Interview with Thibault Damour

0:00 ...and I'll just speak into it and say that it's the 24th of May at a quarter to ten in the morning, and I'm speaking with Thibaut Nemours. That's how you choose. So, well, as I say, we were saying that while it would be nice to have numerical results describing the late stages of the in-Scarland merger of binary systems, at the same time they still seem to be working on that project and as I understand it, in the meantime you're interested in trying to make the analytic work that's been done by you and others extend as far as possible over the whole Yes, so what is the question? So the question is, could you describe a little bit to me what your approach is? Okay, first the motivation is indeed, so a few years ago the motivation new analytical work on cavitational radiation was linked to the binary pulsar data. I mean, there was an urgent problem which really pushed us to push analytical methods beyond what existed to have the full equations of motion at the level where you could see the first terms, radiation reaction terms, together with all the terms of lower order, which had never been done before. I mean, people before had guessed what were the radiation reaction terms, neglecting larger terms before so it was not a satisfactory situation. After that then LIGO, Virgo, because this was, Virgo started in France in fact in the early 1980s there were committees here in 1981-82 just at the moment where I was finishing this work so it was clear that it was interesting of pushing analytical methods towards... It was not so clear what they would be useful to, but as we had, let's say, the analytical tools in hand... In fact, I had to develop new tools for doing this hard calculation at the so-called 2.5 pn approximation of the binary pulsar. So at the time, I took a student, just at that moment, thesis work thinking that probably within this method one could find something to have new

2:30 analytical methods to improve radiation emission now no longer radiation reaction calculations but generation of gravitational waves by similar methods and beyond what was known at the time which was just the quadruple formula plus some formal they were post-newtonian things i mean but in a rather complicated manner and unclear. So I thought, okay, it might be useful. So this is where this thesis with Luc Blanchet, with pushing that now started. Now, this continued successfully for years. I mean, we found this scheme and we developed it. In the meantime, okay, it was not clear to me how useful this would be. I mean, we found a few nice things, but there were corrections to existing things and the brainwashing of the numerical people, all the numerical people in the world were saying we are going to solve the binary neutron star problem and the binary black hole problem so for me this meant I did not need to think too much about these methods because maybe they were not going to be so useful so I had a moment and it's only recently that I really became aware that on one hand LIGO and Virgo are one year ahead and the numerical people although they have been claiming for years to do a lot of fantastic things and they learn many things I don't want to downplay what they did they learn many things but they don't know how to combine all of them to do an actual calculation so I decided to start again seriously about how to use all this analytical knowledge in something really useful and this started in two directions, I should say. The first direction was in the data analysis work I did with Ayer and Satya Prakash after work by a lot of people who said, okay in the problem of computing template waveforms binaries, you have the problem and in particular the work of Thorn, Cutler and company, who attracted the attention of a lot of people that there was a problem of slow

5:00 convergence of post-Newtonian expansions so what people had in mind at the time was, okay, let's consider a binary system, it is it has the dynamics of its own, so there exists a modification of, I mean, the The dynamics which governs the motion of the two objects is not known as an exact thing, but just as a post-Newtonian expansion on one hand. So this is the expansion of the dynamics, even without radiation reaction. For instance, we know that when the two objects come too near to each other, there should happen something like a last stable orbit. I mean, they should suddenly find themselves groundless in the sense that they should have nothing to keep them on circular orbits but this is not known at all for comparable bodies it's well known for a test mass in Schwarzschild when you use this type of post-Newtonian methods you just have like an expansion of the Hamiltonian which governs the two and it's very difficult for an expanded Hamiltonian to find where are the critical points of the dynamics because this is precisely points where the convergence becomes extremely bad in fact infinitely bad First point. Second point, independently of the part of the Hamiltonian which governs the conservative dynamics, the system is losing energy at infinity. So one needs to, in order to keep the phasing correct to high accuracy, not to lose cycles in the templates for gravitational wave detection, you need to be able to integrate the change of phase over many, many orbits. but as the instantaneous change of phase, second derivative of the phase is given again by the post-Newton expansions where the leading term is the quadruple energy loss and then you have sub-correction to the quadruple energy loss this series also, and this was the point of Cutler and Company is slowly convergent and what do you do? so their answer was, and the answer of many people was you need to compute many, many more terms then people started saying you need to compute 10 terms or whatever i mean anything appeared in the literature um okay and this is uh at this point where working with higher and satya prakash i i i try to uh we try to find uh new ways of dealing with this slowly convergent post newtonian series by using resumation methods i mean the the key word there is resumation is to say you should

