Interview with Cliff Will

0:00 Okay, so now it seems to actually be going. And check that. So it's the 18th of March at about 10.30 and I'm talking with Cliff Will. So I guess to start off in chronological order, I'll go back and talk about the more historical stuff that I was interested in. Well, I suppose one of the things I was interested in asking you about was about your paper with Martin Walker on the quadruple of controversy, but I suppose maybe I should start by sort of asking you about the sort of background to the paper, I mean, what were the issues at the time? Well, I mean, obviously, part of the background was the discovery of the binary pulsar, and this paper by Ehlers, Rosenblum, et al., you know, criticizing the quadruple formula, or at least questioning its validity. Now, part of the questions were based upon sort of the point of view of Ehlers and that's cool that, you know, you really want the more mathematical, more rigorous justification for the approximations and so on. Part of it was, of course, motivated by calculations by Arnold Rosenblum that were disagreeing with the waterfall formula. And that was only, well, it didn't specifically motivate Martin and me to respond in some way, but in fact, we had started a collaboration somewhat earlier than that, in some sense by complete fluke, in that one year, I think it was about 1975 or so, Martin was on sabbatical at the University of Alberta, and I was at Stanford at the time, and he invited me up there to give a talk, and I said, I'll come as long as it's before, about October 15th, because it gets too damn cold up there otherwise. Anyway, I went up and talked. But in the course of our conversation, we discovered that Martin is sort of in the more mathematical school of relativity. He thinks in a very formal and mathematical language, and I'm from the Kip Thorne, dirty astrophysics school.

2:30 But we found it actually in talking to each other just during that one day that we sort of hit it off personally and found that we could sort of teach each other some things, and we thought a little bit about doing these post-Newtonian radiation calculations. And so a few years later, I invited him. He was going on sabbaticals, so I invited him to spend six months at Stanford, or a year, actually, at Stanford, working with me. And so we initially did some papers just on, you know, sort of the slow motion approximation for gravitational waves, and there was a technical issue of whether you satisfied a no incoming radiation boundary condition on scry minus. So it was a combination of doing these post-Newtonian calculations with these rigorous Bondi methods for dealing with scry. And so that was kind of a lot of fun to do. And so that sort of had us both interested in these approximation methods and in thinking about making them better. And so, the chronology is a bit hazy at this point, I'd have to look up the papers to think about the chronology. So there was this long-standing paper, Veilers et al., criticizing the formula. Then there was also this series of papers by Cooperstock and his collaborators with another specific counterexample to the quadrupole formula. yes and so that by this time we were back in our home places he was back in Munich but we got to thinking about some of these counter examples so so one of the things we did was to survey the literature of all radiation reaction calculations that we could find this is radiation reaction as opposed to energy flux calculations and to see what was in the literature. We found, of course, lots of wrong answers or answers that disagree with the quadruple formula. And we tried to look in detail at why they got the wrong answer. And we discovered it had to do with how many times you iterate Einstein's equations. In fact, we found that in every case that got the wrong answer, they didn't iterate enough times to get all the terms that contribute. And most of the ones that got the right answer did the right thing. And then there were a few that got the right answer and still did the wrong thing, but made a compensating error,

5:00 including MTW. And so as we were doing all this, we also thought a little bit about the energy flux formula, and that's motivated us to put together this little fissure of letter that sort of claimed that the quadruple formula was correct based on a more rigorous justification of the quadruple formula in retrospect it turns out in some ways it was no more rigorous than anything that had gone previously but at the time I thought it was we thought it was pretty rigorous what was the particular aspect of it that made you feel it was an improvement in terms of rigor of the previous partly because we for a reason completely understood there was in those days a failure to understand whether you had to, whether you needed nonlinear gravity to get the quadruple formula for radiation or whether you could do it using linearized theory. And the rap was that, you know, you use linearized theory, you get, you actually get a formula that is the quadruple formula, but in linearized general relativity, you know, bodies move on straight lines. They don't interact gravitationally with each other. So one of the things we did was to point out sort of carefully how when you iterate Einstein's equations a second time, so put the gravitational field back in and iterate again, those nonlinearities guaranteed that you get the appropriate Newtonian motion of the sources. But at the same time you still end up with the same formal quadruple formula. And we talked a little bit about the issue of whether these integrals that you get can converge or not because you know in a slow motion approximation you calculate multiple moments but the moments contain stress energy of the gravitational field as well as the source itself. The gravitational field extends to infinity and you worry whether or not some of these integrations over this stuff that extends all to infinity whether those intervals converge. And we had some fancy words, as I recall, in that paper about it, but in retrospect, they were no better than any other words that had gone previously. The issue of convergence, we never, I don't think we ever settled. In fact, in my view, it's only been settled recently, in the past three

