Interview with Niall O'Murchadha

0:00 There, and it seems to be working okay. And it's quarter past nine in the morning on the 23rd of August, and I'm speaking with Niela Marku. So, just checking if it's working reasonably well. Yeah. Okay. There's a terrible button on the back that turns the microphone sensitivity way down low. I'm not sure what this is for. For, that's right. About one time, it got smirched accidentally. Yeah, and totally wasted your day. Anyway, what do you want to talk about? Well, I suppose I wanted to start by going a little bit back over just some of the last technical issues revolving around what we discussed last year about your new theory. Yes, yes. And so, in particular, we discussed some of the motivations behind it that it would be possibly a better candidate for a quantizable theory of gravity than G-Z would be. That's right. You probably know this already, but the original proponents of, say, the Wheeler-DeWitt equation as an approach to quantization, the original canonical quantization approach, all of them have, one way or another, said really horrible things about it. Bryce DeWitt attacks it violently at this point, claims that it's completely wrong-headed, the wrong approach, even though, of course, it's the Wheeler-DeWitt equation. He says that this is something that everyone should abandon and run away from as quickly as possible. At the same time, there is a mini-industry left out there of people who still do the Wheeler-Dewitt equation. It turns out that technically there are several major... Do you want me to explain the background of the Wheeler-Dewitt equation? Yeah, I think... Okay, the Wheeler-Dewitt... 3 plus 1, standard canonical gravity, means that you get yourself a P and a Q, and the Q, the position variable, is a 3 metric, and the P, the momentum associated with this, is essentially the extrinsic curvature, and then you end up with a situation that,

2:30 just like as in Maxwell's equations, these are not arbitrarily, you can't choose the P's and Q's, just as you can't choose the E's and B's arbitrarily, you end up having to solve two constraints. These satisfy two constraints, Embedding conditions, the Tracted Gauss-Gudazzi equations, and the two of them then have very different interpretations. One of them, the so-called momentum constraint, says that the momentum is divergence-free, which is just the analogue of div B or div D equals zero, but just one index up. And it's as with, and just for the same reason, in Maxwell's equations tells you that there's an underlying gauge group, which is the standard gauge group of general relativity, the standard gauge group of the electromagnetic theory. In general relativity, the div pi equals zero condition tells you that the thing is three dimensionally covariant, which is what you expect, obviously. You take an initial slice and you choose a pi and a g on that, then you know that if you change the coordinates, the initial coordinates, nothing physical is going to change. And so then the condition that div pi equals 0 is a reflection of that underlying gauge group. The other constraint then is much more complicated, is the so-called Hamiltonian constraint is quadratic. the like you could think of it as the standard energy equation in mechanics you know it's p over 2m plus v equals e right and you get again a p squared over 2m but now it's a pi squared term and then you get a potential term which is the three scalar curvature and then you get nothing, in this case you don't get a total energy but you just get zero And so you have something that looks, as I say, somewhat like the p squared over 2n plus v equals e equation. Now, the idea then was, by Wheeler-Andewitt, was to actually promote this canonical, this classical canonical analysis to a quantum theory.

5:00 And so what you did then was that, as with standard Schrodinger quantization, you promoted the momenta into operators. You left the position variables as classical variables. And so then what you then decided that the configuration space was this super space. initially you started off thinking of your configuration space as the class of all you took a bare manifold and you put all possible a three dimensional manifold you put all possible three dimensional Riemannian metrics on that and then you identified ones which were related by coordinate transformations so you first of all you then looked at your configuration space. And so this would be the so-called super space. This was, you know, people have been using this now since the mid-60s as the configuration space. And then the solution, the classical solution to the Einstein equations you think of as a curve in super space. So this would correspond to a, So I would take a four-manifold and foliate it with three-dimensional slices, and so then I would arrange a three-geometry. With the fixed-coordinate system, you'd initially have a sequence of three metrics, changing three metrics, and then you would allow general-coordinate transformations on each slice. So you would think of it as a sequence of three geometries. And so then you would think of the solution of the, so then the configuration space would be this super space, this set of three geometries on a fixed bare manifold, and then you would then think of a solution to the Einstein equations as a curve in this configuration space. this sounded at least plausible it looked rather like when you actually then went and then of course so then

7:30 then you looked at your wave function as a distribution on super space so you would get yourself a probability of that you would find a particular 3-manifold, right? And so this would be, and then you will then have, and then you then promoted the Wheeler-DeWitt equation to be an operator acting on this wave function. You would turn the momenta, so you would take the g as the g. The metrics would remain the same. you would take the, then you would change the pi into a derivative with respect to g. So you would have a functional of g's, and so you would have a derivative with respect to g, a derivative with respect to g, right, because there are two pi's there. So you get a second derivative with respect to the pi's. And then you would leave the scalar curvature, which is just a function of the metric, as a classical object, as the essentially potential. And so then you would get a second order operator, a double derivative with respect to g's minus a function, the scalar curvature, acting on a wave function, which is a functional of all possible metrics, equals zero. And so that's the Wheeler-Dewitt equation. and then in addition to which you would impose the momentum constraint again as an operator valued object on the wave function and this would just this is very clear because this one just tells you that the configuration space is in fact three geometries rather than three metrics because the momentum constraint means invariant under the coordinate changes. And so then this looked lovely. It turned out of course that this thing was actually absolutely horrible when you looked at it more closely. The fundamental difficulty with it, well there were several fundamental difficulties, but one fundamental difficulty is that this is the analog of the

10:00 time-independent Schrodinger equation. Right? You think about the time-independent Schrodinger equation it's grad squared minus operating on phi equals e phi. Right? The e phi term is gone for reasons which we don't quite understand. But it looks just like that. So there is no... it's a timeless theory. And then the object that you would get would be a time-independent distribution, right? Just as when you solve the hydrogen atom, the time-independent hydrogen atom, you get yourself a distribution of a range of possibilities as to where the electron will be around the proton. But there is no sense in which you actually ever interpret this as a changing electron moving around the proton. You just say, here is the distribution, right? Holds for all time. You don't actually interpret this as an electron ever moving around the proton. So then the solution that you get from the time-independent Schrodinger equation will be this timeless distribution of probabilities. which somehow while we think of the solutions of the Einstein equations as having a time in them the classical theory we think of them as somehow a progression of three geometries labelled with some parameter and so the question is how do I go from the from the classical unique curve in configuration space to this smeared distribution and what you actually do if you think about it in the standard quantum mechanical theory is that you actually look at a superposition either you go to the time dependent theory or you actually can

12:30 say instead of taking a say fixed distribution with, say, fixed angular momentum, right? You actually get all possible. You actually get now a superposition of all possible solutions of the time-independent Schrodinger equation, and you superimpose them one on top of the other. And then the classical path in configuration space emerges as an interference pattern between the various layers of wave functions that you lay down on the single solution. No one has ever managed to make that, in any sense, work for general relativity. There are several major technical difficulties in doing this because it turns out that in GR the object that you get is not a you don't actually get in classical GR in the 3 plus 1 language you don't get a unique curve in super space because I take a given initial data and I progress this using the evolution equations and I get a space-time but now I can somehow as I do this I can somehow change my foliation and I get the same space-time but with a completely different sequence of three geometries they will all be the same classical solution but they will not be represented as the same Corovid super space So the jargon phrase is that you get yourself not a curve in superspace, but a sheaf of curves in superspace corresponding to the single classical solution. Now the question is, how do you represent this in the quantum theory? In some sense, what you're saying, essentially, if I look at superspace, and I look at a classical theory, essentially, all points in superspace can be found as an embedded hypersurface in any one classical theory.