7:30 never use these post-Nutron expansions like everybody was looking at them just as power series. You have to inject some non-perturbative information in the structure of this expansion that you know or that you guess from other reasons and then use that to resum them and this is where we combine information about the analytical structure in the complex plane of some functions to say you need to work with new functions that probably probably like meromorphic in some complex plane first thing and once you guess that a certain function which is given by a power series by perturbation expansion is meromorphic in a complex plane then you have the tool of paddy approximance which tells you you should look for you should factor poles of this function which is meromorphic and paddy approximance is the best thing so at this point the point my own interest was not to continue direct calculations because it was not so clear how far one should go yeah is to say okay let's assume it exists and it exists to to some level is it enough maybe it is enough if you don't use them stupidly as they are but if you resum them in some way and in fact the main result of this work di is work was to prove that For most systems, at the 96.5% level, the phasing was excellent if you just used these resumation methods and we could prove by comparison to other analytical calculations that our resumation methods look very good. So this was the first new twist in my thing, which is not to just push analytical methods, but improve them. Now, more recently, we got beyond this point saying, okay, but maybe there are even better ways of resumming, in particular the Hamiltonian dynamics the part which is not the radiation reaction and this is a new idea that we have developed with Alessandra Bonanno she is now at Caltech but she worked with me three years here at IHS and this is an idea which was taken from early work in the 70s in QED, in quantum electrodynamics by some French people in fact Brésin Hitzigson and Zinsustin, the idea being new in the field, which is not to try to look

10:00 at the two-body dynamics as a two-body dynamics, but to map it, this two-body dynamics, on the dynamics of one body in an external field. So the idea is that you can represent the motion of two bodies as the motion of an effective one body I mean, some fictitious one body effective metric that you don't know in advance but just writing that this body follows a geodesic in this effective metric and that its dynamic should be equivalent in some sense to the two body post-Newtonian expanded equations of motion fix the structure of this effective metric which is not Schwarzschild which is a new object which is a deformation of Schwarzschild and then just writing this you find that the result of this is so close to schwarzschild the the deformation parameter in this problem is the symmetric mass ratio the product of the two masses divided by the square of the sum of the masses and this parameter goes between zero in the test mass limit to one-fourth when the masses are equal to each other which is the strongest deformation from the test mass limit and when this parameter goes to the maximum one-fourth you find that this effective metric differs by infinitesimal quantity, I mean by small quantity, even at the last table orbit of the former Schwarzschild and therefore this gives us good confidence in the fact that our effective, although we cannot prove it, our effective metric description of the gravitational interaction should be reliable down and even beyond the last table orbit, that first we could fix where is this last table orbit and we could integrate the equations of motion past it now combining two things this new effective description of dynamics but then you need to have radiation reaction added because this is what makes you go down from higher orbits i mean the circular orbits go down and they cross the last stable orbit so what pumps the energy out is the radiation reaction and to inject this we use the dis resumed version pade by pade approximants and other tricks of the thing and combining the two our claim now is that we can predict what is the motion of two bodies after they cross the last stable orbit up to the point where they just have half an orbit to go to really coalesce for the two black hole case and this is now the point where numerical people can enter the game and we can stop computing the waveform at this point and

12:30 they should go beyond although we even now go beyond and say okay let's predict at least roughly what happens when you go from 6m to 3m and then at 3m we should see quasi-normal mode swinging and we so we compute a full waveform which is probably very rough at the end but I'm not sure that having discussed a lot in Santa Barbara with numerical people I'm not sure that within the year or year and a half which remains they will be able in fact to do better than what we do now I'm sure that in a few years, numerical relativity would be able to do a lot. But for the initial detectors of LIGO and Virgo, I think the best templates on the market is what we have recently computed analytically. So with these new techniques, you'll be able to take the evolution into almost merger. and could you then sort of fit those onto quasi-normal mode for instance from the close limit approximation in fact what we do at the moment is we are aware of this close limit approximation is a rougher thing which is to say we compute the waveform we have to think what was the limit between the moment where the two bodies are like two point masses moving around and emitting waves like two point masses to the point where one should replace these two point masses by a deformed black hole which is going to ring and in fact we took from existing work on the closed limit approximations invented by Larry Smart first I think and then studied by Price and others by just saying in fact around 3M what means exactly 3M, there exists a sharp transition between the two. So the closed-limit approximation allows to smooth the transition. At the rough level now, we just use a sharp transition, which is we compute two-point masses to 3M. After 3M, we just use a quasi-normal mode, first mode there. And I think, so now I know people in Berlin, in Potsdam, are trying to improve this by using a closed-limit approximation. So that will, I think, round off the transition between the two. What does not exist yet is a numerical calculation from 6m to 3m down to everything.