7:30 or four years. By the current work on post-intentional? Yeah, partly by stuff that we've done here, in which you can, instead of sort of doing these integrals and then letting your integration go to infinity, by explicitly doing integrals that's out to a fixed boundary, say the boundary of the near zone one wavelength away, and then carrying on the integral over the rest of the light cone but using a different integration method and showing that terms from the inner integral that depend on the radius of the boundary that might diverge if you let that boundary go to infinity, those terms are precisely cancelled. In fact, you can show it term by term by corresponding terms that come from this outer integral. So when you actually add up the two pieces, you get a finite answer. even though the individual pieces have terms that depend on this radius of the boundary. So that's one thing. And this is stuff that in fact we're just really doing now in detail and so on. There's a published paper that sort of alludes to it all, but the full details we're still working on, or they're done, but I haven't yet written. Sure. But obviously this has come about because of this need to go to much higher order in post-Newtonian approximation for LIGO, because even at the quadrupole approximation, these so-called divergences that you get are sufficiently tame that you or we, people in the Kip Thorne school, could argue that you could throw them under the rug and be safe. Of course, people from the elder school would say, you know, that's not good enough. But at higher orders, like at second post-Newtonian order beyond the quadrupole approximation, you can't even that are virulently divergent that are there. There's no way to sweep them under the rug. And this is what led us to discover this new way of doing the integrals so that, in fact, they actually cancel. So they have to be dealt with? You have to deal with them, but then we discovered a way to deal with them. So that was the beauty of it. So now there's also this other approach to doing gravitational radiation, which I think is equally good in terms of dealing with divergences and so on, and that's this sort of the Paris approach of Thibaut Amour and Luc Blanchet and their collaborators, sort of a matching approach that I think is every bit as rigorous as ours in dealing with these kinds of problems.

10:00 So the idea that, in some sense, the final story on the quadruple formula But it's really been driven by the need to go to much higher orders where you really have to deal with these problems, whereas before you could kind of sweep them under the rug if you needed to. One of the things I was interested in about the Walker and Will paper and then other papers of that period, like the Ehlers paper, is the way they make some use in the paper of at al particularly give quite a wide-ranging discussion of history and as a matter of fact in one place but i think it's in somewhere else not in that paper ehlers sort of specifically advocates that you know what he's doing is looking backwards because he thinks that physicists are always inclined to forget their history and um and uh in what in some sense reading walk and will not only are you providing an argument as to well here you know as you say at the time trying to reason for believing the political form of result, you're also using the historical, sort of historical argument to buttress that by, as you say, taking a look at all of the previous papers and saying, okay, so here we can kind of identify where people are going wrong and where they're going right, a certain thing. And I was wondering, well, I was wondering how conscious you were of the kind of historical dimension you are? Probably less so than people like Ehlers, partly because I rarely pay much attention to history at that same level. And also, part of it is that, at least in this subject, I have found that what little history that I know about general relativity, I have found that, in fact, there's a lot that's either wrong misplaced about some of the history. I mean, you know, people cite Einstein and some of the things he did, but when I think back about what he did or what he thought about general relativity, I think it's rather misguided in many ways. I mean, partly this whole idea about whether, you know, self-gravitating bodies

12:30 would emit gravitational waves because they move on geodesics. I mean, partly it's motivated because the early calculations of gravitational waves were done using linearized theory. And it's not a consistent theory because it doesn't produce gravitational motion. And so how to deal with this and so on. Well, if you try to cite that history or focus on it too much, there's a danger that you won't break with that history and really realize that it's fully a nonlinear problem, gravitational waves. No matter how you look at it, you have to take the nonlinearities into account. And to some extent, I think that led the Ehlers group a bit astray. because you have to realize one of the co-authors was Peter Havasch, who, with Rosenblum and his others, continued to promote this kind of linearized approach to general relativity. They were really just solving linearized equations. They were doing them to high order in powers of v over c. So it was relativistic in that sense. But they never did it in a non-linear way. In other words, do a second iteration, take that field, and plug it back into the right-hand side and do it again. theory, but to higher relativistic borders. And, you know, so to some extent it was because they were still in this linearized framework, whereas from our point of view it was important to get away from that and to really focus on the non-linearities. If you go to any powers of E or C you wanted, you'd still get the wrong answer because you needed to get those non-linearities. So, but just as a technical point, did that mean, in your view, that it was more or less impossible using this kind of post-linear approach to... Yeah, I mean, absolutely. In fact, I think at least one of the early calculations was one that we wrote down. In fact, there were about six terms that you have to get when you do it in a certain gauge. And they got the four that come from linearized theory, but they would never get the two that come from the next iteration. And it was just impossible. No matter how hard they tried, you know, it's just a fact of life. In fact, we tried in those two papers to sort of give a hand-waving argument based on powers of G as to why, you know, you really had to iterate twice or even three times. It depended subtly on whether you were doing the flux formula or the radiation reaction formula. You really had to iterate non-linearly a number of times to get the full answer

