Interview with Luc Blanchet

0:00 I'll put it there and say that it's the 23rd of May, 2011 a.m., and I'm speaking with Luc Blanchet. So, well, let me begin by asking where things stand now with radiation reactions since I last interviewed you, which I think is about five years ago, maybe. I know there's been a lot of work done in the meantime. Yes, in fact, what has been done is not exactly on radiation reaction, but on the consequence of radiation reaction, which is energy balance, for instance, for conservation laws, or more precisely, some decrease of concert quantities in the source because of radiation reaction. equal to minus the corresponding flux at infinity. And we are basically trying to extend the work concerning the computation of the flux at infinity from binary systems and to equate this flux to a loss of the internal energy of the binary, binding energy binary, the center of mass frame, in order to get the evolution of the phase of coalescing binaries, of inspiring binaries, which is important for Virgo, LIGO and so on. We are doing the computation at the third post-Newtonian order, things are, well for known is the computation at 2.5% order, 1 over C5, plus terms which are due to the tails of waves complete up to 3.5% order, plus you see the Japanese people have consider perturbations of black holes and in the limits of where one of the

2:30 body, the mass of one of the bodies tends to zero, they can compute the perturbation in the post-Nutellian approximation and they can go very far. They can go to 5.5 post-Nutellian level. So this is valid in the limit where the mass ratio tends to zero. And so what is missing, still missing, is the terms in the third post-Newtonian approximation which are vanishing, which vanish in the test mass limit mu goes to zero and so the problem is not complete still it's a very complicated calculation in fact there are two calculations one of the calculation is to get the equations of motion of the binary to 3pn order and the second calculation is to get the flux at infinity For the equations of motion, the equations of motion are obtained, have been obtained, but they depend on still some undetermined coefficients. Two years ago, Jarodowski and Schaeffer published a work on the equations of motion at 3pn order, and they found one ambiguous parameter due to an ambiguity in the regularization of the cell field of pouring particles. And they argued that there is a physical ambiguity there, and so they published equations of quotient, which depend on some undetermined parameters. Since then, we have confirmed the existence of, we have obtained also within a completely different approach, but we have obtained also the equations of motion, and indeed there is, for the moment, an undetermined coefficient.

5:00 So in the binding energy of two point particles at the 3pn order, the binding energy for instance is known, is completely known, except for one coefficient, over 150 or something. So there is only one coefficient, which is of course the most non-linear coefficient, which is a quartically non-linear term, G4. So there is still something missing in the method to get these coefficients. So there are actually 150 terms all together in this 3DM calculation? Yes, let me tell you the precise number if you like, but it's something like that. Yes, and that's just the result. That's just the result. But unfortunately there's one which is actually still undetermined because, and basically you would need a new calculation approach to define that. Yes, yes, probably, yes. So, just, it said in our paper that yes, 164 other terms which are determined, but there is only one in the 3pn energy. So, this coefficient and should be determined, hopefully should be calculated by another term in the future. Now, would it be fair to say that you wouldn't go to the trouble of calculating 164 terms at the third post-Newtonian order if it weren't for the existence of LIGO and Virgo as the primary motivation to produce something that will be useful from the point of view of data analysis? Yes, certainly. This will seem to be not very interesting to go to 3p and order in the equations of motion if there will not be the motivation for LIGO. The formulas are extremely awful in a sense. The quotient of motion involves many, many

7:30 terms with some coefficients which are quite ugly. For instance, for the phase, in the phase phi of t of a binary, you have some coefficients which are, say, 10 or 15 digits over. This is absolutely terrible. That's even worse than there used to be. Yes, so you see these are some formulas like that, you see, for the phase. This one is especially terrible, so I mean, what would be the interest of such coefficients if there is not a practical interest to that. And so the one undetermined parameter, is that likely to be one that would be very important to know from the point of view of creating wave templates, or is it not so? Yes, probably you will discuss with Thibault tomorrow and then he will tell you that there is a difference, that this coefficient is rather important. Tibou is more interested in the location of the last stable orbit for binary black holes and this parameter is important for the determination of the last stable orbit. But we are more interested in the orbital phase of the binary. Right, because that's vital for the depth analysis. Well, if the masses are small enough, if the masses are rather important, the in-spiral phase of binaries will not be in the frequency bandwidth of the detectors, so this is that's important, but for the trans-star binaries it will be important, certainly. Yeah, the phase evolution will be more. So how many people have been working with you on this third post-Detonian calculation? Yeah, this is not finished for the moment, but with the equations of motion we have done this with Guillaume Farré

