I mean the French and the American groups really work independently, we have worked with sort of independent formalisms and the final results were compared and therefore we are very sure that at least there will be no algebraic mistakes. Within the formalism you are sort of sure that you are working consistently so each formalism is consistent because that is what you have made sure of but then the algebra since it has been done independently and you agree on the final coefficients and we trusted it because they are really done independently I think we have to you know do that in our work also so now for example in this particular case when we are working on the 3PN we did it in many different ways for example some things the whole calculation is fairly long the mass movement, it had something like 150 independent terms and each of these terms sort of starts filling out again many other so you know, you sort of say a mess of about 200-300 terms which you want to calculate by a fair amount of algebra, so the calculation was sort of systematically broken down into sort of pieces, I

20:00 handled some of the things by myself, Luke did something else by himself and then we would you know, after doing the calculation, pass on each other's notes and check the other's algebra, spot the things correct. So, and then, then we had a student who was completely independent of us, who computed this by using an algebraic computing program. So, we had something which, and then, so there had to be sort of three check ticks on every calculation. It would be the person who did it, the person who checked it, and the student who would and the whole point is in this particular case one would say why not make the calculation on the machine in the first stage itself, the whole problem is that because of the fact that there are these divergences and so on, unless you know how to compute it, you really the machine you just put something it can give you only as much as you put in it more than that so unless we sort of learnt the lessons by hand and then implemented those features on the machine it would not ever be able to possibly Once you have learned the calculation here for the next order, these techniques then we sort of borrowed. And sometimes when it will become impossible to do by hand, you are now, you know, in a procedure where you have checked the machine calculation by hand also. Right. So therefore, you know, I think we sort of very seriously now have had all these checks. And then I think what also happens is when you try to compute things, and we try to do it by two or three different methods if they are possible, and then try to see what the final answers are right. And every time somebody new joins the game, for example, he invents his own method of doing the calculation and then he checks whether the whole thing matches. So I think the amount of checks is every time you, any possible check which you can do, I think we have been sort of doing. So that's what probably eventually will give us faith on our algebra. But in terms of overall patterns, you know, some, you know, we sort of joke saying that, oh, you know, if the coefficient is 296 upon 250, it's sort of pretty, you know. So you just sort of come up with these notions, you know. And sometimes you sort of find that when terms really look messy and they are not cancelling, obviously there's a small algebraic mistake somewhere. But I don't think that there are sort of overall principles that, well, you know, subjentral symmetry arguments saying that, well, these are the things you expect, the answer. But the final coefficients, I think we can only check by independent algebra. So every time, you know, we do it and probably do it or three.

22:30 So I think over the years, and while we are sort of finalizing the final answer, we have been doing the calculations over and over again. So for example, you know, I did it originally by hand, now again, during my stay, you know, I went over, tried to do the computer, the whole thing all over again by using the machine. So I think that is the only way we can be sure about the algebra. But we finally hope that, again, Cliff's group will independently do the calculation and finally we'll have really independent ticks on the ground. But I think it's one game where there's no other way of doing that. Just to have some checks, yeah. And when you first do a calculation, you do it exclusively by hand and you don't make use of any algebra computer programs? Yeah, exactly. I think that has been our... That's only used as a check. Exactly. But what is happening now is it's becoming more and more impossible to do it by hand. What is happening, you try to sort of first set up the calculation by hand, and then set it up on the machine, try to see if it reproduces it, but then use it too. So at the 3PN, there have been many crucial steps which have been done only by the machine, because it's impossible to do it by hand. So what happens is the smallest sort of module, you do it by hand, and make sure that it works well. Then that program is what gives you the huge coefficient, because the algebraic computing, impossible without algebraic computing. That is, I think, the first time we had. At 2pn, we did everything by hand and was only later checked by the machine. But 3pn, I think the machine has been an important contributor. And what's necessary there is that you have to go through and check out almost as it were the algorithmic steps. Exactly. So that you can tell the machine. And does it become like programming at that point or does one do it sort of interactively? I mean, for example, you know, I think many of the things have been sort of programmed. I mean, one does work sort of interactively, but I think a lot of things can be. For example, I think now, I think, you know, probably you can almost do the 3PN on the machine. I mean, most of the things can be. so this student who worked with Luke I think really did a very good job and which is and basically trying to