15:00 or to guarantee that you got the full answer. and so you know doing it just once was was hopeless and even doing it twice which is finally what Rose Arnold was doing he was trying to calculate a radiation reaction formula using this post linear post this you know what they call it post linear formalism he did iterate a second time he was taking the field and plugging it back in but he wasn't doing it a third time which you need for radiation reaction to get the full answer. Now, no one ever knew why he was getting the wrong answer or got through any of his details, because he never really published a full paper that gave the details. So that's an open question. So from your point of view, quite consciously, you were sort of feeling that there was a danger of getting trapped by the history of the field. Yeah, to some extent. And it may just be my personal view of things, but I think there's a lot of that danger in gravitational physics. I'm not quite sure why. Among some people, of hearkening too much back to the history, which in many ways is different from other fields of physics. where people are not so much concerned by the history. I was thinking of an example like this just the other day. I can't remember it at the moment, but it was a similar case where there seems to be general relativity seems to be a field which has for a long time been dominated by a worry, for example, about formal issues and whether or not this thing really satisfies such and such a condition, in a way that you don't see that much in, say, quantum field theory. In quantum field theory, people did calculations and developed a theory and did all kinds of important calculations and results, and there wasn't quite the same worry about some of these finer points. I mean, there were a few people who did axiomotized things and so on, but it didn't seem to have the dominance that it has in general relativity. a product of the history of the field

17:30 because for so many years there was maybe for so many years it was dominated by mathematicians maybe that's the reason I'm not quite sure why Did you find, since we're discussing the sort of difference between the more mathematical side and the more astrophysical side whatever you want to call it did you find working on just my last question about the Walker did you find any kind of divergence of opinion sort of coming from different viewpoints maybe more convergence of opinion between yourself and Martin Walker well certainly between the two of us there was, I mean I think that by the end of the kind of work we did I would have, I would argue that Martin would have said would have felt much more comfortable about the, you know, rigor mathematical foundation of say the quadruple formula that he did before and that probably Juergen Ehlers would have at that time. I think he felt you know, I think he came a long way toward understanding the issues because I think he understood what goes into these approximation methods and understood from his point of view what you could do to make them more justified and so on. Whereas others on the more mathematical end who weren't willing to get their feet wet would tend to just criticize these things, but without really understanding what was going on. On the other hand, I, of course, got a better appreciation for some of the mathematical issues, too. I mean, just trying to understand the power of some of your mathematics things, too. Was Walker actually in Munich when you were writing? Let's see. That paper, the two Fissor of Letters papers and the Apche letter paper, I think he was still in residence at Stanford. I would have to look back in my calendar. I think the earlier papers we did while he was still in Alberta and such, when I went to Munich and spent about three weeks once, So the earlier stuff we were doing on this Spry Minus business, I think, was done before. And so when he came to Stanford, we were, I think we spent most of that year together. I think that was the year we did those papers and the Cooperstock stuff.

20:00 Yeah, those papers appeared in 1980, 79 to 80. It may well have been the year he was there. And it was after that then that he returned to Munich? Yeah, then he returned to Munich. I was there for some years. I think then I came here to Wash U in 81. And then when it came time for my first sabbatical, I was thinking about going to Munich for six months to work with him. And then I was going to go to Israel for six months and work there. And just before I started formulating my plans, he left physics and went into computers. In fact, moved back to Canada. Did you find, just on the history side, a different approach? Was he more interested in the history side of things coming from the mathematical thing? That's hard to say. He certainly had a better knowledge of historical things than I just, but that's because of the kind of person that he's really broad. He's a really smart guy. He's very broadly knowledgeable about a lot of areas of physics, not just his own. I am in that sense. So I think he had a good sense of the real history and background of the field, but I don't sense that he appealed to it quite the same way as others do. So, well, so we already touched on what you said. It's 11. No, it's 10.45. I have an alarm, which will sound, so. Okay, great. We're not in any danger. so you already touched on the work that you're doing at the moment and you already mentioned also how motivated it is by the need to meet the needs of future detections like LIGO and of course that's sort of the subject that I'm going around and talking to people about now so I suppose maybe I should start by just asking if you could elaborate a bit more on that That is to say, your opinion of what actually are the needs of gravitational wave detection at the moment and what work you're engaged in at the moment. Well, I mean, in terms of the theory, the kind of theory that a bunch of us are working on, the idea is to have these accurate calculations