15:00 Right? If I take superspace now, a set of all possible three geometries, and now take a point in superspace, a metric in superspace, and I take some sort of one single solution of the Einstein equations, there is a high probability that I can find a curve in superspace representing that particular solution which goes through that particular point. So basically, and so this means that the classical theory does not represent a curve, a unit. And this is exactly the opposite of classical mechanics. In classical mechanics, when I throw a stone, a curve a unique curve in the configuration space in general relativity it's smeared out all over the place and so then it becomes extremely difficult to actually and again if you even go say to say an electron a classical electron going around a classical proton it will follow there and so your configuration space is just three space will get a very, you'll get a unique curve. Well, this kind of unique curve has completely vanished in general relativity. Because of this, and this is one of the major, if not the major, fundamental difficulties that people had and still continue to have with implementing the Wheeler-Do-It formulation, that the classical theory is not a curve in the configuration space in any sense. And then somehow gauge fixing, right? Choosing, say, trace cake with constant foliation or whatever your preferred slicing gauge is, is completely antithetical to the spirit of the 3 plus 1 language. Fixing a gauge is somehow breaking the gauge invariance of the theory.

17:30 And so it's somehow wrong. So this has been something that Julian Barber has been thinking about for a long time. And he decided that what he wanted was a theory whose classical trajectories were unique curves in the chosen configuration space. And so he came and bothered me several times about, and he decided for fairly good reasons, I think, as to whether one could find a theory which had this property, that what you would get, that the solution of the classical equations would be a unique curve in the configuration space, not this sheaf of curves. And the language that he felt that this would be best expressed in would be in terms of the so-called Jacobi variation. The initial action formulation of Euler and Malpartois did not have a unique fundamental time in it. And you can see this in something like the Fermat's geometrical optics, right? This shortest path approach. The object that you get from when you do geometrical optics using Fermat's principle is a curve in configuration space. but you don't think of it or you need not think of it as a curve along which the photon moves at a canonical speed you just actually see this line in space you can in fact if you wish to interpret the refractive index as a ratio of velocities actually add a fundamental time to the theory and convert the Fermat's principle from a shortest distance principle,

20:00 a geodesic principle, to a least time principle. But this is an optional added extra, not something that's fundamental to the theory. So then what he wanted was a fundamental theory, a new theory, the configuration space had to be conformal superspace and then he decided that the language in which this was best expressed was in using a Jacobi variation because in the 19th century Jacobi had gone back to the fundamentals and had in fact tidied up the original variational principle, and had in fact put the concept of what's called a parametrized theory, where in fact the theory solution is going to be a parametrized curve, but the value of the parameter is not going to be particularly important. And that this was the kind of theory that we needed to do. And it turned out, in fact, that three people, Byerlane, Sharp, and Wheeler, in 1962, had used the Jacoby Action concept and had written down a Jacoby Action for standard general relativity. And this was the foundation of a game which some people play called the thin sandwich theorem of general relativity where in fact where instead of actually talking about and pi's you actually talk about G's and G dots as your input and so as I say this all comes from the Berlin Sharp Wheeler action so they wrote down an action which gave you standard GR in the thin sandwich language. It turns out that for reasons nobody quite really understands, it turns out that the thin sandwich formulation general activity is absolutely horrible. It in general cannot be solved. So if you give me G and pi

22:30 you can do something with G's and pi's. But if you give me G and G dot You usually can't. And this is one reason why, and I think the fundamental reason why Julian wanted conformal superspace, because the way that we tend to solve the classical GR constraints in the standard 3 plus 1 formulation is using a conformal language or a conformal technique. This is, in fact, in the standard GR language, is, again, something that's not necessary in the sense that it is a useful way of constructing initial data. So you give me some sort of arbitrary objects and then I use this conformer technique, I solve the Lichnerewitz equation and find from these arbitrary objects objects which satisfy the constraints. and the Schneiderwitz equation is a conformal transformation equation it turns out but this of course then once you actually find the initial data you completely forget about the conformal basis and you just rush away as you go and in fact there is no and there is no immediate linkage or no linkage at all between the evolution equations of standard GR and the conformal approach and many people have tried to somehow conformalize the whole thing with new success except people like Helmut Friedrich who's interested in conformal language actually handle technical difficulties in the asymptotically flat regime, where he is interested in these mass hyperboloids, which go null at infinity. And it turns out that in many cases, it's easier to compactify these using a conformal transformation. But this is a very different kind of spirit to the spirit that we are working on.

25:00 But anyway, the situation is that when you looked at the level of the constraints, it's clear that there is something deeply conformal hidden in there. But when you looked at the level of the evolution equations, all this conformal stuff goes away. And so Julian then wanted very badly to see whether one could find an alternative theory of gravity which was completely conformally invariant and whose solution would be a unique curve in the configuration space which would now be conformal super space. And so then basically what happened was that when he bothered me enough, I basically went and looked at the Berlin-Sharp-Wheeler action. And it became clear when you looked at the Berlin-Sharp-Wheeler action and understood what was going on in it, that it was in fact quite straightforward to actually conformalize the Berlin-Sharp-Wheeler action. turn it from a theory which had only three coordinate invariants into a theory in which you had an extra gauge freedom, conformal freedom. A conformal freedom. And so then all I did was take the Berling-Shark-Wheeler action and appropriately modify it to convert the Berlin-Sharp-Wheeler action into something that is completely conformally invariant. Now, it turns out that when you did this, it was clear that there was, in fact, a family of theories which had this conformal invariance. but it turns out that there was one member of this family which was somehow much closer to the BSW action than any other it is the easiest generalization and this is the only one that we have currently

27:30 investigated but you so basically then I just wrote down the conformalized BSW action and then did standard variational principle massaging to it and so it became very easy then once you did that you got a complete theory out of it in the standard way and it turns out then in turn that this complete theory does in fact have the properties that Julian was looking for which was that the solution is a unique curve in the configuration space. The configuration space now is conformal super space, not super space. So that you start off with initial data, and then you've got evolution equations, which are well-posed, and you just turn on these evolution equations, and they just walk across the landscape with a parameter attached to them, and you walk across the same landscape but at a different local speed. That's all that happens. And this, now, of course, this is an interesting game. But it turns out, of course, that this, the solutions of, of course, any curve in conformal superspace is, of course, also a curve in superspace, can be represented as a curve in superspace. And it turns out that the solutions of the new theory, conformal gravity, agree quite closely to at least some solutions of the standard equations of general relativity. So what you have basically is that you've got two theories with different gauges, very different gauge groups. But both of them can be represented by curves in super space. And it turns out that there are, if you choose suitable curves in each theory,

30:00 the two curves actually agree quite closely. And so that means that it turns out that in the new theory, GR, there's a substantial difference between the generalization of, for the compact case, versus the generalization for the non-compact case. so there are actually I suppose one could think of it as two separate theories when you wrote down the BSW action and conformalized it can I write things on the board or will this confuse the machine too much yeah okay let me write down the BSW action that the action and you can find this in the 1962 Fisrael letter, there's a parameter D lambda and then there's an integral over some 3 space right and then there's obviously a square root and then there's a square root of R and there's a square root of T. Now, it turns out that this formulation is exactly the kind of way the thing that you would get from the Jacobi action. In the Jacobi action, you would get a square root of a potential energy term and a square root of a kinetic energy term. and this is this is the three scalar curvature, this object then is effectively the kinetic energy and it turns on and it turns on that T T is basically a GG minus GG times del G del lambda minus a killing form