25:00 get the equation of motion at 3p and order and he's almost sort of there as a part of his thesis last few things which are going to be sort of checked but it's still taking time so but I think it is you can use the machine intelligently enough feed in the insights which you have really get the answers you expect it to get, I think. And that, I think, has been an important feature in this 3PN work. Sounds like a big thesis. Yeah, it's a very, I think, very nice work. Very good work. So you mentioned that there are some coefficients involving huge bodies of algebra that were just done by the machine. Yeah. How do you check in that case? What sort of checks do you use in that case? Two guys would do it independently. look would do it independently, the student would do it independently, they would match the answers. So they'll each use, and to what extreme do you go, or do they try to use different algebraic computing? As much as possible, yeah, exactly. You try to write your own thing, and it's just to be safe. I mean, eventually you'd use the code which is sort of better, but at the beginning, as far as possible, I think they did try to write, you know, be independent of it. for example even sometimes when I use the same code which those guys have done I try to sort of key it independently because many times there's a trivial error and you can't spot 1000 upon some 1003 500 upon 1000 by 3 it can just be trivially there so I think that but ultimately I think there has to be independent groups doing the calculation because independent you know since in the group you're sort of talking to each other I mean your inputs do feed into each other. Sure well I was going to ask because within a group obviously on the one hand it's a collaboration and so there must be exchange between and do you find well I guess well to start off with the necessary interaction for the collaboration how much how important is you know constant physical contact meeting face to face I think this is

27:30 what really happens is I mean in the initial phase when you're setting it up I mean it's very important to be together. Otherwise the project never gets off. But once it is sort of set up, then we find that it can go on immediately. For example, I was in India, I was here in Paris and then we worked long distance. And that of course is the wonder of email and so on. So you can really almost be on very regular contact. But in the initial stage when the project gets off, I think if you don't meet, it doesn't take off very well. Similarly in the final need to be together so that you can make all the checks more elaborately. But in the intermediate phase, in fact in a sense it is good if you are really far away because then it doesn't, you don't influence each other. Right, then you have the independence thing. Exactly. But still you can be in contact. But I think again it would not have been possible if there was no email because sometimes you just want to check is that particular term and is that a typo in your notes or is it, and if you have to meet by regular mail for 15 days I think. I think it's, at least for somebody like me who lives in India, I think it's a real big plus. I mean, in fact, I don't think I would have worked on gravitational waves so intensely if I was not, if I was not, I was not connected to the world by email. Right. It's sort of necessary to have that speed. Exactly. So in a sense, I have more interaction with people in Europe than people across my office because I have more common interests with people here than people not expected. I think it's very wonderful. And do you find that email suffices for pretty much everything? You don't need to use phones much? I rarely tend to use it because, in fact, I somehow find it more that, again, when I write things, I can be much more careful and say exactly what I want and be more precise. I don't perform as well, so I prefer many times to write a detailed point-by-point message and get my collaborator's response. And I'm curious, when writing about technical matters, do you, as it were, write the message in something like tech to get the notation across? Yes, exactly. Usually, that's what happens. You use the tech symbol without really teching. Yeah, tech also has become a part of the short-hand, that's true, that also makes it easy.