22:30 of gravitational waves, primarily from inspiring binaries as the main workhorse system for LIGO, to be used as templates for data analysis. One of the things that we learned, I guess it was discovered by Sam Finn and Kurt Cutler independently, was that in order to do the best job of extracting information from the signal you receive, and to some extent even to do the best job of getting the actual detection of a signal. You need to do a match filtering between a theoretical template and the data, but with a filter that is a very accurate solution of Einstein's equations, not just a quadruple approximation, and that you really need higher order terms, problems, especially in the phasing that's induced by radiation damping. And so this was kind of a clarion call to people to go to the higher orders. Now, the first post-Newtonian order, of course, was done years and years ago by me and Bob Wagoner. And then, of course, we thought it was a totally academic exercise because we saw no hope of ever seeing these corrections. They were then and are still now undetectable in the binary pulsar because they're too small. But we just did it because it could be done. But now, of course, we're way beyond the first post-Newtonian corrections. So that really motivated us. And I guess most of the work has been done by the two groups, the Paris group, using their method that's been developed over many years, and our group here, which is basically an extension of the stuff that Wagoner and I did, which he really started with Ruben Epstein back in the early 70s. But I think along the way, we will have discovered, you know, a way to formulate the theory of gravitational weight radiation from sources that's much more satisfying in many ways than it was before. It's still not sort of rigorous in the kind of Ehlers-type language, but many of the key

25:00 issues that they identified, especially this issue of convergence of the fact that you have integrals that could diverge, that issue I think is now completely taken care of. Issues like how do you guarantee when you're solving for gravitational radiation in a formalism where you rewrite the Einstein equations as a flat space wave equation, which is sort of the standard version of doing that with a non-linear source. So you hold them on linearism on this side of the equation, on this side from your point of view. And the basic equation is a flat space wave equation. Well, how do you guarantee that the waves you get are going to propagate along the true curved null cones when the equation is based on a flat space characteristics? Well, it turns out this stuff we're doing shows exactly how it works. when you calculate the higher order terms you get terms whose effect is to modify the cones in such a way that the radiation really does propagate on the true curve space cones just add up the terms right and you get it it comes out right so a lot of these sort of old issues are only now in some sense being cleared up that's interesting to see that so at the moment I think you said you've gone to second post-inconium order Yeah, the second post-naturian is done, and that was done sort of simultaneously by the two groups. In fact, that was by design. We planned it that way, and then we published a joint paper, because we wanted to compare results, do everything independently, and then compare the final results before we went further. And by miracle, they agreed on the first cut, the first round. It was amazing. But now, again, motivated by the people who think about the data analysis, that you really should be going to third post-Newtonian order. So that's what we're doing. Now, the Paris group is ahead of us in the sense they're almost done. We did not agree to go in lockstep this time. These calculations are so horrendous and so complex that it would be fruitless to try to coordinate them in some way. So we just agreed that if they get it first, that's fine. We're going a little slower, partly because none of them is a department chairman, work on things than I do. So, but we're pushing forward and ultimately we hope to get there.

27:30 And we'll presumably compare the results and hope they agree. But going to V-overseed at 6th, really V-overseed at the 7th, we think beyond the quadrupole formula for the radiation flux. That's a lot of work, I'd say. Yeah, it's quite something. But in some ways it's like analogous to people who calculate the fine structure constant to, you know, calculate all the various loop corrections and the weak interaction corrections to the fine structure constant or the g-2 of the electron, you know, using QCD and QED and so on, because some of these things can be tested with that precision, while here we need that precision to do the optimal job of data analysis. I know from talking to Jim Anderson, while one hand, of course, there's motivation for the data analysis people to push these methods to higher and post-utonian order, I know for I think trying to persuade Jim Anderson to do similar pushing forward with his approximation method, but he was sort of insisting that he wasn't sure that the approximation would continue to be valid up to, beyond a certain point. And obviously, in general, there's obviously a question of the validity of the method of approximation up to, you know, in certain regimes. So I was wondering, at what point do you start to get an issue that you wouldn't be confident about the approximation within, say, the region of compact binary when it's reached the stage in which its frequency is within, the frequency the ways it's emitting is within the LIGO band. Well, I mean, I think there are two questions. One is, one question is the validity of the approximation method, in a technical sense, whether it really does, is an approximation to a solution to Einstein's equations in some suitably defined mathematical sense. And there, I don't know, I probably can't answer that question and in some sense don't care,

30:00 because that's more of a really mathematical question and it's one that's I think very hard to answer but then there's a second question of if you calculate these things up to a certain order how close do you think you are or at what point at what value V over C do you worry that you're not not a good numerical approximation to a solution and there we just don't know because we anything about the say the convergence properties of the series that we're looking at people have looked looked a bit at in the test body limit when one body is small compared to the other it turns out the post Newtonian series for gravitational waves has been pushed up to V over C to the 11th by the Japanese these groups using black hole perturbation theory. So they can go to much higher order in V over C, but they're confined to a test body limit. And there, you know, you look at the series and it doesn't seem to be converging all that well. I mean, numerical coefficients get bigger and bigger in front of the powers of V. At some level, the series is not even analytic. There are powers of log of v. But those we understand. I mean, those would even occur at post-Newtonian approximation because we believe those just proved by tail effects. And so they're... Now, whether a mathematician would say that means that the series is no longer a good series or not, I don't know. I mean, just not analytic, but... So I don't know enough about the formal issue of... the formal theory of series to know if that's good or bad, but it's certainly there. converges and in fact it probably diverges if you were to continue the series you would you know the terms would just get worse and people have thought a little bit about this you know have thought about how how bad will it be for say data analysis with ligo you know to what order i mean in the case of test body, test bodies of course we have an advantage in that there's an exact solution in that you can just generate the purely numerical solution that's only limited by numerical error, round of error. And so people like Eric Poisson and