32:30 Now, with indices appropriately chosen, there's A, B, C, D, A, C, B, D, A, C, A, C, B, D, B, D. right and this is called the DeWitt supermetric this combination and it's the thing that occurs in the Hamiltonian constraint where you have there are two DeWitt supermetrics just to confuse there's this one and there's one with a half in it and they both appear in different formulations of the Hamiltonian constraint constraint where you have the extrinsic curvature where you have R3 is equal to K K minus trace K squared. Right? And that of course as you can see is GABGCD where it's GACG Right? And so that fella is this fella. The other one, of course, is when I write is equal to 1 over g pi pi minus a half trace pi squared. And then, of course, you need a half in here. right anyway this is DeWitt this is the Berland-Sharp-Wheeler action and so then the question is how do I conformally how do I make that conformally invariant and it turns out that basically it turns out that there is a Conformal scalar curvature, which is r minus 8 grads per phi over phi. This goes in the name of the conformal Laplacian of the conformal scalar curvature. If I replace this, if I put that in here, and if I adjust, and then what I did was that I adjusted.

35:00 Julian Barber's had wrote an article I'll find it for you this equation Barber and Bertotti and understanding of what this action meant. The basic idea was that I took two metrics, I took two slices. Right. I took two nearby metrics. and now the action basically told me minimized the separation between these two right, gave me, so that if I gave you g and I gave you g plus del g I would be able to say this would be some sort of measure on configuration space that this would give me a number how close that metric was to this metric. Okay? This is what an action does for you. It gives you a number. It gives you two nearby points in the space, and then the action then gives you a number, which tells you a distance between these two points. Now, the point, however, is that if I write these down as just metrics, then I have, but I don't want to do this, that I could somehow adjust the coordinates on this slice so as to say that this del G here was just a coordinate transformation then I would I would want the measure here to be zero so basically I would want to be able to adjust the coordinates on the second slice and by adjusting them, I would want to be able to minimize the distance. Now, when I adjust the metric, a coordinate transformation

37:30 is just a killing form, right? So basically, I would want to be able to add a killing form here with an arbitrary vector and then adjust the So basically what I do is that I take this measure and I basically vary so as to make the separation between these two as small as possible. And so this is effectively what Berlin Sharp-Wheeler did. Remember there was this there was a del G del lambda minus kW right? and so they varied the action with respect to this W and so what they were doing was just somehow looking at two slices and adjusting the coordinates on the second slice so as to make it as close as possible to the first place, and so then modulated with this sort of weighting factor or something like that, right? And so then when you, so you did standard, so what Berlin-Charpe-Wheeler did was that they did standard Lagrangian tricks on this action, but they basically varied with respect to this W. They minimised the action with respect to this W. And by the way, when you did this, you automatically got the momentum constraint. That's just where the momentum constraint comes out of the theory. But the thing is that now if we wanted a conformally invariant theory, in addition to allowing, so we've got a g and a g plus del g, in addition to allowing coordinate transformations on the second slice, I would also like to allow infinitesimal conformal transformations on the second slice. Okay? And so then you just added, and an infinitesimal conformal transformation is the g. Right? And so basically that's all I did, was that I took the standard theory,

40:00 replaced R by the conformal scalar curvature and replaced this, added this extra term to the kinetic energy term. And now it turns out that this didn't quite work because of the fact that you had to worry about the fact the square root of g will pick up a conformal factor as well, and so then it turns out that the conformal invariant object is x square root of g square root let me call it r and then there will be and it turns out that you have to have a 5 to the 4th here right? to absorb the conformal transformation that appears from that thing basically. But actually, there's another term. Some of it comes from that as well. Now, if I have an action, I want this action to be somehow to give me a reasonable answer. And so now, I'm going to vary this action now with respect to phi, theta, and w. But now, it's clear that I won't be able to that this will not have a minimum that this action because of course if I find a configuration which minimizes it if I multiply phi by a third just multiply that by 1 over 3 then this whole thing goes down by 3 to the power of 4 so I want to prevent this, me being able to just scale this to nothing just by scaling on that value, just multiplying it by a constant. That won't change anything else. And so somehow I have to control to prevent this essentially setting the conformal factor equal to zero, which is the effect of setting the value of the action to be zero. So saying that all things are zero distance apart. way I control that was by effectively controlling the volume. So I basically

42:30 normalized this by dividing this by the conformal volume and then this has to be the power of two thirds just to make that four rather than six. Okay? And so that's the action. And it is clearly, now, it turns out that in the asymptotically flat case, you don't have to do this. You can drop this term completely, and now demand that phi be well behaved at infinity. I can demand, say, that phi goes to 1 at infinity, and then that also prevents me from scaling it to 0. So then, as I say, we have two theories. There's this theory, which works for compact solutions, and there's this theory, which works for the asymptotically flat case, combined with the requirement that phi goes to 1 and infinity. Now, in the asymptotically flat case, the solutions of this theory agree completely with the maximal slicing gauge of general theory. Right? It turns out... So that means that the theory will pass all the standard tests. Obviously, it agrees. Right? So there is no problem in the asymptotically flat case. It is a very different theory. The gauge group of this new theory is completely different from the gauge group of general relativity. But there exists a gauge member of this theory which agrees completely, 100%, with a gauge member of standard GR. But if I make a gauge transformation in one, it will be a completely different object from a gauge transformation in the other, you will no longer see the relationship between the two. So there is a preferred gauge for this theory which agrees with the solution, which gives you a curve in superspace rather than a curve in conformal superspace, a gauge fixing condition, a choice of the conformal factor,

45:00 and this agrees completely with GR. In the compact case, the agreement is not as complete. It only agrees near a moment of maximum expansion, basically. But if I have a theory, a solution of GR, which is going from a big bang to a big crunch, then it will have a moment of maximum expansion and then near that moment of maximum expansion I can find the two theories will agree will agree to second or third order in some parameter or other. Does that mean they only agree when you have some cosmology that's expanding slowly? That's right, that's right, that's right. Exactly. See, the situation is that one could say that in a situation where the Hubble constant goes to zero. You see, at maximum expansion the Hubble constant is zero. So in terms of near a situation so the disagreement between the theories would be to some power of the Hubble constant Now, the advantages of this theory are manifold. As I say, one advantage is the fact that it gets around the problem of the timelessness of the Wheeler-Dewitt formulation. Now you can see, then, that there will be a Hamiltonian constraint. You don't see it, but there will be, because it's going to produce something which looks very much like GR, different. There will be a Hamiltonian constraint, and then you can promote that to a Wheeler-DeWitt equation, and so then the timelessness of this Wheeler-DeWitt equation clearly makes all the sense in the world, because of course the fundamental theory is just a parametrized theory, so then you don't expect, so then the relationship between the classical solution and the quantum solution should be much closer. There is another fundamental advantage which comes from the DeWitt symmetric. The DeWitt, if you look at the Wheeler-DeWitt equation,

47:30 the Wheeler-DeWitt equation is basically g a b g c d minus a half g g a c g g g b d now and now you're you're you're promoting the pies into variation so the variation with respect to g a c variation to g, b, d, right? Minus r, which is a function of the g's, all acting on the wave function. Right. That's the Wheeler-Dewitt equation. Okay? It turns out that this object here, the DeWitt supermetric is not positive definite and this means that the kinetic energy term isn't positive definite which means that there isn't a ground state right that there are infinite number of negative energy modes and so the whole thing it turns out that in the in our theory, the trace pi terms all drop out. If you think about it, it's all maximal slicing. So basically these terms vanish, this term vanishes. And so you get yourself a positive definite kinetic energy and so you have none of these negative energy modes. So the negative term is gone. The negative term is gone. That's right. it turns out by the way that this kind of combination it depends critically on the value of this if it was less than one part it would be okay it's just a question in fact if I break this up into a trace part and a trace free part and just crank it up you'll find that it won't work so at what point when you were working through this in the way that you described did you begin to feel or begin to get excited about it Here are these advantages that look like...