10:00 And I have still an ongoing collaboration with Ballard on the computation of the flux. And there have been also some students here which worked a few months only on the problem. So you don't have that many people working? How long has it taken? I mean, what do you mean? How long has it taken just to, for instance, well, let's say, how long did it take just to get the phase contributions at third position? I mean, the computation is very long. We do it by Mathematica. It is not yet complete. And the computation is very involved. There are many computations of difficult integrals and so on. There are problems like how to maintain the Lorentz invariance of the equations. There is the appearance of logarithms of the distance in the problem. So with logarithms you have arbitrary constants involved. there are several the problems like for instance what will be at four point particular you have a singular functions and when you are seeing in the you have also a delta function because you use use as a source for the calculation you you use delta functions. But very quickly, delta functions get multiplied by singular functions. So this makes no sense in distribution theory. So with Guillaume Phi it was necessary to extend the theory of distribution for a particular class of functions that we are using, and to give a sense to the product of, for example, delta function and a singular function, and also to give a sense to the notion of derivative,

12:30 of distributional derivative in that. So there is a mathematical part, which was rather interesting, in fact, and how to regularize the infinite cell field of point particle in a consistent way, knowing that the field equations are non-linear, so very quickly you have products of singular function, derivative of singular function with themselves, with delta function and so on. So we did this to extend these notions of distributional derivative and delta function to this particular class of functions and we applied this to the equations of motion. So in order to have a regularization which would be well-defined at least. So we could do a well-defined computation but it didn't remove the fact that there is one of the coefficients which is not determined by this method, at least in this stage of development. You mentioned doing the calculations mostly by Mathematica. So does that make it, as it were, take out a lot of the tedium of carrying the terms together and allow you to focus on these conceptual issues such as dealing with irregularities or singularities in logarithmic functions and so on, is that... Yes, indeed. Guillaume developed many programs with Mathematica so we could concentrate on the interesting problems and these ugly coefficients come out from mathematical, so we don't have n computations which would be anyway too long.

15:00 Certainly, I would say that this problem, if you want to try to give a sense to any of the coefficients, to have a well-defined framework, this problem would not be possible, I think, without some algebraic programs. Yeah, I'm sure. That seems well believable. And do you ever have troubles with Mathematica producing, with having bugs in its code? No, no, no. Personally, I am not an expert in algebraic computation, but I have been quite happy with Mathematica and MathTensor, which is a package for tensor indices, which goes with Mathematica. Our computations are quite, yes, are rather simple, I would say that this is simply expanding, collecting terms and adding coefficients and that. But we have been very happy with mathematics. That's interesting. And actually I was speaking last month at Southampton with Ray D'Inverno who was involved in some of the early work at Alderberg. Yes, he's certainly a good expert. Yeah, so it was interesting to hear a little bit about the history of that. And clearly it's had a big impact on this type of difficult calculational work such as you've been involved and as you say, it probably wouldn't be possible to do this unless you had huge numbers of people. to work together somehow to do it. So are there, besides yourself, are there still other groups working on this, the Schaeffer's groups? Sure, sure. There is Jaranovski and Schaeffer. So I don't know if they are pushing further their computation. They are working with the Hamiltonian formulation of general relativity, ADM Hamiltonian.