15:00 So in your newer calculations, does the last stable circuit orbit fall at about 6m? Yes, so the surprising thing is that although there were predictions that varied a lot, I mean, there is the history of where is the last stable orbit for two bodies and the predictions were scattered immensely in the past, which just shows that this is, in fact, a non-perturbative question. And everybody tried to address it either by rough numerical methods or perturbative calculation per post-Neuteronian expansions, and the answer can be completely random. So we cannot claim that we have proven where it is, but what is nice in our calculations is that in our calculations, our answer is a very small deformation of the known answer for the test mass limit so we have this deformation parameter and this gives, although it's not a proof the fact that within one scheme the new point you look for is a very small deformation on the old one and everything looks okay in your calculation, nothing blows up is a good indication that you have it under control If you find an answer which is very far from the initial one and it means you have 100% corrections coming from the perturbation methods that you are never sure you got it correctly, if the answer depends on a very small deformation, I believe this is okay. And indeed, we find that it is not very different from 6m, but it is a little bit inwards in invariant sense. For instance, the frequency is higher. so it means the gravitational force for comparable bodies is not more attractive people like Kider will wise I predicted that there would be this last stable orbit quite a while before the 6M, that is to say for lower frequencies that the two bodies would plunge and that would cut off the signal of Virgo and LIGO in our case this is a little bit higher frequency wise than from a Schwarzschild approximation. And now we are doing the data analysis of this thing with, again, Iyer and Satya Prakash and others. Okay. I should also mention briefly at this point that there exists now a big 3PN problems that all what I said up to now rely on,

17:30 for the conservative dynamics, on the equations of motion that we computed now. 20 years ago nearly, yes, which is the 2pn dynamics and the 2.5pn dynamics, although radiation reaction is improved in a heuristic manner, but for the part which is, let's say, time reversal invariant in the dynamics, now there are two groups in the world trying to push the 2PN calculations V4 over C4 to the 3PN V6 over C6 corrections to Newton's law for the conservative part Yaranovsky and Schaefer obtained in 98 within the ADM formalism an Hamiltonian for this but they found surprisingly that it is given by very complicated integrals that you expected but which are very bad divergences they don't converge and there is no clear mathematical way of giving them a unique meaning in fact I had spent quite some time proving when I was working on the binary pulsar that although they are also divergent integrals they are under control you can show that although you use some tricks and AIT continuation to deal with them in fact they correspond uniquely to the unique physical answer and you can prove it is unique and that the mathematics you do to compute it is not ambiguous and gives the correct answer so there was no problem but now at 3pm there is something that nobody understands there are more nasty divergent integrals than before and even when you spend time thinking about it you don't see a way of regularizing them uniquely and in fact Schaefer and Yaranovsky they said compute all the terms there are hundreds of terms in the Hamiltonian but two of them they are given by such nasty integrals that we need after regularization to put an arbitrary coefficient in front of in front of this because if we regularize those divergent integrals in various manners we get different answers that differ by numerical coefficients therefore it means two numerical coefficients in this Hamiltonian are not known today and we give them names and we compute what we can and then we put in arbitrary parameters. So this was what started to be true in 98. In the meantime, Luc Blanchet and his students have launched on the

20:00 same problem and although they did not publish much they obtained a lot of results there. They were hoping to get a unique answer. I don't think they get a unique answer and now I think they came to this view that although they tried a lot, they did not get a unique answer but at least the good news is that one of the two arbitrary coefficients is indeed uniquely fixed this was shown independently in work by Luc Blanchet and his students and by us in fact by Jarnowski, Schaefer and myself where if you require In our work, what we do is that we have an Hamiltonian, and we say, but we are solving a relativistic problem, and therefore, let me... So, yes, so I was saying that, so there were two arbitrary coefficients, unknown coefficients, ambiguous coefficients, as we call them. So recently, we found in our approach that we have this Hamiltonian, but now, because we deal with a relativistic problem, solving Einstein's equations with asymptotically flat boundary conditions there should still be some representation of the Poincaré group acting on the system because after all the binary system could move in the galaxy with some velocity so it should be boost invariant it should be Poincaré invariant translations, rotations in space-time the full Poincaré group and by imposing this but although the new thing is that we don't work in harmonic coordinates so we don't have a known explicit representation of the Poincaré group because we have a 3 plus 1 split so we distinguish time and space so apparently for years for me it was a mystery we lose the explicit nice 4 dimensional symmetry of Einstein theory but it should be somewhere there and we found a way of implementing it and saying there should be some representation acting in space and by imposing this, this fix uniquely a coefficient in the Hamiltonian and we have been in communication with Luc Blanchet and since then he has also sent for publication a paper on this and we get the same answer. So anyway, the conclusion from this is that there exists now one and only one unknown coefficient in 3pn dynamics and recently then we decided to say okay, maybe as this coefficient is one among hundreds of coefficients