50:00 That's right, that's right. Yeah, yeah. I think fairly early on, what happened to me was that it turns out that, as I said, there are a complete family of theories depending on the action that you write down. And the value... I suppose you could think about it as to how you put in the scalar curvature. Right? So instead of R, square root of R, I could replace that by RPN and then the phi term here which is the thing that needed the V term here changes depending on A. And it turns out that the first theory I worked out was the one for which this coefficient here was 0 It turns out that I think if this is r squared, rather than square root of r, then the coefficient here gets to zero, and you don't need to normalize it all, and you have a much simpler theory. And so what I did was that I worked out this simple theory first, and it looked very interesting. But then I realized that it didn't match gr at all. There's no way. and then I decided that I had to go back and look at the basic theory the one that fitted most closely to GR, the one that was just the natural generalisation of Bernadette Sharp-Wheeler lo and behold, suddenly I found that that it and when I realised that it agreed completely with GR in the asymptotically flat case with this ansatz of putting phi equal to 1 at infinity then suddenly I realized that this was something really interesting or at least I felt it was something that was really interesting because suddenly now there are currently it is floating in limbo I think in my mind halfway between a real counter theory to GR something that people have to take seriously and check whether you can actually distinguish between the two theories

52:30 or a theory which is going to be just a toy model where we will learn how to do the wheeler-de-wit stuff in a simpler context and maybe learn how to do the more difficult one later on this is very ambiguous and it's not going to emerge for several years as to whether which of these two but I honestly can't see it dying as I say at worst it will live on as a place where people how to do something about quantum gravity. At best, it could be a serious counter. It's going to come back down to the situation where somehow the big bugbear is the Hubble constant. Because this theory that we have has basically no Hubble constant in it. It's easy to put a cosmological constant in it, But it's very difficult to see how to put... Julian keeps arguing that once we put matter in, which of course we haven't done at all, life will become more interesting somehow, and that it might well be that one could, in particular situations, have that the effect of matter be equivalent to having a Hubble constant. But, you see, the point is that if you take that sort of theory seriously, you have a fundamental theory, Fermat's principle for optics. It gives you a curve in configuration space. There is a... And you can always add something to the theory, an interpretation of the refractive index, and get yourself now a theory which allows you to see something,

55:00 which converts the theory from something static, right, to something dynamical, right? As in Fermat's principle, you can convert by using, you can convert the line in configuration space, the ray that the laser colors in space, to something along which you can at least visualize the photons moving, right? always and in many cases once you add that interpretation it may be that the theory in some sense becomes simpler right there's no difficulty with with doing that if you actually but but then the question is that how we interpret the information that's coming to us is whether we interpret the information that's coming to us as something fundamental or whether it's just an interpretation. Whether the fact that we think we are moving in a four-dimensional manifold with a preferred absolute global time, at least absolute local time, is something that is fundamental and forced on us by the theory or whether it's something that makes the analysis easier is the key question, really. You know, I drop that and I watch it fall. Now, that has a particular curve in super space. Now, if I a Newtonian time to this I can actually see that the speed of that object obeys a very simple law right? The speed increases linearly with time and so if I used some non-Newtonian I would find that the relationship between the velocity and the points along the trajectory are, you get a more complicated formula. Of course, I can do it, right? There's nothing

57:30 that prevents me from doing it. But it's also true that by adding this Newtonian time, I get a particularly simple representation of the curve. Whether I should think of this as whether this is something fundamental or something cosmetic is the question. and these are not questions that are going to be answered ever this question is to whether there is a universal time which exists external to all our theories or whether any time that exists must be something that is somehow internally generated by the theory. From my point of view, it seems to me that the second view, that the idea of importing something external, which somehow has an existence and a validity completely independent of the observations that we make, is something that makes me a bit twitchy, to be honest. Sure. I think that in many ways the idea that somehow the global time is something that makes the actual observations fit together more neatly is in fact a better way of thinking about it than thinking about some sort of universal time which exists independently of our theory entirely. But this is clearly something which is clearly a major problem that has bugged people for generations and will continue to bug people for generations. So at the present moment you've just circulated a draft? I've circulated a draft. I've got responses back. I have rewritten the draft and sent it off to FISRAV Letters about two weeks ago. I have not put it on the net.

1:00:00 We decided to wait until the FISRAV Letters responded before we put it out on the net. I was going to, in the meantime, write a much longer article, which I haven't gotten around doing yet where I would go through the Jacoby action in detail, go through the Berlin Sharp Wheeler action in detail and, you know, do all the, try and collect all the background material that one would need to but this has been sliding and sliding but in some sense It illuminates the thing that's going on just to do standard single particle mechanics in the Jacobi language and see how much of what you're doing is somewhat generic to this approach of doing mechanics. For example, I wrote down the Hamiltonian, and it was clear that the Hamiltonian generated the equations of motion. so I started out with an action vary the action to get the momenta and wrote down the Euler-Lagrange and got the constraints by varying the various things and wrote down the Euler-Lagrange equation which corresponded to that action and then showed that the Euler-Lagrange and showed that the equations then preserved the constraints that you see in GR and then I then replaced the G's by the pi's basically replaced the del G's by the momenta and so wrote down the equations of motion in a Hamiltonian form if one could use that language and then I went back and I looked at the Lagrangian and the standard approach and constructed the Hamiltonian and then showed that the Hamiltonian generated the Hamiltonian equation, right?