17:30 So they published Hamiltonian at 3PN. I don't know if they are pushing this to higher order. I don't know. There is Cliff, there is Cliff Wheel, and the student, I think that's called Patty, I don't know, but I know that he's working also on the same problem. I don't I don't know what is the status of the world. And do you talk much to these other groups or just sort of compare results at the end? We have some interactions sometimes. I think we have some comparisons at the end. I mean the methods are rather different. For the equations of motion, our method using harmonic coordinates is completely different from the Hamiltonian, ADM Hamiltonian method. Probably Cliff will use the method using harmonic coordinates also, but he probably uses a regularization which is different from us, which is of course very good in the sense that the comparison will be more powerful. And when you do compare results, for instance you mentioned Yarnovsky and Schaefer having previously found this undetermined property, have they always come out the same up to now? Oh, yes, yes. The computation is in complete agreement for all what we know. For the equations of motion, at least we have checked for the energy of the binary at 3 p.m. for circular orbits, which is the case of inspiring magnaries, and there is complete agreement. For the flux, for instance, we are in complete agreement with the Japanese work on the perturbative limits at 3pn, for instance. These coefficients, these glide coefficients are the same. That's impressive. Yeah, that's very convincing.

20:00 So returning then to the practical side, the practical application to detectors, do you think that going to 3, to this level of accuracy, say for post-Newtonian in the phase, for instance, and so on, is likely to be sufficient from the point of view of data analysis? Will it provide, say, some sort of templates which are accurate enough to enable signal It's not sure. It depends on the masses. It depends on which detector you have. If you have four laser, for instance, detector in space, I'm not sure that these orders for the post-Utelian approximation are sufficient at all. what the Caltech group obtained is that this level of approximation say 3pn is sufficient for neutron star binaries advanced for the other types of source for when you have more when the masses are more important or if you have Lisa instead of it's not abuse you might need more and is that because Lisa in the case of Lisa this type of work would apply to supermassive black holes Is that because you have, with the, in the case of LIGO, with the larger masses, you'd have fewer in spiral cycles and holes, so you'd have less time in which to build up the signal. And so in that instance also, it would be more important to know this undetermined quantity

22:30 because that, you were saying, tells you something about where the last stable orbit is going to be where the inspire lands and you enter this plan. So do you have a program in mind to try to determine this difficult parameter? Uh, yes, yes, but I have no idea if this can succeed, in fact, that's not fair. We would like, yes, indeed, to obtain it by a method which is a follow-up of our method, using some expressions valid not only for point particles, but for extended bodies. and for extended bodies, if it would be possible to reduce the computation for extended bodies, in principle, if this would be possible, this would give value of these coefficients without any regularization. So the idea is that because, so if I understand correctly, then maybe this undetermined parameter, the difficulty is somehow connected with the infinite subfield of the point particle. So you're just going to make it not a point particle. And in that case, is there a difficulty, can you also, if you're dealing with an extended body, do you need an equation of state, or does it not matter if your extended body is a neutron star or a black hole? Yes, certainly you need a consistent model for the interior of stars. In fact, you will need some formulas which are valid for any stress energy inside the stars. And then the radius of the body should turn to zero in a consistent way with the interior.

25:00 So you have to define a sequence of bodies whose size is shrinking to zero in a consistent way, which is probably difficult. You need to assume, for instance, some spherical symmetry of the bodies before shrinking them to zero, but some spherical symmetry in which frame and so on. And at 3PN, of course, there are many difficult term integrals of iterated terms, which could be computed because there was some delta functions, which simplifies very much computation. but with extended bodies, this simplification is not a lot. You mentioned that from time to time you've had students working for brief periods of the problem. So do you find that there are parts of the problem which are quite well understood and can sort of be divided off? from the rest and hand it to a student who is not, say, familiar with the whole. Yes, this is true. There were some computations by Mathematica which were clear and so the student could have a short period staying here and do these computations. So I'm curious, just from, I suppose, the sociological point of view, if one didn't have Mathematica, and therefore anyone still wanted to do that to this problem, and therefore the solution maybe was to get a lot of people to do it, would it be possible to divide up the whole problem into sort of little pieces which people could work on independently and and then bring it all together? Well, it's difficult to say. In our approach, I don't know further approach, of course, I'm only speaking of the .. In our approach, now that the computation by Mathematica has been done, say, for the equations of motion,

27:30 for the multiple moments, still it is not completely finished. Even now that it has been done, we could redo it by small pieces and do what you suggest. It would be true. But before it was done, it would have been difficult to imagine how to do this. In our approach we didn't know how to do the computation and so we did some parts in the wrong way and it was necessary to redo it in a better way and then some subtleties linked with the regularization for instance were found and then we were obliged to redo it again. The equations of motion were computed long ago, but we discovered that they were not Lorentz invariants. They didn't satisfy the Lorentz invariants, also the harmonic coordinates maintained the Lorentz invariants. And so we found that, in fact, there are subtleties linked with the regularization, that the regulation was breaking the Lorentz invariance at some stage, and so we were obliged to redo things. So it took, in fact, a long time to get the right invariants, for instance. So two years ago, I think that it would not have been possible to divide the computation in several websites. So, I was going to ask if you are involved or likely to be involved in the data analysis side itself, say... Not very much. So, who are the people who are mostly...