22:30 maybe it is totally negligible in any way, physical quantity you can ask our resumation methods for determining where is the last stable orbit, maybe even when you vary this coefficient between, let's say, minus 10 and 10 which is its natural range of values, although it's unknown, looking from the other coefficients in the Hamiltonian maybe, anyway, the prediction of the last stable orbit you get from this is so little different from what we got before that I don't care, I don't want to spend time on spending a year of computing this coefficient if it makes a 1% difference in the last phasing of something in our most recent work, we find that this coefficient is crucial in changing things. In fact, it is so crucial, that is to say, when it varies, you can get answers that now vary by 30% or 50% or even more for even 200% for the location of the last stable orbit. But then it means a paradox. it means that something which comes from the 3pn approximation modifies a lot what you got from 1pn plus 2pn which you do not expect if the resumation methods were good resumation methods this would be unacceptable so now there exists a dichotomy either the resumation methods we use are bad are not sufficient because they cannot resum the 3pn or in fact the value the correct value of this unknown 3pn coefficient and this is what I believe should be a small correction to all predictions. And if you assume that, you can now fix again numerically with some approximation what must be the 3pn unknown coefficient such that it is a natural extension of the 2pn results. There is a technical basis for doing that. I mean, we compare various predictions, various ways of predicting LSO quantities, last table orbit quantities, and they all converge if this unknown 3pn has a certain value around minus 9. So at this point, I think this is an interesting technical problem, but most probably I think this coefficient is indeed around minus 9. We even make a conjecture about its exact value. It is still technically quite interesting to compute it. I had shown many years ago in my Lesouch lectures that there should not be any ambiguity at 3 pn because the first ambiguity, the first really unknown physical coefficients which comes in in the interaction of two bodies

25:00 should come from what I call the love number, which is there should be a tidal interaction between the two objects, and it's at the tidal level. That is to say, one body should be able to raise a tide on the other body and therefore to deform it from Schwarzschild-type things to something with a quadrupole moment induced by the tidal field of the first body. And now this induced quadrupole moment will react on the other body by changing the 1 over r field by a quadrupole time. And therefore there should be a monopole, quadrupole, induced quadrupole interaction. By order of magnitude, at what level for two compact bodies, like two black holes, at which post-neutronial level this arises? This is at the 5 pn, if I remember correctly, 5 pn level, not at all 3 pn. And at this level, there should be an unknown dimensionless coefficient, which, for instance, should take the value 1.2 for some neutron stars, an equation of state-dependent value and for a black hole it would have a fixed universal value let's say 1 or 0 depending on how you normalize things so at this level you should be able to see whether you deal with two very condensed stars or glue balls or whatever or two black holes but below this level my claim was that there should be no free parameters in the dynamics of two bodies and therefore all coefficients in the Hamiltonian should be uniquely fixed and therefore it is unacceptable to have these unknown 3pn coefficients and therefore my conclusions is that by in fact using the type of matching methods i've been using years ago which is to match the strong field regions of the black holes or neutron stars to their outside field by implementing them now to 3pn and not to 2pn as i was doing there should be a unique way of computing all coefficients in the 3pn dynamics and therefore of computing this coefficient but just technically it's a very complicated problem conceptually also people have not really written down all the things you need just to to do a calculation before doing a calculation you need to have clear ideas on how to set up a thing so now there exists this interesting technical problem i hope that the i'm also working on it at the moment among various other things and okay that would be nice to but i hope the answer will confirm our results that where finally it won't affect any of the predictions we made at 2 p.m. now.

27:30 Otherwise, the situation is very complicated, but also very interesting. It means analytical methods are facing a difficult time, that you don't know how to make predictions, and you don't know how to resum, and really we would be lost, and we would wait for numerical calculations to do things. So you think it probably is possible to infer the value of this parameter on the basis that there is no problem at 3. Yes, and it should be minus 9 or something like that in our notation. But there's still some possibility that there's something completely unexpected. Yes, if it is plus 9 instead of minus 9, then it makes a difference. Although probably we are now looking at this, what I said, it generates instabilities when you look at, although these are invariant quantities like the location of the last stable orbit, We are now doing the data analysis that we know from our work on the transition between the inspiral and the plunge that when this deformation parameter knew the symmetric mass ratio is maximal, one-fourth, the effect of radiation reaction is so strong compared to the effect of the conservative dynamics that the transition is not at all a sharp transition. It's not like the bodies are going down on lower circular orbits up to, let's say, the last stable orbit, and then suddenly they plunge. The transition is smooth. They start falling before, above 6M, and already at 6M, they fall in and they plunge in. And this we have described by technical means. And therefore, we know this. It means the precise location of the last stable orbit is not critical because there is this continuous process. So it blurs things. And therefore, even at the present level, but we are still working on this, this unknown parameter probably has not much effect anyway. But still, it's a nice intellectual thing. I mean, if you think of analytical methods, one wants to resolve this problem. When dealing with data analysis issues, do you work closely with the Virgo people? Good question. And it happens that the structure of the Virgo collaboration, although I was linked to the mere existence of the Virgo project at the beginning because I was in all the committees that pushed Virgo initially, they are now working in like a closed environment.