1:02:30 You know, the standard closed loop that you have to go through. Except that I've got a graduate student who's doing a master's degree, just like you were, and he's going through this, and he came in yesterday and told me something I knew along, that there was a damn factor of two that kept coming up when you tried to construct the Hamiltonian equations from the Hamiltonian. And then eventually I went back and looked at the Jacobi action for mechanics and discovered that you had to put in that factor of 2 by hand. That in fact the standard approach, where you wrote the Hamiltonian as PQ dot minus L, quite work in the Jacobi language. I'm sure if I went and read Lanchos, I'd find this factor of two there as well. But somehow I was bothered by this factor of two, and suddenly it became clear that somehow the Hamiltonian was not quite PQ dot minus L, but half PQ dot minus f, you know. And you could see it very clearly, as I say, in just single particle action. And so it seems to me worthwhile going and writing all these things out in as explicit and concrete a way as one can. But as I say, this is not the end. This is clearly the beginning. are many, many non-trivial problems still associated with quantum gravity. I can write down, as I say, a Wheeler-DeWitt equation for this theory, and it's clear what it is. But the problem is, do you know anything about factor ordering problems? Well, not much. Look at it. It's very simple. If you write down the momentum, the classical momentum, let's ignore the trace term. There's a G g times del pi pi. Right? And we replace that by g g del g del g. Right? But now classically

1:05:00 I can write that as pi pi g g. Right? And so now when I do it here I get del del g del and so clearly this differs from this because this derivative acts on this g in another way function over here and so when I actually work out so the difference, or I could put the g in the middle and so this is called the factor ordering problem which you actually take the classical Hamiltonian object and do the translation, it may well be that there are many equivalent representations of the classical Hamiltonian, which give you inequivalent quantum Hamiltonian. And so these are, this is known, as I say, this is known as the factor ordering problem, and there are something that people have run into in all possible theories. But this clearly has to be faced up to. So, I guess briefly, the people that you sent the draft paper out to, did you get a positive response? Oh, very mixed. Some people, and it became clear that the people who, for example, let me name names, Karel Kuchas felt very threatened by it. Not because he had any technical objections to it, because he found it vaguely threatening. It was very interesting to watch, and this is something I would, I think, I see it myself. I think that if you are somehow attached to a particular theory, then when other theories come along,

1:07:30 which somehow may try and displace view of life, then this is hard stuff, right? And so the responses I got were incredibly varied depending on, I think, the degree to which the people were attached to standard GR. I think that would be a general rule. and people like Lee Smolin thought it was wonderful because Lee doesn't give a damn about GR while Carol found it deeply threatening because he is very attached and has spent all his life trying to understand and interpret and view GR in a particular form and context and I think this will be That seems to me to be my reading of the development of any new theory. I will expect to get this kind of very widespread of... The 30-year-old punks don't give a damn. The 60-year-old wise men will feel very pushed indeed. and even amongst them so there's a generation I would, yes and the people who responded by and large were the younger generation the people I sent it out to many people and many of these people say people of my own age and of them the only person who has responded is Carol say I sent it to Bob Warren I sent it to John Friedman I sent it to Vince Moncrief And in most cases, I got a very neutral, I look at this later and respond kind of answer. I can understand. Look, life is short. But as I say, the people who responded most positively were Klaus Kiefer, Domenico Giulini, people like that.

1:10:00 People who are not, who are looking at other theories from GR, who are not particularly wedded to GR. Most of the answers, most of the responses I got where technical editorial, you know, people said that I had introduced terms before I defined them, that I had changed the meaning of letters as I went along, you know, things A fairly low order that, for example, Ted Jacobson pointed out quite rightly that I should emphasize that the BSW theory was GR. Because it was somehow implicit in the way I had written it down that the equations you got from the Berlin-Charles-Wheeler theory were standard GR. But he felt that it was very important that one should actually say this explicitly. Things of this kind that there are... Because, of course, it's very easy to run away from your audience. And suddenly you've been working at something, even in this case for six months, and suddenly you find yourself already within the six months taking things for granted, which six months ago you would have found difficult. It's one of these situations where... Plenty of time. It's one of these situations where it's interesting, as I say. I can, if you're interested, I can drag out the various responses of people and show them to you. in that kind of nitty-gritty? Yeah, it might be interesting to do that. Because everything has ended up on my email account somewhere or other. The only person who's been communicating heavily by fax is Julian, and so there are... And I've been sending him things. He doesn't know tech, which is a drawback,

1:12:30 and so then if I want to send him an equation, who write it out and fax it to him. But all the people who've been communicating with us have been using emails. But as I say, they... I suppose that's something we can always do electronically. We can always do electronically. As I say, I've saved them all here, but you can... And some of the... but as I say by and large well obviously no one said this is completely wrong and this is where you are making your mistake this answer just didn't come and because if anybody tells me this no I just won't believe them you know in any case we hardly expect that at this stage people are going to be able to respond in that kind of concrete way. That's right. It would take a long time before people would really have had to go over at it themselves. That's right, really sit down and actually think about what the equation is. I am off to Chapel Hill in September on the 7th. And so I will try very hard to get Jimmy to focus on it. getting Jimmy to focus on it now is, this is, it's easier to say this than to actually do it I know, but this is something that I would really like to as you say, life is short people aren't going to begin focusing it on until it's reached a certain level of public prominence as it were for instance so the publication of the paper presumably might galvanize that's right we never know what it is that's going to encourage people to just read this is Carol's response to the situation Okay.

1:15:00 But can you see, when you actually went through that, much of the things he said there valid and correct but all of them were presentational rather than and so once I once I went through and got the final version for publication well for submission I went through all of these things and tried to try to at least face up to these complaints, difficulties that people had. But this is this kind of situation where... And, of course, people have tried to... Let's see what I can find out. You can see old Julian Bauer. False Kiefer, you know, just... Just to this kind of

1:17:30 I just think You know, it's clear that he saw, I think, much more clearly what we were trying to do than Carole did. Because, in some sense, I think he is not... We also... There's a Giudini one that I saw just after it here. And in addition to the generational difference in the responses that you observed, do you think there's any difference do you think one can predict probabilistically predict the difference in response based on background do you think all of us are more likely to respond actively than people coming from a more quantum field theory background yes yes this would be obviously because remember remember what's going on if you actually think about it we are throwing out completely the Lorentz group The local gauge group is no longer space-time. The local gauge group, we still have a four-dimensional gauge group, but it's now, it's three geometry and a conformal three geometry, right? Time is gone. Any time that enters the theory comes via, as I say, a cosmetic, there's a cosmetic time, there's obviously a quote-unquote natural time in the theory, But the naturalness is making the equations look nicer rather than giving some sort of fundamental basis. And so this will, I think, upset classical GR people far more than it will upset quantum people. You know, quantum people don't understand why GR is, you know, what's the point of this GR.

1:20:00 There is, interestingly, and I don't understand this, a remnant of special relativity in the theory, because if you if I take flat space time it turns out that all the maximal slices of flat space time are the Lorentz, is the Lorentz gauge right, if you think about it, if I take flat space time I've got the standard flat slices, right, and these are clearly maximal but the question is how many maximal slices are in flat space time, and it's just the boost of flat slices. That's all. This is a famous result of, this is the Bernstein conjecture in mathematics, that in fact there are no other maximal slices in flat space time but the flat slices. In other words, the vanishing of trace pi implies the vanishing of all of pi if the object is four-dimensionally Riemann flat. As I say, this is... But it means that somehow there is a... in the asymptotically flat case a global Lorenz group but there isn't a local Lorenz group anymore just to get pre-history you were saying it was about six months Julian came here a year ago now and talked to me he was on holidays and he wrote to me and he was visiting somebody he knew down in Cove and so he said he wanted to come up and spend the day with me and then he came to Dublin to give a talk and then he came down again to talk to me in March or something like that and then the second time he came it became clear to me that he had

1:22:30 I understood much better what he wanted to do there was clearly you see when you talk to Julian you will find a completely different mode of thought and a way of thinking that I'm not used to at all because he deals entirely in ideas without equations, which is something I find very bizarre. I write down an equation first and then sort of hit it a few times. And so the idea that you could somehow invent a theory without equations is something that I find difficult to... At the same time, it's clearly been very fruitful. yeah it's amazing really how but it's a situation where the theory is you see it's something that he has been thinking about and you know there is there's much done Someday, I will read this object, but it's clear anybody who has been thinking seriously about the fundamentals of quantum gravity has, at some level or other, to confront that particular problem. The question is, how do you do it? Sure. and this in fact has given in fact is I think the great opening