30:00 I was curious because I noticed that with LIGO and with GEO most of the data analysis is being tackled by theorists and I was wondering if the same situation applies with Virgo or whether it's more the experimentalists who are interested in it. In LIGO, who are the theorists? I know, of course, Kip is very much involved. Kip is involved, but also people like Bruce Allen and Sam Field and so on, whose background is primarily in theory. Oh, yes, absolutely. But they devote their time to the data analysis. Oh, yes, yes, yes, very much. But they come originally from... Exactly. Alan Wiseman for instance, indeed data analysis is a so important issue that I could not personally do work on that without devoting my time to it, so for the moment I would not choose this, I prefer to... And so when, as it were, considering what are the most important elements of the calculations that you are engaged on from the point of view of data analysis, Do you mostly go by, do you, so when judging, you know, for instance, as we said, one of the most important features generally considered, from the point of view of data analysis, to know is the phase evolution of the inspiration and this of course has been pointed out quite a long time ago now but do you sort of hear from people who are more closely involved with the death analysis do you still find them telling you well you know maybe you should be able to it would really be important if you could find this term for us and that sort Yes, I discuss often with people like Satya for instance, or Albert Einstein Institute in Potsdam.

32:30 There are people like Vekiu, Alessandra Papar, so I discuss often with them for instance. they are also some people from LISA detector these people have pointed out recently that the harmonics, higher order harmonics are also important at least for LISA. All people are using only the dominant harmonics at twice orbital frequency, but other harmonics should be considered also. Especially from the point of view of Lisa? Yes, for Virgo and LIGO it's not very much important. And are there people involved with Virgo that you have talked to about the data analysis issues that are relevant to it? unfortunately for us the Virgo group has moved now to the south of France, to Nice because they are closer to the experiment in Casina we had a meeting a few months ago with people with Alain Vrier, Jean-Yves Vinet and Milano, and these are the people who are doing most easy data analysis. So now you actually go to meet them every so often because they're far away. Yes, sometimes. We meet with the meetings. They organize the meetings and they invite us and we discuss. So, when this work on the third post-Newtonian expansion is completed, do you see yourself still working on issues closely related to gravitational ray detection or would

35:00 you like to? Yes but I'd like to be more involved again on the general formulations, not only for binary systems but for more general sources and issues related with radiation reaction. And also these problems related with the non-linear effects in the radiation field, which are for the moment not known completely. One could investigate what is the general form of these effects. to any order that seems to look at the generalization of some formulas that we have and to see if they apply more generally to any order. It's important because if you have a formula which is valid for any order I mean you can just you can you can ask if it is valid in a sense to within the exact theory that you see if you have a formula which is when something if you can have some formulas for the whole post-Newtonian expansion or you can ask yourself if this would be a feature which be valid in the case of an exact solution that you don't know about. Because some parts of the formalism are valid is valid for any order of approximation formally. You can define an infinite formal series of approximations and all the terms of that series are defined. You don't control if the series is convergent or divergent or you don't know but in a formal expansion you can say what are all the terms of the series so in a sense this will be

37:30 valid in a more general sense than simply an approximation would be interested Are you interested, internally, since you mentioned the perturbative work where one deals with a large central body and only a small perturbing mass, are you interested in the radiation reaction problem in that regime at all? the radiation reaction should follow from so this would be for an extended body isolated body which emits gravitational waves and which reacts on itself because of the emission so we we define we can define the post-Nutonian expansion within that body of the inner field And on the other hand, we know the exterior field generated by that body, the radiation field, which satisfies the outgoing radiation at infinity and so on. And the radiation reaction follows from matching between the exterior field and the inner field and so this gives terms which have to be added to the Poissonian metric inside the body and these terms are associated with radiation reaction. So I would like to have maybe a general form for these terms and maybe one can apply this again to binary systems but only by computation done using the equations of motion with radiation reaction and not a computation of the flux So it would be without an energy balance. Yeah, exactly. So in a sense, you will prove that the energy balance was correct. That would be interesting. But it's only a long-term project.