30:00 And I tend to use fax more because, into a phone, again, if I have to use a phone, I prefer a fax, because sometimes you don't want to key in all the equations, but you would like to collaborate to see it, but then you can write it and it's faster, so I find So I use a combination of fax and email rather than phone. and during the initial period when being in the same place is so important is that sort of as it were a stage in which the apparatus of the causation is being developed between the collaborators essentially somebody has an idea saying that this is how we will go this is what we have and this is how we should go and then you sort of decide this is how we go then you set up the basic notation in terms of which the final solution will be sort of written and then you develop a strategy on how to handle we call this the zoo of terms which you have because different terms have to be handled differently so it's really different beasts so in a sense I find that the most important thing that you break up your calculations by your previous experience into bits, then you say, well, you know, this beast is handled by this method which we've already developed, so we just go along this. And then, you know, the next one is this. And these are the new terms for which we don't have anything, so we have to think about it. So I think those things get decided in the first stage. And in the case of the newer beasts where you need new techniques, would they usually hopefully be developed in the initial stage? No, as they go on, you start off with doing the things which you know, which usually are easier but long because there are many of them of that kind. So in terms of what you are thinking, instead of just letting time pass because these projects seem to take long, you start doing things which you know while at the same time thinking about the new guys who have to be handled. Usually it turns out that the newer guys are handled at the later stages. does it happen then that different people in the collaboration may think of different methods of handling sometimes it has been, yeah it can happen that's true

32:30 in which case they probably will just fall through which is probably useful that's useful, exactly, the whole point is whenever you can do something by different methods when comparing between another group such as the Cliff Will group in St. Louis in the case, say, of the 2PM, where I suppose this whole process has been gone through completely. How much contact is necessary desirable in that case? Do you try not to communicate at all up to a certain point? No, we don't sort of, you know. No, I think what really happened, even in that particular case, is that, you know, if you, in general, to talk to the other person is sort of useful because though you really might not be agreed on the details, you might still be able to, for example, suppose in some particular point you are stuck, but when you talk to the other person, you realize, hey, this particular problem can be solved in this particular way. So I think it does help in going, though in a sense the independence is lost a little, but I think also since now there is a deadline that you have to finish before the thing. to sort of discuss in general even in the intermediate series and I think that's what's happening that every time you run a teacher you say, oh, what are the terms you have what are the problems and so on what have you sorted out what have you not sorted out and then I think when the other person has some input I think at a conceptual level you can borrow it and adapt it to your own thing so I think it has been useful but that's how it works actually so every time I meet Cliff I tell him, okay, this is what I'm stuck with and he tells me, okay this is maybe something which we can do, this is what we did and it has been sort of useful. So, what really, in fact, I didn't mention this, so on the one hand I have this very strong interaction with the French group of Damur and Blasley and Tito Damur, but also So I have some project, we worked on a way to sort of check the consistency of the flux calculation and how much you can use the far zone fluxes to infer the local expression for the reactive acceleration. This is some project which Jeff and I sort of initiated and which we have found as a

35:00 useful way to check the consistency of the radiation of local radiation reaction with the balance procedure but it is something which has sort of given us very on the one hand it's sort of just a check in a sense because you can't really determine all the coefficients in the reactive acceleration, some of them remain undetermined but it tells you that well if you have to have consistency between the local dynamics and the fluxes then the acceleration have to this particular form and the coefficients which you cannot determine usually turn out to be gauge coefficients in the sense that if you change your coordinate system those coefficients anyway would change. So it turns out that you know most of the expressions which you have for the reactive acceleration just correspond to different gauges. So you can elaborate that well you know different radiation reaction formula can differ in the values of so many parameters. So it has been a very useful way to check the consistency between the local expressions for reacceleration and the power zone fluxes. Now, whenever we do this particular calculation, it sort of tries to, it can make peace between some equation of motion calculation, which Cliff is doing, something which Luke Nashay is doing, something else which I am sort of doing, and we have to, and each of these things feed into each other. For example, suppose I am looking at some balance equation, then it sometimes happens that at some particular order somebody has sort of made a small gauge transformation and has really gone off to another gauge when you're trying to check the consistency of the balance equations immediately you spot that that is what has really happened so some information which somebody has can be checked with what we so this is the kind of things which we keep sort of exchanging about every time you get some calculation because you know what you normally do is that you work at some particular order you fix the center of mass to that particular order by you know setting the center of mass coefficient equal to zero so which means you have to determine the coordinate system to that order of accuracy that means either the 2pn accuracy or 3pn accuracy and so on so for doing that you have to calculate for example the dipole moment of the field by taking the mass dipole setting it equal to zero you can get something. Now that calculation has to feed in into your calculation of the gravitation wave generation. That has to be consistent with what you do with the equation of motion. So every time