1:25:00 you know I think things like string theory progressed really in the last 20 or 30 years, largely because people have run into really hard problems in the so-called standard approach to GR. It's interesting, and I don't know what the meaning of it, that this burst of articles from Abbe Ashtekar about doing something completely different. This idea of an isolated horizon. If you look at the web there's been three or four articles recently by Abbe on something. Is this just something he has just taken up and is going to, you know, just as is a sign that he has shifted loop theory which is not the same as string theory approach to quantum gravity I don't know but it's interesting to see how difficult quantum gravity has become in terms of actually making any progress and this I think is an opportunity I think the ground is ready for an alternative theory in a way that might not have been ready ten years ago. I think people, as I said, the people who do quantum gravity are definitely looking for a new idea. so there's a receptive audience this is, of course I haven't had the receptions yet I'm sure it's hard to know but it would not surprise me if people ready to

1:27:30 to try something new it would be interesting to see for me the situation is that as I say it's in limbo currently because I'm I'm waiting myself to see what will happen and I'm waiting to see whether what visor of letters say. And then, of course, I've been, as I say, not... All I've been doing, really, is gardening on the original article, trying to make sure that there aren't any... trying to take as many of the errors and omissions and ambiguities out of it as possible, Rather than trying, as I say, because the one thing that would be extremely interesting is to quantize the Schwarzschild solution. And I'm not sure that I know how to do that in this theory. Because, of course, you see, since asymptotically flat theories in GR or agree with asymptotically flat theories in conformal gravity in the maximal gauge, then it's clear that the Schwarzschild solution is a solution of both theories. And so it would be interesting to see whether one could quantize. Because people have been trying to quantize. is this Carol Kuchach quantization to Schwarzschild's solution article, this one, which is now five years old. And that has spawned a string of articles. There are dozens and dozens and dozens of articles now after coming out, following on from this article. And so it would be interesting

1:30:00 whether I could mimic it somehow in the new theory and see what would emerge. Because of course the interesting thing would be a number. Do you want to put math into this? Whether you would get yourself a quantizer. You see, this is I'm just looking at them. That's another, that's a Karel imitation. And, you know, there's a whole stream, you know, this kind of thing floating around, You know, you end up with, you know, there's a lot of stuff going on out there in this area, and I don't understand it, and I'm not sure. Julian has written a book, which will be coming out in the fall. You can see the name. This is a preprint of it in which he is pushing in a much more general way the whole concept of, as I say, His end of time is the fact that the, not an end of time, but rather that one should think of parameterized theories. and that the time is some sort of artifact which we impose on the theory rather than a fundamental external observable. But whether, as I say, he's written this popular book and he's got some

1:32:30 high power publisher willing to pay him a large amount of money for it so he's it will be interesting to read it it does the problem with it is that of course as he said himself that he would much prefer had our work been done a year ago because of course much of the this kind of stuff would fit very naturally into it, but he says that just you know do you know Julian at all? I think I met him most briefly at a history of GR that's what he does so I'm hoping to look him up an independent scientist He lives in a farmhouse north... Do you know where Banbury is? Yeah. Well, you know, he lives sort of five miles outside Banbury in this tiny... One could call it a village, but really it doesn't have a shop. It's got a phone box, but just that's all, and a collection of houses. And so he's been living all his life as a Russian translator must have told you this that's he was you know these people who translated scientific Russian journals and so that's what he lived on and then used the money then to take you know three months a year to think about other problems but his major he has done a great deal of work on the history of astronomy and the history of gravity in general he said I remember interestingly enough saying that he read Kuhn's book not the structure of scientific revolutions but the one about the history of astronomy the Copernican revolution I can't remember what the name of it And he said that, in fact, that he was very impressed by it until he went to it. He actually went and read the original papers. And he said, Kuhn was all wrong.

1:35:00 He said that the guy just didn't understand the relationship, he said, between the pre-Copernicean and the Copernicean and later on the Keplerian ideas was much more complicated and complex than, and that in some sense that people would like to think of Kepler, he felt, as a sort of a revolutionary figure rather than as someone in a very strong line of, you know, that once you actually went and looked, that the level of analysis that the people were doing prior to Kepler was in fact, it was wrong, he said, but very sophisticated. That these people weren't fools, sort of knaves, I think people like to think of somehow heroes and in many ways Kepler is a hugely important figure yeah people do like to simplify well if you have a few more minutes I wanted to since we kind of discussed this briefly earlier I just wanted to bring up the gravitational waves bit. Yes, yes, certainly. Go on. So what we were discussing just before we started was the idea of trying to derive the quadruple form, but by not dealing with, by dealing with a system whose oscillations or motions or whatever are powered by some non-gravitational That's right. So you talked about the idea that you had to take, if you like, a binary system, but put a strut between it. That's right, that's right. So you actually have a mechanical sort of system. System, that's right. So whenabouts were you... This was triggered, as I say, it would have been in the late 70s, I think, I would have been interested in this, because, as I said, the person who first drew my attention to it was Demetrius Christodoulou, that we were writing the Booth theorem, and so he and I were hanging around together quite a lot,

1:37:30 and we discussed this, and it became clear that somehow that there was a mathematical, if not a physical difficulty with actually deriving the quadruple formula from the Einstein equations. that somehow the mathematical difficulties clearly were much deeper than the people who were doing the calculations wanted to believe. Because, of course, if you look at the original Einstein formula, proof, it's proof by fiat. He basically said, this is the answer. You know? And it's a sign, of course, of his skill that, in fact, it almost certainly is the answer. The binary pulsar data fits a dream, you know, really works wonderfully well. And so because of that, we're in a situation, I think, where we have the right answer, which of course makes life much easier now the question is going from the raw data from the raw theory to the right answer in a sequence of logical steps is clearly much easier than actually rushing out into the unknown because this is one of my many You know, it's rather like Carol, as I was describing earlier. Anyone who tells me the quadruple formula is wrong, I just won't believe them, bluntly. Right. You know? Okay, okay, maybe, if nothing else, I don't, I think we're going to have to, I will, it'll take me a long time to believe someone who tells me is wrong I think that's a more honest statement but my instant response

1:40:00 when I see these articles saying there's a factor of two there it's just not there there may be a 5% a correction a 5% correction due to due to the mass distribution rather than but I think that at the point approximation, where we actually think of the, at least at the test particle approximation, it has to be right. It just can't not work, I think. And you still see papers with a factor of two difference today, or is that more so? Oh, I think these are gone, more or less. But there was a period all the way through the 80s in which somehow, pick a number, this was at least my feeling. It was something that I never followed with much care, I admit. But it seemed to me that there was clearly a subculture of people who wanted to do these things. And the other thing that I find is that partly, that even the people who are regarded as credible, I find it very difficult to understand exactly what they're doing. I find, say, Gerhard Schaefer, people of that kind. I'm sure they're doing good stuff, but I always lack an understanding as to exactly what exactly is being approximated. And I know this is a background problem in my case, but I would like someone to write down and say, we are doing the Einstein equations, and these are the approximations we are making. And start from that kind of simple statement. bigger you know that's because for example what is being approximated in PPN I never any feeling