32:30 others have thought a little bit about, you know, the approach to the exact solution. If you go to third post-Natonian, fourth post and fifth post-Natonian, how good do you do or how badly do you do by truncating at a certain level in terms of signal-to-noise issues with LIGO. Not formal mathematical issues, but just how accurately will you determine that you have a signal? How accurately will you measure the masses of the bodies and so on by truncating at a certain level? And the answer seems to be that if you truncate at the second or third post-Newtonian order, you're pretty good. Where pretty good means, you know, 90% in terms of some sort of defined factor that they calculate whatever yeah so that's sort of a quick and dirty thing that says that things are okay but certainly would satisfy a mathematician so again it's a question of what what you're looking for you said that you're not particularly interested in the question of the formal and you did allude there obviously to a kind of a practical method of trying to estimate the convergence of the series, but what other, what else would, or what are the factors that would tend to convince you that it's worthwhile pushing forward with the approximation, given that, as you say, you're not interested in the best of formal validity, but what would be the sort of, as it were, the physical grounds for validity? Well, I mean, in some sense, one, the considerations that would go into going even further would be age, not in my home. You know, these things really get unmanageable, just in terms of the number of turns. They're really horrendous calculations. I mean, this 3 p.m. is going to be a real bear to do. 2 p.m. is bad enough. So there, it's just a practical question of investment versus the game, and luckily sort of all these different ways of looking at the problem suggest that third post-Newtonian is really all you are likely to need for the purpose of LIGO. And so I plan to quit at that point once we get the third post-Newtonian. I think, my own opinion is it's pretty unlikely that anyone will be able to prove some sort of a theorem about these series

35:00 and their convergence or their relationship to, you know, putative exact solutions of GR or anything like that. I mean, some theorems have been proved in certain special cases about, you know, by Christodou and other people like that, But those are very well-defined situations and problems where they sort of set things up in the first place in a very formal, well-defined way. But this is not a well-defined problem, even from the start in some ways. We approximate these bodies as point masses just to make life simple, although we know that's not a good thing to do, but it seems to work. We don't get too much into the issue of what the system was doing in the infinite past. We sort of assume that it was some sort of a wide binary system, but the argument is that its behavior sufficiently far in the past doesn't affect its present behavior. And so, you know, there are ways in which we don't... there's enough sort of dirt built in at the beginning that I can't imagine you doing much formal and besides you only have three terms in the series and we're in third post-Newtonian order what can you prove about a series with only three terms so that's that's hard I mean it's just in this one case of test bodies where we do have the exact solution and you can make a comparison but even there I don't think There's much to be proved in a formal sense. Should I add you to that? Sure. So I should be done around 12.30 if you want to continue on. Okay, I'll come back. If you have more to do. And so what I'll do is I'll come back down here, and then at 1.00 I have to go over 1.00 or 1.15 or so. I'll have to take off. But if I plan to do that, we can pick it up. Great, let's do that then. Thanks a lot. So, it's still the 18th of March, and a quarter to one, and I'm resuming talking with Clifley. Everything seems to be okay. So, well, we have been discussing your ongoing work, advancing the post-Newtonian formulas,

37:30 and in order to, as you say, provide templates for future data analysis with detector-side I was curious to know if the need to go much further in what you said of course was a very complex kind of series of calculations had altered the working methods of the community anyway. Does the fact that the computations are more intensive mean that you have to have a greater number of people working? and does that raise issues? I mean, well, not necessarily. In a practical matter, it hasn't been that I have one student helping me work on these things. So it's not a large kind of enterprise. I mean, it certainly could be one. We could always use more people to help in these kinds of calculations. But it's less of an effort that requires large people where you have all these big teams dealing with codes and all the various issues that surround them with different people having different expertise and so on. So it's even the work that the Paris Group does is still one or two people, I mean one person and a graduate student, just plowing away. So it hasn't changed much in that respect. How much of it, well, I know that Kip was always keen to, I think he's always keen to sort of get other groups doing independent calculations, I guess basically the whole burden at the moment is being taken by two groups, and as you say, there's definite effort to try and make sure that everything is in agreement between the two groups. is that more or less an expression of the difficulty of the work that it's more or less down to two groups? Yeah, I think so. I mean, nobody else is nuts enough to take this on. But there's sort of another group surrounding Gerhard Schaefer in Germany that is doing similar stuff, although the method is basically quite close to sort of a variant of the method that Blanchet and de Boer worked on. I'm not sure exactly how to fit that into