30:00 they want to do things among themselves and to have their own data analysis thing so I am in good communication with all of them and I inject the information I'm a friend of many of the key people there like Alain Brier, Michel Davier and they know everything I do when I do them but I don't collaborate with them on what they really plan for data analysis I'm not worried about it might be a little bit worrying because we are not very far from the thing because the LIGO people are more organized towards an open structure where they want all the help they can get from theorists from this data analysis point of view and data analysts there is this thing, I mean there is this LIGO science collaboration and all that and I'm part of that I mean I'm in the thing and I collaborate with Satya Prakash who is a key data analyst now And therefore, I am more connected with what happens, and I check very carefully via Satya Prakash that what LIGO now is planning for the implementation of the templates will incorporate the latest new things that I'm confident is the best on the market. I'm not sure that this is the truth, but I'm sure it is the best on the market. So I want to be sure that LIGO has that. And I'm sure that at some point, Virgo will just have the same level of thing as LIGO and the information will circulate. So I work just indeed more with the LIGO type of data analysis, and not directly with Virgo, but I'm sure Virgo will follow at some point. So Virgo then preferred to have the actual experimentalists involved in the project working on their data analysis? Yes, on other people. They have this collaboration, so they say within this collaboration there are people working on that, and I don't know them. They are not known to me by their outside works. They did not contribute new things like people like Satya Prakash did in the field. I'm sure they are good. But at some point I will check to be sure, I mean, if things really get urgent, that they get the best templates. I mean, so it's enough for me to be sure that somewhere in the world somebody is developing the templates and has the codes, to do the best thing i know and then i will tell people you should use that otherwise you will lose signals so these people in virgo don't really come from a relativity background they come from

32:30 other other areas yes that's true also that within virgo they don't have people coming from a relativity background and I'm now trying to I mean like for instance some of my students have permanent positions in France so they are available for interesting work for Virgo and LIGO. Others don't have yet permanent positions like Alessandra Bonanno and I'm trying to help with the fact that it would be very good if she gets a permanent position in Europe in France or in Italy although now if she gets a permanent position in the States this is nearly as good but that would be even better for Bianco if she has a position around here with internet and all that now it's not so important all this work that we talk about this know-how from analytical calculations once you publish it it is available for everybody the know-how of numerical matter that even if you say I obtain this if you don't have really the code and if you don't know how to make it work maybe it's useless to everybody else but for these analytical methods this is more spread out in the world so and you think that especially on the analytics side you're having email and internet and that's that level of communication actually with publications all makes it sufficient for people to really effectively exchange So I understand then that, and from what you say also, that Virgo, like LIGO, is expected to come online in a year or two? Okay. And do you think there are any likely, based on your knowledge of the two detectors, that there's likely to be any much great difference in the effective data analysis techniques for the two detectors or are they so similar that you can really treat them as... In principle, the fact that the Virgo noise curve, even for the initial Virgo is flatter and goes and better at low frequencies makes data analysis more complicated because, for instance, for these binaries, you need to keep the phasing for longer

35:00 because you start having a better signal than LIGO before and before means many more cycles and you are not so good when you go to the last cycle as LIGO but for instance for massive binaries it's exactly equivalent between the two but in principle there are more stringent requirements on the template and we are also keeping this in mind in developing a bank of templates although it just means that probably in one case need a finer grid for templates than in LIGO but that's easy to do I mean they have any way to have techniques hierarchical techniques or you do not okay you generate the bank of filters when you need it so you just generate what you need I myself I just want to keep aware of the key issues in in what is important and to be able to ask experts like Satya Prakash what they do and what they intend to do. I don't want to spend time on this because I don't think I can provide new ideas for this really data analysis thing. Well, this is perhaps another question since I'm asking you what you think about what other people do, but do you have any impression as to why there's this difference between the models that Virgo and LIGO operate on the data analysis side of the sort of open and a closed normal is it just ok so one should ask them evidently but let's say there are two evident differences which come from the history of the people in the group in the two groups in the states although in both groups some of the leaders come from particle physics because at some point everybody that they needed to have people used to big collaborations. So they needed to take people from former big collaborations. Like, for instance, in France, Michel Davier has been directing big collaborations at CERN, and Barry Barish in the States. Okay, so you have the same type of people. Now, it is true that in, like, the CERN-type, accelerator-type collaborations, they have a very closed culture, that they have in-house theories, for instance, they know what happens for other theorists outside they always use their in-house theorists

37:30 and their own developed codes so so this culture is i think what somebody like michelle davier is taking from particle physics background into the virgo that is they have the idea this is the way it works in particle physics and therefore it will work the same way we don't need such a close interaction we don't need help immediately from outside so i think this is this historical reason now in the states there is the same background but there is the famous and you are very well aware and harry collins is very well aware of that famous historical fact that joe weber announced the detection of gravitational waves long ago and and nobody confirmed it okay and this was an important i mean i think everybody in the states in laggo is afraid of that something like that might happen again and that the diminishes very much the credibility of the entire field they about the field, they are pumping out a lot of money from NSF and therefore they have to be very open, there is the criticism from everybody else I mean the potential criticism and therefore they are very well aware of that and they want therefore to play a very open thing that this is a big scientific project for many scientists and the help of everybody is needed rather than a close thing so this Weber thing I think is somewhere important that they want to play an open game, let's say, and not a closed game. But I'm sure Virgo now will be obliged to more and more play. They are already doing an international collaboration between them, and that will open things out at some point. Just to change the subject completely for a minute, I'm somewhat interested in talking to Harry, we were both interested in the question of theory testing. in gravity and I know you've been very involved with the binary pulsar over the years and of course famously one of the I guess the earliest papers on the decay of the binary pulsar included quite a bit about theory testing with Rosen's biometric theory. I was curious if there were any other theories that were tested or even falsified by by binary pulsar data in your experience, or that were considered at any stage, that they might be testable by some of the later binary pulsar ones?