37:30 somebody does something you can ask somebody else has some other intermediate result with which it has to be consistent. So I think this has been a very useful way in which we sort of trade information. Everybody has got to that particular frame in a different way but we know that each of us has to be sort of consistent and so we do that a fair amount of many times that whenever we get to some particular part which you have calculated the first time we try to see if somebody else has something else with which you can check it kind of intermediate checks that I think is I was going to ask in fact about say for example something like gauge choices if there is necessary to coordinate between the groups to some extent or whether people choose their own gauges what really happens is you choose your gauge our own calculation so I think what is important and I think that freedom is very important so what is really important is to be aware that this choice has been made and not really put together this result of x with the other result of y without really realizing that really they are in the two different gauges so I think it's important to be aware where these gauges choices can make a difference and the higher you go I think things become more and more complicated for example up to 2pm For example, it's only the even terms in the transformation. But when you go beyond 2.5, there can be a 2.5 PN contribution to the gauge. And therefore, that can start affecting the flux term at 3.5 PN. And therefore, unless you're really keeping track of things properly, you will get small mismatches. So, whenever the balance equations don't match, you always find there's a very small effect, but they don't match. not match correctly. And I think slowly we are reaching orders of accuracy where these very small effects have to be very carefully taken. I think that's a challenge actually. So at the 2PN case for example how long winded or if it was at all was the comparison between the final comparison as it were between the results of the St. Louis group and the results of the group? I think that was in a sense I think of maybe a total timescale for about a couple of years, I think. It was all over. Finally, the chips, I think, were done. But I think the 3PN is still going on for the last three, three and a half years.

40:00 I think we started somewhere at the end of 96. And even one group has not completed the calculation. We are probably reasonably ahead. is handling the equation of motion I think they're still doing the generation then Schaefer has some terms in the equation of motion but again it is not complete so I think 2pn it was it's very easy in a sense now and out of those 2 years is you mentioned of course But is it mostly, you know, you spend the two years working fairly independently and then in a fairly short period at the end compare? In fact, I think in the case of the 2PN, I think after we got the result, we just checked that. I think there was probably a contact somewhere in between at some meeting, I think, Cliff and Luke met and there was some probably exchange about the way the different potentials should be chosen to simplify the calculation. There was hardly any exchange, as far as I know. And the final results were just compared. And was the comparison very cut and dry? It's very odd. This is the expression for farzone flux. I think probably there was maybe one thing, which is a small thing which didn't sort of match. But I think as far as I remember, in the circular orbit case, which was the thing which we all worked on, things just worked out. Just the answer. I think it just matched. I was comparing with Cliff, there was one thing which was not matching. Again, it's turned out to be just some stupid factor of half, which was missed out because of symmetrization. I think Cliff just missed out something. And for some time, we were not sure why things were mismatched. But again, I think. So at the 2pn, I think the matches have been quite good. Yeah, that seems pretty impressive. The final expression was compared, and we were really. And is it likely to be more difficult at the 3 p.m. case, just because there are more... I think it's really dread. If we don't match, how are we going to start tracing, it's not

42:30 going to be easy. Yeah, it's going to be difficult to go back through it, yeah. And you mentioned that part of the checking process was within a given collaboration at any rate was checking each other's notes and looking at each other's notes. Does that involve, is that an easy thing to do? I mean, I know people who write code, for instance, will often say it's very hard to look at somebody else's code. Yeah, I mean, I don't know. at least since I started working with this particular group one good thing which both people and I think probably just because of their experience is that when you do these long calculations fairly detailed the notes are sort of came so I think it becomes much more easier to things have to be very systematically done and we write it so that the other person can easily follow everything but it is a conscious effort I think the thing that people insisted should be done and I think we just follow that thing that's why each one of us can just follow the other's notes and just do for example sample so every step is sort of written down so I'm just trying to check something which for some project with people intermediate step is written. So you can sort of really check. Because otherwise, you know, it is impossible. Also, for example, it helps in the sense that, you know, somebody does an independent character and he says, you know, no, I don't agree with this. Even for me, it is easy to just go back and check, whereas if it was not systematic enough. So one good thing is that even when we don't match, it's very easy for us to check where the error was and correct it. Almost in a day, for example, if somebody, you know, tomorrow there's some problem there and this particular coefficient doesn't match usually we can spot it in a couple of days and finally come to an agreement so I think it's just so you sort of hunt back through exactly so all of us have our files with dates and page numbers and so on and usually everyone has a copy of the other's notes so you know we have never had any long term problems with this in fact we find it very difficult