40:00 this scheme and he's really just calculating equations of motion at this point not gravitational wave forms so it's sort of a quasi-third effort but it's just not clear how we can compare the results through rather different languages and so on but I mean of, you know, in terms of the sociology of the field, it's also, despite the fact that it's very important to have these templates, in some ways it's not as sexy an area to think about than, say, numerical relativity. Right. I mean, a lot of what we do is really just grungy work, keeping track of, you know, thousands of turns, making sure that you ever made a mistake along the way, and then so on. We use a lot of algebraic computation techniques to help out. Right. But it doesn't have quite the cachet that, say, the numerical relativity approach to inspiring black holes and colliding black holes has. So it's sort of necessary, but not particularly fashionable. Yeah. Maybe people figure that two groups are taking care of it, so they don't have to think about it. Yeah, and it's a fairly narrow question, trying to answer this one thing to the third post-Antonian order. I think we all have a handle on it. You know, I don't think it's a subject that has quite the future, say, that the numerical relativity has. I think we're going to get an answer, and then that'll be the end of it, move on to something else. And would it be fair to say that basically pretty much the only major motivation would be the necessity of producing a more accurate template? Yeah, I mean, I think the side benefit will be a better handle on gravitation radiation theory and some of the sort of formal issues surrounding it. But I don't think those alone would have motivated any of us to go to as high order as we have. When you mentioned the algebraic computation techniques and so on, how, and I guess it's only in very recent times, that kind of automated methods of doing algebra have been available how much of an influence does that have it has a big influence I can't say that you thought all the whole calculation is done that way certain aspects still require the

42:30 human you know intuition to do certain things machine can't do but other manipulations are fairly routine and automatable and so we we make use of very extensively. I mean it reaches a point where you do certain things and you're adding up terms and you've got thousands of terms and you have to take big expressions and manipulate them with certain operations that are well defined. Clearly the only way to do that is by machine so we do that a lot. In fact the student I have is even more adept than I am. He's using fancy stuff to really do things in a fairly elegant way I think. Do you still do, this is a practical question to Chris, do you still do fairly significant areas of calculation just with pen and paper? Oh yeah. Yeah, I mean there's notebooks there. They're essentially all written by hand. I was pretty sure that would be the case if it occurred to me. Maybe you always be put in. Certain things, I mean it's just certain things that algebraic, I mean it's not, it's because a lot of stuff that's written down is not so much algebraic it's you know intuition or you know combining two terms in a certain way that if the machine combined them you'd end up with a mess and you wouldn't know what that you're doing but when you combine them yourself in a way that may you know you suddenly see that everything is perfect and works out right the machine is pretty dumb in that regard. There are certain things where the human intelligence is still needed. How important does checking the computer's results presumably have a lot of fun? Well, I don't know. I suppose one assumes that the programs don't have bugs. We know that some of them do. On the other hand, I think that the kinds of things we're doing, which are just basically basic differentiation, algebra, adding, subtracting, are things where I would presume there are no real bugs. I think, I'm not a real expert on these things, but some of my sense was that the bugs that have been found in things like Mathematica are for very high level operations. And what we do is not high level, it's really just making sure that you add, you know, 150 terms and get them to promote the right answer.

45:00 I've certainly been impressed with the accuracy of these things, as you say, for very standard types of calculations. but since you're not too worried about the question of looking for bugs in the program or checking if there are likely to be bugs in the program is it generally the case that the output that the program gives are you sort of confident that the output that the program would give would look wrong if there were bugs sometimes, sometimes things just look wrong but other times you couldn't tell the expression may look right it's got all the terms you expect to occur but the question is 2 thirds or 4 fifths is the coefficient the right one and somehow there's no way to know except by checking with someone else even within our group stuff I did with Alan Wiseman for the 2 p.m. and stuff we're doing now for 3 p.m. we do things somewhat independently too so there are various checks along the way to be sure that we're right So, ultimately, it's a question of having independent calculations of one degree or another, too. Yeah. Can you... Oh, yeah, well, I guess I was going to ask about the... broader issue of data analysis, is that a subject that you have taken much of an interest in? I've taken a bit of an interest at the level of thinking about ways in which you can use mass filtering to do certain things in gravity like test scalar tensor gravity, I haven't thought much about sort of the other end of it, the issue of how big and how fast those computers do you need to handle the data, what are the optimal strategies for taking bits of data and piecing them out and so on. There are people thinking about that. It's not clear that there are enough people yet thinking about those issues because they've