40:00 Okay, the big news now in the binary pulsar over the last year or so is that, and because I've been involved with that, you know, for historical things, that the first paper ever published on the binary pulsar was our paper with Wim Hofini in 1974, published in 1974, and in it we were pointing out that an interesting thing to see would be spin precession, the fact that the pulsar is a gyroscope, and therefore by spin orbit coupling you should see this spinning top precessed in space, and as you see a spot of light coming from the pulsar, that should change in time, and we computed the first estimate of what are the time scales for this. This has been observed for the first time last year, a spin precession in the binary pulsar by Cramer in Germany and then confirmed by Joe Taylor and Joel Weisberg. But this is not a quantitative test. I was just saying now it is a qualitative test that indeed you have seen spin precession so you confirm that pulsars are spinning neutron stars, let's say, and that spin precession is indeed part of what is in general relativity. In principle, this should be a test of different things. Now, to answer your question, And I always felt, it's true that, for instance, some of the important papers, the first one was by Doug Erdley, and then after that, Cliff will work with them, pointing out that the pulsar would be a very good probe of many different theories. I was always not very confident that the theories they were shooting at were very interesting. The first, in fact, the first paper, Doug Erdley, was speaking about Jordan Fiat's Bransdicke theory, scalar field and then people like cliff will extended to many other theories i think that among all alternative to generativity still the addition of a scalar field is the most interesting in this class and and now but this has been shot down by many tests now but there remains now this argument that we found with sasha with first can not vet in the first context and then sasha that Einstein plus scalar gravity has an attractor point in its evolution,

42:30 in its cosmological evolution, a fixed point of its evolution, which is generativity. That is to say, if you start with a theory which at the Big Bang is 100% different from Einstein's theory because there exists a scalar field which is coupled with a strength of other unity compared to Einstein, so like if you made a light deflection experiment at the Big Bang or something like that, the difference for the unity in the prediction but then when you let it evolve with the expansion of the universe now the coupling constant which measures the strength of this new scalar interaction tends naturally to zero so it is a nice mechanism which says that really at the fundamental level there could be a scalar field but today you cannot see it it is nearly extinguished and now my my own interest is that really i spent years thinking about what are interesting deviations from And I think, because I don't think Einstein is the final description of gravity, for the main reason, okay, one reason is that you never expect that a theory at any moment is the exact answer. There are always, I think, layers, an infinite number of layers in physics, and we are just scratching one layer after the other one. That's my general view of physics, which means that everything can go wrong tomorrow, but maybe not tomorrow, maybe in a century or so. But we have a clear indication that now there exists a conflict between quantum mechanics and gravity, quantizing gravity. This challenge, the only hope we have now to do it, and it's a very rich hope, is string theory, which I consider as one of the most interesting things in physics, and I'm now working more than 50% on string theory related things, the consequences of string theory for the gravitational sector. One evident consequence of string theory for gravity, as was in fact first pointed out in the first paper by Scherck and Schwartz in 1974, where they proposed that string theory, which existed in another context, was to be interpreted as a fundamental theory, where the fundamental string scale was like the Planck scale, and therefore that the strange object, which was a massless spin-to-field that nobody knew what to do in particle physics with, in that theory was to be interpreted as the graviton, In the same paper, they say, yes, there exists Einstein's gravity, so it's a fantastic prediction of string theory, which is already verified, but it predicts that there are partners of the graviton, like the dilaton, a scalar field,

45:00 and other fields like the antisymmetric tensor B-min-U, which is now revealing also all the richness of its structure, non-commutative geometry. But if you concentrate on the dilaton modification of Einstein's theory, by itself it's a very important conceptual idea, I think, conceptually very nice and a nice generalization of Einstein theory and the main consequence of having the dilaton is not to have a Jordan-Fiertz-Brenz-Dicke theory because Fiertz first understood that's the history of the so-called Brrenz-Dicke theory in the States Jordan proposed a theory where the scalar field existed and then Fiertz in 1956 realized that this field was violating the equivalence principle by a quantity which was unacceptable just from constant in cosmologically and then he proposed artificial models where you modified this theory so that you did not have a violation of the equivalent principle and this became publicized later as the brand sticky theory but that was invented by fiat in 1956 but now let's go back to point number one jordan was right that the most generic unified models they violate the equivalence principle the dilatonin string theory the first thing it does it's a long-range field the equivalence principle and therefore we have to face the fact that if there exists something true in string theory it predicts that there are a long-range modification of Einstein theory which violates the equivalence principle and therefore the most interesting test for me of Einstein theory are not tests now coming from the binary pulsar or coming from a solar system test but test of the equivalence principle because a very small violation of the equivalence principle is generically predicted and we have found models in which there could be a violation as small as you want which would have escaped detection up to now i should maybe add that okay this is now my position but uh for four years i i worked showing that uh somebody knocked yeah just a moment we yes that yes I think the binary pulsar has been extremely useful in showing that it opened new qualitatively new tests of Einstein theory which are strong field tests and independently of any theory in fact my big paper with Joe Taylor at some point was to show that you do not need to have in mind specific theories