45:00 that are done on the machine, because in the machine you cannot be so systematic, right? So I find it very difficult to check things on the machine, because you go back and trace, whereas here you know what will be, what you are going to do, and so on, so somehow you have been, for example if I send this to somebody, when I collaborate and wants to check it, and I can just go over it and give this, and normally what happens is you don't notice, but you don't carry over a factor of two or carry a minus sign. If somebody else reading it immediately spots it so it becomes very easy. So it often happens that a collaborator will spot them. Yeah, exactly. So that's what happens. So if I send this, if I'm working on this with Luke, he will look at it and then say, well, you know, something wrong here, you know, the final answer should be because he won't tell me, you know, what the thing is. He'll say, but the final answer is wrong because this particular term should be this. Right. And then I just have to sort of go back problem is. And usually one spots the errors. But would it be quite different now, say, when one makes a comparison with, say, Cliff's group? Yeah. There, as I said, only the final answer will be compared. That is the whole idea. And usually it'll be up to them, and you separately look back through your own. Exactly. Because it's impossible to do that. So, and I think therefore, as I said, the internal consistency really is what the group will have to, you know, particular group will have to make sure but the final answers which is what the user will be interested in that we should be in agreement so that has in fact and I think beyond that it's almost impossible to make a check unfortunately that's what scares me sometimes other than the authors is there anybody else in the world who has really made sure that everything in that paper is right it's something which really worries me sometimes whether even the referee everything which an author has written. Sure, and I suppose in principle, it's it's just not going to the referee can't obviously spend the three years that it takes to do this. So they're not going to see everything anyway. But I don't know. Sure. So I think the only serious checks get done when somebody new or a student joins a group. Because when a student joins a group, he's sort of forced to go over some things and then and that, so that's why we look forward to younger people who come to do projects.

47:30 So normally when they come, they say, okay, hey, why don't you check something that other group has done? So then the student, you know, has the patience, or you say, you check my own calculation, but independently. And then I think sometimes, you know, you do notice that some stribute, you know, errors have been there, which fortunately didn't affect the final results. But, you know, they could be, they could affect things at the next order. So I think every time somebody else comes along, new comes along to join the group, I think it's a good opportunity to make a check. And I think those checks, I think we try to do all the time. So for example, when somebody will do 3pn, all the 2pn results, he will check. So the coefficients get checked once more. So every time a new entrant is there in the field, I think the old things get checked all over again. That's a good thing. And I'm curious as to, so these notes, for instance, here would be the actual working notes in the sense that the calculation is done on these notes, but they're not fair copies that are made of scrap notes or anything. Everything is actually done. This is done, yeah. In fact, many times when the calculation is long I do a rough thing and then it is a little bit painful but try to follow. For example, this might not be the final page. I might have on that day done a calculation and then made mistakes maybe thrown it away or then done it again. But this one probably would be something that I'd fight up so that anytime you want to go back available and all everybody in that group has that thing you know they have their file so that you can go back to you know 1996 December and know what has been done so I think it's that it's a fairly well documented right things which are done by hand yeah it's interesting uh but you mentioned that in the case of uh the output of the computer program yeah it's actually difficult to tell sort of what process what the computer's doing yeah that's just something yeah There you can only compare the final sort of results and otherwise I really don't know. It's also not very easy to look at what the other fellow did and so somehow I find it as far as the computer is concerned it's not as easy to check what somebody else has done than when by handwritten notes. Probably it's just the density of my, I mean I don't know why it is true but somehow, In fact, I find it difficult even to check what I have done on the computer. Not very easy to do. It's just maybe a mental block.