47:30 got to be resolved by the time the light goes on the air, but I think there are people starting to think about it. But I'm sort of more interested in the interface between the data analysis and sort of the basic physics questions that you could answer. So I mean, I've done a little bit of mass filtering and doing these fissure matrices and so on that people do, but that's a little level stuff. Well, given that you've thought a lot about the question of experimental in relativity, how big of an impact do you think LIGO and similar detectors will have on that area? Is it a case that it provides a certain amount of interesting results in that way, or would it be a more fundamental revolution in how many tests of relativity I mean, it's hard to characterize it quite so black and white. I mean, I think you'll be able to do tests of general relativity. The level of precision and so on will depend on what is detected and so on. But just being able to test general relativity in the radiative regime, in the strong field regime, where the sources are really black holes and you're seeing stuff coming from near the horizon, highly dynamical relativistic space-times and so on. So I think that will provide sort of new tests of general relativity, probably not in the sense of the precision tests of the solar system, but maybe conceptual tests, some with modest precision, but I think it's unlikely that you'll ever get the kind of precision that we can get nearby so it's just that you'll be doing things in a new regime for example unless one is extremely lucky you can't put a better bound on scalar tensor gravity using say binary in spiral by looking at the gravitational waves with LIGO than you can in the solar system you might in a really favorable case but run-of-the-mill cases you won't do any better than the solar system but still, being able to place a bound based on the difference in gravitational wave damping between scalar tensor gravity and general relativity in a binary system of two neutron stars

50:00 is still to me an interesting result even though it's not as accurate as what you get from deflection of light by the sun in terms of actually constraining that specific theory so it's not sort of going to revolutionize things but I think it will add a new element to experimental gravity because it has a different quality in the sense that it's not got the precision of the position of everything and the stuff I did recently on the graviton mass I mean one can put a bound on the graviton mass that's certainly better than you can do in the solar system you can put a bound on a Yukawa type gravitational potential which bounds the mass of the graviton in some sense so it's kind of a static test. You can actually do better with space-based gravitational wave antennas, LISA-type antennas. You can do marginally better with LIVA than you can with the solar system. But still, it's a test that involves the fact that if the graph time is massive, it probably gets more slowly than if it's massless, and you're measuring this time-of-flight effect. So that's a totally new way of measuring something about the gravitational wave gravitational interaction is there what kind of status do you think tests of rival theories of gravity have at this point for you is it a question that you really there are still rival theories that you think are really serious rivals or is it more well I think the emphasis is slightly different than it used to be many interesting rival theories of the kind that we used to think about in the 70s and 80s. Here, I think the story is a little different in there's now this possible rival scalar tensor formulation of gravity that comes from super strength theory. Now unfortunately, the predictions at the sort of low energy limit of the tests we think about are very uncertain because the models have just haven't been developed enough. But people who do string theory say it's certainly possible. I mean, string theory generically predicts that the theory of gravity is not general relativity, but a scalar tensor theory. But the real issue is what's the mass of the scalar field, what's the coupling strength, blah, blah, blah. But if things are right, you could get testable effects in various experiments.

52:30 And one of the most promising ways to at least probe sort of this string theory regime is using improved tests as the equivalence principle and so that's why people are talking about satellite test as well as really approved by six orders of magnitude which because these theories generically violate the equivalence principle at some level but it could be zillions of times smaller than you could ever hope to achieve even in a space experiment but no one knows it's all all bets are off basically and so it's an interesting way to probe that machine for us improving solar system tests by maybe an order of magnitude, gamma and beta and ppm parameters won't do that much to really look at this specific class of theories so in principle at any rate detectors like MAGO could provide solar system based? Depends on the source and I mean it all depends on signal-to-noise ratio and you know. I mean what you need to test scalar tensor gravity is a neutron star black hole inspired. It can't be two black holes and it can't be two neutron stars. It has to be one of each. It has to be an asymmetric system. Asymmetric in just in terms of mass but also in terms of... Asymmetric in terms of sort of binding energy per unit mass of the two stars, gravitational binding energy. This produces dipole gravitational radiation in scalar tensor of gravity. We don't know the event rate for such objects. It's undoubtedly less than the neutron-neutron star in spiral rate, but no one knows how much less. So it could be an event that we could wait 100 years to detect. But if you detect with good signal-to-noise, you could get a very good bound on the scalar tensor theory. And would that be a decisive test, or is there enough flexibility? It's hard to tell, but in 50 years, other experiments may have improved to some degree. There's talk of doing some experiments in the solar system that could measure gamma, the PPM parameter, to part 10 to the 5. When that happens, I'd be skeptical that this gravitational wave test could reach that level.