47:30 you can show that the binary pulsar is giving you strong field tests even if and they might be useful one day and we have now all those strong field tests that show that Einstein theory is valid in the strong field regime so we can be confident that Einstein theory describes strongly self-gravitating objects like neutron stars correctly and there are models of it where we made models with scalar fields again like for instance we had models where a theory with a scalar field would be in weak field conditions indistinguishable from Einstein theory you could give me any small number then all the tests would be satisfied but in the binary pulsar they would have 100% deviation which have not been seen and therefore this somewhat artificial construction shows that the binary pulsar constrained strong field gravity and constrained it in a way which pushes you again in the pure Einstein case so from this point of view I am convinced that now we should make the kind of decision heuristic or, how do you say, not philosophical but philosophy of science, epistemological decision that Einstein theory is, as a block, has been confirmed as a block that it won't be modified internally by big things. the answer of the that Einstein's is part of the truth that the full block of Einstein's theory is there, the G-munu and the R-munu but the interesting question is that there could still be extra fields, even long range fields that for the moment have weak couplings to matter and have not been seen but in some experimental range might make interesting deviations and the two experimental ranges that I see is very small, high precision deviation of the equivalence principle like testing whether all bodies fall in the same way in the gravitational field of the Earth you might see a small difference and for years I have been working on pushing people to do after the idea had been launched by others, in particular in Stanford to do space experiments to test the equivalence principle in space and now I'm happy to see that France has agreed I mean that the CNES Centre National d'Etudes Spatiales in France 2004 a satellite it's not a confirmed date a so-called microscope satellite to test in a non-chariogenic experiment to a part in 10 to the 15 that all bodies fall in the same way

50:00 and in the future I hope that the full cryogenic project called STEP satellite test of the equivalence principle which would be an international NASA-ISA Stanford-led collaboration would test to a part in 10 to the 18 the same thing although it's not yet decided so there is room there for improvements by a factor of thousand and then a factor thousand more a factor a million to test the equivalence principle so for me that's the most interesting test of anstein theory the other interesting thing i should quote for history is that recently there has been excitation excitement about some millimeter deviation from anstein which is definitely a possibility that some gravity might be modified below the millimeter although in fact it has already to be below the micron so it's very difficult to do any experiment but that's in principle quite an interesting range and the third interesting range for me is early cosmology because even if all the deviations from Einstein's theory now are negligible too small too weakly couple or too short range when you go back in the big bang they become of all their unity again because the time scales and the space scales become small again and we have now to face that all the cosmology of the 20th century has been based off Einstein and the idea of inflation is really 100% based on one key element in Einstein theory but in string theory this key element is changed inflationary mechanism does not work in the same way and therefore probably we need new ideas in string cosmology which is one of my works and recently a few weeks ago with Mark Eno that you saw just a few minutes ago we have found that for instance the generic solution of Einstein's, the stringy Einstein equations near the Big Bang, was infinitely complicated as an infinitely chaotic structure of the same type as what Belinsky, Halatnikov, and Lifshitz found many years ago in four-dimensional generativity. But the history there is that Belinsky, Halatnikov, and Lifshitz for years have been claiming that the generic solution of Einstein's equation in four space-time dimensions is infinitely oscillatory, this BKL behavior but it has been found in between by other people that this oscillatory behavior is quenched and disappears if you do either two things if you go to higher dimensions of space time and or if you have a scalar field and as string theory is both in higher dimension

52:30 and with a scalar field, the dilaton people assume that string cosmology was simple not chaotic but what we found is no, for delicate reason there are other fields in string theory and when you take into account all the fields and the so-called ramon-ramon forms and the form fields, then you get chaos so for me, this opens it's just to say that for me gravity has still a rich structure and cosmology is a new type of cosmology string type of cosmology is something which we don't really know how to even launch, how to tackle because the theory is more complicated theory. We don't know what should be the state at the Big Bang, which field should be excited. So this is for me a very interesting subject for my future research. And maybe you can get gravitational waves from all that. Sure. So, yeah, so gravitational wave detectors could prove to be useful. And in fact, I maybe also point out that this idea that people say repeatedly that One of the main motivations for doing gravitational wave experiments is that we don't really know what exists out there and there might be sources we did not think of which might emit more gravitational bursts than what we think. We have had recently an example of this because with Alex Villenkin we discovered that a source which was supposedly known for years which is cosmic strength, if they exist, they emit new type of gravitational wave bursts that people had neglected but which are very important sources for LIGO and Virgo and LISA which people had not thought of in the 20 years of discussion of cosmic strength so it's just one, I'm not sure cosmic strength really exists at the level needed but this shows that indeed a new idea that really the gravitational wave spectrum could be richer than what people thought and so we should be open for new things You mentioned a paper with yourself and Taylor where you discuss this question of, you know, theory testing is still important, where you don't necessarily have a theory that you're going to falsify in mind. Yes, it's what we call, we distinguish in this paper, a phenomenological discussion of pulsar tests, trying to do some, let's say, low-level epistemology, which is to say, okay, we have the question of data, and what do we do with the data, what does it mean testing a theory?