50:00 Well, is there some sense in which the computer is a bit more like an outsider that you're comparing with as opposed to a collaborator in the sense that you can compare with the computer's final result, but you really can't get his thinking? Yeah, maybe that is. So you mentioned that from the early 90s at any rate you became conscious of projects like LIGO and detector projects as an audience for the work that you were doing. Does it go beyond that? Do you see results from LIGO or other detectors influencing your work in any way or is it still for you more that you're interested in more theoretical techniques it if that's useful but yeah no yeah i mean as far as i'm concerned i mean definitely now i'm sort of excited is that you know that what one is working on maybe of you know direct use to whatever the detector will need but as i said once this project gets over i mean i'm not really sure i mean i also i was hoping that i mean once you i got into this particular project i also felt obliged in a sense to really finish this particular work because you knew it was sort of needed and that it would make a big difference in the detectability of the signals if these pieces were modelled so in a sense one said okay it's an activity on which one should spend some time nobody else is sort of doing it so I think I felt in a sense obliged to sort of finish this particular But after this, I don't know, really. But there seem to be so many things. I somehow thought that once the 3PN project was over, maybe I would move on and maybe start looking at some other kind of problems. But it looks like that things are not going to be as simple as we thought they would be. Things like effects of maybe eccentricity spin and so on, which originally people said were peripheral to the issue, on which I have spent some... I've had a student who worked on the eccentric boundaries very much, or a lot in detail, not for the 2p inaccuracy. In fact, basically, he's finished his work on the eccentric boundaries case up to 2p inaccuracy to the level at which things which can be done.

52:30 But when we started doing, when he started working on it more as a check on the formalism rather than anything else, but by the time he finished, he sees that suddenly he started looking, people talking about sources of text and histories and situations where they'll be important. And therefore I can see that there are again a few more projects which I'm involved in, which I'm in a sense obliged to complete because they seem to be again important. So I probably can make an exit in a few years. So how much longer do you think it will take to, how close are you now to completing the 3pm? it will be over, but the last bit of check, I mean, still is underway. I think there is a few discrepant terms which we are not really being able to nail down. I think that's what Luke is really doing. This is this work on the equation of motion, which I hope the student is doing. The final checks on that are being done. Because once that is done, And then we in principle have all the formulas for the wave generation, the three, the cars and flux is there. The only thing is the equation of motion is necessary to compute some, the time derivative and finding a defined answer. Right. But the mass movement is almost completely computed and checked. So once this equation of motion is finalized, I think we are in business, so we are hoping But as I said, we only hope that this small discrepancy is only an algebraic discrepancy which can be nailed. Sure. But if it is not, then I don't know the time scale. That's the statement, Luc Blanche is checking the class, but we hope that maybe by the year I have my own 3pm, it's the first time, yeah, but I do really wish somebody else also independently confirms these formulas. And if you had to include other things like eccentricity, for instance, or just to include eccentricity, that would be a whole other order of effort? Yeah, it's, yeah, and probably now I think we have most of the things to do, the eccentric case also, I think, maybe, might not. this equation of motion is finalized in fact it is