1:42:30 because somehow when I look at it I always get the horrible feeling that it's really the speed of light and I know this somehow can't be right but at the same time I've never had any feeling that it's something else the PP you know somebody should sit down and say this is for example Can one prove that if you take enough P's, that you'll get GR? Right? So what we have is a theory, right, which is Newtonian mechanics. We have another theory, which is GR. And then we are approximating the Newtonian theory by essentially replacing, by sort of in some sort of ad hoc way, adding a spin-to field to it. And then somehow the idea is that by doing the self-corrections often enough, we're getting a bigger and bigger theory. The question is whether this bigger and bigger theory is converging to the target theory. It's something that I never see. It may be something that people have gone... As I say, it's something I don't... I haven't embedded myself in the field. But I have some terrible feeling that somehow... that there is a... I'm missing... Because somehow, if I, as an outsider, were doing this, surely the right thing to do is to take GR and approximate it, rather than taking Newtonian mechanics and approximating it. That's part of the problem, maybe it was Amos who said this, that one's approximating to a theory that one doesn't know yet. That's right. One has GR, but one doesn't actually have the general relativistic problem motion solved. So you don't actually know where you're going in some sense. Yes, yes, that's right. But it also means that any PPN calculation or PPPN or whatever

1:45:00 is somehow can't be trusted. You know, I listened, as I said, I was hanging out with Gerhard Schaefer recently, and it's clear that somehow, in their case, the fact that two very different calculational techniques give the same answer is seen as validating the result. And I, you know, you don't want to burst out laughing, but somehow this is not the way we do either physics or mathematics. You see, the problem is that traditionally physicists could walk away from these problems and whistle, because they could do their experiments, they could get their lines, they could get their scattering angles, they could do the damn experiment, they could get the numbers, and then they had some sort of ad hoc theory with several ad hoc assumptions which delivered the same answer, and this then in turn validated the ad hoc assumptions and the ad hoc generalizations. And this is the way physics has always progressed, right? We used direct delta functions for 50 years without worrying about... Because they worked. And you could... They were being tested day in, day out in the furnace of the experimenter's lab, right? They were living up to their billing, you know? And each time... gave us a great deal of confidence about the calculation techniques, say the approximation methods to the Schrodinger equation, you use some sort of, you truncated something or other and you just threw it away and paid no attention to it and then you got an answer which agreed within 1% to the data that the experimenter gave you and this, as I say,

1:47:30 justified and GR is exactly not in this situation. We are doing quasi-experiments in the sense of doing some sort of analysis two different ways and then we are using the fact that the answers that emerge from the two different analyses agree being the equivalent of the experimenter. And it's not right. I just feel that somehow, until and unless we actually start getting realistic data from realistic experiments, I think this whole approximation scheme approach is going to always be something that makes me, at least personally, very nervous. So if, for instance, we look at forthcoming experiments like LIGO and gravitational wave detectors, Could there be a problem with the way that the experimental data is derived, that it's too dependent on the approximations? For instance... Oh, yeah. This is going to be a serious problem, isn't it? That the analysis... You see, the data is going to be heavily mangled to extract something out of the data. Now, if the data... You see, this is really a terrible problem because if you didn't mangle the data very much, then you would have some confidence, as I say. but when the way that you mangled data is in some sense very strongly determined by the theory then somehow if the mangled data doesn't fit can you see the problem?

1:50:00 at the same time if they you know a lovely fit then we'll all feel happy it's something which at least in principle and I think in all honesty people do think about this and in principle as well the failure of the numerical people to actually produce anything realistic is, I think, a major problem. Because if we had these... You see, here there are two completely different approximation techniques being used, right? There are the analytical approximators who are truncating series, and there are the numerical approximators who are truncating numbers. And this is a very different kind of operation. And it's clear that these two operations, if these two operations were to start giving the same answers, then, again, this would be at least a much more credible overlap than two different theorists coming up with the same answer, or two different numerists coming up with the same answer. but I don't see the numerical people delivering anything for ages so if when you have LIGO online and it's producing data and you're filtering the data with a bunch of templates which are derived from post-Newtonian extensions and you feel that you've got a hit or a possible detection then there's a possible problem there because And, of course, you end up with the situation where, and this is something extremely difficult to test, you will want to ask somehow, what happens if I tweak my template? Does the hit go away? And what is a reasonable amount to tweak the template

1:52:30 so that the hit does go away? And this is something which, because at the same time it's clear that, given my prejudices, that the binary, if I take a neutron star and think about this as an extended object rather than a test object, the changes I would think that I would expect to the quadruple formula are in fact very small right 0.01% we're talking about a situation where so that far a so that say that you actually were working out a radiation reaction for say a neutron star orbiting a black hole and you then used the exact point quadrupole formula and you found then an orbit and a period and changes of period and all these good things, like amplitudes, right? Now if you were to take that same formula for the quadruple formula and multiplied it by 1.01 and multiplied it by 0.99 and ran the same calculation again. And the question then that arises is whether these two, these three templates actually differ by much over some extended period. or differ by much in the regime in which the overlap occurs with the experiment. That's really the test, obviously. You can throw away the parts of the template which are not visible to LIGO. You're really only looking for a range of frequencies. And so that would be a very crude way of somehow checking the kind of situation that I'm thinking about.

1:55:00 So the question is, what number do I have to multiply the quadruple formula by so as to change it from a hit to a non-hit? I suppose basically the answer is that the number is quite small or that a small change because in fact it turns out that such is the difficulty of detecting that's right, I would expect that number that number could well be extremely small and you actually depend on getting a lot of cycles that's exactly right That's right. You're sunk. That's right. And so that means then, now, we should be able to, if we were orders of magnitude people, we should be able to estimate the error that you're making in treating the neutron star as an extended body rather than as a test body, we should be able to get some sort of feeling for at least the orders of magnitude of that number. And then the question is, then somehow it's a play between numbers, isn't it? I'm not for a moment saying that this is not, that this is a non-answerable question. believe this is a question which we can reasonable physicists answer in a reasonable fashion and reasonably say the following whether a hit is a credible hit or a non-credible hit never the only at the same time and this would be for a single if they got dozens of then you start thinking having more faith in the template the template fit

1:57:30 you see if they get only one hit I think the basic answer is that we will say oh how nice but if they get ten hits then suddenly you know, then that raises the threshold of credibility enormously. Because basically the template appears to be working. Working, that's right, yeah. This is the lab scenario, whereby we can't justify, we may not be able to justify the arguments that went into constructing the template, but the template seems to be working I suppose one could make the argument then that because you have no independent means of knowing when the gravitational wave actually passed through it could be that the template is working too well and that it's making false hits oh yeah but what you end up doing then under those circumstances is doing the kind of tweaking I'm talking about you're tweaking it by 1% in either direction and then seeing what happens seeing if it goes away or seeing if you get another 10 hits and then you're clearly then you lose it again right? But these are questions which, now, they may not be feasible, right? This is not, but nevertheless, it's given the actual lack of faith that I have in the approximation schemes, it's difficult for me to visualize other ways of doing this. than by this kind of testing and it'll work however given the the politics of the time there will be a huge amount of pressure on the people doing the experiment

2:00:00 to announce positive hits right that's right between the and this is interesting in the sense that what you actually need is a situation where the where you need some sort of Chinese wall between the data analysis people and the construction or between the the runners between the experiment the people working the instrument and the people who are analysing the data I remember this and of course this is impossible but I remember someone who tried very hard was that Ray Davis the man who was finding the neutrinos and not finding the solar neutrinos worked very hard to actually And this was, of course, a very hot topic at the time. And I remember him, he worked extremely hard to make his data and his experiment available to external people that you could actually, you know. And it seems to me, in some sense, that what you really need is a kind of a situation where somehow, for example, will the raw, raw data be available to the public? No, I think it's the basic answer, but they still seem to be working out exactly what they're going to do, but yeah, no. Yeah, you know, this would be, you know, the situation is that whether I could log in online and just copy out the jiggles. I think that would definitely be no. Yeah. In fact, one of the things that a lot of people seem to be doing is taking an alternative tack to the notion of whether there's a... Because in a way, at the moment, there's a natural Chinese wall between many of the Dapha House people and the instrumentals. at the moment are theorists. That's right, yeah. So they actually know nothing about the instrument. That's right, that's right.