55:00 So we distinguish a level where we extract from the data Universal tests, which are phenomenological tests, things that if you don't know the theory, you know they test something, but you don't know what, but you can at least confirm Einstein's theory. For instance, if Einstein confirmed this theory, you are fine. It should, but you don't know what it tests. And other tests, so-called theory-dependent tests, where we say, okay, let's now introduce explicitly parameters to describe theories, and now we will constrain directions in theory space. So we distinguish carefully between these two things. when did that paper appear? 1992, I can give you a copy but at the same time you said in the later context of looking for ways that it still is useful to have models of potential theories yes, to keep alive the thing, I think the existence of alternative theories is very useful In fact, for me, a comparison that I always have in mind is, like for instance, if you see just one color in a room, okay, then it looks pink and that's all. But if you have two shades of color, a pink of type 1 and a pink of type 2, you notice immediately there exist subtle differences. And therefore, comparing two things is useful for seeing better what was the original thing. So even if alternative theories of gravity are bad or things like that, even in that case, they are useful in seeing better structures, important structures in the theory. So even bad theories can be very good, and a lot of the bad theories that have been contrasted to Einstein's theory have been useful in understanding structures in Einstein's theory, in fact. So it's always useful for me never to have one only dominant theory, but always to have alternative things to compare to. I'm not very familiar with it, but I remember somebody mentioning that, for instance, Norvitt had said that Gravity Probe B might say something useful about string theories. Do you regard that experiment as one that might have? uh this is linked to what our common work with i mean ken has changed his mind on the importance of this because of our collaboration the understanding we had together of these long range fields and the fact that you could see things so uh so i agree with that but it's still

57:30 uh gravity probe b is important because he's advancing by two orders of magnitude the measurement of a parameter in principle any parameter could go wrong something like that But now, within all the schemes, I myself as a theorist would consider likely that in our low energy world, the only modification of branching activity I can expect are by observable in GPB, are by long-range fields. And now, these long-range fields are already so constrained by experiment that I know in advance that if there exists a scalar field, its coupling has to be much lower than what GPB can see. if it is any field from string theory which is long range, I already know from the 10-12 test of the universality of free-fold that its coupling to matter has to be smaller than 10-7 which means that gamma-1, the post-Newtonian parameter gamma-1 has to be smaller than 10-7 from known experiments. This is my preferred, even in this extreme thing where there would be dilatant type things, long range at this level, which would be just below the equivalence principle test this is below what GPB can see so although you can make maybe other models GPB has to stand on its own feet but it's not for me the most important thing now I prefer really a step I mean a test of the equivalence principle to 10 minus 18 for me is much more enthusing than but anyway it has to use this cryogenic thing the technology of gpb so gpb is a necessary first step to do it and it has to work and it has to prove the technology and then this technology can be used for this experiment and i should also say that when i was asked to write a letter and we'll stop there about gpb what was for me the main motivation for doing gpb i did not want to quote any theories and things like that but i said there exists for me a conceptual importance which is an analog of the Foucault pendulum when in the 19th century Foucault in France here in Paris invented the idea that by a pendulum you could see the rotation of the earth and therefore test the basic idea of Newton that there exists absolute space and that the earth is rotating with respect to that I am sure that at the quantitative level there existed many tests of Newton's mechanics in the solar system that had already proven to experts that Newton's description of the absolute space was correct to a part in 10 to the something

1:00:00 and that Foucault pendulum did not improve this thing but it played an important conceptual role everybody in Paris and then in the world because they repeated Foucault pendulum all over the world it had such a conceptual success they could go in their city see the rotation of the earth by this mechanical experiment so it put the idea of absolute space in the minds of people and for me the main interest of GPB is to put the idea now of soft space fact that the rotation of the earth is making like in jelly or in water making the the space rotate around the earth will make it visible to the minds of people all over the world and for me understanding now Einstein theory the beautiful concept of curved and soft space is very important and is worth the money spending there even if at the quantitative level it's not so interesting I think at the qualitative level it's a very important mind-changing experiment in the history Foucault Pandurum. It's just a little bit more expensive than Foucault Pandurum. But it's very illustrative. Yes. Okay, great. Thank you very much.