55:00 Again, unless you were extraordinarily lucky. So, I don't think it's... I don't think there's this whole new test waiting there to happen, and if you should rush out and do it. so in general the problem would be the precision of the experiments you're allowed to be able to be able to make would be limited but in certain cases where as you say there's a kind of conceptual difference between two tiers they're testing a new regime which I think is useful how much work has to be done on the theory side to sort of prepare the ground for those types of tests, I mean you mentioned of course that on the general data analysis side an awful lot of issues remain to be resolved, but is there and obviously part what would be required would be for instance the work you're engaged on with constructing templates and so on but is there much beyond that? Not a huge amount. I mean, in terms of, you know, doing tests of alternative theories, I mean, some it's already been done. I mean, I've published papers on it, Thibaut Amur, and collaborators have published a recent paper about it. So I think the basic stuff is there, and maybe some refinements could be put in, but nothing, I don't think anything major really needs to be done at this point. The point is I think when the time came, if one were to discover a system that would be particularly ideal for doing tests of these alternative theories then it would not be too difficult to just build the basic theoretical structure you need to then do the job. I don't think 80% of it exists already just from existing work. But I think you could do the rest of it pretty easily. if and when the time, the occasion arose. I guess then the final question I had in my mind was the question of what sort of an impact you see LIGO making to the kind of theory that you're interested in, LIGO or similar detectors, assuming that they're, say, a big success, we'll say,

57:30 I mean, I've been interested in asking peers from different backgrounds how much of an impact they would see that making on their work, and it's ranged from people who think, well, this is going to be it, you know, lots of exciting stuff, too. I don't think it would change my work a whole lot. How much of an impact do you think it would have for someone who you're right? I mean, the answer is it's already had a huge impact. So whether it will have more of an impact or not is not clear. But it's certainly, I mean, essentially all my attention these days is directed toward these issues as opposed, say, to experimental test issues, the kinds of things I used to work on. Apart from writing review articles and such, I sort of don't think much about those questions at all, unless they're in the context of LIGO. I mean, I've thought about testing scalar tensor gravity, but it's in the context of things like LIGO. So I'm really, you know, it's really changed, changed what I've done, you know, turned me toward a new direction in a big way. Now, once it's on the air and data starts arriving, it's hard to know how that will affect me personally. Whether I jump into getting chunks of data and trying to analyze them myself, I tend to doubt that just because it's not really my expertise. But whether, I don't know, I have a clear idea of what I might do on that day when the data starts flowing and people start doing it. So in that sense, I mean, as far as you can tell now, your role is almost that sort of a traditional theorist relationship to experiment in some sense, normative sense in that you're motivated to enable the experiment at this point and be constructing the theory which is necessary to sort of keep it going but then once it's online it's not quite so clear what your role would be in a direct sense some theorists might be involved directly in the data analysis which is kind of unusual it's really unusual for a generality I view that as at this moment as probably unlikely but I think I would agree with what you said. It just occurs to me... That should go in a few minutes. Well, since I've finished the sort of up-to-date thing with that question, it occurs to me to go back a minute and just go back to the

1:00:00 practical form of the business again, to talk about going on from the work that you did that we discussed with Martin Walker and that you did up to around 1980 or so. Subsequent to that, I guess the quadruple form of controversy continued to burn for a while and then I think either ended or petered out in how you choose to look at it. So I was curious to know what you thought were the key issues in sort of bringing it to a conclusion. I mean, convincing presumably the majority of people that the question is that. I mean, obviously, I think one key issue is the fact that the observations agreed with the quadruple formula. Right. I mean, in the end, for whatever its failings in terms of its foundations, it clearly was the correct formula. But also, I think it petered up because of advances. I think to some extent the advances by the D'Amour Blanchet group of putting their own sort of formal foundation behind the quadrupole formula with this matching technique and doing things in terms of these rigorously defined multiple expansions actually based on work that Kip did early on this review article he did in Reason Modern Physics extending that and then finding ways to do this matching between the far zone and the source I think that had enough sort of rigorous foundation, especially since they're French and they tend to do things in rigorous language. I think that went a long way to helping to give the sense that everything was on a solid foundation. And that was sort of work that was done, predated the LIGO stuff. I mean, they were working on these kinds of what they call post-Nunkowskian approaches for many years. Apparently, at least presumably influenced by the bio-referencing. Yeah, yeah. So I think that helped a great deal in terms of satisfying sort of the mathematical foundations of the subject. More so than anything I did during that period, because in some sense I didn't do that much. during sort of the 80s was more interesting in doing experimental gravity and other things and so for us this idea for example

1:02:30 of dealing with these convergent divergent intervals is just something that happened quite recently but I would say that by the mid 80s there was no discussion of quadruple controversy anymore I mean, and besides, not only did there's, I mean, Martin Walker and I wrote a paper and Fizzeroblater's about it, Thibault wrote a paper, Jim Anderson, there's a whole bunch of papers over about a three or four year period, like between 80 and 83, of people claiming from their point of view that the quadruple formula is correct and so on. To some extent that also, you know, helped just by enough people getting on board, helped to support it and settle the whole thing down. Yeah, so this kind of question of sheer numbers would be few enough remaining skeptics and enough people who are all basically happy about the actual answer. Okay. Well, that's it. Thanks very much.