55:00 true for general orbits so it will be complete equation of motion so it might not take much time to discuss the equation of motion the eccentric case 2-3 pin accuracy it's not very difficult probably an extra one more year or so and a half is there any sense in which if you were to take everything that had been developed in the circular case that when you went to the eccentric case it would be possible to automate the process to a much bigger chance. I think that's how we did actually because in the summer we decided to check the calculation once more but then we decided therefore just working with circular orbits we will do the calculation for the general orbits and take the limit rather than so that's how we could automate it very easily. In fact in the 2PN case that's exactly what we did the circular case wasn't completely by hand and checked by the machine. But my student who worked on the elliptic case just used the machine all the time. Because he had a circular limit check, which was done by hand. But therefore, you know, the more complicated cases are being done again by machine, even at the two-peen level. For the elliptic orbits, it's too messy. Right. Yeah. And what code do you normally use? The students who use just simple Mathematica, you know, Maple, in fact, they use Maple. The French group usually use the Mathematica and so many times we sort of, you know, if there are two different people in the collaboration, we let them use different things, Maple and Mathematica in Czech, again, just to make sure that some, you know, peculiar features of the computer system has not really affected the calculation, that also we have done occasionally. What really has happened is, you see, normally you need it to compute the higher time derivatives. So, the programming itself is not very complicated. So, you know, the program, for example, would be sort of complicated, for example, the 3PN case, where you have to write, you know, some code to take care of, for example, the language and integrals. So, there, for example, you have to maybe tell it, you know, how to sort of generate

57:30 all the terms, throw away all the infinite terms, but, and that, as I said, therefore this thesis of E.M. Fay is a nice piece of work where all these things have been done carefully, but the routine calculation of fluxes and so on, I think just need very minimal so the good thing about the machine is it can compute very high time derivatives and simplify things without making mistakes and coefficients and so on as long as you know that it's doing the right thing so I think that's it's not too difficult to do that even in the case, I guess what I was thinking of, is that even in the case where you are automating a problem pretty much, it's still in some sense much more like doing analytic work than like doing numerical work. Yeah, exactly. It doesn't really become very heavily numerical. Exactly, yeah. In most of my work, it sort of has tended to remain analytical most of the time. As you said, I mean, even the computing work tends out to be algebraic, you know, computing and not more than that. It's only in collaborations with Satya, for example, where we look at data analysis implications. In Satya, again, we have had this idea of using party approximants to do data analysis. And recently we were working on Fourier domain representations of these party approximants because they are easier to, more cheaper to sort of compute, and probably the data analysis would prefer that. so that work of course is numerical but then it basically relies very heavily on something else's numerical experience so that was sort of going to be my next question really that as a result of working on this type of work which is so closely well not closely related which has such direct relevance to experiment more towards the data analysis side in a natural way that's what that seems to once you calculate the waveform then you realize that well you know people should know how to best model it

1:00:00 you know you build in all the coordinative features you will expect this waveform to unless you build in those qualitative informations which you know should be there again you will not do as well as you will So, the whole philosophy when we made this proposal for the Pariyyaprakshmi was precisely this, that we know qualitative features that there will be something like plunge, we also know for example that the gravity wave flux shows a sort of divergent behaviour at the light ring. And these qualitative behaviour of these functions should be sort of modelled into your templates because that's how you expect the exact waveform to sort of behave and if you model them then you will do better so our basic philosophy was that and that is what we have consciously implemented in these two pieces of work and again as I said since we've used very much Thibaut's experience with doing the data analysis in analyzing the binary pulsar problems so his insights into that was very useful He'd had that experience. Exactly, which is what really he started us off thinking about it and he tried to explore various suggestions he had. In fact, the first paper which we worked on was really a kind of experiment, a numerical experiment. There were various things which he thought should be tried to model the waveform. We tried various things and then finally picked out what we thought was the best from all those experiments. So it was a very useful process, I think. Yeah, and so with the polyapproximate approach, the idea is instead of just taking your approximate waveform and treating it just as a simple template, you're going to pick certain features out of it and try to use them. And it was the motivation for that because the outlook has, as it were, changed since the early 90s. Say the time of the last three minutes paper. People are more pessimistic now about, say, what you can do with just optimal filtering based on the back of 3pn.