2:02:30 But what I meant, I think also there is a situation where people's... There is a career linkage still. Yeah. You know, if you're a theorist working with LIGO, then it is in your interest that LIGO be successful because, you know... Yeah. And somehow you would... handle this and I know I'm not talking for a moment about dishonesty or fraud or any of these ugly words I'm just talking about natural you know our ability you know the traditional problem of underestimating the errors you know and it's particularly in a situation are somehow uncontrolled which is the feeling I have and as I say if we get ourselves a situation where somehow we get ourselves a bunch of results from LIGO which look credible if we for example see a supernova will they see a supernova? yeah it's close enough Right, but you know, yeah, that's right. Yeah, you know? Yeah, I mean, obviously there's always a possibility of a serendipity that's there for you. That's right, yeah. That's right. But it'll be a long time. I think it's going to be a situation where we're talking really about a generation before all the wrinkles get ironed out, I think. so do you see LIGO and these other experiments as being likely to have any impact on your work in the foreseeable future I would have seen them until I discovered this thing obviously my whole there's been a huge shift you see and there's a whole lot of things lying around that I haven't finished But somehow it's, you know, you're somehow running off in a different direction. And so because of this, you know, I was very interested in doing these hyperbolic schemes that Jimmy York is doing for general relativity.

2:05:00 And it's clear that somehow, you know, there are a million and one hyperbolic schemes. And it's clear that somehow just by doing a weak field approximation, you can actually tidy up the field amazingly. You know, that somehow no one has actually gone and done all the weak field versions of all the hyperbolic theories, you know, and it's easy, you know, it's just a situation. And then this will help you, I think, very clearly distinguish between the theories which are equivalent and the theories which are inequivalent, the theories which are really what they claim to be, first order symmetric hyperbolic, and the theories which aren't. but no one has done that and I was thinking that was one of the things I was supposed to be doing but in fact I was just gone out the door and so in that sense because for a long time I've been interested in the without ever writing a line of code interested in the numerical people and the way they, you know, progress. But at least for the next couple of years, I don't see myself as offering anything in that direction. And is there kind of a symbiotic relationship between people who, in numerical, numericists who actually write code, in numerical relativity people who actually write code, people like yourself wouldn't write the code but for instance would be I suppose in the business of proposing possible algorithms are proposing possible problems it's clear for example that the

2:07:30 I was surprised even though I spent Potsdam the numerical people in Potsdam axisymmetric systems you know a realistic you know a realistic simpler situation they have now but there was a I spent a long time telling them that what they had to do was do, you know, you had to do axisymmetric systems two different ways. You had to do them as axisymmetric systems. So you had to write a code, an axisymmetric code. And then you had to write axisymmetric initial data into your non-axisymmetric code. and then you had an obvious comparison a test as to whether your fully 3D code made any sense and they have now, they are now doing this and it seems to me to be a fairly obvious of actually doing you see this is not This is something where you can actually do a realistic, easier model and use it as a testbed on which to run your full code. And it stopped me as being somehow the obvious place to do it. But it's amazing how slow the numerical community has been to accept advice from the outside. This has always been my experience. Partly, I suppose, because of the investment of time and effort. But this was not a situation where I was suggesting a new method of coding or anything like that

2:10:00 but it took a long time to persuade these people to do this has been my experience all along that the numerical people are by and large very resistant you were saying one reason for this is if you're suggesting a new type of algorithm approach, then obviously they've invested so much in their using code. That's right. They're not going to shift. But even in this case where you're simply suggesting a test. A test, it took a long time to persuade them that this was and, you know, and writing a 2D code is infinitely easier than writing a 3D code. You know, it's just not a big deal. And of course, many people had written 2D codes and the idea then would be that you would run your 3D code with 2D, with axisymmetric and see and then compare it with the outcome of the but currently even in Potsdam now I think all they're doing is solving the constraints in 2D and they're discovering lo and behold this drove them crazy by the way you see they went the whole hog they inputted BrillWave data into their 3D code and tried to solve the constraints and find the horizons, just purely as an initial data problem. No evolution whatsoever. And then they kept finding disagreements between the outcome of their code and the outcomes of other people's codes, right? And, you see, they were forced into this by the fact that their code keeps crashing. And so the theory was that they were hoping hearing earlier than they should anyway anyway it became very messy anyway as to why they were doing this and then they eventually went and they did they wrote a 2d code and lo and behold their

2:12:30 2d code agreed with their 3d code and disagreed with everybody else in the field and it turns out that they were right it turns out that everyone else in the field was in fact raw that that that That, in fact, the people who had done the old 3D codes, Ken Epley, for example, did one way back in the mid-70s. Do you understand the Brill Way of Ansatz? Yeah. And so basically there is an amplitude in there. And so basically you solve effectively the Lishnarevitz equation and then you pump up the amplitude. and then at some value of the amplitude you should get a horizon appearing right so that's what everyone does in these so it's moment of time symmetry and so you're basically putting more and more gravitational wave energy in there and at some value of the amplitude you should be able to get a horizon and then the question is given and so there is and so then the question is they took each all the the functions that each of the other people had tried and then they repeated the calculation with varying amplitudes and you see they had a Lichnerevet solver and they had a horizon finder and so this was a good test but they only did it on their 3D code and sure enough they got answers which were significantly different from the answers in the literature and so then and only then did they go back Then they spent weeks thinking they were wrong. And then they went back, and then they wrote their own 2D code and ran the same data. And as I say, they got agreement with theirs, their 3D code, and disagreement with everyone else. And it turns out, of course, that everyone else was wrong, in fact. That this turned out to be finding horizons, even in 2D, is a non-trivial job. So this is the Einstein group? What? This is the Seidel group? This is the Seidel group, yeah. But it struck me as an example of where

2:15:00 by trying to shortcut where they clearly shouldn't have shortcut because, look, they are going to need these 2D inputs. Anyway, if they're going to do evolution, you know, this is insane somehow, not to have a credible test, but they didn't. And so now, as I said, they eventually wrote a 2D code, first of all, just to solve the constraints, and now they're, presumably they have done, so I haven't been there for a year, they've written an evolution, a 2D evolution code. and so then what they want to do is just run both in parallel and see whether or whether it makes any sense so that was a lot of very interesting things we touched on I should probably release you now oh god it's half past 11 do you want to go and have a cup of coffee?