40:00 Sure, sure. so just to return to something that you mentioned at the beginning so you're going to be moving in the next year or two probably, this is not done for the moment we are discussing moving to the Bachelor Physics Institute in Paris so you were saying that continue the basically the work that you've been doing yes the the people that you'll be held with us that were there mostly astronomer yes like here in fact but there is a an important group of cosmologists the disease there is a team which deals with Planck, Planck Surveyor for cosmic microwave and so the group here of Cosmology is very much interested in this moving to the Institute. But for me it would be exactly the same environment as here in Le Don, they are astronomers. But it's quite exciting to be in this atmosphere of astronomers and astrophysicists. Yeah, it's a good make sense. Do you find that the astronomers are interested in gravitational waves? Oh yes, certainly. that Virgo in France, its budget comes from the particle physics community. I believe that that's the same in the United States for LIGO. LIGO is mainly particle physicists who bring the money to LIGO or support the LIGO project. Well, of course, now it's largely run by former particle physicists, although it's funded by the NSF, which is not many of the big particle physics firms would be funded by a different agency.

42:30 In fact, because the NSF also funds astronomy, generally speaking, in the United States, it has been true, especially at one time, that astronomers were often very anti-LIGO because they thought that it was taking money from them. But that's not true in France. No, I don't. Well, there are some rivalities between the particle physics community and the astronomy physics community, of course, because of question of budgets. But I think that this is quite normal. Yeah. They, um, so Virgo itself didn't have any particular wasn't, you know, particularly singled out by astronomers. No, I didn't think so. Because I think in the case of LIGO in the U.S., there was... In our group, we tried with, for instance, with Eric Gorgoulon, we tried to give several talks to the astronomers, and we tried, and with Silvano Bonanzala, also some important meeting of astronomers we try to to explain what gravitational waves would bring to the atomic so to the atomic community and And did they seem interested in that? Oh yes, yes. What did you present to them as the main benefits? For instance, we discussed very much in CNES, which is a French national space agency. there is a group of theoretical physics for for experiments in space concerning fundamental physics for instance experiments like pharaoh experiments which is an atomic clock which would be put on the space station or experiments like a step or microscope which is an experiment

45:00 which will test the equivalence principle to the level 10 to the minus 50 all these experiments and there is also the astronomy group and we had a lot of discussions between both groups concerning gravitational waves and and especially the participation of the CNES to the LISA project through the ESA, the European Space Agency, which is collaborating with NASA and the LISA. So, LISA in particular is probably something that's of interest. I gather, so there's recently been, this is something else I learned when I was at Southampton, talking to people there, I gather there's been set up a European network of people working on certain aspects of gravitation. Yes, on numerical relativity and gravitational waves. I gather some people have dark are involved in that. Yes, exactly. This is mostly the numerical group here, which I think they will have a postdoc on that network. So you're assigned it now? Well, I was supposed to be... I am involved, but in practice not very much. this is mostly for for numerical simulations this network was has been proposed during I think four years and finally it was accepted this represents a lot of a lot of possibility because many postdocs can work can work during three years so it's it's a big increase of the size of the groups that's right, it is, yes thanks to that in fact when I was at Southampton they were saying the main worry they had was finding enough people to fill yes, yes, exactly to fill up the postdoctoral positions

47:30 which actually I guess brings me to another question I was going to ask you which is, you mentioned some students with you in the past years, at least in graduate students or undergraduates? Guillaume Pai has passed his PhD thesis last year, so he will do a postdoc within this European network. so it's good and where will they go in jenna and so but there was also some students having some stage only for three three months to six months and knowing that the students would do So, this network is already proving useful? Yes, yes, yes. That's good. Oh yes, so I guess the Potsdam, the Alfred Einstein Institute, is the center for that network, right? Yes, exactly. The P.I. for this network is Ed Sider. And you mentioned that you interacted quite a bit with the Potsdam group, didn't you? Yes, I am. Come in! Entrez! Yes, I spent several visits to Potsdam these years. Is that working with the Bernie Schuetz program? Not so much. More on the mathematical relativity side. And I made a review of my work for a book in honor of Jürgen Ehlers, which was edited by Bernschmidt. maybe if you've seen this book. So I was more interacting with these people.