1:02:30 Correct. So our basic point was that one of the very undesirable, one of the undesirable features of just using straightforward dealer approximants is the fact that they don't converge very well. Even an odd order seems to have atrociously different sort of predictions. The 2pn you seem to be doing something, and the 2.5pn you go way off from that. The good thing about the Pa-Day thing is that it makes the convergence smooth. So if 2pn does well, 2.5pn does really better than that, not very bad. So I think there's always this big worry which people have been expressing that, to something but how do you know you are converging to the exact the correct value but I think that as Thibaut keeps emphasizing that is the best anyway you can do because these are the qualitative features we expect the thing to have and we model it and you know if that is wrong well we are wrong but the point is the fact that we have that information and we don't use it is not the right way to sort of go about it so that is his basic point that one should use as much information example if you ask him that well should we model spins and you say well you know if our observations tell us that the value for spins is not really going to be very large for binary pulsar like systems then we should not model that spin we should sort of first make a first cut where we say that it is small you know try to look for it and if we fail then of course you can do the spin effect so to ignore information which is empirically available So it's not the optimal way of going ahead. So that is his basic point. I think we can accept that philosophy. It's not that we are dogmatic about this particular prescription, but we don't have anything better. So the problem of just, say, taking optimal filtering approach without any clever use is that it's not entirely clear So it puts you very closely. Exactly, yeah, that was our worry. And also, for example, you know, as we keep saying, that the numbers can be quite, you know, you can't afford, the event rate is sort of so low, you can't afford to lose one-third of the events just because of doing something stupid, right? The processing. That is the reason, you know, every small amount of overlap

1:05:00 which you can increase, I think one should work towards it. That has been the basic philosophy, yeah. Yeah. So do you find it a different experience working on the type of, on the data analysis work and the various, the type of radiation interaction work now up to 3pm than it was when you were working in the 80s on other areas? No, I definitely, in the sense that I'm definitely more excited about the whole, I mean, there is, yeah, the fact that whatever you're doing has some relevance to an experiment and something which might be sort of seen, I think definitely gives you a different feeling. I definitely feel different, yeah, that's definitely true. and the data analysis side is that something that you would have never been yeah exactly it's not something which I would directly have been involved in but again it's one of those things that when you sort of interact with more people though you're not directly working on that topic and you don't have probably this sole expertise you're alone you would not have worked on those kind of problems now you can contribute something of an exercise which you originally would not have had the opportunity to work on, so I somehow find that, yeah, also a nice, nice part. And I was curious, is there any sense in which the number of collaborators that you have working on these problems now is greater than in your previous experience or...? Yeah, that's definitely true. I mean, in the sense that almost all my previous work was just one person I had a few others but it was not as off and on, meet somebody and work on some particular problem and so on, it's not been such an intense collaboration over a long period of time and has it been an easy process somehow it has somehow the you know I don't know I always had a nice feeling of working within GR itself, somehow I think one of the things which really attracted me to the particular subject was the fact that it was so much easier

1:07:30 to work with people, even older people, there seemed to be a kind of mildness, there is not a ruthlessness of research kind of thing which you always associate with particle physics and so on. So somehow, it's always been easy working with people in GRC. And in the gravity of everything, as I said, I was very fortunate that I had the opportunity to spend time with people who thought about this problem for really long, like, put down, they feel, so I think that really has made a big difference. Yeah. And so how many people, for instance, will be on the paper that you produced on the 3PN equations of motion? This 3PN project had sort of two aspects. There's actually one, which is the equation of motion, which was work done by Lou Blanchet and his student, Dion Faye. And then there is work on the gravity field generation, on which myself and one more student, the student I told you to independently check all our calculations on the machine, we three of us will be working on that. So we are just hoping that when the final thing is produced, the final waveform is produced, so there will be one paper which all of us will write together, and then there are these two modules which will be answered by these two. And for the main body of work, it'd be basically four people. For which one? For the total body of work, as it were, there are basically four main people called five people. So three of us on generation and two on equation, so about five people. So, because one of the, just as an aside, one of the things that seems to happen, at least that's happened on the numerical relativity side, That obviously is the large collaboration, very large, that people have been involved in. And that's true, of course, for the experimenters as well. But obviously for more analytic theorists, they haven't gotten such big collaborations. But there does seem to be a certain amount of more collaborative work. I think one is very, very difficult in this business. I mean, I think it would always be comfortable to have at least two or three.

1:10:00 Okay, well, thank you very much, Baba. I see I've kept you for over an hour, so thank you for your time. It's very enjoyable.