50:00 So I guess on more or less every facet of relativity, the Potsdam center is sort of a big force in European relativity. Yes, it's very pleasant to be a visitor there. I enjoyed very much the visit. I hope that I can continue to. There are many, many visitors. Because I guess the only, certainly up to then, I guess Italy's biggest relativity community in Europe would have been in the Paris area between the different. Well, I don't know. No, no, probably if you can't, if you take only the permanent people in Potsdam, it's not, it's not, there are not so numerous, but considering the number of visitors. Yeah, it's just all of the people who go through. So, the detectors, I guess, are all nearing completion, a lot of work has been done on the various ones, in fact, some instruments at some of the sites are actually up and working. So, how long do you think it will be before the work you've been doing will be actually It's difficult to say because Virgo will have the central interferometer working next year and then the complete interferometer working within two years probably. The distance to which Virgo and LIGO will see in the first stage is, well, is probably

52:30 less than 50 mega parsec. I don't know exactly the exact figure. And so the number of coalescing events is not probably very important at that distance. Also, we don't know about coalescence of black holes, but for the trans stars it's not very, it's around not many. So, really, I have no idea when one will detect a binary, a coalescing binary, for which some theoretical formula will be of some use, but... But it's likely to be when the so-called advanced detector is already, which is still a little bit away. Yeah. And also on the question of applications of the work, do any of the newer work that you've been doing, for instance up to third post-Sytonian order, have relevance for the binary pulsar or system? Well, for the binary pulsar, even the first post-Newtonian corrections for the radiation reaction is much smaller than any kind of noise that you can have, for instance, unknown concerning the propagation of the photons from the pulsar to the Earth. Yeah, so it's simply too small? Yes, it's too small. I mean, speaking of the relativistic corrections in the p-dot of the binary ,, which is relevant for this. Yeah, so it really is true that you're waiting for the detector to come in line for the practical application to come in. But it looks like you're in pretty good shape compared to the numerical people, for instance, or you're a lot closer to... Yes, this is the binary black hole challenge. It's an extremely difficult problem.

55:00 But concerning the post-Mittanian expansion, only on the theoretical point of view, if Larigo and Virgo would, for instance, detect on the next century, on the theoretical point of view, personally, I find that the problems are rather interesting. I mentioned to you that we were obliged to give a sense to some mathematical objects which are not well-defined in some theories. And, well, I think that the problem is rather enjoyable by itself. Yeah. Simply mathematically speaking of that. In fact, speaking of that, I suppose that's a sort of, it's an area where there could be, as it were, a technological spin-off, like they say, of experimental science. Are some of the tools which you've had to develop to overcome, some of the difficulties likely to be used in other areas of mathematical development? This I am not, this I don't know. I don't think so for the answer that I say. Yeah, I was just curious because I would say it's sort of like a symmetry with the experimental side where sometimes they say, well, maybe we'll come up with something that could all be useful to other people Well, I'll be very interested to hear about your progress later on your difficult undetermined problem. If it's possible. Yeah, it sounds like a difficult problem, but I'm sure you'll get there after all the success you've had so far. Or maybe it's a completely different method, but maybe there is a fundamental problem in this method, which arise at 3bm, but it is also possible.

57:30 Do you, since you're going to be using a somewhat different approach within the same general framework, do you have any plans to collaborate with, say, the Schaefer group on this problem? Yes, it's well possible, yes. We have not discussed very much since two or three months, but I would certainly need to discuss with them if there is something possible. In fact, I don't know exactly how we should do this. the project is not very much, for instance, defined. Well, good luck with that, Luke, and thank you very much. Thank you very much to you.